The impact of allocation bias on test decisions in clinical trials with multiple endpoints using multiple testing strategies.

BACKGROUND: Considering multiple endpoints in clinical trials provide a more comprehensive understanding of treatment effects and may lead to increased power or reduced sample size, which may be beneficial in rare diseases. Besides the small sample sizes, allocation bias is an issue that affects the validity of these trials. We investigate the impact of allocation bias on testing decisions in clinical trials with multiple endpoints and offer a tool for selecting an appropriate randomization procedure (RP). METHODS: We derive a model for quantifying the effect of allocation bias depending on the RP in the case of two-arm parallel group trials with continuous multiple endpoints. We focus on two approaches to analyze multiple endpoints, either the Sidák procedure to show efficacy in at least one endpoint and the all-or-none procedure to show efficacy in all endpoints. RESULTS: To evaluate the impact of allocation bias on the test decision we propose a biasing policy for multiple endpoints. The impact of allocation on the test decision is measured by the family-wise error rate of the Sidák procedure and the type I error rate of the all-or-none procedure. Using the biasing policy we derive formulas to calculate these error rates. In simulations we show that, for the Sidák procedure as well as for the all-or-none procedure, allocation bias leads to inflation of the mean family-wise error and mean type I error, respectively. The strength of this inflation is affected by the choice of the RP. CONCLUSION: Allocation bias should be considered during the design phase of a trial to increase validity. The developed methodology is useful for selecting an appropriate RP for a clinical trial with multiple endpoints to minimize allocation bias effects.

Model-based hypothesis tests for the causal mediation of semi-competing risks.

Analyzing the causal mediation of semi-competing risks has become important in medical research. Semi-competing risks refers to a scenario wherein an intermediate event may be censored by a primary event but not vice versa. Causal mediation analyses decompose the effect of an exposure on the primary outcome into an indirect (mediation) effect: an effect mediated through a mediator, and a direct effect: an effect not through the mediator. Here we proposed a model-based testing procedure to examine the indirect effect of the exposure on the primary event through the intermediate event. Under the counterfactual outcome framework, we defined a causal mediation effect using counting process. To assess statistical evidence for the mediation effect, we proposed two tests: an intersection-union test (IUT) and a weighted log-rank test (WLR). The test statistic was developed from a semi-parametric estimator of the mediation effect using a Cox proportional hazards model for the primary event and a series of logistic regression models for the intermediate event. We built a connection between the IUT and WLR. Asymptotic properties of the two tests were derived, and the IUT was determined to be a size [Formula: see text] test and statistically more powerful than the WLR. In numerical simulations, both the model-based IUT and WLR can properly adjust for confounding covariates, and the Type I error rates of the proposed methods are well protected, with the IUT being more powerful than the WLR. Our methods demonstrate the strongly significant effects of hepatitis B or C on the risk of liver cancer mediated through liver cirrhosis incidence in a prospective cohort study. The proposed method is also applicable to surrogate endpoint analyses in clinical trials.

Sample Size Requirements to Test Subgroup-Specific Treatment Effects in Cluster-Randomized Trials.

Cluster-randomized trials (CRTs) often allocate intact clusters of participants to treatment or control conditions and are increasingly used to evaluate healthcare delivery interventions. While previous studies have developed sample size methods for testing confirmatory hypotheses of treatment effect heterogeneity in CRTs (i.e., targeting the difference between subgroup-specific treatment effects), sample size methods for testing the subgroup-specific treatment effects themselves have not received adequate attention-despite a rising interest in health equity considerations in CRTs. In this article, we develop formal methods for sample size and power analyses for testing subgroup-specific treatment effects in parallel-arm CRTs with a continuous outcome and a binary subgroup variable. We point out that the variances of the subgroup-specific treatment effect estimators and their covariance are given by weighted averages of the variance of the overall average treatment effect estimator and the variance of the heterogeneous treatment effect estimator. This analytical insight facilitates an explicit characterization of the requirements for both the omnibus test and the intersection-union test to achieve the desired level of power. Generalizations to allow for subgroup-specific variance structures are also discussed. We report on a simulation study to validate the proposed sample size methods and demonstrate that the empirical power corresponds well with the predicted power for both tests. The design and setting of the Umea Dementia and Exercise (UMDEX) CRT in older adults are used to illustrate our sample size methods.

Power analysis for cluster randomized trials with continuous coprimary endpoints.

Pragmatic trials evaluating health care interventions often adopt cluster randomization due to scientific or logistical considerations. Systematic reviews have shown that coprimary endpoints are not uncommon in pragmatic trials but are seldom recognized in sample size or power calculations. While methods for power analysis based on K ( K ≥ 2 $K\ge 2$ ) binary coprimary endpoints are available for cluster randomized trials (CRTs), to our knowledge, methods for continuous coprimary endpoints are not yet available. Assuming a multivariate linear mixed model (MLMM) that accounts for multiple types of intraclass correlation coefficients among the observations in each cluster, we derive the closed-form joint distribution of K treatment effect estimators to facilitate sample size and power determination with different types of null hypotheses under equal cluster sizes. We characterize the relationship between the power of each test and different types of correlation parameters. We further relax the equal cluster size assumption and approximate the joint distribution of the K treatment effect estimators through the mean and coefficient of variation of cluster sizes. Our simulation studies with a finite number of clusters indicate that the predicted power by our method agrees well with the empirical power, when the parameters in the MLMM are estimated via the expectation-maximization algorithm. An application to a real CRT is presented to illustrate the proposed method.

A multiple-testing procedure for high-dimensional mediation hypotheses.

Mediation analysis is of rising interest in epidemiology and clinical trials. Among existing methods, the joint significance (JS) test yields an overly conservative type I error rate and low power, particularly for high-dimensional mediation hypotheses. In this article we develop a multiple-testing procedure that accurately controls the family-wise error rate (FWER) and the false discovery rate (FDR) when testing high-dimensional mediation hypotheses. The core of our procedure is based on estimating the proportions of component null hypotheses and the underlying mixture null distribution of p-values. Theoretical developments and simulation experiments prove that the proposed procedure effectively controls FWER and FDR. Two mediation analyses on DNA methylation and cancer research are presented: assessing the mediation role of DNA methylation in genLetic regulation of gene expression in primary prostate cancer samples; exploring the possibility of DNA methylation mediating the effect of exercise on prostate cancer progression. Results of data examples include wellL-behaved quantile-quantile plots and improved power to detect novel mediation relationships. An R package HDMT implementing the proposed procedure is freely accessible in CRAN.

Hypothesis test for causal mediation of time-to-event mediator and outcome.

Hepatitis B has been a well-documented risk factor of liver cancer and mortality. To what extent hepatitis B affects mortality through increasing liver cancer incidence is of research interest and remains to be studied. We formulate the research question as a hypothesis testing problem of causal mediation where both the mediator and the outcome are time-to-event variables. The problem is closely related to semicompeting risks because time to the intermediate event may be censored by an occurrence of the outcome. We propose two hypothesis testing methods: a weighted log-rank test (WLR) and an intersection-union test (IUT). A test statistic of the WLR is constructed by adapting a nonparametric estimator of the mediation effect; however, the test may be conservative regarding its Type I Error rate. To address this, we further propose the IUT, the test statistic of which is constructed under the composite null hypothesis. Asymptotic properties of the two tests are studied, showing that the IUT is a size α test with better statistical power than the WLR. The theoretical properties are supported by extensive simulation studies under finite samples. Applying the proposed methods to the motivating hepatitis study, both WLR and IUT provided strong evidence that hepatitis B had a significant mediation effect on mortality via liver cancer incidence.

Generalized multi-SNP mediation intersection-union test.

To elucidate the molecular mechanisms underlying genetic variants identified from genome-wide association studies (GWAS) for a variety of phenotypic traits encompassing binary, continuous, count, and survival outcomes, we propose a novel and flexible method to test for mediation that can simultaneously accommodate multiple genetic variants and different types of outcome variables. Specifically, we employ the intersection-union test approach combined with the likelihood ratio test to detect mediation effect of multiple genetic variants via some mediator (e.g., the expression of a neighboring gene) on outcome. We fit high-dimensional generalized linear mixed models under the mediation framework, separately under the null and alternative hypothesis. We leverage Laplace approximation to compute the marginal likelihood of outcome and use coordinate descent algorithm to estimate corresponding parameters. Our extensive simulations demonstrate the validity of our proposed methods and substantial, up to 97%, power gains over alternative methods. Applications to real data for the study of Chlamydia trachomatis infection further showcase advantages of our methods. We believe our proposed methods will be of value and general interest in this post-GWAS era to disentangle the potential causal mechanism from DNA to phenotype for new drug discovery and personalized medicine.

Use of tolerance intervals for assessing biosimilarity.

A biosimilar is a biological product that is highly similar to an existing approved reference drug and has no clinically meaningful difference from it. Biosimilars are composed of or derived from living cells or organisms. Therefore, they are often sensitive to slight variations in the manufacturing process. Consequently, in demonstrating biosimilarity, it might be inappropriate to focus solely on the mean difference, or ratio of means, while ignoring the variabilities associated with the test and reference products. It is important to account for the entire population of clinical outcomes. Thus, we propose using the concept of tolerance intervals and related hypothesis testing for assessing biosimilarity. Our approach has the advantage of considering entire populations associated with both groups. A real example is used to illustrate our proposed method, and our approach is more stringent than those that employ confidence intervals. This is specifically the case when the mean difference of two drugs is not sufficiently large, but the biosimilar has a higher variability than that in the reference drug.

Permutation-based methods for mediation analysis in studies with small sample sizes.

BACKGROUND: Mediation analysis can be used to evaluate the effect of an exposure on an outcome acting through an intermediate variable or mediator. For studies with small sample sizes, permutation testing may be useful in evaluating the indirect effect (i.e., the effect of exposure on the outcome through the mediator) while maintaining the appropriate type I error rate. For mediation analysis in studies with small sample sizes, existing permutation testing methods permute the residuals under the full or alternative model, but have not been evaluated under situations where covariates are included. In this article, we consider and evaluate two additional permutation approaches for testing the indirect effect in mediation analysis based on permutating the residuals under the reduced or null model which allows for the inclusion of covariates. METHODS: Simulation studies were used to empirically evaluate the behavior of these two additional approaches: (1) the permutation test of the Indirect Effect under Reduced Models (IERM) and (2) the Permutation Supremum test under Reduced Models (PSRM). The performance of these methods was compared to the standard permutation approach for mediation analysis, the permutation test of the Indirect Effect under Full Models (IEFM). We evaluated the type 1 error rates and power of these methods in the presence of covariates since mediation analysis assumes no unmeasured confounders of the exposure-mediator-outcome relationships. RESULTS: The proposed PSRM approach maintained type I error rates below nominal levels under all conditions, while the proposed IERM approach exhibited grossly inflated type I rates in many conditions and the standard IEFM exhibited inflated type I error rates under a small number of conditions. Power did not differ substantially between the proposed PSRM approach and the standard IEFM approach. CONCLUSIONS: The proposed PSRM approach is recommended over the existing IEFM approach for mediation analysis in studies with small sample sizes.

Sequential parallel comparison design with two coprimary endpoints.

A placebo-controlled randomized clinical trial is required to demonstrate that an experimental treatment is superior to its corresponding placebo on multiple coprimary endpoints. This is particularly true in the field of neurology. In fact, clinical trials for neurological disorders need to show the superiority of an experimental treatment over a placebo in two coprimary endpoints. Unfortunately, these trials often fail to detect a true treatment effect for the experimental treatment versus the placebo owing to an unexpectedly high placebo response rate. Sequential parallel comparison design (SPCD) can be used to address this problem. However, the SPCD has not yet been discussed in relation to clinical trials with coprimary endpoints. In this article, our aim was to develop a hypothesis-testing method and a method for calculating the corresponding sample size for the SPCD with two coprimary endpoints. In a simulation, we show that the proposed hypothesis-testing method achieves the nominal type I error rate and power and that the proposed sample size calculation method has adequate power accuracy. In addition, the usefulness of our methods is confirmed by returning to an SPCD trial with a single primary endpoint of Alzheimer disease-related agitation.

Variance component tests of multivariate mediation effects under composite null hypotheses.

Mediation effects of multiple mediators are determined by two associations: one between an exposure and mediators ( S - M ) and the other between the mediators and an outcome conditional on the exposure ( M - Y ). The test for mediation effects is conducted under a composite null hypothesis, that is, either one of the S - M and M - Y associations is zero or both are zeros. Without accounting for the composite null, the type 1 error rate within a study containing a large number of multimediator tests may be much less than the expected. We propose a novel test to address the issue. For each mediation test j , j=1,…,J , we examine the S - M and M - Y associations using two separate variance component tests. Assuming a zero-mean working distribution with a common variance for the element-wise S - M (and M - Y ) associations, score tests for the variance components are constructed. We transform the test statistics into two normally distributed statistics under the null. Using a recently developed result, we conduct J hypothesis tests accounting for the composite null hypothesis by adjusting for the variances of the normally distributed statistics for the S - M and M - Y associations. Advantages of the proposed test over other methods are illustrated in simulation studies and a data application where we analyze lung cancer data from The Cancer Genome Atlas to investigate the smoking effect on gene expression through DNA methylation in 15 114 genes.

Risk-modeling of dog osteosarcoma genome scans shows individuals with Mendelian-level polygenic risk are common.

BACKGROUND: Despite the tremendous therapeutic advances that have stemmed from somatic oncogenetics, survival of some cancers has not improved in 50 years. Osteosarcoma still has a 5-year survival rate of 66%. We propose the natural canine osteosarcoma model can change that: it is extremely similar to the human condition, except for being highly heritable and having a dramatically higher incidence. Here we reanalyze published genome scans of osteosarcoma in three frequently-affected dog breeds and report entirely new understandings with immediate translational indications. RESULTS: First, meta-analysis revealed association near FGF9, which has strong biological and therapeutic relevance. Secondly, risk-modeling by multiple logistic regression shows 22 of the 34 associated loci contribute to risk and eight have large effect sizes. We validated the Greyhound stepwise model in our own, independent, case-control cohort. Lastly, we updated the gene annotation from approximately 50 genes to 175, and prioritized those using cross-species genomics data. Mostly positional evidence suggests 13 genes are likely to be associated with mapped risk (including MTMR9, EWSR1 retrogene, TANGO2 and FGF9). Previous annotation included seven of those 13 and prioritized four by pathway enrichment. Ten of our 13 priority genes are in loci that contribute to risk modeling and thus can be studied epidemiologically and translationally in pet dogs. Other new candidates include MYCN, SVIL and MIR100HG. CONCLUSIONS: Polygenic osteosarcoma-risk commonly rises to Mendelian-levels in some dog breeds. This justifies caninized animal models and targeted clinical trials in pet dogs (e.g., using CDK4/6 and FGFR1/2 inhibitors).

Significance Testing for Allelic Heterogeneity.

It is useful to detect allelic heterogeneity (AH), i.e., the presence of multiple causal SNPs in a locus, which, for example, may guide the development of new methods for fine mapping and determine how to interpret an appearing epistasis. In contrast to Mendelian traits, the existence and extent of AH for complex traits had been largely unknown until Hormozdiari et al. proposed a Bayesian method, called causal variants identification in associated regions (CAVIAR), and uncovered widespread AH in complex traits. However, there are several limitations with CAVIAR. First, it assumes a maximum number of causal SNPs in a locus, typically up to six, to save computing time; this assumption, as will be shown, may influence the outcome. Second, its computational time can be too demanding to be feasible since it examines all possible combinations of causal SNPs (under the assumed upper bound). Finally, it outputs a posterior probability of AH, which may be difficult to calibrate with a commonly used nominal significance level. Here, we introduce an intersection-union test (IUT) based on a joint/conditional regression model with all the SNPs in a locus to infer AH. We also propose two sequential IUT-based testing procedures to estimate the number of causal SNPs. Our proposed methods are applicable to not only individual-level genotypic and phenotypic data, but also genome-wide association study (GWAS) summary statistics. We provide numerical examples based on both simulated and real data, including large-scale schizophrenia (SCZ) and high-density lipoprotein (HDL) GWAS summary data sets, to demonstrate the effectiveness of the new methods. In particular, for both the SCZ and HDL data, our proposed IUT not only was faster, but also detected more AH loci than CAVIAR. Our proposed methods are expected to be useful in further uncovering the extent of AH in complex traits.

Evaluating cardiac risk: exposure response analysis in early clinical drug development.

The assessment of a drug's cardiac liability has undergone considerable metamorphosis by regulators since International Council for Harmonization of Technical Requirement for Pharmaceuticals for Human Use E14 guideline was introduced in 2005. Drug developers now have a choice in how proarrhythmia risk can be evaluated; the options include a dedicated thorough QT (TQT) study or exposure response (ER) modeling of intensive electrocardiogram (ECG) captured in early clinical development. The alternative approach of ER modeling was incorporated into a guidance document in 2015 as a primary analysis tool which could be utilized in early phase dose escalation studies as an option to perform a dedicated TQT trial. This review will describe the current state of ER modeling of intensive ECG data collected during early clinical drug development; the requirements with regard to the use of a positive control; and address the challenges and opportunities of this alternative approach to assessing QT liability.

Design, data monitoring, and analysis of clinical trials with co-primary endpoints: A review.

We review the design, data monitoring, and analyses of clinical trials with co-primary endpoints. Recently developed methods for fixed-sample and group-sequential settings are described. Practical considerations are discussed, and guidance for the application of these methods is provided.

Choice of futility boundaries for group sequential designs with two endpoints.

BACKGROUND: In clinical trials, the opportunity for an early stop during an interim analysis (either for efficacy or for futility) may relevantly save time and financial resources. This is especially important, if the planning assumptions required for power calculation are based on a low level of evidence. For example, when including two primary endpoints in the confirmatory analysis, the power of the trial depends on the effects of both endpoints and on their correlation. Assessing the feasibility of such a trial is therefore difficult, as the number of parameter assumptions to be correctly specified is large. For this reason, so-called 'group sequential designs' are of particular importance in this setting. Whereas the choice of adequate boundaries to stop a trial early for efficacy has been broadly discussed in the literature, the choice of optimal futility boundaries has not been investigated so far, although this may have serious consequences with respect to performance characteristics. METHODS: In this work, we propose a general method to construct 'optimal' futility boundaries according to predefined criteria. Further, we present three different group sequential designs for two endpoints applying these futility boundaries. Our methods are illustrated by a real clinical trial example and by Monte-Carlo simulations. RESULTS: By construction, the provided method of choosing futility boundaries maximizes the probability to correctly stop in case of small or opposite effects while limiting the power loss and the probability of stopping the study 'wrongly'. Our results clearly demonstrate the benefit of using such 'optimal' futility boundaries, especially compared to futility boundaries commonly applied in practice. CONCLUSIONS: As the properties of futility boundaries are often not considered in practice and unfavorably chosen futility boundaries may imply bad properties of the study design, we recommend assessing the performance of these boundaries according to the criteria proposed in here.

Can an early phase clinical pharmacology study replace a thorough QT study? Experience with a novel H3-receptor antagonist/inverse agonist.

OBJECTIVE: The objective of the present study was to compare the effects of pitolisant on QTcF interval in a single ascending dose (SAD) study and a thorough QT (TQT) study. METHODS: The SAD study at three dose levels of pitolisant enrolled 24 males and the TQT study at two dose levels 25 males. Both studies intensively monitored ECGs and pitolisant exposure. Effect on QTcF interval was analysed by Intersection Union Test (IUT) and by exposure-response (ER) analysis. Results from the two studies were compared. RESULTS: In both studies, moxifloxacin effect established assay sensitivity. IUT analysis revealed comparable pitolisant-induced maximum mean (90 % confidence interval (CI)) placebo-corrected increase from baseline (ΔΔQTcF) in both the studies, being 13.3 (8.1; 18.5) ms at 200-mg and 9.9 (4.7; 15.1) ms at 240-mg doses in SAD study and 5.27 (2.35; 8.20) ms at 120-mg dose in TQT study. ER analysis revealed that ER slopes in SAD and TQT studies were comparable and significantly positive (0.031 vs 0.027 ms/ng/mL, respectively). At geometric mean concentrations, bootstrap predicted ΔΔQTcF (90 % CI) were 9.23 (4.68; 14.4) ms at 279 ng/mL (240-mg dose) in the SAD study and 4.97 (3.42; 8.19) ms at 156 ng/mL (120-mg dose) in the TQT study. CONCLUSION: Pitolisant lacked an effect of regulatory concern on QTc interval in both the studies, however analysed, suggesting that the results from the SAD study could have mitigated the need for a TQT study. Our findings add to the growing evidence that intensive ECG monitoring in early phase clinical studies can replace a TQT study.

Testing for parallelism in the heteroscedastic four-parameter logistic model.

For bioassay data in drug discovery and development, it is often important to test for parallelism of the mean response curves for two preparations, such as a test sample and a reference sample in determining the potency of the test preparation relative to the reference standard. For assessing parallelism under a four-parameter logistic model, tests of the parallelism hypothesis may be conducted based on the equivalence t-test or the traditional F-test. However, bioassay data often have heterogeneous variance across dose levels. Specifically, the variance of the response may be a function of the mean, frequently modeled as a power of the mean. Therefore, in this article we discuss estimation and tests for parallelism under the power variance function. Two examples are considered to illustrate the estimation and testing approaches described. A simulation study is also presented to compare the empirical properties of the tests under the power variance function in comparison to the results from ordinary least squares fits, which ignore the non-constant variance pattern.

Establishing assay sensitivity in QT studies: experience with the use of moxifloxacin in an early phase clinical pharmacology study and comparison with its effect in a thorough QT study.

OBJECTIVE: To compare the effect of moxifloxacin as a positive control in a single ascending dose (SAD) study with that in a thorough QT (TQT) study. METHODS: Moxifloxacin was used as a positive control in a SAD study and a TQT study during the evaluation of the QT liability of a new drug. The SAD study had enrolled 24 males and the TQT study 25 males. Both studies intensively monitored electrocardiograms (ECGs) and pharmacokinetic sampling. Effect of moxifloxacin on QTc interval was analysed in each study by intersection union test (IUT) and by exposure-response (ER) analysis and the results compared. Cost-effectiveness of this approach was computed. RESULTS: Analysis by IUT revealed that the maximum mean (90 % confidence interval (CI)) placebo-corrected change from baseline (ΔΔQTcF) in the SAD study and the TQT study were remarkably similar (10.7 (6.5; 14.9) ms vs. 9.09 (6.20; 11.98) ms, respectively). In both studies, assay sensitivity was established by the 90 % lower bound exceeding 5 ms. ER analysis revealed the slopes in both studies to be significantly different from zero and comparable. Bootstrap-predicted effects of moxifloxacin at geometric mean concentrations of ~3000 ng/mL were 8.19 (90 % CI 5.86; 10.7) ms in the SAD study and 7.33 (90 % CI 5.69; 9.70) ms in the TQT study. CONCLUSION: Moxifloxacin can be integrated effectively in a SAD study to establish assay sensitivity, and a TQT study may be replaced by a SAD study which has the required assay sensitivity. Further experience is warranted to verify this conclusion.

Comment and Completion: Implementation of Parallelism Testing for Four-Parameter Logistic Model in Bioassays.

Parallelism testing between two four-parameter logistic curves has been widely discussed over the last decade. Current tests available in common statistical software used in laboratories have been shown to be highly flawed. In 2012, Yang et al. showed an easy way to implement an intersection union test based on confidence intervals on ratios of parameters of both curves. The method was automated using a fully good manufacturing practice-compliant software package. Although the rationale is correct and efficient, a small mistake appears in the computation of the confidence intervals in the paper and may lead to error when implementing the intersection union test in a software package. Because parallelism testing is both a prerequisite for the determination of relative potency of bioassays and a regulatory requirement, it is important to rectify this mistake. In this paper, we show the actual formulas to be used to compute confidence interval on ratios of parameters.