Comparison of methods for survival analysis of dependent data

Analysis of dependent survival data by conventional partial likelihood methods produces unbiased estimates of the regression coefficients but incorrectly estimates their variance. Here we compared the conventional partial likelihood methods with two alternative methods for analyzing dependent survival data. The first alternative method estimated the regression coefficient by the partial likelihood approach but adjusted the variance to account for clustering. The second alternative method used marginal likelihoods to estimate both the regression coefficient and its variance. We evaluated the performance of the three methods using simulated and actual data. Simulated data were used to examine bias, efficiency, type I errors, and power. An Old Order Amish genealogy was analyzed under these models to illustrate their performance on real data. The simulation study showed that all three methods provided unbiased estimates of the regression coefficient, but the efficiency of the estimated regression coefficient varied according to the simulation conditions. The standard partial likelihood method showed increasing type I error as the dependence increased within clusters. Both alternative methods had acceptable levels of type I errors at all dependence levels. In the analysis of genealogic data, the regression coefficient was similar in the three methods showing stable estimates of the regression coefficients. The variance estimates from the alternative methods were slightly different from the conventional method, suggesting a flow level of dependence. This study displays the effect of violating the independence assumption and provides guidelines for using alternative statistical methods.