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This paper studies the optimality of matched-pair designs in randomized controlled trials (RCTs). Matched-pair designs are examples of stratified randomization, in which the researcher partitions a set of units into strata based on their observed covariates and assign a fraction of units in each stratum to treatment. A matched-pair design is such a procedure with two units per stratum. Despite the prevalence of stratified randomization in RCTs, implementations differ vastly. We provide an econometric framework in which, among all stratified randomization procedures, the optimal one in terms of the mean-squared error of the difference-in-means estimator is a matched-pair design that orders units according to a scalar function of their covariates and matches adjacent units. Our framework captures a leading motivation for stratifying in the sense that it shows that the proposed matched-pair design additionally minimizes the magnitude of the ex-post bias, i.e., the bias of the estimator conditional on realized treatment status. We then consider empirical counterparts to the optimal stratification using data from pilot experiments and provide two different procedures depending on whether the sample size of the pilot is large or small. For each procedure, we develop methods for testing the null hypothesis that the average treatment effect equals a prespecified value. Each test we provide is asymptotically exact in the sense that the limiting rejection probability under the null equals the nominal level. We run an experiment on the Amazon Mechanical Turk using one of the proposed procedures, replicating one of the treatment arms in Dellavigna and Pope (2018), and find the standard error decreases by 29%, so that only half of the sample size is required to attain the same standard error.

Summary An empirical likelihood test is proposed for parameters of models defined by conditional moment restrictions, such as models with nonlinear endogenous covariates, with and without heteroscedastic errors and non-separable transformation models. The number of empirical likelihood constraints is given by the size of the parameter, unlike alternative semi-parametric approaches. We show that the empirical likelihood ratio test is asymptotically pivotal, without explicit studentization. A simulation study shows that the observed size is close to the nominal level, unlike alternative empirical likelihood approaches. It also offers a major advantage over two-stage least-squares, because the relationship between endogenous and instrumental variables does not need to be known. An empirical likelihood model specification test is also proposed.

A generalization of the normal scores two-sample test is proposed. The empirical significance level of this test closely approximates the nominal level of significance and it is often more powerful...

A significant body of research has demonstrated that IQs obtained from different intelligence tests substantially correlate at the group level. Yet, there is minimal research investigating whether different intelligence tests yield comparable results for individuals. Examining this issue is paramount given that high-stakes decisions are based on individual test results. Consequently, we investigated whether seven current and widely used intelligence tests yielded comparable results for individuals between the ages of 4–20 years. Results mostly indicated substantial correlations between tests, although several significant mean differences at the group level were identified. Results associated with individual-level comparability indicated that the interpretation of exact IQ scores cannot be empirically supported, as the 95% confidence intervals could not be reliably replicated with different intelligence tests. Similar patterns also appeared for the individual-level comparability of nonverbal and verbal intelligence factor scores. Furthermore, the nominal level of intelligence systematically predicted IQ differences between tests, with above- and below-average IQ scores associated with larger differences as compared to average IQ scores. Analyses based on continuous data confirmed that differences appeared to increase toward the above-average IQ score range. These findings are critical as these are the ranges in which diagnostic questions most often arise in practice. Implications for test interpretation and test construction are discussed.

In survival analysis, data may be correlated or clustered, because of some features such as shared genes and environmental background. A common approach to accommodate clustered data is the Cox frailty model that has proportional hazard assumption and complexity of interpreting hazard ratio lead to the misinterpretation of a direct effect on the time of event. In this paper, we considered Laplace quantile regression model for clustered survival data that interpret the effect of covariates on the time to event. A Bayesian approach with Markov Chain Monte Carlo method was used to fit the model. The results from a simulation study to evaluate the performance of proposed model showed that the Laplace regression model with frailty term performed well for different scenarios and the coverage rates of the pointwise 95% CIs were close to the nominal level (0.95). An application to data from breast cancer was presented to illustrate the theory and method developed in this paper.

In the present paper, we are concerned with introducing a simple method for signal detection problem in one realization of a two-dimensional random field based on the one-dimensional random projection technique. Formally, we provide a Bayesian projection-based approach for signal detection in the two-dimensional Gaussian scale space random field, though it is applicable for higher dimensions. It will be shown by a series of simulation studies that our purposed method, controls the error rate in nominal level and has the high performance for signal detection, and this procedure completely distinguishes between the two hypotheses of “no signal” and the alternative. Also, we provide two applications of the proposed procedure, one from a real dataset of a two-dimensional random field of R-fMRI data of an autistic individual and the other with a two-dimensional random field of fMRI data.

Conventional methods for testing independence between two Gaussian vectors require sample sizes greater than the number of variables in each vector. Therefore, adjustments are needed for the high-dimensional situation, where the sample size is smaller than the number of variables in at least one of the compared vectors. It is critical to emphasize that the methods available in the literature are unable to control the Type I error probability under the nominal level. This fact is evidenced through an intensive simulation study presented in this paper. To cover this lack, we introduce a valid randomized test based on the Kronecker delta covariance matrices estimator. As an empirical application, based on a sample of companies listed on the stock exchange of Brazil, we test the independence between returns of stocks of different sectors in the COVID-19 pandemic context.

Objectives: In clinical practice, many prediction models cannot be used when predictor values are missing. We, therefore, propose and evaluate methods for real-time imputation. Study Design and Setting: We describe (i) mean imputation (where missing values are replaced by the sample mean), (ii) joint modeling imputation (JMI, where we use a multivariate normal approximation to generate patient-specific imputations), and (iii) conditional modeling imputation (CMI, where a multivariable imputation model is derived for each predictor from a population). We compared these methods in a case study evaluating the root mean squared error (RMSE) and coverage of the 95i.e., the proportion of confidence intervals that contain the true predictor value) of imputed predictor values. Results: eRMSE was lowest when adopting JMI or CMI, although imputation of individual predictors did not always lead to substantial improvements as compared to mean imputation. JMI and CMI appeared particularly useful when the values of multiple predictors of the model were missing. Coverage reached the nominal level (i.e., 95 for both CMI and JMI. Conclusion: Multiple imputations using either CMI or JMI is recommended when dealing with missing predictor values in real-time settings. Ó 2021 The Authors. Published by Elsevier Inc. This is an open access article under the CC BY license (http://creativecommons. org/licenses/by/4.0/).

In this paper, the problem of simultaneously testing mean vector and covariance matrix of one-sample population is investigated in high-dimensional settings. We propose a new test statistic and obtain its asymptotic distributions under null and local alternative hypotheses, respectively. Our asymptotic result for proposed test does not need some conditions such as linearity between the sample size and dimension used in existing studies. Simulation results also demonstrate our new test not only can control reasonably the nominal level but also has greater empirical powers than competing tests.

This paper studies the properties of the wild bootstrap-based test proposed in Cameron et al. (2008) for testing hypotheses about the coefficients in a linear regression model with clustered data. Cameron et al. (2008) provide simulations that suggest this test works well even in settings with as few as five clusters, but existing theoretical analyses of its properties all rely on an asymptotic framework in which the number of clusters is “large." In contrast to these analyses, we employ an asymptotic framework in which the number of clusters is “small," but the number of observations per cluster is “large." In this framework, we provide conditions under which an unstudentized version of the test is valid in the sense that it has limiting rejection probability under the null hypothesis that does not exceed the nominal level. Importantly, these conditions require, among other things, certain homogeneity restrictions on the distribution of covariates. In contrast, we establish that a studentized version of the test may only over-reject the null hypothesis by a “small" amount in the sense that it has limiting rejection probability under the null hypothesis that does not exceed the nominal level by more than an amount that decreases exponentially with the number of clusters. We obtain results qualitatively similar to those for the studentized version of the test for closely related \score" bootstrap-based tests, which permit testing hypotheses about parameters in nonlinear models. We illustrate the relevance of our theoretical results for applied work via a simulation study and empirical application.

In this paper, we investigate confidence intervals for the ratio of means of two independent lognormal distributions. The normal approximation (NA) approach was proposed. We compared the proposed with another approaches, the ML, GCI, and MOVER. The performance of these approaches were evaluated in terms of coverage probabilities and interval widths. The Simulation studies and results showed that the GCI and MOVER approaches performed similar in terms of the coverage probability and interval width for all sample sizes. The ML and NA approaches provided the coverage probability close to nominal level for large sample sizes. However, our proposed method provided the interval width shorter than other methods. Overall, our proposed is conceptually simple method. We recommend that our proposed approach is appropriate for large sample sizes because it is consistently performs well in terms of the coverage probability and the interval width is typically shorter than the other approaches. Finally, the proposed approaches are illustrated using a real-life example.

It is more and more important to consider the dependence structure among multiple testings, especially for the genome-wide association studies (GWAS). The existing procedures, such as local index of significance (LIS) and pooled local index of significance (PLIS), were proposed to test hidden Markov model (HMM)-dependent hypotheses under the framework of compound decision theory, which was successfully applied to GWAS. However, the etiology of complex diseases is not only with respect to the genetic effects, but also the environmental factors. Failure to account for the covariates in multiple testing can produce misleading bias of the association of interest, or suffer from loss of testing efficiency. In this paper, we develop a covariate-adjusted multiple testing procedure, called covariate-adjusted local index of significance (CALIS), to account for the effects of environmental factors via a factorial hidden Markov model. The theoretical results show that our procedure can control the false discovery rate (FDR) at the nominal level and has the smallest false non-discovery rate (FNR) among all valid FDR procedures. We further demonstrate the advantage of our novel procedure over the existing procedures by simulation studies and a real data analysis.

To detect a change in the probability of a sequence of independent binomial random variables, a variety of asymptotic and exact testing procedures have been proposed. Whenever the sample size or the event rate is small, asymptotic approximations of maximally selected test statistics have been shown to be inaccurate. Although exact methods control the type I error rate, they can be overly conservative due to the discreteness of the test statistics in these situations. We extend approaches by Worsley and Halpern to develop a test that is less discrete to increase the power. Building on ideas from binary segmentation, the proposed test utilizes unused information in the binomial sequences to add a new ordering to test statistics that are of equal value. The exact distributions are derived under side conditions that arise in hypothetical segmentation steps and do not depend on the type of test statistic used (e.g., log likelihood ratio, cumulative sum, or Fisher's exact test). Using the proposed exact segmentation procedure, we construct a change point test and prove that it controls the type-I-error rate at any given nominal level. Furthermore, we prove that the new test is uniformly at least as powerful as Worsley's exact test. In a Monte Carlo simulation study, the gain in power can be remarkable, especially in scenarios with small sample size. Giving a clinical database example about pin site infections and an example assessing publication bias in neuropsychiatric drug research, we demonstrate the wide-ranging applicability of the test.

Introduction In a five-arm randomized clinical trial (RCT) with stratified randomization across 54 sites, we encountered low primary outcome event proportions, resulting in multiple sites with zero events either overall or in one or more study arms. In this paper, we systematically evaluated different statistical methods of accounting for center in settings with low outcome event proportions. Methods We conducted a simulation study and a reanalysis of a completed RCT to compare five popular methods of estimating an odds ratio for multicenter trials with stratified randomization by center: (i) no center adjustment, (ii) random intercept model, (iii) Mantel–Haenszel model, (iv) generalized estimating equation (GEE) with an exchangeable correlation structure, and (v) GEE with small sample correction (GEE-small sample correction). We varied the number of total participants (200, 500, 1000, 5000), number of centers (5, 50, 100), control group outcome percentage (2%, 5%, 10%), true odds ratio (1, > 1), intra-class correlation coefficient (ICC) (0.025, 0.075), and distribution of participants across the centers (balanced, skewed). Results Mantel–Haenszel methods generally performed poorly in terms of power and bias and led to the exclusion of participants from the analysis because some centers had no events. Failure to account for center in the analysis generally led to lower power and type I error rates than other methods, particularly with ICC = 0.075. GEE had an inflated type I error rate except in some settings with a large number of centers. GEE-small sample correction maintained the type I error rate at the nominal level but suffered from reduced power and convergence issues in some settings when the number of centers was small. Random intercept models generally performed well in most scenarios, except with a low event rate (i.e., 2% scenario) and small total sample size (n ≤ 500), when all methods had issues. Discussion Random intercept models generally performed best across most scenarios. GEE-small sample correction performed well when the number of centers was large. We do not recommend the use of Mantel–Haenszel, GEE, or models that do not account for center. When the expected event rate is low, we suggest that the statistical analysis plan specify an alternative method in the case of non-convergence of the primary method.

Meta-studies are often conducted on empirical findings obtained from overlapping samples. Sample overlap is common in research fields that strongly rely on aggregated observational data (eg, economics and finance), where the same set of data may be used in several studies. More generally, sample overlap tends to occur whenever multiple estimates are sampled from the same study. We show analytically how failing to account for sample overlap causes high rates of false positives, especially for large meta-sample sizes. We propose a generalized-weights (GW) meta-estimator, which solves the sample overlap problem by explicitly modeling the variance-covariance matrix that describes the structure of dependence among estimates. We show how this matrix can be constructed from information that is usually available from basic sample descriptions in the primary studies (ie, sample sizes and number of overlapping observations). The GW meta-estimator amounts to weighting each empirical outcome according to its share of independent sampling information. We use Monte Carlo simulations to (a) demonstrate how the GW meta-estimator brings the rate of false positives to its nominal level, and (b) quantify the efficiency gains of the GW meta-estimator relative to standard meta-estimators. The GW meta-estimator is fairly straightforward to implement and can solve any case of sample overlap, within or between studies. HIGHLIGHTS: Meta-analyses are often conducted on empirical outcomes based on samples containing common observations. Sample overlap induces a correlation structure among empirical outcomes that harms the statistical properties of meta-analysis methods. We derive the analytic conditions under which sample overlap causes conventional meta-estimators to exhibit high rates of false positives. We propose a generalized-weights (GW) solution to sample overlap, which involves approximating the variance-covariance matrix that describes the correlation structure between outcomes; we show how to construct this matrix from information typically reported in the primary studies. We conduct Monte Carlo simulations to quantify the efficiency gains of the proposed GW estimator and show how it brings the rate of false positives near its nominal level. Although we focus on meta-analyses of regression coefficients, our approach can, in principle, be modified and extended to effect sizes more commonly used in other research fields, such as Cohen's d or odds ratios.

Universal and individual two‐sided tolerance intervals that take the inherent structure of normal mixture distributions into account are introduced in this paper for the purpose of monitoring the overall population and specific subpopulations. On the basis of generalised fiducial inference, a Markov chain Monte Carlo sampler is proposed to generate realisations from the generalised fiducial distributions of unknown parameters for obtaining the required tolerance intervals. Based on the simulation results, it is shown that the proposed method can maintain the empirical coverage rates sufficiently close to the nominal level. In addition, a lake acidity monitoring study is used to illustrate the proposed method.

Summary Paradata refers to survey variables which are not of direct interest themselves, but are related to the quality of data on survey variables which are of interest. We focus on a categorical paradata variable, which reflects the presence of measurement error in a variable of interest. We propose a quasi-score test of the hypothesis of no measurement error bias in the estimation of regression coefficients under models for paradata. We also propose a regression-based test, analogous to a simple test proposed by Fuller for instrumental variables. The methods developed can take account of a complex sampling design. In an application with data from the British Household Panel Survey, all tests provide clear evidence of measurement bias in the estimated coefficient of gross pay. In a simulation study, all tests have rejection rates close to the nominal level under the null hypothesis; the quasi-score tests display more power than the regression-based test. The size of the quasi-score test is shown to be robust to some forms of misspecification of the paradata model, both by a theoretical argument and in findings of the simulation study.

This article investigates the homogeneity testing problem of binomial proportions for stratified partially validated data obtained by double-sampling method with two fallible classifiers. Several test procedures, including the weighted-least-squares test with/without log-transformation, logit-transformation and double log-transformation, and likelihood ratio test and score test, are developed to test the homogeneity under two models, distinguished by conditional independence assumption of two classifiers. Simulation results show that score test performs better than other tests in the sense that the empirical size is generally controlled around the nominal level, and hence be recommended to practical applications. Other tests also perform well when both binomial proportions and sample sizes are not small. Approximate sample sizes based on score test, likelihood ratio test and the weighted-least-squares test with double log-transformation are generally accurate in terms of the empirical power and type I error rate with the estimated sample sizes, and hence be recommended. An example from the malaria study is illustrated by the proposed methodologies.

Summary Hypothesis testing in the linear regression model is a fundamental statistical problem. We consider linear regression in the high dimensional regime where the number of parameters exceeds the number of samples (p > n). To make informative inference, we assume that the model is approximately sparse, i.e. the effect of covariates on the response can be well approximated by conditioning on a relatively small number of covariates whose identities are unknown. We develop a framework for testing very general hypotheses regarding the model parameters. Our framework encompasses testing whether the parameter lies in a convex cone, testing the signal strength, and testing arbitrary functionals of the parameter. We show that the procedure proposed controls the type I error, and we also analyse the power of the procedure. Our numerical experiments confirm our theoretical findings and demonstrate that we control the false positive rate (type I error) near the nominal level and have high power. By duality between hypotheses testing and confidence intervals, the framework proposed can be used to obtain valid confidence intervals for various functionals of the model parameters. For linear functionals, the length of confidence intervals is shown to be minimax rate optimal.

Data containing many zeroes is popular in statistical applications, such as survey data. A confidence interval based on the traditional normal approximation may lead to poor coverage probabilities, especially when the nonzero values are highly skewed and the sample size is small or moderately large. The empirical likelihood (EL), a powerful nonparametric method, was proposed to construct confidence intervals under such a scenario. However, the traditional empirical likelihood experiences the issue of under-coverage problem which causes the coverage probability of the EL-based confidence intervals to be lower than the nominal level, especially in small sample sizes. In this paper, we investigate the numerical performance of three modified versions of the EL: the adjusted empirical likelihood, the transformed empirical likelihood, and the transformed adjusted empirical likelihood for data with various sample sizes and various proportions of zero values. Asymptotic distributions of the likelihood-type statistics have been established as the standard chi-square distribution. Simulations are conducted to compare coverage probabilities with other existing methods under different distributions. Real data has been given to illustrate the procedure of constructing confidence intervals.

Ridge regression is a popular method to solve the multicollinearity problem for both linear and non-linear regression models. This paper studied forty different ridge regression t-type tests of the individual coefficients of a linear regression model. A simulation study was conducted to evaluate the performance of the proposed tests with respect to their empirical sizes and powers under different settings. Our simulation results demonstrated that many of the proposed tests have type I error rates close to the 5% nominal level and, among those, all tests except one have considerable gain in powers over the standard ordinary least squares (OLS) t-type test. It was observed from our simulation results that seven tests based on some ridge estimators performed better than the rest in terms of achieving higher power gains while maintaining a 5% nominal size.

Meta-analysis of 2 × 2 tables is common and useful in research topics including analysis of adverse events and survey research data. Fixed-effects inference typically centers on measures of association such as the Cochran-Mantel-Haenszel statistic or Woolf's estimator, but relies on assuming exact homogeneity across studies, which is often unrealistic. By showing that estimators of several widely-used methods have meaningful estimands even in the presence of heterogeneity, we derive improved confidence intervals for them under heterogeneity. These improvements over current methods are illustrated by simulation, and we also study which factors affect the coverage levels. We find that our confidence intervals provide coverage closer to the nominal level when heterogeneity is present, in both small and large-sample settings. The conventional confidence intervals derived under homogeneity are often conservative, though anti-conservative inferences occur in some scenarios. We also apply the proposed methods to a meta-analysis of 19 randomized clinical trials on the effect of sclerotherapy in preventing first bleeding for patients with cirrhosis and esophagogastric varices. Our methods provide a more interpretable approach to meta-analyzing binary data and more accuracy in characterizing the uncertainty of the estimators.

Sample size calculation based on normal approximations is often associated with the loss of statistical power for a single-arm trial with a time-to-event endpoint. Recently, Wu (2015) derived the exact variance for the one-sample log-rank test under the alternative and showed that a single-arm one-stage study based on exact variance often has power above the nominal level while the type I error rate is controlled. We extend this approach to a single-arm two-stage design by using exact variances of the one-sample log-rank test for the first stage and the two stages combined. The empirical power of the proposed two-stage optimal designs is often not guaranteed under a two-stage design setting, which could be due to the asymptotic bi-variate normal distribution used to estimate the joint distribution of the test statistics. We adjust the nominal power level in the design search to guarantee the simulated power of the identified optimal design being above the nominal level. The sample size and the study time savings of the proposed two-stage designs are substantial as compared to the one-stage design.

Testing for equality of two high-dimensional distributions is a challenging problem, and this becomes even more challenging when the sample size is small. Over the last few decades, several graph-based two-sample tests have been proposed in the literature, which can be used for data of arbitrary dimensions. Most of these test statistics are computed using pairwise Euclidean distances among the observations. But, due to concentration of pairwise Euclidean distances, these tests have poor performance in many high-dimensional problems. Some of them can have powers even below the nominal level when the scale-difference between two distributions dominates the location-difference. To overcome these limitations, we introduce some new dissimilarity indices and use them to modify some popular graph-based tests. These modified tests use the distance concentration phenomenon to their advantage, and as a result, they outperform the corresponding tests based on the Euclidean distance in a wide variety of examples. We establish the high-dimensional consistency of these modified tests under fairly general conditions. Analyzing several simulated as well as real data sets, we demonstrate their usefulness in high dimension, low sample size situations.

Though black-box predictors are state-of-the-art for many complex tasks, they often fail to properly quantify predictive uncertainty and may provide inappropriate predictions for unfamiliar data. Instead, we can learn more reliable models by letting them either output a prediction set or abstain when the uncertainty is high. We propose training these selective prediction-set models using an uncertainty-aware loss minimization framework, which unifies ideas from decision theory and robust maximum likelihood. Moreover, since black-box methods are not guaranteed to output well-calibrated prediction sets, we show how to calculate point estimates and confidence intervals for the true coverage of any selective prediction-set model, as well as a uniform mixture of K set models obtained from K-fold sample-splitting. When applied to predicting in-hospital mortality and length-of-stay for ICU patients, our model outperforms existing approaches on both in-sample and out-of-sample age groups, and our recalibration method provides accurate inference for prediction set coverage., Published at Biometrics

It is common practice for auditors to verify only a sample of recorded values to estimate the total error amount. Monetary-unit sampling is often used to over-sample large valued items which may be overstated. The aim is to compute an upper confidence bound for the total errors amount. Naïve bounds based on the central limit theorem are not suitable, because the distribution of errors are often very skewed. Auditors frequently use the Stringer bound which known to be too conservative. We propose to use weighted empirical likelihood bounds for Monetary-unit sampling. The approach proposed is different from mainstream empirical likelihood. A Monte–Carlo simulation study highlights the advantage of the proposed approach over the Stringer bound.

We consider five asymptotically unbiased estimators of intervention effects on event rates in non-matched and matched-pair cluster randomized trials, including ratio of mean counts (Formula presented.), ratio of mean cluster-level event rates (Formula presented.), ratio of event rates (Formula presented.), double ratio of counts (Formula presented.), and double ratio of event rates (Formula presented.). In the absence of an indirect effect, they all estimate the direct effect of the intervention. Otherwise, (Formula presented.), (Formula presented.) and (Formula presented.) estimate the total effect, which comprises the direct and indirect effects, whereas (Formula presented.) and (Formula presented.) estimate the direct effect only. We derive the conditions under which each estimator is more precise or powerful than its alternatives. To control bias in studies with a small number of clusters, we propose a set of approximately unbiased estimators. We evaluate their properties by simulation and apply the methods to a trial of seasonal malaria chemoprevention. The approximately unbiased estimators are practically unbiased and their confidence intervals usually have coverage probability close to the nominal level; the asymptotically unbiased estimators perform well when the number of clusters is approximately 32 or more per trial arm. Despite its simplicity, (Formula presented.) performs comparably with (Formula presented.) and (Formula presented.) in trials with a large but realistic number of clusters. When the variability of baseline event rate is large and there is no indirect effect, (Formula presented.) and (Formula presented.) tend to offer higher power than (Formula presented.), (Formula presented.) and (Formula presented.). We discuss the implications of these findings to the planning and analysis of cluster randomized trials. publishedVersion

Background For differential abundance analysis, zero-inflated generalized linear models, typically zero-inflated NB models, have been increasingly used to model microbiome and other sequencing count data. A common assumption in estimating the false discovery rate is that the p values are uniformly distributed under the null hypothesis, which demands that the postulated model fit the count data adequately. Mis-specification of the distribution of the count data may lead to excess false discoveries. Therefore, model checking is critical to control the FDR at a nominal level in differential abundance analysis. Increasing studies show that the method of randomized quantile residual (RQR) performs well in diagnosing count regression models. However, the performance of RQR in diagnosing zero-inflated GLMMs for sequencing count data has not been extensively investigated in the literature. Results We conduct large-scale simulation studies to investigate the performance of the RQRs for zero-inflated GLMMs. The simulation studies show that the type I error rates of the GOF tests with RQRs are very close to the nominal level; in addition, the scatter-plots and Q–Q plots of RQRs are useful in discerning the good and bad models. We also apply the RQRs to diagnose six GLMMs to a real microbiome dataset. The results show that the OTU counts at the genus level of this dataset (after a truncation treatment) can be modelled well by zero-inflated and zero-modified NB models. Conclusion RQR is an excellent tool for diagnosing GLMMs for zero-inflated count data, particularly the sequencing count data arising in microbiome studies. In the supplementary materials, we provided two generic R functions, called and , for calculating the RQRs given fitting outputs of the R package .

Confidence intervals for the mean of discrete exponential families are widely used in many applications. Since missing data are commonly encountered, the interval estimation for incomplete data is an important problem. The performances of the existing multiple imputation confidence intervals are unsatisfactory. We propose modified multiple imputation confidence intervals to improve the existing confidence intervals for the mean of the discrete exponential families with quadratic variance functions. A simulation study shows that the coverage probabilities of the modified confidence intervals are closer to the nominal level than the existing confidence intervals when the true mean is near the boundaries of the parameter space. These confidence intervals are also illustrated with real data examples.

Phase II immuno-oncology clinical trials screen for efficacy an increasing number of treatments. In rare cancers, using historical control data is a pragmatic approach for speeding up clinical trials. The drop-the-losers design allows dropping off ineffective arms at interim analyses. We extended the original drop-the-losers design for a time-to-event outcome using a historical control through the one-sample log-rank statistic. Simulated trials featured three arms at the first stage, one at the second stage, nine scenarios, eight sample sizes with 5%- and 10%- nominal family-wise error rate (FWER). A numerical algorithm is provided to solve power calculations at the design stage. Our design was compared with a group of three independent single-arm trials (fixed design) with and without correction for multiplicity. Our design allowed strict control of the FWER at nominal levels while the misspecification of survival distribution and fixed design inflated the FWER up to three times the nominal level. The empirical power of our design increased with the sample size, the treatment effect and the number of effective treatments and dropped when more patients were recruited at the second stage. The fixed design with correction showed comparable power, while our design advantageously included more patients to the most promising arm. Recommendations for future applications are given. By taking advantage of the use of historical control data and a time-to-event outcome, the drop-the-losers design is a promising tool to meet the challenge of improving phase II clinical trials in immuno-oncology.