A note on exact confidence interval for causal effects on a binary outcome in randomized trials
A note on exact confidence interval for causal effects on a binary outcome in randomized trials
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关于随机试验中二元结果因果效应的确切置信区间的说明
DOI：
10.1002/sim.6826
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发表时间：
2016
影响因子：
2
通讯作者：
Yasutaka Chiba
中科院分区：
文献类型：
--
作者：
Akiko Takeda;Katsuya Tono;Jun-ya Gotoh;Yasutaka Chiba;Suguru Sekine and Yasushi Nagata;Yasutaka Chiba
Rigdon和Hudgens [1]在他们最近的论文中提出了两种方法来构建二元结果因果效应的基于随机化的置信区间（CI）：归因效应（AE）和反向排列（IP）方法。其100（1 α）%CI是精确的，即包含真实因果效应的概率至少为100（1 α）%。他们使用表I中的数据展示了他们的两种方法，其中X表示治疗，Y表示结果。对于数据，风险差（RD）为33/48 × 11/48= 22/48= 0.4583。相应AE和IP方法得出的95% CI分别为（22/96，61/96）=（0.2292，0.6354）和（27/96，61/96）=（0.2813，0.6354）。后一个95% CI作为精确CI似乎有些不自然，因为上限与观察到的RD之间的差异（61/96 × 22/48= 17/96）等于下限和观测到的RD之间的值（22/48 - 27/96= 17/96），尽管当观测到的RD为33/48 × 11/48= 0.4583时，下限的分布比上限的分布宽。在这封信中，对于表I中的数据，我直观地显示了这两种分布的差异，并且基于两个单独的单侧假设检验，IP方法的95% CI上限过于保守（因此，AE方法的下限和上限都过于保守）。为此，我应用了主分层的概念[2]。让我们假设观察到的数据汇总在表II中的通用二乘二列联表中。设Y（x）表示X= x下每例受试者的潜在结局，nst表示（Y（1），Y（0））=（s，t）的受试者数量，其中s，t= 0，1，nst，x表示nst例受试者中分配至X= x组的受试者数量。这里，考虑（n11，n10，n 01，n 00）=（34，27，0，35）的组合。在该组合下，因果RD为（n11+ n10）/n11（n11+ n 01）/n= 27/96= 0.2813，对应于IP方法的95% CI下限。当每组中分配的受试者数量固定时，
In their recent paper, Rigdon and Hudgens [1] presented two approaches for constructing a randomization-based confidence interval (CI) for the causal effect on a binary outcome: the attributable effect (AE) and inverted permutation (IP) approaches. Their 100 (1Àα)% CIs are exact in the sense that the probability of containing the true causal effect is at least 100 (1Àα)%. They demonstrated their two approaches using the data in Table I, where X denotes a treatment and Y denotes the outcome. For the data, the risk difference (RD) is 33/48À11/48= 22/48= 0.4583. The respective AE and IP approaches yield 95% CIs of (22/96, 61/96)=(0.2292, 0.6354) and (27/96, 61/96)=(0.2813, 0.6354). It seems that the latter 95% CI is somewhat unnatural as an exact CI, because the difference between the upper limit and the observed RD (61/96À22/48= 17/96) is equal to that between the lower limit and the observed RD (22/48À27/96= 17/96), although the distribution of the lower limit would be wider than that of the upper limit when the observed RD is 33/48À11/48= 0.4583. In this letter, for the data in Table I, I show the difference of these two distributions visually, and that the upper limit of 95% CI from the IP approach would be too conservative (and thus, both lower and upper limits from the AE approach would be too conservative) based on the two separate one-sided hypothesis tests. To do so, I apply the concept of principal stratification [2].Let us assume that the observed data are summarized in the generic two-by-two contingency table in Table II. Let Y (x) denote the potential outcome for each subject under X= x, nst denote the number of subjects with (Y (1), Y (0))=(s, t), where s, t= 0, 1, and nst, x denote the number of subjects assigned to the group with X= x of the nst subjects. Here, consider a combination of (n11, n10, n01, n00)=(34, 27, 0, 35). Under this combination, the causal RD is (n11+ n10)/nÀ (n11+ n01)/n= 27/96= 0.2813, which corresponds to the lower limit of 95% CI from the IP approach. When the number of subjects assigned in each group is fixed, the probability that the RD is