Statistical analysis methods for confounded data and clustered time-to-event data
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Confounding effects are a commonly encountered challenge in statistical inference. Ignoring confounders can cause bias in estimation. In practice, confounders are often unknown, which makes applying classical methods to deal with the confounding effect difficult. In the first thesis project, we apply the Gaussian Mixture Model (GMM) to help overcome the difficulty caused by a shortage of information about confounders. A new estimator is developed which shows better performance than the unadjusted estimator with regard to bias and confidence interval coverage probability. In the second thesis project, we consider the bias caused by an informative number of events in a recurrent-event data framework. Wang and Chang (1999) studied this bias and introduced an unbiased Kaplan-Meier-like estimator for recurrent event data. However, their method lacks corresponding rank tests to compare survival estimates among different groups. In this thesis project, we extend three commonly used rank tests to compare within group estimates based on Wang and Chang’s unbiased survival estimator. We also compare the power of our new method and the clustered rank test method which did not consider the informativeness of number of events. In addition, we show how to estimate the hazards ratio based on the log-rank test statistics. The unbiasedness of the log hazards ratio estimator calculated based on the extended log-rank test statistic is confirmed via simulation. In the third thesis project, we extend Firth’s correction method for the maximum partial likelihood estimator (MPLE) to clustered survival data. Heinze and Schemper (2001) showed that Firth’s correction method is applicable to the Cox regression estimates for survival data with small numbers of events or even with the monotone likelihood problem. However, this problem has not been solved in the clustered survival data setting. In this dissertation project, we extend Firth’s correction method by adopting a robust variance estimator to calculate the correct variability and reduce bias for the MPLE estimator in clustered survival data analysis.