Master thesis | Statistical Science for the Life and Behavioural Sciences (MSc)
open access
The Restricted Mean Survival Time (RMST) is a statistic that measures treatment effects which can be used as a replacement for the hazard ratio when the proportional hazards assumption is violated....Show moreThe Restricted Mean Survival Time (RMST) is a statistic that measures treatment effects which can be used as a replacement for the hazard ratio when the proportional hazards assumption is violated. The idea of RMST came from Irwin (1949) [5], and when combined with the formal definition of the survival function, RMST can be defined as the integral of survival function up to a time limit τ . Several different methods for estimating the RMST are available. The Kaplan-Meier method and Cox PH model are the most commonly used methods in survival analysis, and they are also suitable for estimating RMST. This is done by first estimating the survival curve and then calculating the area under it to give an estimation of RMST. To allow a more general population of survival time distributions, a flexible parametric model was introduced by Royston and Parmar (2002) [4]. This flexible parametric model method followed the same method of estimating RMST as the Kaplan-Meier and Cox PH model: a survival function is estimated from the model, then a 15-point Gauss-Kronrod quadrature can be used to calculate the integral of the survival function, which allows estimation of RMST. The final option is a pseudo-observation method proposed by Anderson et al. (2004) [3]. This method first builds a pseudo-observation of RMST for each subject. Then, using the pseudo-observations of RMST as outcome variables, a generalized linear model can be built to describe the relationship between the covariates and RMST. A generalized estimating equation (GEE) method can then be used to estimate the parameters of the generalized linear model [8]. Comparisons between these methods under various simulation scenarios were conducted for this thesis. The Kaplan-Meier method is simple to calculate and performs well with early time limits and low censoring proportions. It is also faster to estimate RMST result than Cox model and flexible parametric model. However, this method lacks the ability to be adjusted for more covariates, so it is only suitable when estimating average RMST difference for a population. The unstratified Cox model performed well in datasets that satisfied the proportional hazards assumption. The stratified Cox model also performed well in our simulated non-proportional hazards datasets. The performance of the flexible parametric model method was similar to that of the Cox model, but it is more time-consuming in the integral calculation step. The pseudo-observation methods offered the shortest computation time among all four methods. However, when estimating RMST difference for a subject with given age and gender, the performance of the pseudo-observation method was worse than either the Cox model or flexible parametric model.Show less
