Conventional methods of sample size calculations in clinical trials with a time-to-event endpoint are based on the logrank test, Cox proportional hazards (PH) assumption, and the exponential distribution. Of these, calculation based on PH assumption is the most popular as it allows for covariate adjustment. In case of non-inferiority (NI) trials, information gained from previously conducted trials is used to decide the allowable margin of non-inferiority. Thereafter, sample size calculations are performed taking this margin into consideration and are often supported by simulations. Considerably large sample sizes are required to conduct a NI trial, sometimes making it difficult to conduct one. In situations where the PH assumption is not appropriate based on information gained from prior studies, we propose a novel method to conduct sample size calculations based on the concept of proportional time (PT). Our calculations are based on simulations conducted using a generalized gamma ratio distribution and provide a viable, clinically appealing alternative to the more traditional methods. We identify situations where our method will be beneficial as compared to the standard designs.