Correct and logical causal inference for binary and time-to-event outcomes in randomized controlled trials.

Targeted therapies tend to have biomarker defined subgroups that derive differential efficacy from treatments. This article corrects three prevailing oversights in stratified analyses comparing treatments in randomized controlled trials (RCTs) with binary and time-to-event outcomes: 1.Using efficacy measures such as odds ratio (OR) and hazard ratio (HR) can make a prognostic biomarker appear predictive, targeting wrong patients, because the inference is affected by a confounding/covert factor even with ignorable treatment assignment in an RCT. As shown analytically and with real immunotherapy patient level data, OR and HR cannot meet the causal Estimand requirement of ICH E9R1. 2.Mixing efficacy in subgroups by prevalence, the prevailing practice, can give misleading results also, for any efficacy measured as a ratio. However, mixing relative response (RR) and ratio of median (RoM) survival times by the prognostic effect, the confounding/covert factor hiding in plain sight, will give causal inference in an RCT. 3.Effects in subgroups should not be mixed on the logarithmic scale, because it creates an artificial Estimand for the whole population which changes depending on how the population is divided into subgroups. Current computer package implementations contain all these oversights. Probabilities, including survival curve probabilities, naturally average within each treatment arm by prevalence. The subgroup mixable estimation (SME) principle fixes the oversights by first averaging probabilities (not their logarithms) within each treatment arm, then computing simultaneous confidence intervals for ratio efficacy in subgroups and their mixtures based on rigorous mathematical derivation, to finally provide causal inference in the form of apps.

Rejoinder for discussions on correct and logical causal inference for binary and time-to-event outcomes in randomized controlled trials.

Our paper differs from previous literature in two ways: 1.We think in terms of clinical consequences, what benefits patients, what harms patients. Our main message is: using a not logic-respecting efficacy measure can potentially harm patients in a randomized controlled trial (RCT), as we prove analytically, and demonstrate with the OAK blood-based tumor mutational burden (bTMB) study. 2.We follow nature, which mixes effects within each treatment arm. Our secondary message is that following nature to mix within each treatment arm first before calculating any efficacy measure between treatments resolves issues. For example, following natural mixing to prove ratio of time is logic-respecting avoids the issue that weights of efficacy measures are implicit solution to an equation that depends on the unknown prognostic effect. More importantly, coding subgroup mixable estimation (SEM) by mixing within each treatment arm first and then calculating efficacy will make marginal and conditional efficacy agree, for logic-respecting efficacy measures (be it a ratio or a difference), no matter the outcome is continuous, binary, or time-to-event. One does not have to choose between marginal and conditional.

Afatinib vs Placebo as Adjuvant Therapy After Chemoradiotherapy in Squamous Cell Carcinoma of the Head and Neck: A Randomized Clinical Trial.

IMPORTANCE: Locoregionally advanced head and neck squamous cell cancer (HNSCC) is treated curatively; however, risk of recurrence remains high among some patients. The ERBB family blocker afatinib has shown efficacy in recurrent or metastatic HNSCC. OBJECTIVE: To assess whether afatinib therapy after definitive chemoradiotherapy (CRT) improves disease-free survival (DFS) in patients with HNSCC. DESIGN, SETTING, AND PARTICIPANTS: This multicenter, phase 3, double-blind randomized clinical trial (LUX-Head & Neck 2) studied 617 patients from November 2, 2011, to July 4, 2016. Patients who had complete response after CRT, comprising radiotherapy with cisplatin or carboplatin, with or without resection of residual disease, for locoregionally advanced high- or intermediate-risk HNSCC of the oral cavity, hypopharynx, larynx, or oropharynx were included in the study. Data analysis was of the intention-to-treat population. INTERVENTIONS: Patients were randomized (2:1) to treatment with afatinib (40 mg/d) or placebo, stratified by nodal status (N0-2a or N2b-3) and Eastern Cooperative Oncology Group performance status (0 or 1). Treatment continued for 18 months or until disease recurrence, unacceptable adverse events, or patient withdrawal. MAIN OUTCOMES AND MEASURES: The primary end point was DFS, defined as time from the date of randomization to the date of tumor recurrence or secondary primary tumor or death from any cause. Secondary end points were DFS at 2 years, overall survival (defined as time from the date of randomization to death), and health-related quality of life. RESULTS: A total of 617 patients were studied (mean [SD] age, 58 [8.4] years; 528 male [85.6%]). Recruitment was stopped after a preplanned interim futility analysis on July 4, 2016, on recommendation from an independent data monitoring committee. Treatment was discontinued. Median DFS was 43.4 months (95% CI, 37.4 months to not estimable) in the afatinib group and not estimable (95% CI, 40.1 months to not estimable) in the placebo group (hazard ratio, 1.13; 95% CI, 0.81-1.57; stratified log-rank test P = .48). The most common grade 3 and 4 drug-related adverse effects were acneiform rash (61 [14.8%] of 411 patients in the afatinib group vs 1 [0.5%] of 206 patients in the placebo group), stomatitis (55 [13.4%] in the afatinib group vs 1 [0.5%] in the placebo group), and diarrhea (32 [7.8%] in the afatinib group vs 1 [0.5%] in the placebo group). CONCLUSIONS AND RELEVANCE: This study's findings indicate that treatment with afatinib after CRT did not improve DFS and was associated with more adverse events than placebo in patients with primary, unresected, clinically high- to intermediate-risk HNSCC. The use of adjuvant afatinib after CRT is not recommended. TRIAL REGISTRATION: ClinicalTrials.gov identifier: NCT01345669.

Design and rationale for the DIVERSITY study: An open-label, randomized study of dabigatran etexilate for pediatric venous thromboembolism.

BACKGROUND: The current standard of care (SOC) for pediatric venous thromboembolism (VTE) comprises unfractionated heparin (UFH), or low-molecular-weight heparin (LMWH) followed by LMWH or vitamin K antagonists, all of which have limitations. Dabigatran etexilate (DE) has demonstrated efficacy and safety for adult VTE and has the potential to overcome some of the limitations of the current SOC. Pediatric trials are needed to establish dosing in children and to confirm that results obtained in adults are applicable in the pediatric setting. OBJECTIVES: To describe the design and rationale of a planned phase IIb/III trial that will evaluate a proposed dosing algorithm for DE and assess the safety and efficacy of DE versus SOC for pediatric VTE treatment. PATIENTS/METHODS: An open-label, randomized, parallel-group noninferiority study will be conducted in approximately 180 patients aged 0 to <18 years with VTE, who have received initial UFH or LMWH treatment and who are expected to require ≥3 months of anticoagulation therapy. Patients will receive DE or SOC for 3 months. DE will be administered twice daily as capsules, pellets, or an oral liquid formulation according to patient age. Initial doses will be calculated using a proposed dosing algorithm. RESULTS: There will be two coprimary endpoints: a composite efficacy endpoint comprising the proportion of patients with complete thrombus resolution, freedom from recurrent VTE and VTE-related mortality, and a safety endpoint: freedom from major bleeding events. CONCLUSION: Findings will provide valuable information regarding the efficacy and safety of DE for the treatment of pediatric VTE. ClinicalTrials.gov registration number: NCT01895777.

Phase 3, single-arm, multicenter study of dabigatran etexilate for secondary prevention of venous thromboembolism in children: Rationale and design.

BACKGROUND: Anticoagulant therapy for venous thromboembolism (VTE) in children is largely based on treatment recommendations for adults. However, differences in both physiology (ie, renal maturation and drug excretion) and developmental hemostasis must be considered when treating children, as such differences could affect dose appropriateness, safety and efficacy. OBJECTIVES: To address these concerns, a study was designed to evaluate the safety of dabigatran etexilate in children requiring secondary thrombus prevention in whom an initial VTE was associated with an identified risk factor that persisted after the acute VTE treatment period. We report herein the rationale and design of the study. PATIENTS/METHODS: This phase 3, open-label, single-arm, multicenter, multinational, prospective cohort study will be conducted in ≥100 children aged 0 to <18 years at ~100 specialist sites worldwide. Children will be treated with dabigatran etexilate for 12 months, or for a shorter duration if their identified VTE risk factor resolves, as per current American College of Chest Physicians recommendations. A nomogram will be used to determine starting doses for each patient. RESULTS: The primary outcomes of the study will be VTE recurrence, bleeding events, overall mortality, and VTE-related mortality. Secondary outcomes will include occurrence of post-thrombotic syndrome, the pharmacokinetics of dabigatran, and the need for dose adjustments during treatment. Data on adverse events during the study will also be collected. CONCLUSION: This study will evaluate the safety of dabigatran etexilate for the secondary prevention of VTE in children, in addition to providing further data to guide pediatric dosing with dabigatran.

Symptom and Quality of Life Improvement in LUX-Lung 8, an Open-Label Phase III Study of Second-Line Afatinib Versus Erlotinib in Patients With Advanced Squamous Cell Carcinoma of the Lung After First-Line Platinum-Based Chemotherapy.

INTRODUCTION: In the phase III LUX-Lung 8 trial, afatinib significantly improved progression-free survival (PFS) and overall survival (OS) versus erlotinib in patients with squamous cell carcinoma (SCC) of the lung progressing during or after platinum-based chemotherapy. Patient-reported outcomes (PROs) and health-related quality of life (QoL) in these patients are presented. PATIENTS AND METHODS: Patients (n = 795) were randomized 1:1 to oral afatinib (40 mg/d) or erlotinib (150 mg/d). PROs were collected (baseline, every 28 days until progression, 28 days after discontinuation) using the European Organization for Research and Treatment of Cancer QoL questionnaire and lung cancer-specific module. The percentage of patients improved during therapy, time to deterioration (TTD), and changes over time were analyzed for prespecified lung cancer-related symptoms and global health status (GHS)/QoL. RESULTS: Questionnaire compliance was 77.3% to 99.0% and 68.7% to 99.0% with afatinib and erlotinib, respectively. Significantly more patients who received afatinib versus erlotinib experienced improved scores for GHS/QoL (36% vs. 28%; P = .041) and cough (43% vs. 35%; P = .029). Afatinib significantly delayed TTD in dyspnea (P = .008) versus erlotinib, but not cough (P = .256) or pain (P = .869). Changes in mean scores favored afatinib for cough (P = .0022), dyspnea (P = .0007), pain (P = .0224), GHS/QoL (P = .0320), and all functional scales. Differences in adverse events between afatinib and erlotinib, specifically diarrhea, did not affect GHS/QoL. CONCLUSION: In patients with SCC of the lung, second-line afatinib was associated with improved prespecified disease-related symptoms and GHS/QoL versus erlotinib, complementing PFS and OS benefits with afatinib.

Continued use of afatinib with the addition of cetuximab after progression on afatinib in patients with EGFR mutation-positive non-small-cell lung cancer and acquired resistance to gefitinib or erlotinib.

OBJECTIVES: In a phase Ib trial, afatinib plus cetuximab demonstrated promising clinical activity (objective response rate [ORR]: 29%; median progression-free survival [PFS]: 4.7 months) in patients with epidermal growth factor receptor (EGFR) mutation-positive non-small-cell lung cancer (NSCLC) with acquired resistance to erlotinib or gefitinib. Here, a separate cohort exploring afatinib plus cetuximab after progression on afatinib is reported. MATERIALS AND METHODS: Patients with EGFR mutation-positive NSCLC who progressed on erlotinib or gefitinib received afatinib 40mg daily until progression, followed by afatinib daily plus cetuximab 500mg/m2 every 2 weeks until progression or intolerable adverse events (AEs). Endpoints included safety, ORR, and PFS. RESULTS: Thirty-seven patients received afatinib monotherapy. Two (5%) patients responded; median PFS was 2.7 months. Thirty-six patients transitioned to afatinib plus cetuximab. Four (11%) patients responded; median PFS was 2.9 months. Median PFS with afatinib plus cetuximab for patients who received afatinib monotherapy for ≥12 versus <12 weeks was 4.9 versus 1.8 months (p=0.0354), and for patients with T790M-positive versus T790M-negative tumors was 4.8 versus 1.8 months (p=0.1306). Fifty percent of patients receiving afatinib plus cetuximab experienced drug-related grade 3/4 AEs. The most frequent drug-related AEs (any grade) were diarrhea (70%), rash (49%), and fatigue (35%) with afatinib monotherapy and rash (69%), paronychia (39%), and dry skin (36%) with afatinib plus cetuximab. CONCLUSION: Sequential EGFR blockade with afatinib followed by afatinib plus cetuximab had a predictable safety profile and demonstrated modest activity in patients with EGFR mutation-positive NSCLC with resistance to erlotinib or gefitinib. CLINICALTRIALS. GOV IDENTIFIER: NCT01090011.

Idarucizumab for Dabigatran Reversal - Full Cohort Analysis.

BACKGROUND: Idarucizumab, a monoclonal antibody fragment, was developed to reverse the anticoagulant effect of dabigatran. METHODS: We performed a multicenter, prospective, open-label study to determine whether 5 g of intravenous idarucizumab would be able to reverse the anticoagulant effect of dabigatran in patients who had uncontrolled bleeding (group A) or were about to undergo an urgent procedure (group B). The primary end point was the maximum percentage reversal of the anticoagulant effect of dabigatran within 4 hours after the administration of idarucizumab, on the basis of the diluted thrombin time or ecarin clotting time. Secondary end points included the restoration of hemostasis and safety measures. RESULTS: A total of 503 patients were enrolled: 301 in group A, and 202 in group B. The median maximum percentage reversal of dabigatran was 100% (95% confidence interval, 100 to 100), on the basis of either the diluted thrombin time or the ecarin clotting time. In group A, 137 patients (45.5%) presented with gastrointestinal bleeding and 98 (32.6%) presented with intracranial hemorrhage; among the patients who could be assessed, the median time to the cessation of bleeding was 2.5 hours. In group B, the median time to the initiation of the intended procedure was 1.6 hours; periprocedural hemostasis was assessed as normal in 93.4% of the patients, mildly abnormal in 5.1%, and moderately abnormal in 1.5%. At 90 days, thrombotic events had occurred in 6.3% of the patients in group A and in 7.4% in group B, and the mortality rate was 18.8% and 18.9%, respectively. There were no serious adverse safety signals. CONCLUSIONS: In emergency situations, idarucizumab rapidly, durably, and safely reversed the anticoagulant effect of dabigatran. (Funded by Boehringer Ingelheim; RE-VERSE AD ClinicalTrials.gov number, NCT02104947 .).

An improved uniformly more powerful exact Fisher-Hayter pairwise comparisons procedure.

Pairwise comparison is a very common multiple comparison problem. It is known that Fisher's LSD test does not control the familywise error rate (FWER) when there are more than three groups to be compared. Improved testing strategies include the Tukey-Kramer (TK) test that eliminates the F-test step and the two-step Fisher-Hayter (FH) test which requires a significant F-test. We propose a modified FH-test that is uniformly more powerful than the original version and relies on exact size α test under the balanced model. We provide simulations to show that the new procedure is preferred to the FH-test and the TK-test.

Sample size determination with familywise control of both type I and type II errors in clinical trials.

The concept of controlling familywise type I and type II errors at the same time is essentially an integrated process to deal with multiplicity issues in clinical trials. The process will select a multiple testing procedure (MTP) which controls the familywise type I error and calculate the per hypothesis sample size such that the "studywise power" is maintained at desired level. The power of a study can be defined in several ways and it depends on the objective. In this article, we provide general guidance on how to make the selection of MTPs and calculate sample size simultaneously. We introduce the concept of strong and weak control of the familywise type II error and generalized familywise type II error. We also proposed the novel Bonferroni+ and optimal Bonferroni+ procedures to allocate per hypothesis type II error. We demonstrated the value of the proposed work as it cannot be replaced by simple simulations. A real clinical trial is discussed throughout the article as an example.

Afatinib versus erlotinib as second-line treatment of patients with advanced squamous cell carcinoma of the lung (LUX-Lung 8): an open-label randomised controlled phase 3 trial.

BACKGROUND: There is a major unmet need for effective treatments in patients with squamous cell carcinoma of the lung. LUX-Lung 8 compared afatinib (an irreversible ErbB family blocker) with erlotinib (a reversible EGFR tyrosine kinase inhibitor), as second-line treatment for patients with advanced squamous cell carcinoma of the lung. METHODS: We did this open-label, phase 3 randomised controlled trial at 183 cancer centres in 23 countries worldwide. We enrolled adults with stage IIIB or IV squamous cell carcinoma of the lung who had progressed after at least four cycles of platinum-based-chemotherapy. Participants were randomly assigned (1:1) to receive afatinib (40 mg per day) or erlotinib (150 mg per day) until disease progression. The randomisation was done centrally with an interactive voice or web-based response system and stratified by ethnic origin (eastern Asian vs non-eastern Asian). Clinicians and patients were not masked to treatment allocation. The primary endpoint was progression-free survival assessed by independent central review (intention-to-treat population). The key secondary endpoint was overall survival. This trial is registered with ClinicalTrials.gov, NCT01523587. FINDINGS: 795 eligible patients were randomly assigned (398 to afatinib, 397 to erlotinib). Median follow-up at the time of the primary analysis of progression-free survival was 6·7 months (IQR 3·1-10·2), at which point enrolment was not complete. Progression free-survival at the primary analysis was significantly longer with afatinib than with erlotinib (median 2·4 months [95% CI 1·9-2·9] vs 1·9 months [1·9-2·2]; hazard ratio [HR] 0·82 [95% CI 0·68-1·00], p=0·0427). At the time of the primary analysis of overall survival (median follow-up 18·4 months [IQR 13·8-22·4]), overall survival was significantly greater in the afatinib group than in the erloinib group (median 7·9 months [95% CI 7·2-8·7] vs 6·8 months [5·9-7·8]; HR 0·81 [95% CI 0·69-0·95], p=0·0077), as were progression-free survival (median 2·6 months [95% CI 2·0-2·9] vs 1·9 months [1·9-2·1]; HR 0·81 [95% CI 0·69-0·96], p=0·0103) and disease control (201 [51%] of 398 patients vs 157 [40%] of 397; p=0·0020). The proportion of patients with an objective response did not differ significantly between groups (22 [6%] vs 11 [3%]; p=0·0551). Tumour shrinkage occurred in 103 (26%) of 398 patients versus 90 (23%) of 397 patients. Adverse event profiles were similar in each group: 224 (57%) of 392 patients in the afatinib group versus 227 (57%) of 395 in the erlotinib group had grade 3 or higher adverse events. We recorded higher incidences of treatment-related grade 3 diarrhoea with afatinib (39 [10%] vs nine [2%]), of grade 3 stomatitis with afatinib (16 [4%] vs none), and of grade 3 rash or acne with erlotinib (23 [6%] vs 41 [10%]). INTERPRETATION: The significant improvements in progression-free survival and overall survival with afatinib compared with erlotinib, along with a manageable safety profile and the convenience of oral administration suggest that afatinib could be an additional option for the treatment of patients with squamous cell carcinoma of the lung. FUNDING: Boehringer Ingelheim.

Idarucizumab for Dabigatran Reversal.

BACKGROUND: Specific reversal agents for non-vitamin K antagonist oral anticoagulants are lacking. Idarucizumab, an antibody fragment, was developed to reverse the anticoagulant effects of dabigatran. METHODS: We undertook this prospective cohort study to determine the safety of 5 g of intravenous idarucizumab and its capacity to reverse the anticoagulant effects of dabigatran in patients who had serious bleeding (group A) or required an urgent procedure (group B). The primary end point was the maximum percentage reversal of the anticoagulant effect of dabigatran within 4 hours after the administration of idarucizumab, on the basis of the determination at a central laboratory of the dilute thrombin time or ecarin clotting time. A key secondary end point was the restoration of hemostasis. RESULTS: This interim analysis included 90 patients who received idarucizumab (51 patients in group A and 39 in group B). Among 68 patients with an elevated dilute thrombin time and 81 with an elevated ecarin clotting time at baseline, the median maximum percentage reversal was 100% (95% confidence interval, 100 to 100). Idarucizumab normalized the test results in 88 to 98% of the patients, an effect that was evident within minutes. Concentrations of unbound dabigatran remained below 20 ng per milliliter at 24 hours in 79% of the patients. Among 35 patients in group A who could be assessed, hemostasis, as determined by local investigators, was restored at a median of 11.4 hours. Among 36 patients in group B who underwent a procedure, normal intraoperative hemostasis was reported in 33, and mildly or moderately abnormal hemostasis was reported in 2 patients and 1 patient, respectively. One thrombotic event occurred within 72 hours after idarucizumab administration in a patient in whom anticoagulants had not been reinitiated. CONCLUSIONS: Idarucizumab completely reversed the anticoagulant effect of dabigatran within minutes. (Funded by Boehringer Ingelheim; RE-VERSE AD ClinicalTrials.gov number, NCT02104947.).

Design and rationale for RE-VERSE AD: A phase 3 study of idarucizumab, a specific reversal agent for dabigatran.

Idarucizumab, a Fab fragment directed against dabigatran, produced rapid and complete reversal of the anticoagulation effect of dabigatran in animals and in healthy volunteers. The Study of the REVERSal Effects of Idarucizumab in Patients on Active Dabigatran (RE-VERSE AD™) is a global phase 3 prospective cohort study aimed at investigating idarucizumab in dabigatran-treated patients who present with uncontrollable or life-threatening bleeding, and in those requiring urgent surgery or intervention. We describe the rationale for, and design of the trial (clinicaltrials.gov NCT02104947).

Dual inhibition of EGFR with afatinib and cetuximab in kinase inhibitor-resistant EGFR-mutant lung cancer with and without T790M mutations.

UNLABELLED: EGFR-mutant lung cancers responsive to reversible EGFR inhibitors (gefitinib/erlotinib) develop acquired resistance, mediated by second-site EGFR T790M mutation in >50% of cases. Preclinically, afatinib (irreversible ErbB family blocker) plus cetuximab (anti-EGFR monoclonal antibody) overcomes T790M-mediated resistance. This phase Ib study combining afatinib and cetuximab enrolled heavily pretreated patients with advanced EGFR-mutant lung cancer and acquired resistance to erlotinib/gefitinib. Patients provided post-acquired-resistance tumor samples for profiling EGFR mutations. Among 126 patients, objective response rate (overall 29%) was comparable in T790M-positive and T790M-negative tumors (32% vs. 25%; P = 0.341). Median progression-free survival was 4.7 months (95% confidence interval, 4.3-6.4), and the median duration of confirmed objective response was 5.7 months (range, 1.8-24.4). Therapy-related grade 3/4 adverse events occurred in 44%/2% of patients. Afatinib-cetuximab demonstrated robust clinical activity and a manageable safety profile in EGFR-mutant lung cancers with acquired resistance to gefitinib or erlotinib, both with and without T790M mutations, warranting further investigation. SIGNIFICANCE: This article reports the results of a trial combining afatinib and cetuximab in patients with acquired resistance and details the first clinical proof-of-concept for the preclinical hypothesis that a significant proportion of tumors in patients with acquired resistance to gefitinib/erlotinib remain dependent on EGFR signaling for survival.

An Application of Graphical Approach to Construct Multiple Testing Procedures in a Hypothetical Phase III Design.

Many multiple testing procedures (MTP) have been developed in recent years. Among these new procedures, the graphical approach is flexible and easy to communicate with non-statisticians. A hypothetical Phase III clinical trial design is introduced in this manuscript to demonstrate how graphical approach can be applied in clinical product development. In this design, an active comparator is used. It is thought that this test drug under development could potentially be superior to this comparator. For comparison of efficacy, the primary endpoint is well established and widely accepted by regulatory agencies. However, an important secondary endpoint based on Phase II findings looks very promising. The target dose may have a good opportunity to deliver superiority to the comparator. Furthermore, a lower dose is included in case the target dose may demonstrate potential safety concerns. This Phase III study is designed as a non-inferiority trial with two doses, and two endpoints. This manuscript will illustrate how graphical approach is applied to this design in handling multiple testing issues.

A new partition testing strategy for multiple endpoints.

To evaluate efficacy in multiple endpoints in confirmatory clinical trials is a challenging problem in multiple hypotheses testing. The difficulty comes from the different importance of each endpoint and their underlying correlation. Current approaches to this problem, which test the efficacy in certain dose-endpoint combinations and collate the results, are based on closed testing or partition testing. Despite their different formulations, all current approaches test their dose-endpoint combinations as intersection hypotheses and apply various union-intersection tests. Likelihood ratio test is seldom used owing to the extensive computation and lack of consistent inferences. In this article, we first generalize the formulation of multiple endpoints problem to include the cases of alternative primary endpoints and co-primary endpoints. Then we propose a new partition testing approach that is based on consonance-adjusted likelihood ratio test. The new procedure provides consistent inferences, and yet, it is still conservative and does not rely on the estimation of endpoint correlation or independence assumptions that might be challenged by regulatory agencies.

Consonant closed likelihood ratio test procedures with application to dose-response study.

Coherence and Consonance are two important concepts in multiple testing procedures (MTP). Closed test is a well-known coherent hypothesis testing procedure, which is not necessarily consonant. In this paper, we propose two consonant closed likelihood ratio tests which are compared with the step-down Dunnett test (SD) and Dunnett-Tamhane step-up test (SU) in several aspects. Simulation and dose-response study examples show that the new procedures have certain advantages over the SD and SU test. For example, the rejection region of our new procedures is larger than that of the SD test particularly when most of the null hypotheses are false. The new procedures control the family-wise error rate (FWER) strongly without the equal correlation assumption, which is a necessary condition for the SU test. In terms of computing effort, the new procedures require similar moderate computation for critical constants as the SU test and they follow the same steps as any closed test procedures. We also provide guideline in applying consonance adjustment in multivariate analysis with mixed model and repeated measurements.

General solutions to consistency problems in multiple hypothesis testing.

Coherence and consonance are the two important concepts to ensure consistent conclusions drawn from multiple tests. Unlike coherence, consonance of a multiple testing procedure (MTP) has not yet received much attention. Although most of the MTPs used in practice are consonant, cases still exist that dissonant tests have to be used due to their unique advantages, for example, the likelihood ratio tests and sum tests. Consonance adjustments are necessary for such tests to avoid difficulty in interpretation. Moreover, in terms of detecting elementary hypotheses, a consonant test procedure is uniformly more powerful than the corresponding dissonant one. In this paper, several general methods using the partitioning principle to construct (strongly) consonant and strongly coherent MTPs are proposed. As a result, any dissonant (but coherent) multiple level α test can be improved by a consonant one without any cost in terms of inferences on elementary hypotheses.