The Sample Size Calculations For Log-rank Test And Cox Regression In Survival Analysis

For a given study, how large sample sizes are needed are of first actual problems to the investigators. Similarly, when we appraise a published experimental result, sample sizes also play an important role for assuring reliability.With improving of the world economy, developing of the public health work, changing of the disease chart and average life span rising, there are more and more clinical trials and follow-up studies on tumor, chronic disease and disease of aged people, which can be sorted as survival data. During the planning stage of these related studies, sample sizes are calculated to ensure that statistical analysis results are accurate and reliable. Sample size calculation is quite complex because of the following reasons: (i) the survival data simultaneously consider the survival status and the survival time; (ii) survival time possibly includes censored data; (iii) the distribution of survival time obviously differs from the common statistical distribution.This study introduced several sample size calculation models applied to survival data: Freedman model, Lachin-Foulkes model, Lakatos model and models applied to Cox proportional hazards regression model. Through simulation experiments, sample size calculation methods which are reliable and effective were selected from the considered methods. This will provide certain scientific basis for researchers to raise the research efficiency and save financial resources.The analysis demonstrated that sample size calculation about survival analysis depends on not only statistical requests and treatment effects, but also many uncertain influencing factors, such as start time of entry, censored data, distribution of the cure time, patients'compliance during experiment, whether the proportional hazards assumption was satisfied and so on. For the specific experiment, the Lakatos model we introduced can make full use of a lot of complicated information that the data provide to fit a unique survival process.This model can adapt complexity and diversity of clinical trial well, and solve the problem that many complicated factors may have effects to sample size.This study also introduced the sample size calculation models about Cox proportional hazards regression model. It effectively solved the sample size calculation problems for Cox regression models used widely in survival analysis.