Flexible models for analyzing correlated And non-normal data with application to Health research

Abstract

Skewed and non-normal data are commonly observed in health research. Usually, the dataset is transformed, censored, or truncated to impose normality, rather than modeling the data in its natural state. Many conventional approaches to modeling lead to incorrect estimates of parameters and standard errors due to the assumptions imposed. This study investigated three statistical problems; Non-normality, Skewness and Correlation under the Generalized Estimating Equations (GEEs) Framework. The general objective was to develop flexible models for correlated and Skewed data in health research. The specific objectives were, to investigate the skewness property of binomial longitudinal data and its application to model infant morbidity under HIV setting, to review cost spending models on outpatient care while assuming independence structure under GEE, to develop mod- els for alternative estimation of the scale parameter under the Generalized Estimating Equations framework, and to propose methods of analyzing clustered inpatient care data that relaxes the non-normality. The study applied; the Burrs-10 distribution and sup- pressor effect assumptions under the GEE to model the correlated infant morbidity data; exchangeable correlation structure to model predictors of distance for inpatient care; and independence correlation structure to model the predictors for outpatient care cost with Bienayme–Chebyshev inequality. The best model selected was the one that displayed the lowest quasi-likelihood under the independence criterion (QICu). The results revealed that skewed logit-GEE under the Burrs-10 distribution was able to show an association between variables which was not identified by the standard GEE. Accordingly, it fitted our imbalanced health dataset better. The study found out that the SL-GEE was supe- rior over the standard GEE when asymmetry was assumed. The main contribution of thestudy is in the development of the algorithm of estimating the skewness parameter for the model. The suppressor effect showed some patterns of the disease, which the conventional approaches failed to reveal. It revealed that gastro intestinal infections were common in the infants exposed to Bacterial Vaginosis. Modelling the distance for inpatient care re- vealed that differences in employment, ability to pay for the service and household size are associated with distance covered to access government facilities. Finally, the best predictors of outpatient care expenses are age, wealth index, marital status, and educa- tion of the household head. In conclusion, the methodologies developed are applicable in modelling of non-normal response variable. The study recommends the reproducibility of the R-codes developed on different health and biomedical datasets.