Truncated product method for combining P-values.

We present a new procedure for combining P-values from a set of L hypothesis tests. Our procedure is to take the product of only those P-values less than some specified cut-off value and to evaluate the probability of such a product, or a smaller value, under the overall hypothesis that all L hypotheses are true. We give an explicit formulation for this P-value, and find by simulation that it can provide high power for detecting departures from the overall hypothesis. We extend the procedure to situations when tests are not independent. We present both real and simulated examples where the method is especially useful. These include exploratory analyses when L is large, such as genome-wide scans for marker-trait associations and meta-analytic applications that combine information from published studies, with potential for dealing with the "publication bias" phenomenon. Once the overall hypothesis is rejected, an adjustment procedure with strong family-wise error protection is available for smaller subsets of hypotheses, down to the individual tests.

Properties of multiple intersection-union tests for multiple endpoints in combination therapy trials.

We consider intersection-union tests involving multiple endpoints in a combination drug trial, for which we control the familywise error rate in the strong sense using closed testing methods. Bonferroni-Holm, Simes-Hommel, and Resampling-Based methods all are considered in this context. Familywise error rate control heuristics are developed and evaluated using a simulation study that is specifically tailored to the intersection-union setting. Both Resampling-Based and Simes-Hommel uniformly outperform the Bonferroni-Holm. Using simulations of power, the choice of Simes-Hommel versus Resampling-Based is seen to depend on the particular alternative of interest. Because it is simpler and has generally good power, we recommend the Simes-Hommel intersection-union tests. The techniques are illustrated using real data from a clinical trial to evaluate a combination asthma therapy.

Using prior information to allocate significance levels for multiple endpoints.

We maximize power in a replicated clinical trial involving multiple endpoints by adjusting the individual significance levels for each hypothesis, using preliminary data to obtain the optimal adjustments. The levels are constrained to control the familywise error rate. Power is defined as the expected number of significances, where expectations are taken with respect to the posterior distributions of the non-centrality parameters under non-informative priors. Sample size requirements for the replicate study are given. Intuitive principles such as downweighting insignificant variables from a preliminary study and giving primary endpoints more emphasis are justifiable within the conceptual framework.

Evaluation of the ability of power to predict low frequency lifting capacity.

An experiment was conducted to examine the role that maximal lifting power has in predicting maximum acceptable weight of lift (MAWL) for a frequency of one lift per 8 h. The secondary aim of the study was to compare the ability of power to predict MAWL to previously used measures of capacity including two measures of isometric strength, five measures of isokinetic strength, and isoinertial capacity on an incremental lifting test. Twenty-five male subjects volunteered to participate in the experiment. The isometric tests involved maximum voluntary contractions for composite lifting strength at vertical heights of 15 and 75 cm. Peak isokinetic strength was measured at velocities of 0.1, 0.2, 0.4, 0.6 and 0.8 m s-1 using a modified CYBEX II isokinetic dynamometer. Isoinertial lifting capacity was measured on the X-factor incremental lifting machine and peak power was measured on the incremental lifting machine by having subjects lift a 25 kg load as quickly as possible. The results indicate that peak isoinertial power is significantly correlated with MAWL, and this correlation was higher than any of the correlations between the other predictor variables and MAWL. The relationships between the isokinetic strength measures and MAWL were stronger than the relationships between the isometric measures and MAWL. Overall, the results suggest that tests used to predict MAWL should be dynamic rather than static.

Weighted multiplicity adjustments for animal carcinogenicity tests.

Sparse data is a difficulty in the analysis of animal carcinogenicity data: it is difficult to detect effects when the background tumor rates are low. The widely used "Haseman rule" and its variants provide more power to tests with low background rates, while maintaining a degree of control over the global false positive rate. In this article we explore the use of these rules, finding global error rates that are unacceptably high for many animal carcinogenicity studies. We provide alternative weighting methods that correct the deficiencies of the Haseman rule, and apply them to carcinogenicity data from a pharmaceutical company.