Detecting an overall survival benefit that is derived from progression-free survival

Abstract

Background: Whether progression-free survival (PFS) or overall survival (OS) is the more appropriate endpoint in clinical trials of metastatic cancer is controversial. In some disease and treatment settings, an improvement in PFS does not result in an improved OS.

Methods: We partitioned OS into two parts and expressed it as the sum of PFS and survival postprogression (SPP). We simulated randomized clinical trials with two arms that had respective medians for PFS of 6 and 9 months. We assumed no treatment difference in median SPP. We found the probability of a statistically significant benefit in OS for various median SPP and observed P values for PFS. We compared the sample sizes required for PFS vs OS for various median SPP. We compare our results with the literature regarding surrogacy of PFS for OS by use of the correlation between hazard ratios for PFS and OS. All statistical tests were two-sided.

Results: For a trial with observed P value for improvement in PFS of .001, there was a greater than 90% probability for statistical significance in OS if median SPP was 2 months but less than 20% if median SPP was 24 months. For a trial requiring 280 patients to detect a 3-month difference in PFS, 350 and 2440 patients, respectively, were required to have the same power for detecting a real difference in OS that is carried over from the 3-month benefit in PFS when the median SPP was 2 and 24 months.

Conclusions: Addressing SPP is important in understanding treatment effects. For clinical trials with a PFS benefit, lack of statistical significance in OS does not imply lack of improvement in OS, especially for diseases with long median SPP. Although there may be no treatment effect on SPP, its variability so dilutes the OS comparison that statistical significance is likely lost. OS is a reasonable primary endpoint when median SPP is short but is too high a bar when median SPP is long, such as longer than 12 months.

Figure 1

Three typical examples of Kaplan-Meier progression-free survival (PFS) curves and associated overall survival (OS) curves from the simulations. Each row of plots is an example of a single simulated trial. The leftmost plot shows PFS, simulated to have median PFS of 6 months (control) and 9 months (experimental). The other three plots in each row show OS and differ only in median SPP (6, 12, and 18 months). The hazard ratios and P values shown are those observed for the single simulated example. These three examples were typical of the simulations carried out. PFS and OS were compared by the log-rank test, and all statistical tests were two-sided. HR = hazard ratio; med = median. Solid line = control arm; dashed line = experimental arm.

Figure 2

Probability of statistically significant differences in overall survival (OS) as a function of median survival postprogression (SPP). The three curves were indexed by the power for detecting the actual median progression-free survival (PFS) benefit that was simulated, 6 vs 9 months (ie, powers of 90%, 85%, and 80%).

Figure 3

Sample sizes required for detecting a statistically significant difference in overall survival by median survival postprogression (SPP). The three curves were indexed by the power for overall survival (ie, powers of 90%, 85%, and 80%).

Figure 4

Association between progression-free survival (PFS) and overall survival (OS) for a single simulation of 67 trials. Each study had a randomly selected sample size and PFS hazard ratio, which remains fixed across scenarios while median survival postprogression (SPP) times were allowed to vary (0, 3, 6, 9, 12, 18, and 24 months). Hazard ratios (HRs) for PFS and OS were estimated with a proportional hazards model, and the correlation was estimated from a linear regression model weighted by the number of patients in each trial. The size of the circle is relative to the total sample size of the study. The diagonal line is the fitted weighted linear regression line.