Paired Survival Data
Paired survival data can arise in two situations in comparative effectiveness research. In the first, data may be naturally paired or patients may be prospectively assigned to treatment. In the second, large registries may be available to investigators for treatment comparisons so smaller subsets of the data base are used for comparisons. These non-randomized prospective data sets need some means of adjusting treatment arms for imbalances in non-controllable factors effecting outcome. Matching of patients on these factors is one common approach to making adjustments.
In survival studies matched pairs studies may have problems when some of the cases are lost to follow-up and in all studies matching has problems when some covariates have missing values. Many methods have been proposed for the survival analysis problem. It is not clear in a given situation which of these methods is best.
Often investigators have collected data in small pilot studies that are used to compute sample sizes for a large scale study. For many studies this data includes covariate or explanatory information in addition to the main effect of interest. This covariate information makes estimates of the standard error as a function of the sample size difficult. Two problems present themselves with this scenario. First, while it is well known that the standard error is a decreasing function of the sample size, n, the exact functional form in complex sampling schemes is unknown.
When the preliminary data is used to estimate a sample size and the preliminary data is used in the analysis an adjustment to the type one error must be made to account for the multiple uses of the data in both the design and analysis stage. This will mandate that testing of the main effect be performed at a modified significance level. These modified significance levels are found by Monte Carlo methods.