Sample Size Considerations for the Evaluation of Prognostic Factors in Survival Analysis

When the role of a new prognostic factor is investigated, careful planning of an appropriate study is required. This includes an assessment of the power of the study in terms of sample sizes. An adequate analysis of the independent prognostic effect of a new factor has to be adjusted for the existing standard factors. With survival time as endpoint this will usually be done with the Cox proportional hazards model. Sample size and power formulae in survival analysis have been developed by Schoenfeld for randomized treatment comparisons. In the analysis of prognostic factors the covariates included are expected to be correlated with the factor of primary interest. In this situation, the existing sample size and power formulae are not valid and may not be applied. In this paper, Schoenfeld's formula is first extended to the situation where a correlated factor is included in the analysis. The validity of the resulting approximate asymptotic formula is investigated for its asymptotic behaviour by numerical integration and for its finite behaviour by simulation. Second, an approximate formula for sample size and power is provided to detect an interaction between the interesting and a second correlated factor. This extends the formula for independent effects. Finally, the approach is illustrated by an example on the prognostic impact of DNA ploidy and other factors in advanced ovarian cancer.