Estimating time to first episode of malaria among infants in Uganda in the presence of alternative link functions
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This study concerns estimating time to first malaria episode in the presence of alternative link functions. The main objective of this dissertation was to evaluate the proportional hazards assumption for all the covariates and also evaluate the link function between the log hazard and the covariates. The study used primary data on infants obtained from selected health facilities in Mukono and Wakiso districts. Methods on Proportional Hazards and alternative link functions were used on this time to event data. Findings from the research show that the proportional hazards assumption for all the covariates in the model was not met. Covariates including education status, breastfeeding status, residence, water status and house floor met the proportional hazards assumption whereas mosquito net status did not. Also, the link function between the log-hazard and covariates provided evidence that the link was non-linear and the Royston-Parmar flexible parametric model with 5 degrees of freedom was selected as the best link. Significant explainers including breast feeding, mosquito net and house floor status used in this model provided the appropriate link with time to the event. Results indicate that infants whose mothers reported to sleep under an ITN had a significantly lower risk of first malaria compared to those that do not (HR=0.632, p=0.015). Infants that were breast feeding had a significantly lower risk of first malaria before 12months compared to those that were not (HR=0.338, p=0.000). Also infants born to mothers who boil drinking water had a significantly reduced risk of getting first malaria before 12months compared to those that did not (HR=0.440, p=0.004). The researcher recommends that efforts by the government and other stake holders are needed to create public awareness on the importance of breast feeding, mosquito net use and boiling water to reduce the risks of malaria among infants. The study also recommends modelling using restricted cubic splines on the log cumulative hazard scale for all proportional hazard models to accurately capture the complex shape of the baseline hazard.