**Mapping of Pneumonia Disease in Malaysia Using Poisson-** **Gamma Model **

**1****Ijlal Mohd Diah&**^{1,2}**Nazrina Aziz* **

* Corresponding author:

1Department of Mathematics and Statistics, School of Quantitative Sciences, UUM College of Arts and Sciences, Universiti Utara Malaysia, 06010, Sintok, Kedah Darul

Aman, Malaysia.

2Institute of Strategic Industrial Decision Modelling (ISIDM), UUM.

**Abstract **

Bayesian models have been used as one of the estimation techniques for smoothing relative risks estimation for disease mapping. One of the most commonuses of Bayesian methodology in disease mapping is Poisson-gamma model. This paper begins with a brief introduction of pneumonia disease. Then followed by a review of methodology used in this paper that is Poisson-gamma model which used to estimate the values of relative risk.Then, the results will be shown into a map to show pneumonia risk areas. The risk areas can be shown clearlythrough disease map. Thus, the objective of this study is to estimate the value of relative risk for pneumonia based on Poisson-gamma model. Pulau Pinang, Perak, Selangor, Kuala Lumpur &

Putrajaya, Sabah, Labuan and Sarawak are categorized as low-risk of pneumonia occurrence, while Terengganu and Negeri Sembilan categorized as high-risk areas.

**Keywords: disease mapping; pneumonia; relative risk; Poisson-gamma model **

**1. ** **Introduction **

This paper demonstrates and discusses the used of the most common and earliest
Bayesian method that is Poisson-gamma model in disease mapping.First, we explain
about pneumonia. This is followed by description of Poisson-gamma model that was
suggested by Lawson et al.^{1}.Pneumonia is an infection in one or both lungs which
inflames the air sacs with pus or fluid.It can be causedby different type of organisms
which include viruses, bacteria and fungi^{2}.However, the most common cause for
someone to get pneumonia is caused by bacterial pneumonia known as Streptococcus
pneumoniae and viruses. These viruses include the new virus which is now already
became outbreak worldwide that is Coronavirus-2019 (COVID-19), which may
trigger pneumonia and can become serious. Forchildren under 5 years old, the most
well-known cause of pneumonia are viruses. Eventhough viral pneumonia usually is
just minor, however it can become most terrible in some case^{2}.Both bacterial and viral
pneumonia are contagious which mean that they can transmit the disease from a
person to anothervia air when a person inhales airborne droplets from a sneeze or
cough of an infected person. It also can be transfered to others through contact with
objects or surfaces that are contaminated with bacteria or viruses.When someone is

infected with pneumonia, it will show symptoms such as chest pain when cough or
breathe, fever, chills, shortness of breath, and coughing that produce mucus^{2}. The
symptoms can be varied from minor to serious depend on factors such as age, type of
organisms that causes the inflammation, and overallcondition of health. For mild
symptom, it shows like a normal flu or cold, but it last longer.

The severity of pneumonia can range from mild to life-threatening. Infants and
young children especially under-age of five, people aged 65 years and older, and
people with weakened immune systems are the higher risk group and can become
most serious for them if they are being infected with pneumonia^{2}. Pneumonia has
been recognized as top five diseases that causes of death globally with 2.6 million in
2017^{3}. About 15% from these 2.6 million are deaths among children under-age of
five. About 1 child dies of pneumonia every 39 seconds and this made it become
number one killer among the leading infectious disease cause of death for children
under-age of five^{4}.These 2.6 million of deaths concentrated in South Africa, South
East Asia, and sub-Saharan Africa. Even though pneumonia is a preventable disease,
but it kills more children than other infections. It also recognized as a common cause
of death for elderly where in 2017, about 1.13 million of deaths are among adults
aged over 65 years^{3}. According toDepartment of Statistics Malaysia, pneumonia has
been listed as top three diseases that cause death in Malaysia^{5}. In 2019, 145,419 cases
had been reported with 7,542 number of deaths^{5}. Pneumonia also been reported as top
three causes of death for children under-age of five.If this situation persists, it will
affect the number of future populationsif it is not control where we will be facing
ageing population as there are more people aged 70 years and older than there are
children under-age of five in the future.

It is necessary to look into this problem as complication for those who infected
with influenza and Corona Virus Disease 2019 (COVID-19) can lead someone to get
pneumonia disease^{5}. Both can contribute to the increase in the number of pneumonia
cases. Pneumonia disease might become outbreak if it does not control as the number
of pneumonia cases can be increase due to other diseases.

Current approach used in Malaysia to estimate the low and high-risk areas of pneumonia is by monitoring based on the reportedoverall number of cases in each state. However,this approach only showed general information without consider other important factors such as number of population and geographical areas.

One of the important tools in public health research is disease mapping where it
can be help in controlling and alsoas the stopping strategies for a disease^{6}. Disease
mapping can be seen as a descriptive picture of pneumonia’s burden in some
geographical areas.Besides, it can help showing areas that need more attention from
government especially in term of health supply and medical treatment.In this study,
Empirical Bayes approach specifically Poisson-gamma model are used where this
approach arehighly recommended in the use of small area estimation as it smooth the
relative risk and provides the measures of uncertainty associated with this relative risk
estimation and the modeling can take into account the spatial autocorrelation. The
approach to smoothing in Bayesian approach is by borrowing strength values from
geographically referenced neighboring values.

**2. ** **Materials and Methods **

In this study,the relative risk values are computed using WinBUGSsoftware. This
software is a program created to implement Bayesian inference on statistical problem
using computations of Markov Chain Monte Carlo (MCMC)^{1}.Findings of this study
are presented in form of table and graph. A map of the pneumonia risk will be
displayed to show the high-low risk areas depend on the values of relative risk which
are estimated. ArcGIS software is used to produce the map.For the Poisson-gamma
model,the prior parameters values, α and *β are unknown and are assumed to have *
exponential prior distributions with values of hyperparameter 0.1^{1}. The prior expected
relative risks in this study using this model is equal to 1.

*2.1 Poisson-gamma Model *

One of the initial Bayesian methods is Poisson-gamma model that has been
suggested by other researchers to be used to overcome the weakness of the
Standardized Morbidity Ratio(SMR)method^{1}. Poisson distribution is used as this is
the fundamental model for count data. Here,i=1,2,…,M represent the study areas
whilej=1,2,…,Trepresent the time period.Assumingthat the numberof new
infections,y* _{ij}* followsthe Poisson distribution over a period of time, with mean and
variance,e

_{ij}*θ*

*. In this model, the expected number of new infectives is expressed as*

_{ij}*e*

*ij*and the relative riskis expressed asθ

*ij*, hence:

*y*_{ij}*|e*_{ij}*, θ*_{ij}*~Poisson (e*_{ij}*θ** _{ij}*) (1)

The parameter of the relative risk has a gamma prior distribution withα and β parameters:

*θ**ij**~ Gamma(α, β) * (2)

Based on this Poisson-gamma model, the expected posterior relative risk will be one of the outputs of the analysis.

*2.2The Data Set *

In this study, the data set wasgivenby the Department of Statistics and Ministry of Health in Malaysia. This Poisson-gamma model are implemented to pneumonia data from year 2010 until year 2019in form of the number of cases for 13 states in Malaysia that are Perlis, Kedah, Penang, Perak, Selangor, Negeri Sembilan, Melaka, Johor, Pahang, Terengganu, Kelantan, Sabahand Sarawak and three federal territories that are Kuala Lumpur, Putrajaya, and Labuan. However, in this study, both territories and states are informed as states for simplicity. In this study, for Putrajaya state pneumonia data are included in the data for the states of Kuala Lumpur where it is written as Kuala Lumpur& Putrajaya.

**3. ** **Results **

Figure 1 shows the estimatedresultsof the relative risk value for 15 states in Malaysia. From the graph, most statesshow the relative risk values more than one from year 2010 until 2019 which implies that the susceptible people in these states tendtogetpneumonia disease compared with people throughout thewhole population.The relative riskin this study isdefinedas the conditional probability that a person inside anareabecome infected with the disease divided by the conditional

probability that a person in the whole population become infected with the disease.

From the graph, Sabah and Sarawak has relative risk close to one for most epidemiology weeks, which means there is no significant difference in terms of the likelihood that the people in these states and within the whole population to contract with pneumonia disease. Conversely, for Selangor, Kuala Lumpur & Putrajaya and Pulau Pinang, these three states have relative risk value less than one for most epidemiology weeks which shows that people within thesestates are less probable to get pneumonia disease when compared to wholepopulation in Malaysia.

0.500 1.000 1.500 2.000 2.500

**R** **e** **la** **ti** **ve** ** R** **is** **k**

**Relative Risk Estimation of Pneumonia in ** **Malaysia**

**Fig. 1Plots of time series for the relative risk estimation using Poisson-gamma **
**model for 15 states in Malaysia. **

Numerical values for the relative risk are shown in Table 1 for year 2019.

From Table 1, susceptible personsin the state of Terengganu has the highest risk of getting infected with pneumonia disease with 1.651 value of relative risk. In contrast withsusceptible persons in Pulau Pinangwhere it recognized to bethe lowest risk areawith value of 0.559.

**States ** **Relative risk **

Perlis **1.458 **

Kedah **1.094 **

Pulau Pinang **0.559 **

Perak **0.922 **

Kuala Lumpur & Putrajaya **0.710 **

Selangor **0.682 **

N. Sembilan **1.521 **

**Table 1. Estimation of Relative Risk forPneumonia for Year 2019 **

Figure 2 shows the choropleth pneumonia map that showhigh-low risk areas for the occurrence cases of pneumonia for 15 states of Malaysia for year 2019. Each state is allocated with one of five different levels of relative risk, starting from very low to very high risks with intervals of [0.0,0.5), [0.5, 1.0),[1.0,1.5), [1.5,2.0) and [2.0, ).

Here, very low risk is represented bythe brightestshade and for very high risk, it is represented by the darkest shade to differentiate the levels of relative risk.

**Fig. 2. Relative risk estimation map forpneumonia disease using Poisson-gamma **
**modelfor year 2019 **

Figure 2 demonstratesthe map ofPoisson-gamma. From the map, the stateofNegeri Sembilan and Terengganu have high risk areas. Perlis, Kedah, Johor, Pahang and Kelantan have been identified as medium risk areas. The other statesare identified aslow risks.There is no state identified as very high risk and very low risk area.

**4. ** **Conclusion **

It very important to estimate the values of relative risk in orderto monitor and control the spread of pneumonia, especially in Malaysia. In this study, Poisson- gamma model has been used to estimate the relative risk values, which this model is one of the initial approach of Bayesian in estimating the relative risk. The results for

Melaka **1.066 **

Johor **1.099 **

Pahang **1.375 **

Terengganu **1.651 **

Kelantan **1.491 **

Sabah Labuan

**0.978 **
**1.178 **

Sarawak **0.983 **

this study are shown in form of graph, table and also map. From the map, it givesobvious picture of areas withhigh-low risks. To conclude, there is no state that has been identified as very high-risk and very low-risk area. Terengganu and Negeri Sembilan highest risk area while Pulau Pinang, Perak, Selangor, Kuala Lumpur&

Putrajaya, Sabah, Labuan and Sarawak show the lowest risk areas of contracting
pneumonia. Based on the study by Lawson et al., they demonstrated the use of
Poisson-gamma model in their study and itis shown that a map issmootherwith less
extreme values of the relative riskcompared when using SMR method^{1}.This Poisson-
gamma model still has its own drawbacks where the covariate adjustment is difficult
and there is no likely to deal with spatial correlation between risks in adjacent areas.

Hence, this urges researchers to purpose other approachesto estimate therelative risk values.The map should be seen as atool which canhelp to inform and direct government strategy for monitoring and controlling pneumonia disease.

**Acknowledgements **

The authors would like to thank Universiti Utara Malaysia and also family membersfor thesupport of this study.The authors also acknowledge support from the Department of Statistics Malaysia andMinistry of Health Malaysiafor the data.

**References **

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3. GreensladeL. The Missing Piece: Why continued neglect of pneumonia threatens the achievement of health goals. JustActions Report; 2018.

4. UNICEF. Pneumonia: A child dies of pneumonia every 39 seconds. 2019 [cited 2020 April 12]. Available from https://data.unicef.org/topic/childhealth/pneumonia/

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