American Journal of Mathematics and Statistics
p-ISSN: 2162-948X e-ISSN: 2162-8475
2023; 13(2): 84-98
doi:10.5923/j.ajms.20231302.03
Received: Nov. 7, 2023; Accepted: Nov. 20, 2023; Published: Dec. 13, 2023

Doreen Laurent1, Hamad Zahor Hamad2
1Lecturer Department of Mathematics and Actuarial Studies, Institute of Finance Management, Dar Es Salaam, Tanzania
2Assistant Lecturer Department of Mathematics and Statistics, The University of Dodoma, Dodoma, Tanzania
Correspondence to: Doreen Laurent, Lecturer Department of Mathematics and Actuarial Studies, Institute of Finance Management, Dar Es Salaam, Tanzania.
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Copyright © 2023 The Author(s). Published by Scientific & Academic Publishing.
This work is licensed under the Creative Commons Attribution International License (CC BY).
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Health insurance is considered to be an essential part of health care financing around the world and one of the mechanisms to achieve universal health coverage. However, in Tanzania, the coverage of health insurance among women aged 15-49 years is very low. This study examined the spatial distribution patterns of health insurance uptake among women of reproductive age. This study used secondary data derived from the 2015 TDHS-MIS whereby 13,266 reproductive-age women used as the sample. The Bernoulli model was adopted by applying Kulldorff methods using the SaTScan software to analyse the purely spatial clusters of uptakes of health insurance. ArcGIS version 10.3 was used to visualize the distribution of health insurance coverage across the country. The generalized estimating equation (GEE) logistic regression model was used to assess factors associated with uptake of health insurance using SAS version 9.4. The study found that the distribution of health insurance uptake among women aged 15-49 years had spatial patterns and clustered across the country. Women from Mainland Tanzania were about eleven times more odds of purchasing health insurance compared to those from Zanzibar. Place of residence, wealth index, level of education, marital status, age, visits to health facilities, and watching television were the important factors associated with health insurance coverage among reproductive-age women in Tanzania. Stakeholders should act on factors that reduce the chance of health insurance uptake by taking coherent and harmonized actions such as strengthening financial fortification through national health packages, sharing the experience with the regions having higher health insurance coverage, and increasing awareness and confidence of potential in the systems, which may encourage them to join.
Keywords: Health insurance uptake, Spatial modelling, Women of reproductive age, Tanzania
Cite this paper: Doreen Laurent, Hamad Zahor Hamad, Spatial Modelling of Health Insurance Uptake Among Women of Reproductive Age in Tanzania, American Journal of Mathematics and Statistics, Vol. 13 No. 2, 2023, pp. 84-98. doi: 10.5923/j.ajms.20231302.03.
test was used to test an association between categorical variables at
. ArcGIS version 10.3 was used to visualize the distribution of health insurance coverage across the country. The generalized estimating equation (GEE) logistic regression model was used to assess factors associated with uptake of health insurance using SAS version 9.4, whereby variables with a p-value ≤ 0.05 were declared as significant associated factors of uptake of health insurance. Statistical adjustments were made to get robust standard errors since the sampling procedures in the TDHS involved stratification and clustering (Kulldorff, 2006; Diggle at el., 2020).Geographic visualization using maps is a powerful tool for providing a visual representation of the distribution of health insurance coverage. This form of visualization allows for the exploration and analysis of spatial patterns and disparities in access to health insurance across different regions. The use of maps for geographic visualization of health insurance coverage enhances the understanding of the spatial dynamics of healthcare access. This approach not only aids in identifying areas of concern but also supports evidence-based decision-making, helping to shape more targeted and effective health policy interventions. As technology continues to advance, interactive and dynamic mapping tools further empower stakeholders to explore, analyze, and address issues related to health insurance coverage on a geographical scale.One key advantage of using maps for geographic visualization is the ability to convey complex information in a way that is easy to understand. Moreover, geographic visualization facilitates the representation of geographical clusters or hotspots with high or low health insurance coverage rates identified by SaTScan. This information can be crucial for targeting interventions and policy initiatives to areas where they are most needed.The Bernoulli model was adopted by applying Kulldorff methods using the SaTScan software to analyse the purely spatial clusters of health insurance uptake among women of reproductive age. The Bernoulli model is the statistical model that assesses the probability of an event occurring in different units, such as census tracts or counties. The model was used to analyze binary data such as the presence or absence of an event. In the context of health insurance, individuals or households are often categorized as either covered or not covered. So, the Bernoulli model assesses the probability of an event (having health insurance) occurring in different spatial units. By applying this model, researchers can identify areas where the likelihood of having health insurance significantly deviates from what would be expected by random chance. The Kulldorff method, on the other hand, is a spatial scan statistic used to detect clusters or spatial patterns of events. This method compares the observed number of cases (e.g., individuals with health insurance) within a circular window that systematically moves across the study area against the expected number based on the overall distribution. The method identifies clusters with higher or lower rates than expected, and it calculates statistical significance to determine whether these clusters are likely due to random chance. In this study, the number of cases in each location had Bernoulli distribution whereby women without health insurance were taken as controls (coded “0”) while the others taken as cases (coded “1”) variable to fit the Bernoulli model. A Likelihood ratio test statistic was used to determine whether the number of observed insured cases within the potential cluster was significantly higher than the expected or not, such that the scanning window with the maximum likelihood taken as the most likely high performing clusters. The clusters were identified using p-values and likelihood ratio based on the Monte Carlo (Kulldorff, 2006).Scan statistics are a class of statistical methods used for detecting and locating clusters of events within a given data set. They are particularly useful in fields such as epidemiology, spatial statistics, and quality control. One notable feature of scan statistics is their ability to adapt to the underlying distribution of the data such coverage of health insurance, making them versatile in various applications. One common method often compared with scan statistics is the spatial autocorrelation analysis. Spatial autocorrelation examines the degree of similarity in health insurance uptake among nearby locations. While both methods aim to identify patterns and clusters of health insurance coverage, scan statistics specifically focus on identifying circular or elliptical clusters, making it suitable for these types of spatial patterns.In contrast, kernel density estimation is a non-parametric method commonly used for visualizing the spatial distribution of events. While scan statistics explicitly identify statistically significant clusters, kernel density estimation provides a smooth estimate of the health insurance coverage intensity across the entire study area. This method is not as useful as scan statistics since is mostly used for gaining a comprehensive understanding of spatial patterns without focusing solely on localized clusters. Hence, in this study Scan statistics were deemed powerful for pinpointing specific clusters with high or low health insurance coverage. However, other methods, such as spatial autocorrelation, space-time permutation scan statistics, and kernel density estimation, offer complementary insights and may be more appropriate for certain types of spatial analyses.Generalized Estimating Equation (GEE) is the statistical technique that models clustered binary outcome with set of independents variables while accounting for correlation among the subjects within a cluster (Diggle et al., 2020). In health-related studies, individuals within the same community, household, or other groups may share similarities that can influence the outcome of interest, such as health insurance uptake. The GEE approach allows researchers to model these correlations, providing more accurate estimates of the associations between predictor variables and the likelihood of obtaining health insurance.Unlike standard logistic regression, the GEE logistic regression model provides robust standard error estimates, even in the presence of correlated data. This is particularly important when dealing with observations that are not independent, as failing to account for correlation can lead to inaccurate parameter estimates and overly optimistic assessments of statistical significance. By using GEE, researchers can obtain more reliable and unbiased estimates of the effects of various factors on health insurance uptake.Therefore, this study employed this model since had binary outcome (covered or not covered with health insurance) and the unit of sampling was the household, in which all the eligible women in the sampled households were sampled thus bringing in a cluster of household members who are likely to have similar background characteristics. Thus, the assumption of independence of observations within a cluster did not hold because the subjects share the same cluster. Therefore, for a clustered binary outcome a Generalized Estimating Equation (GEE with logit model) became a candidate model to account for Logit model:
Hypothesis:
Where;
These are all 10 independent variables that are state, place of residence, age, marital status, education level, wealth index, visit to health facility, reading newspaper, listening to radio and watching television.
These are coefficients of logistic regression that explain the magnitude of association between dependent variable and independent variables.
It is the chance of women to uptake the health insurance.![]() | Figure 1. Prevalence of Health Insurance Coverage among Women aged 15-49 in Tanzania, 2015/2016 TDHS-MIS |
![]() | Figure 2. Proportion of Health Insurance Coverage by Region of Residence among Reproductive Age Women Based on the 2015/2016 TDHS-MIS |
![]() | Table 1. Distribution of Health Insurance Coverage among Women of Reproductive age by Baseline Characteristics and Place of Residence, 2015/2016 TDHS-MIS |
![]() | Table 2. Crude and Adjusted Odds Ratios of Health Insurance Coverage among Women of Reproductive age in Tanzania (Pooled Sample), 2015/2016 TDHS-MIS |
![]() | Table 3. Significant spatial clusters with a high and low rate of health insurance coverage among women of reproductive age in Tanzania, 2015 TDHS-MIS |
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