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样本量计算

方法简介

样本量估算是临床试验设计的核心环节，直接影响试验的检验效能和可行性。

常用设计类型

设计 检验假设 关键参数
优效性 H0: Δ ≤ 0 效应量 δ, α, β
非劣效性 H0: Δ ≤ -margin margin, α, β
等效性 H0: |Δ| ≥ margin margin, α, β

代码实现

# 两样本均值比较（优效性）
power.t.test(
  delta = 5,           # 组间差异
  sd = 10,             # 标准差
  sig.level = 0.05,    # α
  power = 0.90,        # 1-β
  type = "two.sample",
  alternative = "two.sided"
)

# 两样本率比较
power.prop.test(
  p1 = 0.6,
  p2 = 0.4,
  sig.level = 0.05,
  power = 0.80
)

# 生存分析样本量
library(survival)
power_ct <- powerSurvEpi(
  n = NULL,
  time = 24,
  event = 0.8,
  hr = 0.7,
  alpha = 0.05,
  power = 0.90
)

from statsmodels.stats.power import TTestIndPower, NormalIndPower

# 两样本 t 检验
power = TTestIndPower()
n = power.solve_power(
    effect_size=0.5,   # Cohen's d
    alpha=0.05,
    power=0.90,
    alternative='two-sided'
)
print(f"每组所需样本量: {n:.0f}")

# 率的比较
from statsmodels.stats.proportion import proportion_effectsize
es = proportion_effectsize(0.6, 0.4)
n = NormalIndPower().solve_power(es, power=0.80, alpha=0.05)

proc power;
    twosamplemeans
        groupmeans = 10 | 15
        stddev = 10
        power = 0.90
        alpha = 0.05
        npergroup = .;
run;

proc power;
    twosamplefreq
        groupproportions = (0.6 0.4)
        power = 0.80
        alpha = 0.05
        npergroup = .;
run;

关键参数

  • 效应量：临床 meaningful difference，非统计学最小可检测差异
  • α：通常双边 0.05
  • β：通常 0.10-0.20（power 80-90%）
  • 脱落率：需在计算样本量基础上调整：N_adj = N / (1 - dropout_rate)

相关可视化