Wu M C, Lan K K
Biostatistics Research Branch, National Heart, Lung, and Blood Institute, Bethesda, Maryland 20892.
Biometrics. 1992 Sep;48(3):765-79.
The spending function approach proposed by Lan and DeMets (1983, Biometrika 70, 659-663) for sequential monitoring of clinical trials is applied to situations where comparison of changes in a continuous response variable between two groups is the primary concern. Death, loss to follow-up, and missed visits could cause follow-up measurements to be right-censored or missing for some participants. Furthermore, the probability of being censored may be dependent on the parameter value of the response variable (informative censoring). We propose to compare treatment effects by comparing areas under the expected response change curves between the two groups. When the response curves are linear as a function of time in both groups, this comparison is equivalent to comparing the rates of change in the response variable. Covariances of the sequential test statistics are derived. Conditions for having independent increments are presented. For studies designed to evaluate long-term treatment effects, spending functions obtained by shifting the usual spending functions (Kim and DeMets, 1987, Biometrika 74, 149-154) to the right and then rescaling to the remaining interval are also proposed. Such a shifted spending function is applied to the monitoring plan for the Lung Health Study (Anthonisen, 1989, American Review of Respiratory Diseases 140, 871-872).
Lan和DeMets（1983年，《生物统计学》70卷，659 - 663页）提出的用于临床试验序贯监测的花费函数方法，被应用于以比较两组连续反应变量变化为主要关注点的情况。死亡、失访和错过就诊可能导致部分参与者的随访测量出现右删失或缺失。此外，删失的概率可能取决于反应变量的参数值（信息删失）。我们建议通过比较两组预期反应变化曲线下的面积来比较治疗效果。当两组的反应曲线作为时间的函数呈线性时，这种比较等同于比较反应变量的变化率。推导了序贯检验统计量的协方差。给出了具有独立增量的条件。对于旨在评估长期治疗效果的研究，还提出了通过将通常的花费函数（Kim和DeMets，1987年，《生物统计学》74卷，149 - 154页）向右移动然后重新缩放到剩余区间而获得的花费函数。这种移位的花费函数被应用于肺部健康研究的监测计划（Anthonisen，1989年，《美国呼吸系统疾病评论》140卷，871 - 872页）。
