A Strategy for Stepwise Regression Procedures in Survival Analysis with Missing Covariates

The selection of variables used to predict a time to event outcome is a common and important issue when analyzing survival data. This is an essential step in accurately assessing risk factors in medical and public health studies. Ignoring an important variable in a regression model may result in biased and inefficient estimates of the outcomes. Such bias can have major implications in public health studies because it may cause potential risk factors to be falsely declared as associated with an outcome, such as mortality or conversely, be falsely declared not associated with the outcome. Stepwise regression procedures are widely used for model selection. However, they have inherent limitations, and can lead to unreasonable results when there are missing values in the potential covariates.In the first part of this dissertation, multiple imputations are used to deal with missing covariate information. We review two powerful imputation procedures, Multiple Imputation by Chain Equations (MICE) and estimation/multiple imputation for Mixed categorical and continuous data (MIX) that implement different multiple imputation methods. We compare the performance of these two procedures by assessing the bias, efficiency and robustness in several simulation studies using time to event outcomes. Practical limitations and valuable features of these two procedures are also assessed. In the second part of the dissertation, we use imputation together with a criterion called the Brier Score to formulate an overall stepwise model selection strategy. The strategy has the advantage of enabling one to perform model selection and evaluate the predictive accuracy of a selected model at the same time, all while taking into account the missing values in the covariates. This comprehensive strategy is implemented by defining the Weighted Brier Score (WBS) using weighted survival functions. We use simulations to assess this strategy and further demonstrate its use by analyzing survival data from the National Surgical Adjuvant Breast and Bowel Project (NSABP) Protocol B-06.