Sample Size Calculation For Marginal Proportional Hazards Model

The calculation of sample size has always been a topic of close interest because it plays an important role in trials and clinical research in medicine.A reasonable sample size can determine the success or failure of a clinical trial.In general,people mainly study the sample size under the standard proportional risk model and the sample size under the time-dependent covariate model,but there are few studies on the calculation of the sample size of the marginal proportional risk model.In this paper,the generalized estimating equation is used to study the method of calculating the sample size under the marginal proportional hazards model,which is mainly to simulate the data with certain correlation between repeated observations in the cluster,and calculate the sample size under the marginal proportional hazards model.Compare and analyze the simulated results of the sample size and the true values under the standard proportional hazards model.This paper mainly consists of five parts: The first part introduces the background and significance of the topic,as well as the research and analysis of the sample size calculation of the proportional hazards model by various researchers in domestic and abroad.The second part is about the generalized linear model and the proportional hazards model.The theoretical knowledge is summarized,and then the estimation methods of regression parameters in the two models are introduced.In the third part,the method of calculating the sample size by using the generalized estimating equation is discussed,then the calculation method and steps of the sample quantity under the marginal proportional hazards model are derived.In the fourth part,the simulation study shows the comparison of sample capacity under different correlation structures,censoring rates and different models.The final part analyzes the clinical research of different types of patients with nephrotic infection.