Studies with stratified cluster designs, called complex surveys, have increased in popularity in medical research recently. With the passing of the Affordable Care Act, more information about effectiveness of treatment, cost of treatment, and patient satisfaction may be gleaned from these large complex surveys. We introduce three separate methodological approaches that are useful in complex surveys.;In Chapter 1, we propose a method to create a simulated dataset of clustered survival outcomes with general covariance structure based on a set of covariates. These measurements arise in practice if multiple patients are measured for the same doctor (the cluster) across many doctors. The method proposed in this chapter utilizes the fact that Kendall's Tau is invariant to monotonic transformations in order to create the survival times based on an underlying normal distribution, which the practicing statistician is likely to be more comfortable with. Such a simulated dataset of correlated survival times could be useful to calculate sample size, power, or to measure the characteristics of new proposed methodology.;In Chapter 2, we introduce a method to compare censored survival outcomes in two groups for complex surveys based on linear rank tests. Since the risk sets in a complex survey are not well defined, our proposed method instead utilizes the relationship between the score test of a proportional hazard model and the logrank test to develop the approach in these complex surveys. In order to make this method widely useful, we incorporate propensity scores in order to control for possible confounding effects of other covariates across the two groups.;In Chapter 3, we develop a method to reduce bias in a logistic regression model for binary outcome data in complex surveys. Even in large complex surveys, if the domain is small, a small number of successes or failures may be observed. When this occurs, standard weighted estimating equations (WEE) may produce biased estimates for the coefficients in the logistic regression model. Based on incorporating an adjustment term in the weighted estimating equation, we are able to reduce the first-order bias of the estimates.
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