Exact Inference and Multiple Testing

Exact tests, sequential analysis, and error-rate control for clinical and genetic hypotheses

2026-06-07 18:16 PDT

Overview

Exact inference methods – procedures whose Type I error is guaranteed without large-sample approximation – are essential in settings where sparse data, small samples, or discrete outcomes make asymptotic chi-square and z-tests unreliable. This has long been a defining theme of the lab’s statistical methodology work, beginning with early papers on Fisher’s exact test for general r×2 tables and extending through unconditional exact procedures, sequential analysis, and error-rate control in multiple-testing contexts.

The applied motivation spans clinical trials with rare events, genetic association studies with Hardy-Weinberg equilibrium constraints, and interim analyses requiring formal stopping rules.

Current work

  • Fisher’s exact test for general r×2 tables. Exact conditional inference for two-way tables with more than two rows, including algorithms for exact p-value computation and power analysis under unequal sample sizes.

  • Unconditional exact tests for 2×2 tables. Comparison of unconditional exact procedures (Barnard, Boschloo) with the conditional Fisher test; power analysis and sample-size implications for trials with binary endpoints.

  • Fisher exact power with unequal N. Power analysis for exact tests under planned allocation imbalance.

  • Sequential analysis and repowering. Formal sequential testing procedures for clinical trials with planned interim looks, including sample-size re-estimation and repowering after an underpowered trial result.

  • Multiple comparisons. Error-rate control procedures (Bonferroni, Holm, Benjamini-Hochberg, closed testing) for clinical trials with multiple primary or secondary endpoints.

  • Hardy-Weinberg equilibrium testing. Exact tests for Hardy-Weinberg equilibrium in genetic association studies, with power evaluation for common allele-frequency configurations.

Methods

Exact conditional and unconditional tests; network algorithms for exact p-value computation; Monte Carlo power evaluation; sequential probability ratio tests (SPRT) and group sequential designs with alpha-spending; Bonferroni and Holm-type closed testing procedures.

Software

  • zzfisher – Fisher’s exact test for r×2 contingency tables, with exact power analysis and p-value computation.

Publications

This is one of the oldest and largest threads in the publication record. The full publications list can be filtered by exact-inference, hypothesis-testing, or confidence-intervals to browse the relevant papers, which span work from the early 1980s through the present.