A clinical trial design using the concept of proportional time using the generalized gamma ratio distribution

Abstract

Traditional methods of sample size and power calculations in clinical trials with a time-to-event end point are based on the logrank test (and its variations), Cox proportional hazards (PH) assumption, or comparison of means of 2 exponential distributions. Of these, sample size calculation based on PH assumption is likely the most common and allows adjusting for the effect of one or more covariates. However, when designing a trial, there are situations when the assumption of PH may not be appropriate. Additionally, when it is known that there is a rapid decline in the survival curve for a control group, such as from previously conducted observational studies, a design based on the PH assumption may confer only a minor statistical improvement for the treatment group that is neither clinically nor practically meaningful. For such scenarios, a clinical trial design that focuses on improvement in patient longevity is proposed, based on the concept of proportional time using the generalized gamma ratio distribution. Simulations are conducted to evaluate the performance of the proportional time method and to identify the situations in which such a design will be beneficial as compared to the standard design using a PH assumption, piecewise exponential hazards assumption, and specific cases of a cure rate model. A practical example in which hemorrhagic stroke patients are randomized to 1 of 2 arms in a putative clinical trial demonstrates the usefulness of this approach by drastically reducing the number of patients needed for study enrollment.