A comprehensive open-source library for exact required sample size in binary clinical trials.

We describe how we are creating a new and comprehensive R library solving the problem of exact sample size determination of RCTs. A crucial prerequisite for the trial protocol is a priori sample sizes that bound the test size below a target (often 5%) and the test power above a target (often 80%). Approximate formulas are available for binary trials but the target test size and power are often violated by standard methods for even quite large sample sizes.

Exact confidence limits after a group sequential single arm binary trial.

Group sequential single arm designs are common in phase II trials as well as attribute testing and acceptance sampling. After the trial is completed, especially if the recommendation is to proceed to further testing, there is interest in full inference on treatment efficacy. For a binary response, there is the potential to construct exact upper and lower confidence limits, the first published method for which is Jennison and Turnbull (1983).

Tests for noninferiority trials with binomial endpoints: A guide to modern and quasi-exact methods for biomedical researchers.

Applied statisticians and pharmaceutical researchers are frequently involved in the design and analysis of clinical trials where at least one of the outcomes is binary. Treatments are judged by the probability of a positive binary response. A typical example is the noninferiority trial, where it is tested whether a new experimental treatment is practically not inferior to an active comparator with a prespecified margin δ.

A new method of identifying target groups for pronatalist policy applied to Australia.

A country's total fertility rate (TFR) depends on many factors. Attributing changes in TFR to changes of policy is difficult, as they could easily be correlated with changes in the unmeasured drivers of TFR. A case in point is Australia where both pronatalist effort and TFR increased in lock step from 2001 to 2008 and then decreased.

Accurate p-values for adaptive designs with binary endpoints.

Adaptive designs encompass all trials allowing various types of design modifications over the course of the trial. A key requirement for confirmatory adaptive designs to be accepted by regulators is the strong control of the family-wise error rate. This can be achieved by combining the p-values for each arm and stage to account for adaptations (including but not limited to treatment selection), sample size adaptation and multiple stages.

Accurate confidence limits for stratified clinical trials.

For stratified 2 × 2 tables, standard approximate confidence limits can perform poorly from a strict frequentist perspective, even for moderate-sized samples, yet they are routinely used. In this paper, I show how to use importance sampling to compute highly accurate limits in reasonable time. The methodology is very general and simple to implement, and orders of magnitude are faster than existing alternatives.

Bootstrap and second-order tests of risk difference.

Clinical trials data often come in the form of low-dimensional tables of small counts. Standard approximate tests such as score and likelihood ratio tests are imperfect in several respects. First, they can give quite different answers from the same data.

A more powerful exact test of noninferiority from binary matched-pairs data.

Assessing the therapeutic noninferiority of one medical treatment compared with another is often based on the difference in response rates from a matched binary pairs design. This paper develops a new exact unconditional test for noninferiority that is more powerful than available alternatives. There are two new elements presented in this paper.

A new exact and more powerful unconditional test of no treatment effect from binary matched pairs.

We consider the problem of testing for a difference in the probability of success from matched binary pairs. Starting with three standard inexact tests, the nuisance parameter is first estimated and then the residual dependence is eliminated by maximization, producing what I call an E+M P-value. The E+M P-value based on McNemar's statistic is shown numerically to dominate previous suggestions, including partially maximized P-values as described in Berger and Sidik (2003, Statistical Methods in Medical Research 12, 91-108).

Exact one-sided confidence bounds for the risk ratio in 2 x 2 tables with structural zero.

This paper examines exact one-sided confidence limits for the risk ratio in a 2 x 2 table with structural zero. Starting with four approximate lower and upper limits, we adjust each using the algorithm of Buehler (1957) to arrive at lower (upper) limits that have exact coverage properties and are as large (small) as possible subject to coverage, as well as an ordering, constraint. Different Buehler limits are compared by their mean size, since all are exact in their coverage.

Unconditional efficient one-sided confidence limits for the odds ratio based on conditional likelihood.

We compare various one-sided confidence limits for the odds ratio in a 2 x 2 table. The first group of limits relies on first-order asymptotic approximations and includes limits based on the (signed) likelihood ratio, score and Wald statistics. The second group of limits is based on the conditional tilted hypergeometric distribution, with and without mid-P correction.

Exact one-sided confidence limits for the difference between two correlated proportions.

We construct exact and optimal one-sided upper and lower confidence bounds for the difference between two probabilities based on matched binary pairs using well-established optimality theory of Buehler. Starting with five different approximate lower and upper limits, we adjust them to have coverage probability exactly equal to the desired nominal level and then compare the resulting exact limits by their mean size. Exact limits based on the signed root likelihood ratio statistic are preferred and recommended for practical use.