Improved Confidence Intervals for Fixed Term Survival Probabilities in a Small Two-Arm Trial

Abstract BackgroundThe confidence interval for survival probability at a fixed time point provides valuable information on how the subject performs in terms of survival rate. However, in a two-arm trial when the sample size in each group is small or when the distribution of events that occurred within the group is skewed, the confidence interval might become very unstable, and thus may not provide accurate information for estimating survival rate. In addition, when there are other covariates available in the dataset, it is important to select those significant variables and include them in the model. On the other hand, researchers such as physicians who pay more attention to the final result often analyze the treatment group and control group separately, which may lead to inaccurate prediction. MethodsIn this study, two treatment groups are combined, and the group indicator variable is considered as a covariate and is included in the model for computation. Yuan and Rai’s adjusted effective sample size methods are further extended along with Cox proportional hazard model, Weibull model, and log-logistic model to compute predicted fixed-term overall survival probabilities and corresponding confidence intervals with other covariates adjusted. Simulations are conducted to obtain coverage probability. ResultsIn a single model, Wilson-Peto provides better confidence intervals than Kaplan-Meier, especially in the middle and later stages. In addition, AC-Peto produces better coverage probability at all time points. In a multivariate model, the log-logistic method provides both better confidence intervals and coverage probability than Cox regression model at all stages.ConclusionsThis paper provides a guideline on how one should correctly analyze survival data with the most appropriate method. Depending on the dataset, it is important to consider methods other than traditional Kaplan-Meier and Cox regression models when evaluating survival outcomes.