截断混合高斯分布入组模式下生存资料样本量估计

Sample Size Estimation for Survival Trials with Truncated Gaussian Mixture Distribution Accrual

目的在入组间期长的生存资料临床试验中,受试者入组速率可能受招募广告宣传等多因素影响而存在反复波动,本文采用截断混合高斯分布拟合这种入组速率变化并估计该入组模式下需要的样本量。方法在指数分布生存时间和指数失访假设下,采用多重积分法推导受试者入组速率服从截断混合高斯分布时的事件发生率及样本量计算公式;分别计算截断混合高斯分布中均值、方差、权重分配变化时样本量变化情况;通过Monte Carlo模拟对采用均匀分布估计波动入组速率可能引起的试验检验效能损失及对提出样本量计算公式的稳健性进行评价。结果截断混合高斯入组模式下各高斯组分的均值越小、均值较小高斯组分的方差越小、权重越大,需要的样本量越小,即受试者入组速率高峰出现较晚或早期入组速率波峰窄小时需要更多的样本量;采用均匀分布拟合波动入组速率可能会引起不同程度的试验检验效能不足,而在截断混合高斯入组模式计算的样本量下试验检验效能基本能稳定在预期水平;截断混合高斯入组模式还可以近似恒定入组速率,单调增或减入组速率等情况。结论截断混合高斯入组模式及提出的样本量计算公式具有较好的稳健性,适用性更广,可以用于生存资料临床试验样本量估计。

Objective In survival trials with long accrual duration,patient accrual may be affected by many factors such as enrollment propaganda,then the accrual rate may change as a wavy curve.To approximate the fluctuant accrual rate,we propose a novel accrual model named truncated Gaussian mixture distribution (GMD) accrual and deduce the corresponding sample size estimation method. Methods Under the assumption of exponential distributed survival time and time to drop-out,the expected event rate of each arm is calculated by multiple integral and the sample size calculation formula of truncated GMD accrual is derived.The impacts of truncated GMD parameters,i.e.,means,variances and weight allocations,on sample size are explored.Monte Carlo simulation method is adopted to investigate the impact of fluctuant patient accrual on power and the performance of the proposed sample size calculation method. Results For truncated GMD accrual model,small Gaussian component means and former Gaussian components with small variances and large weight will lead to smaller sample size.More patients would be required when the accrual rate peaks appear at the late phase of the accrual duration or the early accrual rate wave is narrow and small.Approximating the fluctuant patient accrual rate with uniform distribution indiscriminately would decrease the power of trials to varying degrees,while the proposed method has been proved with satisfactory performance under a series of scenarios.The truncated GMD accrual can also approximate the constant,increasing or decreasing accrual rate well. Conclusion The proposed sample size estimation method for truncated GMD accrual has good robustness and wider applicability,it can be used to estimate the sample size of survival trials.