TITLE:
Sample Size Calculation of Exact Tests for the Weak Causal Null Hypothesis in Randomized Trials with a Binary Outcome
AUTHORS:
Yasutaka Chiba
KEYWORDS:
Causal Inference, Conditional and Unconditional Exact Test, Potential Outcome, Two-by-Two Contingency Table
JOURNAL NAME:
Open Journal of Statistics,
Vol.6 No.5,
October
8,
2016
ABSTRACT: The main purpose in many randomized trials
is to make an inference about the average causal effect of a treatment.
Therefore, on a binary outcome, the null hypothesis for the hypothesis test
should be that the causal risks are equal in the two groups. This null
hypothesis is referred to as the weak causal null hypothesis. Nevertheless, at
present, hypothesis tests applied in actual randomized trials are not for this
null hypothesis; Fisher’s exact test is a test for the sharp causal null
hypothesis that the causal effect of treatment is the same for all subjects. In
general, the rejection of the sharp causal null hypothesis does not mean that
the weak causal null hypothesis is rejected. Recently, Chiba developed new
exact tests for the weak causal null hypothesis: a conditional exact test,
which requires that a marginal total is fixed, and an unconditional exact test,
which does not require that a marginal total is fixed and depends rather on the
ratio of random assignment. To apply these exact tests in actual randomized
trials, it is inevitable that the sample size calculation must be performed
during the study design. In this paper, we present a sample size calculation
procedure for these exact tests. Given the sample size, the procedure can
derive the exact test power, because it examines all the patterns that can be
obtained as observed data under the alternative hypothesis without large sample
theories and any assumptions.