The Effects of Overstration on the Stratified Log Rank Test for Survival Analysis

摘要

Survival analysis concerns the characterization or comparison of one or more distributions of the time to a well defined event. The log-rank test is the most common method used to compare the survival distributions of two samples. When data within the two groups are stratified according to some risk factors, then a stratified log-rank test is employed. udStratified analysis is a procedure used to compare outcomes in different groups while at the same time correcting for the effects of confounders. It is one way to ensure that important prognostic factors are equally distributed among different treatments.udThe ordinary log-rank test is known to be conservative when treatments have been assigned by a stratified design. The stratified log-rank test is valid even when the sizes of strata differ. Schoenfeld and Tsiatis modified the log-rank test with a variance adjustment reflecting the dependence of survival on strata size. Their method is shown to be more efficient than the ordinary stratified log rank test when the number of strata is large, and it remains valid when the censoring distributions differ across treatment groups.udIn this thesis, we investigate these three log-rank tests for survival analysis. The effect of the stratum sizes on each type of analysis is evaluated using simulated data. udOur results show that the modified log rank test is beneficial for stratified survival analysis in most cases especially when there are large numbers of strata and the strata sizes get small. The statistical power of the modified log-rank test is relatively stable even with very small strata sizes and high strata effects. udThe public health relevance of this thesis is that the modified log-rank test we investigated and implemented using the R programming language provides an alternative and more efficient way to accommodate higher amounts of stratification in analyzing survival data. More efficient statistical methods indirectly have public health impact as such methods lead to analyses which better identify treatments, interventions or factors that influence health outcomes. Such analyses are commonly used in clinical trials and other studies which influence public healthud