和《使用Bootstrap法计算自举置信区间》的想法差不多，通过暴力枚举来计算临床研究的样本量，以两组生存分析为例。

Logrank对数秩检验

require(survival)
f_surv_logrank = function(df){
    # df 包含 group time status 三列
    # group 类型为 factor
    # status 0 表示未发生结局事件 1 表示发生结局事件
    surv_obj = with(survival::Surv(time = time, event = status), data = df)
    surv_fit = survival::survfit(surv_obj ~ group, data = df)
    surv_diff = survival::survdiff(surv_obj ~ group, data = df)
    res = list(pv = 1 - stats::pchisq(surv_diff$chisq, length(surv_diff$n) - 1),  # p值
                surv_fit = surv_fit,  # 绘图用
                surv_obj = surv_obj)  # 为了兼容惰性求值
    return(res)
}
f_surv_logrank_plot = function(res){
    require(survminer)
    surv_obj <<- res$surv_obj  # 为了兼容惰性求值
    survminer::ggsurvplot(res$surv_fit, conf.int = F, pval = T, risk.table = T, ncensor.plot = TRUE)
}

模拟计算

f_surv_logrank_simulation_Group = function(N, Median_Survival_Time, Lost, Duration_Accrual_Time, Duration_Total_Time){
    time = stats::rexp(N, rate = log(2) / Median_Survival_Time)  # 生存时间服从指数分布
    status = rep(1,N)  # 到生存时间发生结局事件
    # print(median((survfit(Surv(time, status) ~ 1))))
    EnrollT = stats::runif(N, min = 0, max = Duration_Accrual_Time)  # 招募时间服从均匀分布
    calender_time = time + EnrollT  # 发生结局的日期
    idx = calender_time > Duration_Total_Time  # 研究终止时未发生结局事件
    status[idx] = 0
    time[idx] = Duration_Total_Time - EnrollT[idx] # 实际参与试验的时间
    # print(median((survfit(Surv(time, status) ~ 1)))) # 如果 Accrual_Time + Median_Survival < Total_Time，结果不变
    loss = stats::rexp(N, rate = Lost)  # 失访时间服从指数分布
    idx = loss < time  # 失访的人
    status[idx] = 0
    time[idx] = loss[idx]
    # print(median((survfit(Surv(time, status) ~ 1))))  # 结果改变
    return(list(time = time, status = status))
}
f_surv_logrank_simulation_Power = function(n_C, Median_Survival_Time_C, Lost_C, 
                                           n_T, Median_Survival_Time_T, Lost_T, 
                                           Duration_Accrual_Time, Duration_Total_Time, Simulation_Cycle, Alpha){
    df = data.frame(group = factor(c(rep('Control',n_C), rep('Treatment',n_T))), 
                    time = rep(0,n_C+n_T), 
                    status = rep(0,n_C+n_T))
    sum = 0
    for (i in 1:Simulation_Cycle) {
        C = f_surv_logrank_simulation_Group(n_C, Median_Survival_Time_C, Lost_C, Duration_Accrual_Time, Duration_Total_Time)
        T = f_surv_logrank_simulation_Group(n_T, Median_Survival_Time_T, Lost_T, Duration_Accrual_Time, Duration_Total_Time)
        df$time = c(C$time, T$time)
        df$status = c(C$status, T$status)
        if(f_surv_logrank(df)$pv < Alpha){
            sum = sum + 1
        }
    }
    return(sum/Simulation_Cycle)
}
f_surv_logrank_simulation_Sample_Size = function(n_C_min, n_C_max, Median_Survival_Time_C, Lost_C, 
                                                   TvsC, Median_Survival_Time_T, Lost_T, 
                                                   Duration_Accrual_Time, Duration_Total_Time,
                                                   Simulation_Cycle, Alpha, Power, err=0.01){
    mid = floor((n_C_min + n_C_max) / 2)  # 以防没有进入循环
    while (n_C_min < n_C_max) {
        mid = floor((n_C_min + n_C_max) / 2)
        simulation_Power = f_surv_logrank_simulation_Power(mid, Median_Survival_Time_C, Lost_C, 
                                       as.integer(mid * TvsC), Median_Survival_Time_T, Lost_T, 
                                       Duration_Accrual_Time, Duration_Total_Time, Simulation_Cycle, Alpha)
        print(paste("mid:", mid, "simulation_Power:", simulation_Power))
        if (abs(simulation_Power - Power) < err) {
            return(mid)
        }else if(simulation_Power < Power) {
            n_C_min = mid + 1
        }else {
            n_C_max = mid - 1
        }
    }
    return(mid)
}

参数说明

Power = 0.9  # 检验效能 = 1 - 第二类错误的概率
Alpha = 0.05  # 第一类错误的概率
Median_Survival_Time_C = 6  # 对照组的中位生存时间
Median_Survival_Time_T = 8  # 试验组的中位生存时间
Duration_Accrual_Time = 8  # 入组完成用时
Duration_Total_Time = 18  # 总试验用时
Lost_C = 0.05  # 对照组随访单位时间后发生失访的概率
Lost_T = 0.05  # 试验组随访单位时间后发生失访的概率
TvsC = 1 # 试验组的样本量:对照组的样本量 1:1 = 1
Simulation_Cycle = 100  # 模拟的循环次数，越大越准确

检查效果

f_surv_logrank_simulation_Power(441, 6, 0.05, 
                                442, 8, 0.05,
                                8, 18, 1000, 0.05
)
# PASS的结果是 0.9
f_surv_logrank_simulation_Sample_Size(0, 1000, 6, 0.05, 
                                1, 8, 0.05,
                                8, 18, 1000, 0.05, 0.9
)
# PASS的结果是 441