Sensitivity analysis approaches for incomplete longitudinal data in a multi-centre clinical trial

The first major contribution of the thesis is the development of sensitivity analysis strategy for dealing with incomplete longitudinal data. The second important contribution is setting up of simulation experiment to evaluate the performance of some of the sensitivity analysis approaches. The third contribution is that the thesis offers recommendations on which sensitivity analysis strategy to use and in what circumstance. It is recommended that when drawing statistical inferences in the presence of missing data, methods of analysis based on plausible scientific assumptions should be used. One major issue is that such assumptions cannot be verified using the data at hand. In order to verify these assumptions, sensitivity analysis should be performed to investigate the robustness of statistical inferences to plausible alternative assumptions about the missing data. The thesis implemented various sensitivity analysis strategies to incomplete longitudinal CD4 count data in order to investigate the effect of tuberculosis pericarditis (TBP) treatment on CD4 count changes over time. The thesis achieved the first contribution by formulating primary analysis (which assume that the data are missing at random) and then conducting sensitivity analyses to assess whether statistical inferences under the primary analysis model are sensitive to models that assume that the data are not missing at random. The second contribution was achieved via simulation experiment involving formulating hypotheses on how sensitivity analysis strategies would performed under varying rate of missing values and model mis-specification (when the model is mis-specified). The third contribution was achieved based on our experience from the development and application of the sensitivity analysis strategies as well as the simulation experiment. Using the CD4 count data, we observed that statistical inferences under the primary analysis formulation are robust to the sensitivity analyses formulations, suggesting that the mechanism that generated the missing CD4 count measurements is likely to be missing at random. The results also revealed that TBP does not interact with the HIV/AIDS treatment and that TBP treatment had no significant effect on CD4 count changes over time. We have observed in our simulation results that the sensitivity analysis strategies produced unbiased statistical inferences except when a strategy is inappropriately applied in a given trial setting and also, when a strategy is mis-specified. Although the methods considered were applied to data in the IMPI trial setting, these methods can also be applied to clinical trials with similar settings. A sensitivity analysis strategy may not necessarily give bias results because it has been mis-specified, but it may also be that it has been applied in a wrongly defined trial setting. We therefore strongly encourage analysts to carefully study these sensitivity analysis frameworks together with a clearly and precise definition of the trial objective in order to decide on which sensitivity analysis strategy to use