On the empirical choice of the time window for restricted mean survival time

The t-year mean survival or restricted mean survival time (RMST) has been used as an appealing summary of the survival distribution within a time window [0, t]. RMST is the patient's life expectancy until time t and can be estimated nonparametrically by the area under the Kaplan-Meier curve up to t. In a comparative study, the difference or ratio of two RMSTs has been utilized to quantify the between-group-difference as a clinically interpretable alternative summary to the hazard ratio. The choice of the time window [0, t] may be prespecified at the design stage of the study based on clinical considerations. On the other hand, after the survival data have been collected, the choice of time point t could be data-dependent. The standard inferential procedures for the corresponding RMST, which is also data-dependent, ignore this subtle yet important issue. In this paper, we clarify how to make inference about a random “parameter.” Moreover, we demonstrate that under a rather mild condition on the censoring distribution, one can make inference about the RMST up to t, where t is less than or even equal to the largest follow-up time (either observed or censored) in the study. This finding reduces the subjectivity of the choice of t empirically. The proposal is illustrated with the survival data from a primary biliary cirrhosis study, and its finite sample properties are investigated via an extensive simulation study.     

钙离子对PSII颗粒放氧活性的影响

外加5 mmol/L Ca~(2 )可以使菠菜PSⅡ颗粒的放氧活性增高。PSⅡ颗粒经EGTA透析、低pH值、光照、2 mol/L NaCl等处理后,放氧活性下降,同时,这些颗粒的钙含量也相应降低。但当外加 5 mmol/L Ca~(2 )时,可使这些颗粒全部或部分地恢复放氧活性。PSⅡ颗粒中存在的钙对放氧起着重要作用;钙在PSⅡ颗粒中的结合位点不止一个,其结合状态有紧密和松散之别。