Modeling the trend of reported malaria cases in Kisumu county, Kenya

Study design and setting

A cross-sectional survey using routinely reported national Programme data on malaria cases in the DHIS2 platform, as reported by health facilities in Kisumu County was conducted from January 2014 to December 2017.

Kisumu County is located in the former Nyanza Province and its headquarters are in Kisumu City, which is situated approximately 370 km west of the Kenyan capital, Nairobi. According to 2009 census, Kisumu County had a population of 968,879 people and covers an area landmass of 2085.9 km² and 567 km² covered by water.

Study population and eligibility of participants

The study population included individuals at risk of malaria in Kisumu County.

All patients confirmed to have malaria by laboratory test were recruited in the study and patients diagnosed with ailments other than malaria were excluded.

Sample size determination

The Fisher et al. (1998) formula was used to determine the sample size for the study as follows:

Whereby:

n = is the desired sample size (if the target population is over 10,000) and Z = 1.96 which corresponds to 95% confidence level. p = is proportion of patients confirmed to have malaria by laboratory test while q = is (1-p) is proportion of patients confirmed not to have malaria by laboratory test. d = standard error at 95% confidence limit (0.05). Since the proportion of patients confirmed to have malaria by laboratory test (P) was not known, it was estimated to be 50% (Mugenda & Mugenda, 2013)

Therefore, based on the given figures

n = 384 laboratory-confirmed malaria patients

Data collection and study variables

Any patient who was referred to the laboratory by the clinical officer/nurse after presumptive diagnosis of malaria and fulfilled the criteria for inclusion was enrolled in the study.

Secondary data of all laboratory-confirmed malaria cases as reported by all Health Facilities was downloaded from the District Health Information System (DHIS2) using the standard application programming interface provided. The data included weekly number of malaria cases. Patients testing Positive for malaria was the dependent variable and the predictors were locality, Time in years and Total number of patients tested for malaria. The predictors were assessed as given in Table 1. A conceptual framework depicting the predictor-outcome relationship is displayed in Figure 1.

Figure 1. Conceptual framework.

Ethical considerations

Considering that secondary data was used, there was no interaction with human participants in this study. However, all the personal information generated from this study was treated with a lot of confidentiality. Approval to carry out the study was granted by the Ethics Research Committee at Kenyatta National Hospital/University of Nairobi (P511/05/2019). Permission to use the DHIS2 data was also granted Health Management Information Systems (HMIS) at the Ministry of Health Kenya (Ref. No.MOH/F/DHSMEI/01 Vol.I(17)).

Minimization of biases

Data was downloaded from the DHIS2 using the standard application programming interface provided. Each facility’s data was visually cross-checked subjected to range and limit tests to confirm obvious outliers or errors in transcription.

Statistical analysis

Weekly facility-level data on malaria parasitological testing were extracted from the Integrated Disease Surveillance and Response (IDSR) registry through the DHIS2 platform. The analysis involved checking for completeness, consistency and accuracy of the data. This include descriptive, trend analysis and time series analysis (ARIMA). The ARIMA model was used and applied to time series data of malaria reported cases in Kisumu County.

Based on the Box-Jenkins approach, model building involved ascertaining the order of the AR and MA components which was guided by the Auto Correlation Function and partial correlation coefficients plots. Dicker Fuller and Shapiro-Wilk test were used to test for stationarity and normality respectively. Additionally, Pearson’s Chi-square was used to test the goodness of fit of both Poisson and negative binomial regression models.

The influence of time in years, total number of patients tested and locality on the number of malaria cases was evaluated. Frequency distribution of each variable and each category for each of the categorical variables was calculated and presented using R statistical software version 3.5.1. A significant count model negative binomial regression model was used to measure the effect of each of the predictor variables on the number of malaria cases and the incidence rate ratio (IRR), was reported. The statistical significance was measured using the 95% confidence interval and P-values. Missing data was addressed using single imputation method.

Descriptive statistics of the study data

The study included 384 reported malaria cases in the final analysis, for the period January 2014 to December 2017. A line graph illustrating reported malaria cases from 2014–2017 is shown in Figure 2. Figure 3 shows the trend in weekly reported malaria cases.

Figure 2. Line graph illustrating reported malaria cases from 2014–2017.

Figure 3. Trend in weekly reported malaria cases.

Model identification

The procedure for model building involved ascertaining the order of the AR and MA components. This was guided by the auto correlation function and partial correlation coefficient plots based on the Box-Jenkins approach.

The autocorrelation function in Figure 4 of malaria reported cases from 2014 to 2017 at 95% confidence level spikes significantly at lag 1, 2, 3 and 4. After lag 4 it cuts off, implying that the moving average component of the ARIMA model of order 4 (MA= 4) would be needed to describe this data set.

Figure 4. The autocorrelation function of reported malaria cases.

The partial autocorrelation function in Figure 5 at 95% confidence level significantly spikes at lag 1 and then quickly cut off, implying that the autoregressive component of the ARIMA model is of order 1 (AR=1).

Figure 5. The partial autocorrelation function of reported malaria cases.

The ACF and PACF plots in Figure 4 and Figure 5 respectively suggest that a MA = 4 and AR =1 would be needed in describing this data set as coming from a moving average and autoregressive process, respectively.

Testing for stationarity

A constant mean, constant variance and a constant autocorrelation structure signifies a stationary series. The test for stationarity using augmented Dicker Fuller test as shown in Table 2 depicts that the time series is stationary with a significant p-value of 0.01.

In comparing the Akaike information criterion (AIC) values of the five likely ARIMA models depicted in Table 3, it was deduced that model ARIMA (2, 0, 1) is the best model for the data since it has the lowest AIC value of 5581.917.

Shapiro-Wilk normality test results (p-value ≤ 0.0001) in Table 4, depicts that the residuals are normally distributed. Consequently, it can be inferred that the true mean of the residuals is approximately equal to zero and there is a constant variance among residuals of the selected model.

Modeling incidence of malaria cases results of regression analyses

Table 5 shows the residual deviance for the fitted Poisson regression was given as 26219 on 373 degrees of freedom. To check the fit of the fitted Poisson model, the value of the residual deviance 26219 on 373 degrees of freedom was considered as observed in Table 5 $\frac{26219}{373}=70.29223,$ a dispersion parameter of 70.29223 is an indication that the data is over-dispersed as the value is far greater than 1. This implies that the model is not fit because the mean and variance of the response variable are not equal. If the mean and variance were equal, the residual deviance should be approximately equal to the degrees of freedom.

In this case, the assumption of mean equal to variance of the Poisson random variable was violated and so, a negative binomial regression model was deemed suitable and practical as they cater for over-dispersion. Also, they allow the likelihood ratio and other standard maximum likelihood tests to be applied. The fitted Poisson model had an AIC value of 29318 and a null deviance of 115777 on 383 degrees of freedom. Table 6 represents parameter estimates after validating the Poisson regression model using negative binomial regression model since the assumptions of Poisson regression was not met.

The AIC of this model is 5345.2, a deviance of 411.59 on 373 degrees of freedom also following the chi-square distribution D~^χ2(n-p) degrees of freedom. The dispersion parameter was found to be 1.10346 as shown in Table 7. It was observed that the negative binomial was actually the best model which fit the incidences of malaria as the dispersion parameter given by Poisson regression model had been reduced from 70.29223 to 1.10346, an indication that the assumptions of Poisson regression were not met.

ln (Incidence) = 5.185 – 0.1155(Nyakach) – 0.4613(Kisumu East) – 0.0829(Muhoroni) + 0.3357(Seme) + 0.3001(Nyando)– 0.375(Kisumu Central) – 0.1022(Year2015) – 0.09154(Year2016) − 0.3084(Year2017) + 0.0008181(Total Tested)

Table 5 below shows the goodness of fit results, which clearly indicates that negative binomial regression model is a better fit for the incidence of malaria compared to the Poisson model. To begin with, the ratios of deviance and Pearson chi-square to degree of freedom $\frac{D}{DF}{\sim }^{{\chi }^2}(\text{n}-\text{p})$ for the Poisson model are far greater than 1, which is an indication of over-dispersion and thus Poisson is not adequate for modeling such data.

Subsequently, $\frac{D}{DF}{\sim }^{{\chi }^2}(\text{n}-\text{p})$ negative binomial model ratios are both close to one which exhibits a good fit to the data. Additionally, Pearson chi-square, the lower deviance, and the larger log likelihood values of negative binomial are against those of Poisson. Together all of them share a similar conclusion of favoring the negative binomial model.

From the Table 4, Adjusting for Kisumu East, Muhoroni, Seme, Nyando, Kisumu Central, years 2015, 2016, 2017 and the total number of patients tested for malaria, the average number of reported malaria cases in Nyakach is e-0.1155(0.8909), 11% less than those in Kisumu West Sub-County.

Adjusting for Nyakach, Muhoroni, Seme, Nyando, Kisumu Central, years 2015, 2016, 2017 and the total number of patients tested for malaria, the average number of reported malaria cases in Kisumu East is e-0.4613(0.6305), 37% less than those in Kisumu West Sub-County.

Adjusting for Kisumu East, Nyakach, Seme, Nyando, Kisumu Central, years 2015, 2016, 2017 and the total number of patients tested for malaria, the average number of reported malaria cases in Muhoroni is e-0.0829(0.9204), 8% less than those in Kisumu West Sub-County.

Adjusting for Muhoroni Kisumu East, Nyakach, Nyando, Kisumu Central, years 2015, 2016, 2017 and the total number of patients tested for malaria, the average number of reported malaria cases in Seme is e0.3357(1.3989), 40% more than those in Kisumu West Sub-County.

Adjusting for Seme, Muhoroni Kisumu East, Nyakach, Kisumu Central, years 2015, 2016, 2017 and the total number of patients tested for malaria, the average number of reported malaria cases in Nyando is e0.3001(1.3499), 35% more than those in Kisumu West Sub-County.

Adjusting for Nyando, Seme, Muhoroni Kisumu East, Nyakach, years 2015, 2016, 2017 and the total number of patients tested for malaria, the average number of reported malaria cases in Kisumu Central is e-0.375(0.6873), 31% less than those in Kisumu West Sub-County.

Adjusting for Kisumu Central, Nyando, Seme, Muhoroni Kisumu East, Nyakach, years 2016,2017 and the total number of patients tested for malaria, the average number of reported malaria cases in the year 2015 is e-0.1022(0.9028), 10% less than the year 2014.

Adjusting for Kisumu Central, Nyando, Seme, Muhoroni Kisumu East, Nyakach, years 2015,2017 and the total number of patients tested for malaria, the average number of reported malaria cases in the year 2016 is e-0.09154(0.9125), 9% less than the year 2014.

Adjusting for Kisumu Central, Nyando, Seme, Muhoroni Kisumu East, Nyakach, years 2015, 2016 and the Total number of patients Tested for malaria, the average number of reported malaria cases in the year 2017 is e-0.3084(0.7346), 27% less than the year 2014.

Adjusting for Kisumu Central, Nyando, Seme, Muhoroni Kisumu East, Nyakach, years 2015, 2016 and 2017, the average number of reported malaria cases e0.0008181(1.0008) increases by 0.08% for every increase in the number of patients tested for malaria.

Significance of the predictors

Kisumu East Sub-county is statistically associated with the incidence of malaria while adjusting for Nyakach, Muhoroni, Seme, Nyando, Kisumu Central, Years 2015, 2016, 2017 and the Total number of patients Tested for malaria (p-value ≤0.0001)

Seme Sub-county is statistically associated with the incidence of malaria while adjusting for Kisumu East, Nyakach, Muhoroni, Nyando, Kisumu Central, Years 2015, 2016, 2017 and the Total number of patients Tested for malaria (p-value = 0.0001)

Nyando Sub-county is statistically associated with the incidence of malaria while adjusting for Kisumu East, Nyakach, Muhoroni ,Seme, Kisumu Central, years 2015, 2016, 2017 and the total number of patients tested for malaria (p-value = 0.0006)

Kisumu Central Sub-county is statistically associated with the incidence of malaria while adjusting for Kisumu East, Nyakach, Muhoroni, Nyando, Seme, years 2015, 2016, 2017 and the Total number of patients Tested for malaria (p-value = 0.0024)

Controlling for all other covariates, Nyakach and Muhoroni localities do not show any significant association with the incidence of malaria in Kisumu County (p-value = 0.205, 0.339) respectively.

The year 2017 is statistically associated with the incidence of malaria while adjusting for Kisumu East, Nyakach, Muhoroni, Nyando, Seme, Kisumu Central, years 2015, 2016 and the total number of patients tested for malaria (p-value = < 0.0001)

Controlling for all other covariates, the years 2015 and 2016 do not show any significant association with the incidence of malaria in Kisumu County (p = 0.153 and p = 0.2014, respectively).

The total number of patients tested is statistically associated with the incidence of malaria, while adjusting for Kisumu East, Nyakach, Muhoroni, Nyando, Seme, Kisumu Central, years 2015, 2016 and 2017 (p-value ≤ 0.0001)

Trend analysis

Preliminary and further analysis in this study, investigated the change in the yearly trends of malaria incidence in Kisumu County from 2014 to 2017 to determine if there is any increase or decrease in malaria reported cases. A trend analysis was applied to the weekly malaria reported cases and the appropriate ARIMA model fitted. The yearly cases have exhibited a continuous increasing trend except in 2017, where there was a decrease. The recorded yearly malaria cases for this study were also cyclical, for instance, the year 2016 represent an increase in cases over the years 2014 and 2015, whilst the year 2017 exhibited a decline compared with all other years.

This increase may be due to improvements in the reporting system by health facilities over time, non-usage of mosquito nets by the residents and low socioeconomic status of the population (Adenomon, 2014). This fluctuating incidence recorded yearly could also be attached to the people not being careful about the illness or inconsistencies by the health care authorities in the management of the illness. The decreasing trend in 2017 could be due to an increase in the use of mosquito nets, general improvement in the malaria awareness by the population of Kisumu owed to the intensive campaigns in malaria education by several organizations. Climatic changes could have also attributed to this(Anokye et al., 2018).

The overall pattern of the reported malaria cases as reported by this study had seasonal variations. Weekly cases towards midyear recorded the highest number of cases, whereas the first weeks of the year recorded the lowest number of cases. This could be as a result of heavy rainfall experienced in the months of April, May, June and July, which is usually the rainfall season in Kisumu, and the temperature associated with rainfall seasons.

This confirms the findings of Craig et al. (1999) and Zhou et al. (2004) who revealed that that climate is a major factor in explaining the incidence of malaria. According to Zhou et al. (2004), the incidence of malaria is influenced by rainfall since mosquitoes need stagnant water for a complete life cycle. At the same time, Mabaso et al. (2007) also discovered that rainfall seasonality as well as minimum temperature are related to the number of Plasmodium falciparum-infective bites got by an individual annually or during a season.

The best fitted time series model developed for predicting the number of weekly reported cases of malaria was ARIMA (2, 0, 1). This suggests that ARIMA (2, 0, 1) can be utilized as a forecasting model to predict the future values of a series. ARIMA works best when data exhibits a constant pattern over time with a minimum amount of outliers (Labys, 2006). Researchers can use this model to forecast malaria reported cases (Mabaso et al., 2001). Nonetheless, it should be updated from time to time with the incorporation of current data.

Significance of predictor variables on malaria incidences

Accordingly, the study investigated the association between time in years, locality and total number of patients tested for malaria in Kisumu using weekly malaria data from 2014 to 2017.

The study results revealed that residing in Kisumu East, Seme, Nyando and Kisumu Central sub-counties were statistically associated to the incidence of malaria as compared to residing in Kisumu West sub-county. Residing in Muhoroni and Nyakach sub-counties were not statistically associated with the incidence of malaria as compared to residing in Kisumu West sub-county. The different localities have demonstrated inequalities in malaria incidence mainly due to variations in access to health services, urbanization and wealth distribution. This is similar to findings by Galactionova et al. (2017), who identified regional inequalities in the coverage of malaria interventions because of the inequality of the wealth distribution within and across many countries.

Many studies have also established that there is less access to services in the rural areas compared to the urban areas, leading to less reported malaria cases from the rural sub-counties. This makes this variable a useful determinant of malaria incidence since some localities are more urban than rural and vice versa.

Generally, there was fluctuation in malaria incidences during the last four years. The year 2017 was statistically associated to the incidence of malaria as compared to the year 2014. Whereas 2015 and 2016 were not statistically associated with the incidence of malaria as compared to the year 2014. Several factors may be responsible for seasonal changes, for example climatic changes, ecologic and environmental factors, social and economic determinants such as change in health care infrastructure. Availability of health facilities and drug resistance also have an impact on incidence of malaria. Although there were different malaria control activities in each year, such as activities to decrease incidence of malaria, insecticide indoor spraying, distribution of ITNs, massive malaria control campaigns and distribution of ITNs the prevalence is still constant. This is similar to findings by Alemu et al. (2012).

There was a significant association between the total number of patients tested for malaria and the incidence of malaria. Though urban areas have normally been at lower risk of malaria, unpredictable and unplanned population growth has been a key factor in making urban or peri-urban transmission an increasing problem .This could explain the high malaria incidence in 2016.This finding is consistent to a study carried out by (Knudsen & Slooff, 1992).

Trends analysis

The objective of this research was to determine the factors associated with the incidence of malaria in Kisumu County over time, given the locality where the patients sought health facility intervention, time in years and the total number of patients who were tested for malaria. The study utilized weekly malaria reported cases data from IDSR Disease Surveillance registry, for the period January 2014 to December 2017 in Kisumu County. Reported malaria cases confirmed by laboratory test was used in the analysis and modeling.

A seasonal pattern was observed in the malaria incidences in Kisumu County. ARIMA (2, 0, 1) model was found to be the best fit statistical model to predict malaria incidences in Kisumu County. The results found from this study offer useful information for policy makers to be able to effectively implement timely and effective malaria preventive and control measures.

Significance of predictor variables on malaria incidences

Goodness of fit model assessment criteria were used in selecting which model will fit the malaria reported cases better by exhausting both Poisson and negative binomial regression models. The negative binomial regression model was found to fit the data better than the Poisson regression model, based on the results. In modeling the incidence of malaria, the quality of the Poisson model was estimated using the AIC. The AIC value produced was 29,318, the deviance was 26,219 and a dispersion parameter of 70.29 showing an over-dispersion in the data leading to a violation of one of its main assumption of the equality of mean and variance parameters. It became a necessary to validate the Poisson regression models using negative binomial because of over-dispersion.

The results obtained suggested that Kisumu East, Seme, Nyando, Kisumu Central localities, the year 2017 and the total number of patients who underwent a laboratory confirmation test for malaria were significant factors for incidence of malaria in Kisumu County over time. Whereas, Nyakach, Muhoroni localities, the years 2015 and 2016 were not significant factors for malaria incidences. The findings provide better insight of environmental and socio-economic effects on malaria and provide important information for malaria prediction. Nonetheless, there is need for additional studies to consider which other factors influence the incidence of malaria notwithstanding environmental and socio-economic factors. Likewise, health professionals practicing in Kisumu County should be encouraged to regularly review and report cases of malaria in their facilities. This is because, reporting rates, completeness and the consistency of malaria reported cases remain extremely low and importantly was poorer in localities where malaria is endemic.

Source data

The data can be obtained from the Integrated Disease Surveillance and Response (IDSR) registry through the DHIS2 platform, using the standard application programming interface provided https://hiskenya.org/dhis-web-commons/security/login.action. Weekly facility-level data on malaria parasitological testing were extracted from Kenya DHIS2 between January 2014 to December 2017.

Access to the raw dataset is possible upon placing a formal request to the Ministry of Health, Kenya (emailing pshealthke@gmail.com), since the platform is kept under restricted access.