Stepwise Procedure for Toxicological Assessment Based on Ratio of Mean Differences for a Normally Distributed Data

We propose a new stepwise confidence set procedure for toxicity study based on ratio of mean difference. Statistical approaches for evaluating toxicity studies that properly control familywise error rate (FWER) for difference of means between treatments and a control already exist. However, in some therapeutic areas, ratio of mean differences is desirable. Therefore, we construct stepwise confidence procedure based on Fieller's confidence intervals for multiple ratio of mean difference without multiplicity adjustment for toxicological evaluation. Simulation study revealed that the FWER is well controlled at prespecified nominal level α. Also, the power of our approach increases with increasing sample size and ratio of mean differences.

Using multiple outcomes in intervention studies for improved trade-off between power and type I errors: the Adjust NVar approach

Background The CONSORT guidelines for clinical trials recommend use of a single primary outcome, to guard against the raised risk of false positive findings when multiple measures are considered. It is, however, possible to include a suite of multiple outcomes in an intervention study, while controlling the familywise error rate, if the criterion for rejecting the null hypothesis specifies that N or more of the outcomes reach an agreed level of statistical significance, where N depends on the total number of outcome measures included in the study, and the correlation between them. Methods Simulations were run, using a conventional null-hypothesis significance testing approach with alpha set at .05, to explore the case when between 2 and 12 outcome measures are included to compare two groups, with average correlation between measures ranging from zero to .8, and true effect size ranging from 0 to .7. In step 1, a table is created giving the minimum N significant outcomes (MinNSig) that is required for a given set of outcome measures to control the familywise error rate at 5%. In step 2, data are simulated using MinNSig values for each set of correlated outcomes and the resulting proportion of significant results is computed for different sample sizes,correlations, and effect sizes. Results The Adjust NVar approach can achieve a more efficient trade-off between power and type I error rate than use of a single outcome when there are three or more moderately intercorrelated outcome variables. Conclusions Where it is feasible to have a suite of moderately correlated outcome measures, then this might be a more efficient approach than reliance on a single primary outcome measure in an intervention study. In effect, it builds in an internal replication to the study. This approach can also be used to evaluate published intervention studies.

Smoothed Nested Testing on Directed Acyclic Graphs

Summary We consider the problem of multiple hypothesis testing when there is a logical nested structure to the hypotheses. When one hypothesis is nested inside another, the outer hypothesis must be false if the inner hypothesis is false. We model the nested structure as a directed acyclic graph, including chain and tree graphs as special cases. Each node in the graph is a hypothesis and rejecting a node requires also rejecting all of its ancestors. We propose a general framework for adjusting node-level test statistics using the known logical constraints. Within this framework, we study a smoothing procedure that combines each node with all of its descendants to form a more powerful statistic. We prove a broad class of smoothing strategies can be used with existing selection procedures to control the familywise error rate, false discovery exceedance rate, or false discovery rate, so long as the original test statistics are independent under the null. When the null statistics are not independent but are derived from positively-correlated normal observations, we prove control for all three error rates when the smoothing method is arithmetic averaging of the observations. Simulations and an application to a real biology dataset demonstrate that smoothing leads to substantial power gains.

A Stepwise Procedure for Toxicity Studies Based on Ratio of two means

This paper proposes a stepwise confidence set procedure for identifying equivalence or safety of compounds in a toxicity study under heteroscedasticity of variances for a normally distributed data. The problem of statistical methodology for drug safety is the control of the familywise error rate (FWER). Hence, we construct a confidence set procedure for toxicological evaluation and incorporating the partitioning principle with a case of heteroscedascity of variances under normal assumption. Our simulation studies demonstrated that the power of the procedures for heterogeneity of variances increases with increasing in ratio of means.

Identifying Minimum Effective Dose Under Heteroscedasticity

We propose a stepwise confidence procedure for identifying minimum effective dose (MED) without multiplicity adjustment.Stepwise procedures strongly control the familywise error rate (FWER) which is a critical requirement for statistical methodologies in identification of MED. The partitioning principle is invoked to validate the control of the FWER. Our simulation study indicates that the FWER was properly controlled in the case with balanced design but failed in some cases of sample sizes for situations of unbalanced design. In addition, the power of the procedure increases with increasing mean of ratio differences and the sample sizes.

193 Substitution of Expensive Protein Sources by Soybean Meal Supplemented with a β-mannanase Enzyme Results in Improved General Clinical Health Score During the Post-weaning Period

β-Mannans are strongly anti-nutritive polysaccharide fibres found in most vegetable feed ingredients. The objective of the study was to compare piglet performance and antibiotic use between a Control group, fed a conventional 2-phase diet, and an Enzyme treated group, fed an adapted 2-phase diet including a β-mannanase enzyme (Hemicell™ HT; Elanco). A seven-week feeding trial was conducted with 320 pigs in two rotations of 160 piglets in 20 replicate pens of 8 pigs. Two different 3-phase diets were compared: a standard 3-phase control diet and an adapted 3-phase diet including a β-mannanase enzyme included at 300 g/tonne. The following adaptation were made: Phase-1 (weeks 1–3): 0.15% potato protein concentrate and 2.00% Danex [extruded soybean meal (SBM)], was replaced with SBM 48%, Phase-2 (weeks 4–7): β-mannanase was formulated to replace 63 kcal/kg NE. Standard piglet performance parameters (ADWG, ADFI, FCR) and antibiotic use were recorded. All data analyses were performed using R version 3.6.3 (R Core Team, 2020). All tests were performed at the 5% level of significance. When multiple testing was involved, the nominal 5% Familywise Error Rate (FWER) was used. Throughout the trial and within each phase, ADWG, ADFI and FCR were not significantly different (P > 0.05) between Control and Enzyme group. No mortality occurred and no antimicrobials were used in either of the treatment groups. Inclusion of a β-mannanase in nursery diets with an adapted formulation, by replacing expensive protein sources by soybean meal, or reducing the NE content by 63 kcal/kg, resulted in similar piglet performance post-weaning with reduced mortality and less antimicrobials used.

Identification of Minimum Effective Dose based on Ratio of a Normally Distributed Data under Heteroscedasticity

Efficacy and safety study is of practical importance in modern drug development. It is a key component in evaluating the safety of food additives or pesticides, and assessing the effectiveness and safety of drugs. In most of the various statistical procedures, homogeneity of variances among different dose levels was required. This paper without a need for multiplicity adjustment proposes a stepwise confidence set procedure for estimating Minimum Effective Dose (MED) of drugs based on ratio of population means for normally distributed data under heteroscedasticity. The procedure employed Fieller’s (1954) method and obtained individual confidence intervals for identification of MED. The procedure is applied to a data of an experiment that was published by Ruberg (1989) where the effect of a new compound is measured by an increase in the weight of a particular organ in mice. Simulation study was carried out and results indicate that the procedure controls the familywise error rate (FWER) strongly. Power of the procedure increases with increasing ratio of means and sample size.

Online control of the familywise error rate

Biological research often involves testing a growing number of null hypotheses as new data are accumulated over time. We study the problem of online control of the familywise error rate, that is testing an a priori unbounded sequence of hypotheses ( p-values) one by one over time without knowing the future, such that with high probability there are no false discoveries in the entire sequence. This paper unifies algorithmic concepts developed for offline (single batch) familywise error rate control and online false discovery rate control to develop novel online familywise error rate control methods. Though many offline familywise error rate methods (e.g., Bonferroni, fallback procedures and Sidak’s method) can trivially be extended to the online setting, our main contribution is the design of new, powerful, adaptive online algorithms that control the familywise error rate when the p-values are independent or locally dependent in time. Our numerical experiments demonstrate substantial gains in power, that are also formally proved in an idealized Gaussian sequence model. A promising application to the International Mouse Phenotyping Consortium is described.

The Romano–Wolf multiple-hypothesis correction in Stata

When considering multiple-hypothesis tests simultaneously, standard statistical techniques will lead to overrejection of null hypotheses unless the multiplicity of the testing framework is explicitly considered. In this article, we discuss the Romano–Wolf multiple-hypothesis correction and document its implementation in Stata. The Romano–Wolf correction (asymptotically) controls the familywise error rate, that is, the probability of rejecting at least one true null hypothesis among a family of hypotheses under test. This correction is considerably more powerful than earlier multiple-testing procedures, such as the Bonferroni and Holm corrections, given that it takes into account the dependence structure of the test statistics by resampling from the original data. We describe a command, rwolf, that implements this correction and provide several examples based on a wide range of models. We document and discuss the performance gains from using rwolf over other multiple-testing procedures that control the familywise error rate.

Multiple Comparison with a Control Using Step-down Procedure

The purpose of this research was to compare the efficiency of single-step procedures and the step-down procedures in order to test for multiple comparison with a control group. Four tests; Dunnett test, Step-down Dunnett test, Bonferroni test and Bonferroni-Holm test, was considered. The performance of these tests was evaluated in terms of the family wise error rate, any-pair power and all-pairs power. A Monte Carlo simulation was performed with repeated 10,000 times. The results showed that the familywise error rate of all test statistics closed to the nominal level. The empirical power of step-down procedures were higher than the single-step procedures, and the step-down Dunnett test gave the highest power.