# Spatio-temporal Event Studies for Air Quality Assessment under Cross-
sectional Dependence

Paolo Maranzano111University of Milano-Bicocca (Milano, Italy) & Fondazione
Eni Enrico Mattei (Milano, Italy<EMAIL_ADDRESS>Matteo
Pelagatti222University of Milano-Bicocca (Milano, Italy);
<EMAIL_ADDRESS>
###### Abstract

Event Studies (ES) are statistical tools that assess whether a particular
event of interest has caused changes in the level of one or more relevant time
series. We are interested in ES applied to multivariate time series
characterized by high spatial (cross-sectional) and temporal dependence. We
pursue two goals. First, we propose to extend the existing taxonomy on ES,
mainly deriving from the financial field, by generalizing the underlying
statistical concepts and then adapting them to the time series analysis of
airborne pollutant concentrations. Second, we address the spatial cross-
sectional dependence by adopting a twofold adjustment. Initially, we use a
linear mixed spatio-temporal regression model (HDGM) to estimate the
relationship between the response variable and a set of exogenous factors,
while accounting for the spatio-temporal dynamics of the observations. Later,
we apply a set of sixteen ES test statistics, both parametric and
nonparametric, some of which directly adjusted for cross-sectional dependence.
We apply ES to evaluate the impact on NO2 concentrations generated by the
lockdown restrictions adopted in the Lombardy region (Italy) during the
COVID-19 pandemic in 2020. The HDGM model distinctly reveals the level shift
caused by the event of interest, while reducing the volatility and isolating
the spatial dependence of the data. Moreover, all the test statistics
unanimously suggest that the lockdown restrictions generated significant
reductions in the average NO2 concentrations.

Keywords: Multivariate Time Series, Spatial cross-sectional dependence, Event
Studies, Air quality, Abnormal concentrations

##  1 Introduction

###  1.1 Event Studies and Statistical Intervention

Event studies, hereafter ES, are statistical tools used to assess whether a
particular event of interest induced abrupt changes in the level (level shift)
or in the volatility (volatility shift) of one or more relevant time series
(Campbell et al.,, 1998). Such events may be either artificial, such as the
introduction of a new policies or interventions (e.g., the effect of traffic
limitations on road traffic and air quality or restrictive measures on
mobility), or natural events (e.g., environmental extreme events).

ES ground on two main pillars. The first pillar is the interrupted time series
(ITS) paradigm (McDowall et al.,, 2019), in which we assume that at a certain
known date an event (e.g., treatment or intervention) occurred, dividing the
time series into two parts, one before and one after the event. The occurrence
date is labeled as the event date and is assumed to be known. The final goal
of an ES is to state if the event of interest generated a statistically
significant impact on the time series under consideration. The event can be
permanent or temporary and it ca be gradual or abrupt. Usually, ES focus on
abrupt changes. The second pillar is the offline hypothesis testing methods of
Basseville and Nikiforov, (1993), in which a without change scenario (i.e., no
abrupt changes occurred in the observed data) is compared to a with change
scenario (i.e., the data were statistically significantly affected by some
shock or event). The two scenarios are compared through a statistical
hypothesis testing procedure. Considering ES for level shift, under the null
hypothesis H0, we state that there are no abnormal variations in the average
level due to the event occurrence, whereas the alternative H1 suggests the
existence of abnormal variations after the event of interest. In the former
case, the variations can be attributed to the randomness in the data.

ES are directly connected with branches of statistics involved into the impact
assessment of policies and unexpected shocks, such as the Statistical
Intervention Analysis (Abraham,, 1980), hereafter SIA. Indeed, ES and SIA can
be considered as complementary, but also competing, tools. ES methodology
combines a regression-based approach for parameter estimation enforced with a
validation strategy and robust hypothesis testing to return insights about the
sign of the shock and its statistical significance. SIA is used to quantify
the impact of the event through a model-based inferential approach. However,
the average effect generated by the event is estimated by regression
techniques and its statistical significance is assessed by classic hypothesis
tests (e.g., t-test for regression coefficients). In ES, the event impact is
quantified as pointwise change (i.e., at a given time instant) or cumulative
change (i.e., over a window of subsequent observations) in the time series of
interest. Both ES and SIA are based on the ITS paradigm, however, whereas in
ES much emphasis is placed on robust estimation of the significance of
variances, statistical intervention places great emphasis on defining the form
of the intervention and on ensuring an unbiased estimate of the effect.
Accordingly, it is reasonable to consider the combined use of ES and SIA for
policy impact assessment. For example, one can adopt ES as a preliminary tool
to identify the presence (or absence) of shocks in the time series and then
quantify the change that has occurred using statistical intervention tools.

Both ES and SIA follow a model-based reasoning, but adopt very different
strategies for computing the test statistics. ESs for level shifts follow a
forecasting-based approach in which the level before and after an intervention
are compared to assess whether the estimated difference is statistically
significant. The ES test statistics are computed using the forecast errors on
future observations at the event date. Such approaches are standard, for
example, in assessing structural breaks in public and macroeconomic policies
(Guglielminetti and Rondinelli,, 2021). The standard procedure for ES is to
segment the timeline into two consecutive subsamples: the first part of the
time series is used to estimate the parameters of the regression model (i.e.,
the estimation window), while the second part is used to quantify the effect
of the intervention without re-estimating the model (i.e., the event window).
To produce unbiased parameter estimates, the estimation window must be
unaffected by the intervention/event. For level shift ESs, if the event truly
generated a significant effect, post-event observations should diverge from
model-based forecasts. Therefore, the forecast (residual) errors should
exhibit a pronounced change in the level shift. In contrast, if the variation
is random, the forecast and actual values should almost coincide and the
residuals should have zero mean. From the sampling perspective, ES approach is
similar to modern statistical learning techniques for temporal data, in which
a portion of the time series is used for in-sample model training and
parameter estimation, whereas performance is evaluated over successive out-of-
sample periods in cross-validation (Bergmeir et al.,, 2018). While ES use a
validation strategy, in SIA the model’s parameters are estimated employing all
available observations, that is, the entire time series. The classic approach
to SIA identifies the level (or volatility) shift in time series using a
regression framework in which an intervention covariate is introduced to
quantify the anomaly. The covariate can take the form of a dichotomous
variable (pulse or constant effect), ramp (linear effect), or dynamic ARMA-
like filter (Box and Tiao,, 1975; Abraham,, 1980). If a model in parametric
form is fitted, the significance of the event is reflected by the statistical
significance of the parameter associated with the intervention covariate.

###  1.2 Event Studies for Environment and Energy

We focus on the analysis of air quality data and the application of ES
techniques to detect shocks in observed airborne pollutant concentrations
following unexpected exogenous events. While statistical intervention analyses
are common tools in studying the air quality (Fassò,, 2013; Grange and
Carslaw,, 2019; Petetin et al.,, 2020) and the impact of pollution mitigation
policies, ES are only recently receiving attention in pollution-related
fields, such as energy and oil commodity markets. For example, Demirer and
Kutan, (2010) use the ES methodology to examine the behavior of crude oil spot
and futures markets around the OPEC conference, as well as US strategic
petroleum reserves announcement between 1983 and 2008. Zhang et al., (2009)
use ES to test the impact of extreme events, such as the Gulf War in 1991 and
Iraq War in 2003, on crude oil price volatility. Further, in Zha et al.,
(2018) the authors aim at assessing the impact of refined oil price
adjustments to control air pollution in China between 2014–2015. In addition,
ES methods have recently received great attention in climate policy analysis.
Looking at the macroeconomic perspective, one can refer to the paper by
Barnett, (2019), in which the impacts of climate policy risk exposure on
observable market outcomes such as oil production, stock returns, and oil
prices are analyzed. In Diaz-Rainey et al., (2021), the authors examined the
effect of policy interventions associated with Paris Agreement (agreement and
ratification) and the election of Donald Trump (election and withdrawal from
agreement) on stock returns of oil and gas companies. Other researchers
focused on the effect of climate polices on stock returns and investment
portfolios. We recall, for example, Borghesi et al., (2022) examining the
behavior of green and brown portfolios around green policy-related
announcements launched by European governments in 2020 to alleviate the
adverse effect of climate change; Birindelli and Chiappini, (2021), which
examined investor reaction toward eight EU policy announcements over the years
2013–2018 on a large sample of EU firms; and Huynh and Xia, (2020), which used
ES to analyze the effect of climate change news on individual corporate bond
returns.

None of the previously cited studies directly examine the case of local
pollutant concentrations. Moreovor, they employ standard regression techniques
for time series under the assumption of cross-sectional independence (i.e.,
the series are independent of each other). In this paper we are interested in
ES applied to multivariate time series characterized by high cross-sectional
(spatial) and temporal dependence. In particular, we are interested in
concentrations of airborne pollutants observed on geo-referenced monitoring
networks located on specific territories. In this case, cross-sectional
dependence (CD) is a direct consequence of the spatial correlation between the
sampling points in space. Indeed, it is reliable to assume that control units
located at close distances record similar values under the same environmental
conditions.

Since the data are characterized by a well-defined spatial and temporal
structure, a key feature of this paper is the implementation of an appropriate
geostatistical modeling approach to model the relationships between the
pollutant concentrations across space and time. In addition, the focus is on
the statistical significance of observed variations in the average value under
autocorrelated data across space and time, and on the methods used to correct
for these issues. Quantification of impact is a secondary objective.

Specifically, we aim at targeting two issues. The first concerns the
definition of Event Studies specific to the case of air quality. In this
regard, we propose to extend the existing taxonomy on ES, mainly deriving from
the financial field, by generalizing the underlying statistical concepts and
then adapting them to the case of airborne pollutant concentrations. This task
is performed by assimilating the concentrations of a specific pollutant
observed in a given time $t$ at a given monitoring station $s$ to the stock
returns observed for a stock $i$ at time $t$. Thus, by analogy with the
definitions of normal and abnormal returns (Ball and Brown,, 1968), we propose
the definition of normal, abnormal, and cumulated abnormal airborne pollutant
concentrations. The second issue addresses the problem of adjusting ES against
cross-correlation when dealing with spatially distributed observations. To
address the spatial cross-sectional dependence, we adopt a twofold adjustment
with respect to classical ES frameworks. First, we use a linear mixed spatio-
temporal regression model, namely the Hidden Dynamics Geostatistical Model or
HDMG (Calculli et al.,, 2015), to estimate the relationship between observed
concentrations and several exogenous factors, such as meteorology and calendar
effects, while accounting for the spatio-temporal dynamics of the data. To
exploit the improvements guaranteed by the spatio-temporal modelling, the HDGM
is compared with purely temporal regression models (i.e., not adjusted for
spatial dependence). Second, we apply and compare a series of sixteen ES test
statistics, both parametric and nonparametric, some of which directly adjusted
for cross-sectional dependence. Expectations are for greater consistency in
corrected statistics than in unadjusted ones. Extending robust ES to the
spatio-temporal context is an improvement that can provide great benefits to
projects whose goal is to assess the impact of policies in space and time. A
valid example is the AgrImOnIA project (https://agrimonia.net/), whose
objectives include the analysis of the relationship between livestock and air
pollution through geostatistical models, as well as scenario analyses
regarding the expected effect on particulate matter concentrations deriving by
reductions of pollutant emissions in the agricultural sector (e.g., efficient
manure management, increased organic farming techniques).

The remainder of this paper is organized as follows. In Section 2, we propose
the definitions of normal (expected) concentrations, abnormal (unexpected)
concentrations, and cumulated airborne pollutant concentrations. In Section 3,
we discuss the effect of CD on the test statistics and present the twofold
adjustment strategy for CD data in ES. In Section 4, we present the HDGM and
discuss its interpretation and the major benefits of its implementation. In
Section 5, we present an empirical application of ES analysis concerning the
effect of the lockdown restrictions imposed on air quality in the Lombardy
region (Italy) in response of COVID-19 disease spread in 2020. The aim was to
test whether traffic and mobility restrictions significantly affected the
average daily levels of NO2 concentrations collected at 83 ground monitoring
stations. The results support the hypothesis of a generalized reduction of the
average oxide concentrations in the region. Finally, Section 6 concludes the
paper and proposes future development strategies for ES in spatio-temporal
frameworks.

##  2 Event Studies taxonomy for air quality assessment

Let $s=1,\ldots,N$ be the index for cross-sectional units, where $N$ is the
total number of spatial locations in the sample, and let $t$ be the time index
$t=T_{0},\ldots,T_{1},T_{1}+1,\ldots,T$. Recall that ES rely on a validation
strategy performed by splitting the whole temporal sequence into two
subsamples, namely the estimation window and the event window. Observations in
the estimation window are used to estimate the model parameters, while those
in the event window are used to assess the event’s effect.

Let’s denote the time index for the first available observation as $T_{0}$,
the time index for the last observation included in the estimation window as
$T_{1}$, and the time index for the last observation in the event window with
$T$. Moreover, assumes that the event date coincides with $T_{1}+1$ and that
the last observation of the event window coincides with the last available
observation $T$. The set $\Omega_{0}=T_{0}+1,T_{0}+2,\ldots,T_{1}$ (with
cardinality $\tau_{0}$) will denote the set of time indexes for the estimation
window, while the set $\Omega_{1}=T_{1}+1,T_{1}+2,\ldots,T$ (with cardinality
$\tau_{1}$) will denote event window. Eventually, the set
$\Omega=\Omega_{0}\cup\Omega_{1}$ has cardinality $\tau=\tau_{0}+\tau_{1}$ and
represents the full sequence of time indexes.

Let Cst be the observed airborne pollutant concentrations observed at time $t$
at the monitoring station $s$. Moreover, let Xst be a set of conditioning
information collected at time $t$ at the same station $s$. Notice that the set
Xst can include station specific information (e.g., local weather
measurements, traffic data, land cover) and information common to all the
sensor (e.g., calendar effects) or further variables measured at aggregate
geographical level. Assuming the existence of a statistical relationship
between the concentrations and conditioning information, for each spatial
sampling point $s$ and time stamp $t$, the normal concentrations (NCst) can be
defined as the conditional expected value of Cst with respect to Xst, i.e.

$NC_{st}=E[C_{st}\rvert X_{st}]\qquad\forall t\in\Omega.$ (1)

It follows that the abnormal concentrations at time $t$ for station $s$ (ACst
or $\varepsilon_{st}$) are defined as the difference between the observed
concentrations at time $t$ and the normal concentrations at time $t$ for
station $s$:

$AC_{st}=\varepsilon_{st}=C_{st}-E[C_{st}\rvert
X_{st}]=C_{st}-NC_{st}\qquad\forall t\in\Omega.$ (2)

The abnormal concentrations in the event window $\Omega_{1}$ can be
interpreted as the abnormal values of $C$ not explained by the conditioning
information Xst, and potentially generated by the event of interest.

Finally, by the term cumulated abnormal concentrations we mean the cumulative
sum of abnormal concentrations in a given time window. When the cumulative
window coincides with the event-window, we refer to cumulated abnormal
concentrations in the event window, hereafter CAC${}_{s\Omega_{1}}$. The
cumulated abnormal concentrations for station $s$ over the event window
$\Omega_{1}$ are defined as follows:

$CAC_{s\Omega_{1}}=\sum_{t=T_{1}+1}^{T_{2}}{AC_{st}}.$ (3)

##  3 Addressing cross-sectional dependence in ES

Cross-sectional dependence is the outcome of the strong spatial correlation
naturally exhibited by observations collected on geo-referenced monitoring
networks located on specific territories. Recall the Tobler’s First Law of
Geography (Tobler,, 1970), ’Everything is related to everything else, but near
things are more related than distant things’ (spatial autocorrelation
principle). The law also applies to air quality, as it is reasonable to assume
a strong spatial correlation in air quality of geographically close areas
(Montero et al.,, 2021). Also, recall the Third Law of Geography (Zhu and
Turner,, 2022) ‘The more similar geographic configurations of two points, the
more similar the values (processes) of the target variable at these two
points’. Therefore, by analyzing the measurements recorded in monitoring
networks belonging to specific regions and assuming very similar environmental
conditions, it is realistic to state that the concentrations of airborne
pollutants observed in monitoring stations located at close distances will be
very similar.

According to Dale and Fortin, (2009), ecological data are often affected by
positive spatial dependence, giving rise to more apparently significant
results than the data justify. When the observations are affected by positive
cross-sectional dependence, the significance rates of the classic ES
parametric test statistics are oversized (i.e., the test rejects too often).
On the contrary, in the presence of negative cross-sectional dependence ES
tests are undersized (i.e., the test rejects too few). The same considerations
hold when observations are affected by temporal autocorrelation (Lee and
Lund,, 2004, 2008), or when considering correlated paired samples (Dutilleul
et al.,, 1993; Zimmerman,, 2012). Size-distortion effects still hold when
negligible levels of cross-correlation are observed (Pelagatti and Maranzano,
2021b, ). Considering ES applied to environmental policy evaluation, over-
rejection leads to the erroneous identification of a statistically significant
effect caused by the event of interest. Certainly, using regression techniques
to compute the abnormal concentrations can reduce the average correlation
significantly. However, because of the strongly similar environmental and
geographical conditions (Zhu and Turner,, 2022) of the region, even after
filtering the confounding effects there may be enough average correlation to
severely bias any parametric statistic.

To address the spatial cross-correlation issue, we adopt a twofold adjustment
compared to classic ES frameworks.

The first adjustment concerns the modelling (regression) step. Usually, ES
literature assumes a linear relationship among the response variable and the
covariates. Moreover, the relationship is often estimated in a univariate
framework, that is, for each location $s$ the observed concentrations are
modelled as linear functions of the set of conditioning information Xst. This
is equivalent to assuming that the concentrations observed at the stations are
mutually independent (which is rather unlikely given the physical-chemical
characteristics of the atmospheric phenomenon). Also, in linear regression
contexts, estimates of regression coefficients could be biased due to not
explicitly modelled spatial structures into the residuals (Paciorek,, 2010).
Since ES statistics are calculated from the predicted residuals, the presence
of confounding spatial correlation can adversely affect the values of the
statistics and their uncertainty. We aim at relaxing the independence
assumption by explicitly modelling the spatio-temporal dynamics of the NO2
concentrations though a common spatio-temporal process describing the
evolution of airborne pollutant concentrations measured on the network. We use
a linear mixed spatio-temporal regression model, namely the Hidden Dynamics
Geostatistical Model (HDMG) (Calculli et al.,, 2015), to estimate the
relationship between observed concentrations and several exogenous factors,
such as meteorology and calendar effects, while accounting for the spatio-
temporal dynamics between the observations.

The second adjustment refers to the hypothesis testing step. In line with the
reasoning of Lee and Lund, (2008), in Dale and Fortin, (2002) and Dale and
Fortin, (2009) the authors proposed a strategy to mitigate the CD effect by
adjusting the test statistics for the effective sample size, that is the
extent to which the test statistic must be deflated to achieve the correct
rejection rate. The strategy we adopt is related to the one proposed in
Zimmerman, (2012) for t-tests on two related populations. Rather than
operating on the information contained in the observations (i.e., effective
sample size), we propose to use CD-adjusted test statistics directly adjusting
for spatial cross-sectional dependence by means of a cross-correlation measure
for multivariate time series. We apply and compare the set of ES test
statistics presented and discussed in Pelagatti and Maranzano, 2021b . The
proposed statistics test the null hypothesis of absence of level shift in the
cumulated abnormal concentrations ($CAC$). The list of ES we used includes
both cross-sectionally adjusted statistics and non-adjusted statistics.
Moreover, among the considered statistics, we included both parametric and
non-parametric specifications. In particular, we considered nonparametric
statistics belonging to the family of rank-based statistics (Kolari and
Pynnönen,, 2011; Luoma,, 2011; Hagnäs and Pynnonen,, 2014). Since we model the
spatio-temporal dependence at the estimation stage, the residual cross-
correlation is expected to be very small. Therefore, all the adjusted
statistics should be straightforward in identifying (or not identifying) the
statistical significance of the effect. Statistics that do not account for the
dependence should nevertheless be robust, but not as robust as the adjusted
statistics.

In Table 1 we list the ES test statistics proposed or analyzed by Pelagatti
and Maranzano, 2021b  and that we use in the empirical analysis. The table
includes the name of the statistics, a bibliographical reference and a
statement regarding the adjustment for cross-sectional dependence. An extended
discussion on the statistical properties, as well as simulated and empirical
results about their performances, of each statistic is available in the same
article.

Table 1: Test statistics for H0: $E[CAC_{\Omega_{1}}]=0$ Cross-sectional | Specification | Statistic | Reference
---|---|---|---
adjustment
Not-adjusted | Param. | cross_T_Test | Brown and Warner, (1985)
Not-adjusted | Param. | crude_dep_T_Test | Brown and Warner, (1985)
Not-adjusted | Param. | T_skew | Brown and Warner, (1985)
Not-adjusted | Param. | Z_patell | Patell, (1976)
Not-adjusted | Param. | Z_BMP | Boehmer et al., (1991)
Not-adjusted | Nonpar. | Z_grank | Kolari and Pynnönen, (2011)
Not-adjusted | Nonpar. | CumRank_Z | Corrado, (1989)
Adjusted | Param. | Z_patell_adj | Kolari and Pynnönen, (2011)
Adjusted | Param. | Z_BMP_adj | Kolari and Pynnönen, (2011)
Adjusted | Nonpar. | T_grank | Kolari and Pynnönen, (2011)
Adjusted | Nonpar. | Z_grank_adj | Kolari and Pynnönen, (2011)
Adjusted | Nonpar. | CumRank | Corrado, (1989)
Adjusted | Nonpar. | CumRank_mod | Corrado and Zivney, (1992)
Adjusted | Nonpar. | CumRank_T | Corrado and Zivney, (1992)
Adjusted | Nonpar. | CumRank_Z_adj | Hagnäs and Pynnonen, (2014)
Adjusted | Nonpar. |  P1 | Pelagatti and Maranzano, 2021b
Adjusted | Nonpar. |  P2 | Pelagatti and Maranzano, 2021b
Adjusted | Nonpar. | Corrado-Tukey adjusted | Pelagatti and Maranzano, 2021b

Spatial dependence can be measured in several ways (we suggest referring to
the review paper by Lee, (2017) for a detailed discussion about strengths and
weaknesses of autocorrelation and bivariate spatial correlation measures). The
most intuitive measure of correlation over space is the Moran’s Index (Moran,,
1950), which can be seen as the correlation coefficient for the relationship
between a variable and its neighbouring values. Global Moran’s I is a
generalization of Pearson’s correlation coefficient with geographical weights
(Chen,, 2013). The very close analytical link between Pearson’s coefficient
and Moran’s index was first scrutinized by Wartenberg, (1985). Later, a
bivariate spatial correlation measure was proposed in Lee, (2001) as a
smoothed version of Pearson’s correlation capable of capturing both bivariate
point-to-potint association and univariate spatial autocorrelation. The CD
adjusted statistics in Table 1 correct the spatial dependence using Pearson’s
linear correlation coefficient. While this is an approximate aspatial measure
of autocorrelation, it can still provide a straightforward indication of the
direction (sign) of the relationship and its strength. Indeed, the bivariate-
spatial correlation can be expressed as a fraction of Pearson’s linear
correlation coefficient, which acts as an upper-bound (Lee,, 2001).

##  4 HDGM for Event Studies

We assume that data are generated by a spatio-temporal process
$\\{Y_{st}\in\mathds{R}:s\in D,t=1,\ldots,T\\}$, where $D$ is the spatial
domain and $t$ represents a discrete point of time. The Hidden Dynamics
Geostatistical Model, namely the HDGM (Calculli et al.,, 2015), entails a
random-effect term $w_{st}$ modelling the spatial and temporal dependence, a
fixed-effect term $v_{st}$ accounting for all exogenous regressive effects and
an error term $\varepsilon_{st}$. The univariate HDGM is specified as follows:

$Y_{st}=v_{st}+w_{st}+\varepsilon_{st}$ (4)

with $\varepsilon_{st}\sim N(0,\sigma^{2}_{\varepsilon})$ being the error
vector that is assumed to be independent and identically distributed (I.ID.)
across space and time. The error sequence is supposed to have a zero mean and
a constant variance $\sigma^{2}_{\varepsilon}$ and Gaussian distribution. The
fixed-effects mean term can be specified as follows:

$v_{st}=X_{st}\beta,$ (5)

where $X_{st}$ is the $(n\times p)$-dimensional matrix of $p$ covariates at
location $s$ and time point $t$ and $\beta$ is a vector of $p$ fixed-effects
parameters. The random effects term $w_{st}$, which accounts for the spatio-
temporal dependence in the random process $Y_{st}$, is described by a
Markovian autoregressive temporal process plus a spatially correlated random
effects $\omega_{st}$ with Gaussian distribution

$w_{st}=gw_{st-1}+\omega_{st}\,$ (6)

where $\lvert g\rvert<1$ represents the first-order temporal autocorrelation
parameter. The element $\omega_{st}\sim N(0,\Gamma)$ is a Gaussian Process
independent in time with zero mean and covariance matrix

$\Gamma(s,s^{\prime})=\nu\rho(\lvert\lvert s-s^{\prime}\rvert\rvert,\theta)\,$
(7)

where $\nu>0$ is the random effects variance (shape parameter), $\rho$ is a
Matérn spatial covariance function which depends on the distance between pairs
of observations, i.e. $\lvert\lvert s-s^{\prime}\rvert\rvert$, and $\theta>0$
is the spatial dependence parameter. HDGM allows both univariate and
multivariate specifications (Fassò et al.,, 2021), but also a functional
specification called f-HDGM (Wang et al.,, 2021). Each specification relies on
a state-space representation with the related Kalman Filter algorithm. For
recent reviews on Kalman filtering for spatio-temporal models see Ferreira et
al., (2022), Jurek and Katzfuss, 2022a , and Jurek and Katzfuss, 2022b . The
maximum likelihood estimates of the parameters are computed using the EM
algorithm, which is implemented together with the parameter variance-
covariance matrix computation in D-STEM package Wang et al., (2021) for
MATLAB.

The HDGM has been extensively used in many empirical contexts, such as air
quality policy assessment (Fassò et al.,, 2021), bike-sharing system
comprehension (Piter et al.,, 2022), and off-shore coastal profile
measurements for beach monitoring (Otto et al.,, 2021). In addition, the HDGM
model, combined with land use regression techniques, has been used in Taghavi-
Shahri et al., (2019) for spatio-temporal interpolation of missing
observations outperforming conventional interpolation techniques.

##  5 Assessing the impact of COVID-19 lockdown measures on air quality in
Lombardy

To fight the spreading COVID-19 disease across the country, the Italian
government imposed a total lockdown (Presidenza del Consiglio dei Ministri
Italia,, 2020) from 9$th$ March to 18$th$ May 2020. This period, also denoted
as first wave COVID-19 lockdown, was characterized by the closure of all non-
essential activities and enterprises, and by the minimization of individual
mobility and social distancing (Pelagatti and Maranzano, 2021a, ). As a direct
consequence of the limitations, a generalized reduction of car traffic and
personal travel for the entire country was observed (Finazzi and Fassò,,
2020).

Numerous studies have shown how general lockdown imposed by governments have
generated strong and significant reductions in pollutant concentrations
worldwide Higham et al., (2020); Zangari et al., (2020); Nakada and Urban,
(2020); Xin et al., (2021), particularly in large urban centers (Baldasano,,
2020; Rossi et al.,, 2020). The Lombardy (Northern Italy) case study received
a significant scientific interest. In particular, the studies by
Collivignarelli et al., (2020); Cameletti, (2020); Fassò et al., (2021);
Maranzano and Fasso, (2021); Granella et al., (2021) showed that, due to the
restrictions on mobility, oxides concentrations registered statistically
significant reductions (up to 50%) throughout the region. On the contrary,
particulate matter remained stable or slightly reduced over the entire period.
This indicates that the major emission sources of particulate matter in the
region are other than vehicular traffic and industrial production. Consider,
for example, the role of agriculture and livestock farming, which, through the
production of ammonia, generates significant amounts of secondary particulate
matter (Lovarelli et al.,, 2020, 2021).

###  5.1 Sample and event definition

We are interested in analyzing the effect of the lockdown restriction on NO2
concentrations registered in Lombardy. The null hypothesis we are testing is
that the restrictions did not have any effect on the cumulative abnormal NO2
concentrations during the lockdown period (i.e., $CAC_{s\Omega_{1}}$ have null
mean value). The alternative hypothesis is that the cumulated abnormal
concentrations registered a significant reduction during the event-window
(i.e., $CAC_{i\Omega_{1}}$ have negative mean value). Therefore, the
hypothesis test is unilateral on the left tail. Our expectations about the
tests are twofold. Previously existing literature confirmed significant
reductions in NO2 levels in Lombardy. Thus, a statistically significant
negative sign of the statistics is expected. As for dependence, we expect the
cross-sectionally adjusted statistics to be moderate in absolute terms when
compared to the unadjusted statistics. As we will see later, the empirical
correlation of pollutants is remarkable, so that the unadjusted statistics
tend to lead to over-sized tests.

We considered the average daily concentrations of NO2 collected in $N=83$
ground stations belonging to the ARPA Lombardia network (Maranzano,, 2022).
Air quality measurements were collected using the ARPALData package (release
1.2.2 available on CRAN) of the statistical software R (R Core Team,, 2020).

We performed ES analysis using daily observations from 1st January 2018 to
18th May 2020. We recall that the lockdown period during the first wave of
COVID-19 lasted 70 days, from 9$th$ March and 18$th$ May 2020. Although the
event window is very long, we can credibly assume that there were no other
overlapping events capable of hiding the impact of the restrictive measures
during the period. Moreover, by controlling through regression for possible
exogenous effects, several confounding factors typical of environmental
series, such as changes in meteorology or calendar events, were isolated.
However, as a further test regarding the choice of the windows, we performed a
sensitivity analysis by estimating the models with various combinations of
estimation window and event window. We evaluated the following scenarios:

  * •

Exact lockdown period: estimation window from 1st January 2018 to 8th March
2020 ($\tau_{0}=798$ days) and event window from 9th March 2020 to 18th May
2020 ($\tau_{1}=70$ days)

  * •

Anticipated lockdown period: estimation window from 1st January 2018 to 29th
February 2020 ($\tau_{0}=790$ day) and event window from 1st March 2020 to
18th May 2020 ($\tau_{1}=78$ days)

  * •

Restricted lockdown period: estimation window from 1st January 2018 to 15th
March 2020 ($\tau_{0}=805$ days) and event window from 16th March 2020 to 16th
May 2020 ($\tau_{1}=61$ days)

The results of the three scenarios were mutually consistent. The diagnostics
on the estimated models showed very similar characteristics and did not reveal
structural differences in the time series. Both magnitudes and significance of
the test statistics remained of the same order and were absolutely comparable.
The overall assessment of lockdown effects remained unchanged. Therefore, only
the results referring to the exact lockdown period scenario, i.e., considering
an estimation window between 1st January 2018 and 8th March 2020 and event
window from 9th March 2020 to 18th May 2020, will be shown and commented on in
the following sections. The full results of the three scenarios are available
in Supplementary Material S1.

Table 2 reports key descriptive statistics for the Pearson’s linear
correlation index ($\rho$) of NO2 concentrations observed in the sample. The
average cross-sectional correlation at regional level for NO2 is about 60%,
thus able to heavily bias classical ES statistics (see the discussion in
Pelagatti and Maranzano, 2021b, , regarding the effect of even a small
correlation on size and power of ES tests).

Table 2: Descriptive statistics for NO2 concentrations observed at the 83 stations included in the sample and regarding the period January 2018 - May 2020. | Min | 25% perc | mean | Median | 75% perc | Max
---|---|---|---|---|---|---
$\rho$ | -0.327 | 0.464 | 0.579 | 0.632 | 0.737 | 0.953

###  5.2 Spatio-temporal modelling and diagnostics

The covariates included in the fixed-effect component of the HDGM were chosen
among those available from the Copernicus ERA-5 reanalysis database (Sabater,,
2019). ERA-5 provides observations with a $0.1^{\circ}\times 0.1^{\circ}$ grid
spatial resolution. To each air quality station, we associated the
meteorological measurement observed in the cell where the station is located.
To explain the airborne pollutant concentrations, we considered a set of nine
meteorological and land cover variables: average daily temperature
($\mbox{}^{\circ}C$), daily cumulative precipitation (mm), relative humidity
($\%$), atmospheric pressure (Pa), eastward and northward component of the
wind (m/s), geopotential height (m2/s2) as a proxy of altitude, and high and
low vegetation covering (measured as one-half of the total green leaf area per
unit horizontal ground surface area, cf. Sabater,, 2019). While the
geopotential height and land cover are time invariant, the weather covariates
are all time-varying.

Pollutant concentrations are strongly seasonal phenomena. In particular, they
consistently follow the cyclical pattern of climatic seasons. Statistically,
they are characterized by annual seasonality and intra-weekly seasonality. In
the case of hourly measurements, concentrations are also affected by intra-day
seasonality. The inclusion of the weekend dummy in the list of covariates
allows us to control for typical reductions observed during the weekend, while
the use of temperature serves as a proxy for the climatic season. In the case
of NO2, the use of temperature is not sufficient to suitably capture the
annual cycle. To resolve this issue, we decided to include short- and long-
term lags of the time-varying covariates. In detail, we included the 1-day,
2-day and 365-day lagged values of temperature, rainfall, pressure, wind speed
and relative humidity among the regressors. Altogether, the total number of
covariates is 28.

In order to assess the effectiveness of spatio-temporal modelling, we compared
the HDGM performances with those that would be obtained by ignoring the
spatial dependence in the estimation stage, while keeping active the the
temporal dynamics of the concentrations. We compared the spatio-temporal model
with two classes of univariate linear models. First, we considered a multiple
linear regression with i.i.d. errors. Second we model the air quality through
a linear regression model with ARMA disturbances, or regARMA (Zinde-Walsh and
Galbraith,, 1991; Veleva et al.,, 2020; Vadrevu et al.,, 2020). Specifically,
the regression models we considered are as follows:

  * •

HDGM: HDGM as defined in Equations (4)-(7)

  * •

regAR1: regARMA with AR(1) dynamics

  * •

regARMA: regARMA with optimal ARMA dynamics

  * •

lm: linear regression with i.i.d. errors

Note that, while for the regAR1 model the ARMA structure is pre-determined,
regarding the optimal regARMA the ARMA specification is automatically detected
using the Corrected Akaike Information Criterion (AICc) at each monitoring
site. Dealing with daily data we restricted the ARMA specifications to orders
in the range ARMA(0,0)–ARMA(7,7). Thus, we allow the concentrations not
explained by the regressors to be affected by their past values up to seven
days and random shocks occurring within one week of the date.

Both the regAR1 and the linear regression model can be seen as special cases
of the HDGM model. In fact, by assuming that the temporal dynamics of the
errors is of type AR(1), and assuming absence of spatial correlation, HDGM
becomes a regARMA(1,0) model with common (pooled) coefficients across
stations. Finally, assuming both spatial and temporal incorrelation, the HDGM
model degenerates into a pooled regression model with i.i.d. errors. Thus, lm,
regAR1 and HDGM can be considered nested models. The optimal regARMA model is
here included as we assume that the temporal autocorrelation is very strong
and the use of a simple AR(1) dynamics can be insufficient to suitably capture
the persistence.

Eventually, in order to maintain as much comparability as possible, we decided
to use a common set of spatio-temporal covariates to be included in the fixed-
effects component of each model.

Figure 1 shows the estimated abnormal concentrations using the four models
both in the estimation and event windows.

Figure 1: Estimated abnormal concentrations using HDGM (upper left panel),
optimal regARMA (upper right panel), regAR1 (lower left panel) and linear
model (lower right panel). Estimation window: 1st January 2018 - 8th March
2022. Event window: 9th March 2022 - 18th May 2022.

The insights provided by the chart are manifold. First, the HDGM model is the
only one to distinctly reveal the level shift caused by the event of interest.
There is a reduction of about -12$\mu g/m^{3}$ between the average of the
estimation window and the event window. This difference is close to zero in
the case of the optimal regARMA model and is estimated to be around -5$\mu
g/m^{3}$ in the other two cases. The reduction estimated with HDGM is the only
one consistent with that estimated in other studies (Lonati and Riva,, 2021;
Bontempi et al.,, 2022). Second, the abnormal concentrations of HDGM were the
least volatile among the four. In fact, the range in the estimation window is
between $\pm 10\mu g/m^{3}$ and is constant for the entire period (no
heteroskedasticity). Moreover, the abnormal concentrations are poorly
seasonal. Pure time series models show seasonality in the residuals, which are
highly volatile. Graphical analysis leads unquestionably to the dominance of
the spatio-temporal model over those that do not model spatial correlation.

Table 3 reports diagnostics computed on abnormal concentrations within the
estimation window. Our goal was to identify the capacity of the models to
adequately capture the spatio-temporal characteristics of NO2 concentrations.
Therefore, we focused on indicators of centrality, dispersion, shape and
dependence of the ACst within the estimation window. We considered the
following set of diagnostics: Pearson’s linear correlation index ($\rho$) for
cross-sectional dependence; shape indices (i.e. skewness and kurtosis); sample
mean ($\mu$); standard deviation ($\sigma$); temporal autocorrelation at
various lags (i.e., $\phi_{1}$ is the autocorrelation coefficient 1-day lag,
$\phi_{3}$ is the autocorrelation coefficient 3-day lag, $\phi_{7}$ is the
autocorrelation coefficient at 7-day lag, $\phi_{14}$ is the autocorrelation
coefficient at 14-day lag and $\phi_{21}$ is the autocorrelation coefficient
at 21-day lag). Finally, the Outliers quantity calculates the percentage of
outliers over the total using the Hampel filter (Pearson et al.,, 2016).
Statistics are calculated as the average value over the $N=83$ univariate time
series.

| HDGM | regARIMA | regAR1 | lm
---|---|---|---|---
$\rho$ | 0.02 | 0.37 | 0.34 | 0.35
$\mu$ | -0.00 | 0.02 | 0.01 | -0.00
$\sigma$ | 1.40 | 6.23 | 6.40 | 8.02
Skewness | 0.22 | 0.18 | 0.23 | 0.36
Kurtosis | 6.32 | 5.17 | 4.94 | 4.18
$\phi_{1}$ | -0.30 | -0.00 | -0.04 | 0.56
$\phi_{3}$ | -0.01 | 0.01 | 0.06 | 0.30
$\phi_{7}$ | 0.06 | 0.08 | 0.15 | 0.30
$\phi_{14}$ | 0.05 | 0.05 | 0.10 | 0.18
$\phi_{21}$ | 0.02 | 0.04 | 0.07 | 0.14
Outliers | 3.43 | 2.51 | 2.75 | 1.60
Table 3: Descriptive statistics for abnormal concentrations ($AC$) of NO2
within the estimation window (1st January 2018 - 8th March 2020). Each
statistic is computed as the average value across the $N=83$ time series.
$\rho$ is the Pearson’s linear correlation, $\mu$ is the sample mean, $\sigma$
is the sample standard deviation, $\phi_{l}$ is the temporal autoccorelation
coefficient at lag $l$ days, and Outliers is the percentage of values
classified as outliers.

The table suggests considerations that are consistent with Figure 1. The HDGM
residuals are (on average) cross-sectionally uncorrelated, while the other
models show residual cross-sectional correlation. The very short-term (1-day)
temporal serial correlation not zero for HDGM, while it is very close to zero
for regARMA models. As the lag increases, the optimal regARMA model and HDGM
keep the autocorrelation very low, while the regAR1 model and lm do not clean
the residuals adequately. The variance of abnormal concentrations for HDGM is
the lowest ever and is about 1/3 of the others, which confirms what the series
graphs showed earlier (in which the range was the most compact of all). The
shares of outliers are also very small.

In summary, we can state that the HDGM spatio-temporal model is extremely
useful in solving the problem of spatial dependence by slightly sacrificing
the very short term spatial autocorrelation (while the medium to long term
spatial autocorrelation is preserved). This result may be due to the model
definition itself. HDGM is built to model only the AR(1) dynamics. If the
dependence is strong, covariates play a key role. In contrast, the regARIMA
model with optimal choice of lags easily fits the high persistence by
increasing the lags in the model.

###  5.3 Test statistics for NO2 concentrations

Table 4 reports the estimated test statistics on NO2 average concentrations
during the event window. The reported significance levels are computed using
the quantiles of a standard Normal distribution at level $\alpha$.

ES_stats | CD | HDGM | regARMA | regAR1 | lm
---|---|---|---|---|---
P1 | Adj | -16.69*** | -3.75*** | -9.39*** | -14.57***
P2 | Adj | -20.57*** | -3.21*** | -8.60*** | -13.77***
Corrado_Tuckey | Adj | -22.76*** | -9.46*** | -15.12*** | -15.86***
Z_patell_adj | Adj | -29.41*** | -11.32*** | -20.31*** | -22.95***
Z_BMP_adj | Adj | -11.43*** | -2.24** | -2.88*** | -2.83***
T_grank | Adj | -14.79*** | -11.9*** | -15.12*** | -15.26***
Z_grank_adj | Adj | -26.37*** | -3.74*** | -9.9*** | -14.29***
CumRank | Adj | -27.62*** | -3.92*** | -10.37*** | -14.97***
CumRank_mod | Adj | -79.69*** | -3.95*** | -11.07*** | -17.37***
CumRank_T | Adj | -112.38*** | -20.99*** | -56.94*** | -88.11***
CumRank_Z_adj | Adj | -42.45*** | -3.68*** | -9.77*** | -16.08***
cross_T_test | Unadj | -25.81*** | -3.56*** | -9.43*** | -16.2***
crude_dep_T_test | Unadj | -13.75*** | -15.07*** | -25.86*** | -23.39***
T_test_skew | Unadj | -210.02*** | -20.51*** | -54.54*** | -101.06***
Z_patell | Unadj | -60.82*** | -3.66*** | -10.07*** | -18.41***
CumRank_Z | Unadj | -39.70*** | -3.96*** | -10.81*** | -16.24***
Z_grank | Unadj | -5.22*** | -2.24** | -2.87*** | -2.82***
Z_BMP | Unadj | -7.94*** | -1.61 . | -3.04*** | -3.37***
Table 4: Estimated ES statistics for NO2 concentrations within the event
window (9th March 2020 - 18th May 2020). Symbols ’***’, ’**’, ’*’ stand for
statistically significant at levels 1%, 5% and 10%, respectively. The symbol
’.’ stands for not statistically significant at 10%.

Overall, the estimated values are consistent with the expectations, both in
terms of sign and magnitude. Regarding the signs, all the estimated statistics
report a negative value, meaning the presence of a reduction in the average
NO2 concentrations at regional level due to the lockdown period. Estimations
for HDGM, regAR1 and lm are always statistically significant at 1% level. The
statistical significance for the optimal regARMA are slightly lower,
especially for the unadjusted statistics (e.g., $Z_{BMP}$ and $Z_{grank}$).
This result is consistent with the findings observed in Figure 1, which showed
that the difference between the averages of the two periods was very close to
zero. Eventually, considering the HDGM, in absolute values, all the unadjusted
statistics are smaller than the cross-sectionally adjusted statistics. This
finding is also consistent with expectations. Having explicitly modeled cross-
sectional dependence in estimation, which led to a near-zero Pearson
correlation index in the estimation window, the adjusted statistics result in
very high values by construction. However, adjusting the ES statistics remains
the most consistent and statistically valuable alternative.

##  6 Conclusions and future developments

We presented new empirical findings regarding the application of ES methods to
the case of strongly cross-sectional dependent multivariate time series. Our
interest focused on cross-sectional dependence resulting from the strong
spatial correlation naturally exhibited by geo-referenced observations, such
as air quality measurements collected from ground monitoring networks.

The major points we raised were as follows. First, we generalized the
statistical concepts underlying ES and adapted them to the case of airborne
pollutant concentrations. In this regard, we provided definitions of normal
and abnormal airborne concentrations by exploiting the analogy with the
concept of abnormal returns typical of financial literature. Second, we
discussed the role of (spatial) cross-sectional dependence in ES by proposing
a twofold strategy to overcome its drawbacks. In principle, we proposed to
analyze time series interconnected by a strong spatial correlation through a
geostatistical spatio-temporal model, namely the HDGM. This model allows to
exploit the relationship among the response variable and a set of exogenous
covariates, while accounting for the spatio-temporal dynamics of the
observations. Additionally, the HDGM was compared with three purely temporal
models not explicitly accounting for the spatial dimension. As a second step,
we suggested to investigate the abnormal concentrations through a set of
sixteen ES statistics in order to determine the significance of the event of
interest. Among the ES statistics used, some of them were specifically built
to deal with cross-sectionally dependent observations.

The adjustment strategy was applied to the empirical case of NO2
concentrations registered in Lombardy through the ARPA air quality monitoring
network. We considered as the event of interest the lockdown restrictions
imposed on mobility and socio-economic activities during the first wave of the
COVID-19 pandemic. The main interest was to state if the lockdown generated
significant reductions in the average concentrations of NO2, i.e., we tested
for a level shift after the event date. Our findings can be summarized as
follows. First, the HDGM was the only one that distinctly reveals the level
shift caused by the event of interest. The other models, in fact, showed much
more limited reductions. Moreover, the abnormal concentrations of the HDGM
were the least volatile among those computed. Second, the HDGM was the only
one of the four specifications to fully isolate the spatial dependence of the
data, leading the average CD of the abnormal concentrations to be zero.
However, the very short-term temporal autocorrelation (i.e., 1-day lag)
persisted. Third, all the proposed test statistics, both adjusted and
unadjusted for CD, unequivocally revealed a reduction in NO2 concentrations
due to the lockdown imposed in Lombardy. The robustness of this reduction was
established through a sensitivity analysis of the test statistics with respect
to the start and end dates of the event.

Future studies that apply Event Studies methodology for spatio-temporal data
should regard the spatio-temporal dependence between observations intensively.
We focused on modelling NO2 concentrations using the univariate HDGM. However,
other models could be implemented. Consider, for example, the fixed rank
smoothing spatio-temporal random effects model (Katzfuss and Cressie,, 2011),
hierarchical spatio-temporal models based on INLA (Fioravanti et al.,, 2021;
Saez and Barceló,, 2022) and Dynamic Spatio-Termporal Models (Wikle et al.,,
2019). The second strategy involves the use of multivariate models to jointly
analyze multiple response variables (e.g., different types of pollutants) that
are mutually correlated. This approach would provide an opportunity to exploit
the cross-correlation among responses to further improve predictions in the
event window. Consider as examples the multivariate extension of HDGM (Fassò
et al.,, 2021) or spatio-temporal VAR models (Ferreira et al.,, 2022).
Eventually, the ES test statistics could be explicitly adjusted for the
spatial cross-correlation (Chen,, 2015) and spatio-temporal cross-correlation
(Ma et al.,, 2006; Gao et al.,, 2019) measures, instead of linear correlation
measures.

## Data and codes

All the results presented in this paper can be reproduced using R and Matlab
software. Data and codes have been uploaded in the journal’s database. Data
and codes are available at the following Google Drive link:
https://drive.google.com/drive/folders/1fXImuCvOpP7orvfuSeGwDa-
GcuNyOf-H?usp=sharing.

## Supplementary materials

This paper is accompanied by a single supplementary material: Full results of
the event date sensitivity analysis (S1).

## Declarations

  * •

Funding: this research was funded by Fondazione Cariplo under the grant
2020-4066 ”AgrImOnIA: the impact of agriculture on air quality and the
COVID-19 pandemic” from the ”Data Science for science and society” program.

  * •

Conflict of interest/Competing interests: the authors declare that they have
no competing interests

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# Bone Marrow Cytomorphology Cell Detection using InceptionResNetV2

Raisa Fairooz Meem  Khandaker Tabin Hasan

###### Abstract

Critical clinical decision points in haematology are influenced by the
requirement of bone marrow cytology for a haematological diagnosis. Bone
marrow cytology, however, is restricted to reference facilities with
expertise, and linked to inter-observer variability which requires a long time
to process that could result in a delayed or inaccurate diagnosis, leaving an
unmet need for cutting-edge supporting technologies. This paper presents a
novel transfer learning model for Bone Marrow Cell Detection to provide a
solution to all the difficulties faced for the task along with considerable
accuracy. The proposed model achieved 96.19% accuracy which can be used in the
future for analysis of other medical images in this domain.

###### keywords:

Transfer Learning , Bone Marrow Cell Detection , InceptionResNet

###### PACS:

0000 , 1111

###### MSC:

0000 , 1111

††journal: arXiv

[inst1]organization=Department of Computer Science, American International
University Bangladesh,addressline=Dhaka, city=Dhaka, country=Bangladesh

[inst2]organization=Department of Computer Science, American International
University Bangladesh,addressline=Dhaka, city=Dhaka, country=Bangladesh,
email=<EMAIL_ADDRESS>
Explore the application of Transfer Learning for Bone Marrow Cell Detection

##  1 Introduction

A haematological diagnosis is mainly based on a bone marrow analysis [17]. It
is carried out to investigate a haematological problem that is clinically
suspected, as part of lymphoma staging procedures, and to evaluate the bone
marrow response to chemotherapy in acute leukaemias. It is also examined in
myelodysplastic syndrome (MDS) and myeloproliferative neoplasm (MPN) to detect
several factors such as dysplastic cellular morphology, blast excess, and
cellularity of the subject etc. [22]. A hematopathologist will gather data
from the various parts of a bone marrow investigation and combine it with
clinical data to arrive at a final diagnostic interpretation. There are
currently no clinical-grade solutions for bone marrow cytology, even though a
number of commercial computational pathology workflow support systems have
been created for the analysis of peripheral blood cytology. The reliability of
a disease diagnosis depends on the accuracy of identification of
histopathological image slides for which, a computerized process, namely
machine learning can be an affordable yet efficient solution, replacing the
dependency on human experts [21]. Bone marrow aspirates are more sophisticated
cytological specimens than blood film cytology. Aspirates have a limited
number of cytologically useful regions, a large amount of non-cellular debris,
and a wide variety of cell types that are frequently aggregated or
overlapping. This has made computational pathology problems related to bone
cytology somewhat difficult [2].

Malignant and nonmalignant illnesses affecting the haematopoietic system can
be diagnosed by examining and differentiating the cell morphologies of the
bone marrow (BM). Despite the availability of numerous advanced techniques,
including cytogenetics, immunophenotyping, and increasingly molecular
genetics, cytomorphologic evaluation is still a crucial initial step in the
diagnosis of many intra- and extramedullary diseases. Since the process has
proven challenging to automate, in a clinical workflow, human experts are
still primarily responsible for microscopic analysis and single-cell
morphological classification. Manual evaluation of BM smears, however, can be
laborious and time-consuming and is greatly reliant on the knowledge and
experience of the examiner, particularly in cases when the results are
unclear. As a result, the availability and expertise of qualified experts is a
constraint on the number of high-quality cytological examinations, although
examiner classifications have been found to be vulnerable to significant
inter- and intrarater variability. Furthermore, the procedure is challenging
to combine with other diagnostic techniques that provide more quantitative
data because the analysis of individual cell morphologies is fundamentally
qualitative [12].

Deep learning techniques for object detection include regional CNN (R-CNN),
and fast and Faster R-CNN. These methods rely on region proposals for object
recognition, followed by a different technique like object classification,
which makes them difficult to train and ineffective computationally [2]. Deep
learning models, in particular convolutional neural networks (CNN), are
extensively employed for picture categorization tasks [1]. But the main
obstacle to widely applying it for the medical image analysis sector is the
unavailability of large datasets as small datasets for training lead to
overfitting results or convergence [15]. Assigning individual bone marrow
cells or non-cellular objects to one of the multiple discrete classes based on
sophisticated and nuanced cytological traits presents another challenge in
object categorization. In MDS, when morphological dysplasia causes subtle
cytological alterations, this complexity rises. Many tried to solve the issues
by fine-tuning the Faster R-CNN. This method, however, proved to be
inefficient operationally and is probably not adaptable to a clinical
diagnostic workflow. To enable bone marrow aspirate cytology, unique,
effective, and scalable computational pathology methodologies are required.
Approaches that add full end-to-end automation, that is, from raw images to
bone marrow cell counts and classification [2].

Transfer learning (TL) gained the attention of researchers working on medical
image analysis in recent years. Transfer learning is a branch of CNN that has
had its weights initialized before and can be trained quickly and accurately
due to being trained on a bigger dataset. The main advantage of using transfer
learning is that instead of starting from scratch with the random
initialization, the weights used can be applied to categorize another entirely
different dataset [5]. Most commonly used models are often trained on the
ImageNet dataset, a massive collection of images created for use in the
development of visual object recognition software. The project has manually
annotated over 14 million photographs to identify the things they depict, and
at least one million of the images also include bounding boxes. Although the
actual images are not ImageNet’s property, the database of annotations for
third-party image URLs is freely accessible. A deep CNN model that has
previously been trained on a huge dataset is used for the procedure. The CNN
model is further trained (fine-tuned) using a new dataset that has fewer
training images than the previously trained datasets. While the latter layers
of CNN models concentrate on more abstract features, the first layers of CNN
models frequently learn features like edges, curves, corners, etc. Frequently,
the remaining layers are relocated to carry out a new classification while the
completely linked layer, SoftMax layer, and classification output layer are
discharged [16]. Transfer Learning was a common option when the available
dataset was small since it did not require huge datasets to train the model
with randomly initialized weights from start [6].

Inception and ResNet, two of the most effective models, were combined to
create the well-known TL model known as ResNet. This model, which was
developed using the ImageNet database, substitutes batch normalization for
convolutional layer summation. To prevent overfitting, input units are set to
0 at random in the dropout layers during the training phase. In order to use a
one-dimensional data array in the subsequent layers, the model additionally
employs a flattering strategy. The same procedure is used to generate a
feature vector from the output data. By connecting to the classification
model’s final layer, the model creates a fully connected layer with a batch
size of 32 and a ”binary cross-entropy” loss function [7].

In this study, a small dataset of bone marrow smears is analyzed using
InceptionResNetV2 to find the cells suggestive of different haematological
illnesses. This article is divided into five sections: the second section
highlights the relevant improvements made in this field to date; the third
describes the research’s methods and supplies; the fourth examines the
findings; and the fifth closes with recommendations for further research.

##  2 Literature Review

Recently, Convolutional Neural Networks (CNN) and Deep Learning (DL) are being
utilized extensively for medical image analysis. Naturally, the use of
Transfer Learning (TL) is also promoted in this field, given that it provides
a workaround for the need for huge training datasets.

To offer the most recent status of this subject, Morid, Mohammad Amin et al.
[8] reviewed selected articles published after 2018 on the utilization of
different ImageNet-trained transfer learning models for the analysis of
clinical images. According to their analysis, the use of models depends on the
type of images that are being processed. For X-ray, endoscopic, or ultrasound
pictures, for instance, Inception models are often utilized, whereas VGGNet
performs comparably better for OCT or skin lesion images. No matter the type
of image or organ, the top 4 models are Inception, VGGNet, AlexNet, and ResNet
in order of most frequent usage. Only 3 papers mentioned the InceptionResNet
model because it is a relatively novel method.

The literature assessment undertaken by Kim, Hee E., et al. [11] also
supported the choice of Inception and ResNet models. They assessed 425
articles on medical image classification using transfer learning models that
were published till 2020, and the result indicated the usefulness of these
models considering the scarcity of data. Their study on reducing costs and
time for clinical image detection provided some interesting outputs such as:
1. for most transfer learning models, fine-tuning only the last fully
connected layers provides a better result than starting from scratch. 2.
Unfreezing the convolutional layers while maintaining a low learning rate from
top to bottom manner can improve the overall performance of the model.
According to their study on various models used in the selected articles,
Inception and ResNet models were proven the most effective feature extractors
which are able to provide impressive accuracy even after reducing the time
required and computational costs.

Faruk, Omar et al. [7] applied 4 different transfer learning models, namely
Xception, InceptionV3, InceptionResNetV2, and MobileNetV2 for tuberculosis
detection using X-ray images. Each model consists of three MaxPooling2D
levels, four Conv2D layers, a flattened layer, two dense layers, and a ReLU
activation function. With a few tweaks in the final layers, the thickest and
last layer, SoftMax, functions as an activation layer. Layers like average
pooling, flattening, dense, and dropout are used to customize the results.
InceptionResNetV2 outperformed the other 4 models in terms of accuracy
(99.36%).

Matek, Christian, et al. [12] proposed a model named ResNeXt to classify Bone
Marrow Cell Morphology. ResNeXt replicates a structural component that
combines several transformations with the same topology. In addition to the
depth and width dimensions, it also highlights cardinality (the size of the
set of transformations) as a new dimension in comparison to ResNet. They
preferred this particular model as it was previously applied for categorizing
peripheral blood smears. They selected only 32 cardinality hypermeters for the
research. They used a single-centre strategy, preparing all the BM smears
included for training in the same laboratory and digitizing them using the
same scanning tools. The network reported in this study performs in a highly
encouraging manner where the external validation shows that the strategy is
generalizable to data gathered in various settings, albeit being difficult due
to the small amount of available data.

Yu, Ta-Chuan, et al. [17] proposed a deep CNN architecture to automatically
identify and classify Bone Marrow cells. The dataset consisted of Liu’s
stained images of bone marrow smears of patients at the National Taiwan
University Hospital. The proposed model considered and applied several factors
such as group normalization, colour shift, Gaussian blur etc. for various
tasks such as model training or augmentation of data and achieved 93.6%
accuracy.

Rahman, Jeba Fairooz, and Mohiuddin Ahmad [20] conducted a comparative study
on 4 transfer learning models, namely AlexNet, VGG-16, ResNet50, and
DenseNet161 to detect Acute Myeloid Leukaemia (AML) that is mainly
distinguished by the traces of immature leukocytes in blood and bone marrow.
They modified the applied models using a binary classifier and ReLu for
activation as they aimed to detect mature and immature leukocytes only. Among
the models, AlexNet achieved an accuracy of 96.52% for detecting leukocytes.

Many of the research works on haematological disease analysis focus on Acute
Lymphoblastic Leukemia (ALL) Cell detection. It is a type of cancer that
damages organs and tissues involved in blood production and the blood
circulation system as well. It damages the production of healthy white blood
cells that are responsible for protecting the body from various diseases [19].

Kumar, Deepika, et al. [4] proposed a Dense CNN model for accurate
identification of ALL and Multiple Myeloma and compared the performance with
multiple machine learning methods, namely, Support Vector Machine (SVM),
VGG16, Naïve Bayes, Random Forest (RF), Decision Tree (DT) etc. Adam Optimizer
was used to train the model consisting of multiple Convolution, Pooling, and
Connected layers with Sigmoid loss function. The model achieved an accuracy of
97.25%.

Liu, Ying, et al. [18] and Ramaneswaran, S, et al. [23] both applied transfer
learning models for classifying ALL Cells. Liu, Yin, et al. applied
InceptionResNetV2 as a backbone network to identify lymphoblastic leukaemia
cells using 2 stages deep bagging ensemble learning technique while
Ramaneswaran, S, et al. used InceptionV3 as the feature extractor with XGBoost
Classifier instead of SoftMax. Liu, Ying, et al. trained the model using the
bagging ensemble learning to minimize data imbalance and produced two separate
models that were later combined to enhance the final performance. The model
achieved an F1 score of 0.88 for classifying the cells. The hybrid InceptionV3
with XGBoost Classifier model proposed by Ramaneswaran, S, et al. achieved an
accuracy of 97.9%.

Abir, Wahidul Hasan et al. [9] conducted a comparative study on the
performance of several transfer learning models for identifying ALL cells. The
models were InceptionV3, InceptionResNetV2, ResNet101V2, and VGG19. They
applied Local Interpretable Model-agnostic Explanation (LIME) algorithm and
XAI to ensure the reliability and validity of the proposed model. They applied
a stratified k-fold cross-validation technique to remove the imbalance in the
dataset for class distribution. InceptionV3 model achieved 96.65% accuracy for
the validation set, outperforming the other models, though for the training
set, InceptionResNetV2 had the highest accuracy (99.14%).

Tayebi, Rohollah Moosavi, et al. [2] proposed a You-Only-Look-Once (YOLO)
model for automated bone marrow cytology. An end-to-end system based on deep
learning was created for the experiment. The model automatically detects
regions that are suitable for cytology from a digital whole slide image of a
bone marrow aspirate, and then it identifies and categorizes every bone marrow
cell in each region. This comprehensive cytomorphological data is represented
by a cytological patient fingerprint known as the Histogram of Cell Types
(HCT), which quantifies the probability distribution of bone marrow cell
classes. The proposed system provided an impressive accuracy considering
region detection (0.97 accuracies and 0.99 ROC AUC), cell detection and cell
classification (0.75 mean average precision, 0.78 average F1-score, and a log-
average miss rate of 0.31).

Loey, Mohamed, Mukdad Naman, and Hala Zayed [10] claimed to achieve 100%
accuracy in leukaemia detection using transfer learning models. They applied 2
models for the task. The first model used AlexNet for feature extraction and
several classifiers, namely SVM (Linear, Gaussian, and Cubic), DT, Linear
Discriminants (LD) and K-NN for the classification process. The model with
SVM-Cubic achieved the highest accuracy among other classifiers (99.79%). The
2nd model used AlexNet both for feature extraction and classification. This
model achieved 100% accuracy in detecting leukaemia using blood cell image
slides.

In conclusion, the field of brain and lung illness detection, particularly
different types of cancer, uses TL models most frequently. However, because of
how well they worked, researchers started using them to find problems in other
organs as well. We are motivated to conduct more studies in this area because
several models have demonstrated outstanding accuracy in the identification of
haematological diseases from Bone Marrow Cell images.

##  3 Methodology

###  3.1 Dataset

The dataset from the work of Matek et al, [14] consists of 171,375 cells from
bone marrow smears of 945 patients stained with the May-Grünwald-
Giemsa/Pappenheim stain that has been de-identified and expertly annotated.
The cohort’s diagnosis distribution includes a range of haematological
conditions consistent with the sample entry of a sizable laboratory with a
focus on leukaemia diagnostics. A brightfield microscope with a 40x
magnification and oil immersion was used to get the images. 20% of the
dataset, chosen at random, was used for the thesis. The images are divided
into 21 categories based on the haematological disease or aspect they present.
The categories are mentioned in Table 1.

Table 1: List of Haematological diseases cell images of which are included in the dataset Abbreviation | Meaning
---|---
ABE | Abnormal eosinophil
ART | Artefact
BAS | Basophil
BLA | Blast
EBO | Erythroblast
EOS | Eosinophil
FGC | Faggott cell
HAC | Hairy cell
KSC | Smudge cell
LYI | Immature lymphocyte
LYT | Lymphocyte
MMZ | Metamyelocyte
MON | Monocyte
MYB | Myelocyte
NGB | Band neutrophil
NGS | Segmented neutrophil
NIF | Not identifiable
OTH | Other cells
PEB | Proerythroblast
PLM | Plasma cell
PMO | Promyelocyte

###  3.2 Evaluation Criteria

To evaluate the performance of the transfer learning model, a confusion matrix
was utilized where four types of output were considered- True Positive (TP)
where an output accurately identifies the existence of a condition, True
Negative (TP) meaning an output correctly indicates the absence of a
characteristic, False Positive (FP) where the existence of a condition is
falsely indicated and False Negative (FN) where the output wrongly identifies
the existence of a condition. The concept of the confusion matrix is further
explained in Table 2:

Table 2: Explanation of TP, TN, FP, and FN I/O | Output Negative | Output Positive
---|---|---
Input Positive | False Positive (FP) | True Positive (TP)
Input Negative | True Negative (TN) | False Negative (FN)

Five criteria are used to evaluate the output: accuracy, loss, precision,
recall, and AUC.

The evaluation of how closely the expected result matches the actual result is
called Accuracy, expressed as a percentage. It is computed by dividing the sum
of true positive and true adverse events by the total number of outcomes that
could occur:

Accuracy = (TP + FN) / (TP + TF + FP + FN)

The degree to which predicted values accord with one another is known as
Precision. One can determine the true positive by dividing the true positive
by the sum of true and false positives.

Precision = TP / (TP + FP)

The gross number of true positives is divided by the total number of true
positives and false negatives to determine the Recall value of an experiment.

Recall = TP / (TP + FN)

For this experiment, ‘32’ was selected as the batch size along with only 5
epochs. Google Colaboraty was used as the experiment’s coding platform, which
also utilized GPU runtime. ‘Categorical Loss Entropy’ was selected for the
experiment. According to Zaheer et al [13], the Adam optimizer, derived from
’Adaptive Moment’ outperforms all the other optimizers in terms of accuracy
which is why it was selected for this experiment.

##  4 Output Evaluation

Table 3: Evaluation of InceptionResNetV2 for Bone Marrow Cell Detection Set | Loss | Accuracy | Precision | Recall | AUC
---|---|---|---|---|---
Training | 5.7916 | 96.39% | 0.6214 | .6171 | 0.8472
Validation | 7.2734 | 96.19% | 0.6 | 0.5968 | 0.8297

The result points out several things- first, the difference between the
accuracy of training and validation sets is very little (0.2%). The loss
values are quite high for both sets, even more in the case of the validation
set (7.2734). Precision and recall values for both sets are almost similar,
even with each other.

##  5 Conclusion

Transfer learning models reduce the possibility of false detection along with
the complexity, human participation requirements, required time etc. which is
beneficial for biological image segmentation and can ensure that everyone,
including those with minimal resources, receives competent medical care. The
paper examines the effectiveness of the InceptionResNetV2 model for bone
marrow cell detection, a crucial component of the analysis of blood disorders
that have not received enough attention from researchers who are curious about
the potential uses of transfer learning models in this field. To better
understand them, other criteria were applied to the output the model produced.
The chosen model had a 96.19% accuracy rate. This work points to potential
areas for further research, such as:

  * 1.

Comparing several transfer learning models to see whether any model can
outperform the InceptionResNetV2 models.

  * 2.

A follow-up investigation to improve InceptionResNetV2’s Bone Marrow Cell
Detection accuracy.

  * 3.

Other bone diseases and illnesses in other organs can be detected using the
InceotionResNetV2 model.

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