Simulations-Based Least Required Sample Size and Power in Clinical Trials with Time-to-Event endpoint and Variable Hazard

Abstract

Two of the pivotal design parameters for planning clinical trials with time-to-event outcome(s) are sample size and power. Attention needs to be placed on the hazard function (which characterizes the rate at which events occur and can be constant, decreasing, and/or increasing in time). This work employs simulation(s) of real scenarios of randomized studies to generate time-to-event variables with specific hazard characterization, obeying the Weibull function which accommodates variable hazard situations. Our aim is to determine the least required sample size and power values, based on simulating two independent samples of Weibull distributed responses, differing by various postulated hazard patterns (constant, decreasing, or increasing in time), different scale parameter values, and follow-up periods.

Keywords: Hazard; Simulation; Statistical Power; Time-to-event; Weibull.

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Figure 2:

Typical hazard functions of Simulated Sample size100 per group, Decreasing Hazard (shape=0.8), HR= 0.5, Follow-up=4

Figure 3:

Typical Survival distributions with Simulated Sample size100 per group, shape=2.0, HR= 0.5, Follow-up=4

Figure 4:

Typical hazard functions of Simulated Sample size 200 per group, Constant Hazard (shape=1.0), HR= 0.5, Follow-up=5

Figure 5:

Typical hazard functions of Simulated Sample size100 per group, Increasing Hazard (shape=2.0), HR= 0.5, Follow-up=4 Years

Figure 6:

The converse is observed when evaluating changes in power as a function of scale parameters

Figure 7:

It goes without saying that these observational findings require future study to substantiate.