Showing papers in "Biometrical Journal in 2020"

Meta-analysis of the difference of medians.

Abstract: We consider the problem of meta-analyzing two-group studies that report the median of the outcome. Often, these studies are excluded from meta-analysis because there are no well-established statistical methods to pool the difference of medians. To include these studies in meta-analysis, several authors have recently proposed methods to estimate the sample mean and standard deviation from the median, sample size, and several commonly reported measures of spread. Researchers frequently apply these methods to estimate the difference of means and its variance for each primary study and pool the difference of means using inverse variance weighting. In this work, we develop several methods to directly meta-analyze the difference of medians. We conduct a simulation study evaluating the performance of the proposed median-based methods and the competing transformation-based methods. The simulation results show that the median-based methods outperform the transformation-based methods when meta-analyzing studies that report the median of the outcome, especially when the outcome is skewed. Moreover, we illustrate the various methods on a real-life data set.

Network meta-analysis of multicomponent interventions

Abstract: In network meta-analysis (NMA), treatments can be complex interventions, for example, some treatments may be combinations of others or of common components. In standard NMA, all existing (single or combined) treatments are different nodes in the network. However, sometimes an alternative model is of interest that utilizes the information that some treatments are combinations of common components, called component network meta-analysis (CNMA) model. The additive CNMA model assumes that the effect of a treatment combined of two components A and B is the sum of the effects of A and B, which is easily extended to treatments composed of more than two components. This implies that in comparisons equal components cancel out. Interaction CNMA models also allow interactions between the components. Bayesian analyses have been suggested. We report an implementation of CNMA models in the frequentist R package netmeta. All parameters are estimated using weighted least squares regression. We illustrate the application of CNMA models using an NMA of treatments for depression in primary care. Moreover, we show that these models can even be applied to disconnected networks, if the composite treatments in the subnetworks contain common components.

Power gains by using external information in clinical trials are typically not possible when requiring strict type I error control.

Abstract: In the era of precision medicine, novel designs are developed to deal with flexible clinical trials that incorporate many treatment strategies for multiple diseases in one trial setting. This situation often leads to small sample sizes in disease-treatment combinations and has fostered the discussion about the benefits of borrowing of external or historical information for decision-making in these trials. Several methods have been proposed that dynamically discount the amount of information borrowed from historical data based on the conformity between historical and current data. Specifically, Bayesian methods have been recommended and numerous investigations have been performed to characterize the properties of the various borrowing mechanisms with respect to the gain to be expected in the trials. However, there is common understanding that the risk of type I error inflation exists when information is borrowed and many simulation studies are carried out to quantify this effect. To add transparency to the debate, we show that if prior information is conditioned upon and a uniformly most powerful test exists, strict control of type I error implies that no power gain is possible under any mechanism of incorporation of prior information, including dynamic borrowing. The basis of the argument is to consider the test decision function as a function of the current data even when external information is included. We exemplify this finding in the case of a pediatric arm appended to an adult trial and dichotomous outcome for various methods of dynamic borrowing from adult information to the pediatric arm. In conclusion, if use of relevant external data is desired, the requirement of strict type I error control has to be replaced by more appropriate metrics.

Time-dependent mediators in survival analysis: Modeling direct and indirect effects with the additive hazards model

Abstract: We discuss causal mediation analyses for survival data and propose a new approach based on the additive hazards model. The emphasis is on a dynamic point of view, that is, understanding how the direct and indirect effects develop over time. Hence, importantly, we allow for a time varying mediator. To define direct and indirect effects in such a longitudinal survival setting we take an interventional approach (Didelez, 2018) where treatment is separated into one aspect affecting the mediator and a different aspect affecting survival. In general, this leads to a version of the nonparametric g‐formula (Robins, 1986). In the present paper, we demonstrate that combining the g‐formula with the additive hazards model and a sequential linear model for the mediator process results in simple and interpretable expressions for direct and indirect effects in terms of relative survival as well as cumulative hazards. Our results generalize and formalize the method of dynamic path analysis (Fosen, Ferkingstad, Borgan, & Aalen, 2006; Strohmaier et al., 2015). An application to data from a clinical trial on blood pressure medication is given.

Adaptive seamless clinical trials using early outcomes for treatment or subgroup selection: Methods, simulation model and their implementation in R.

Abstract: Adaptive seamless designs combine confirmatory testing, a domain of phase III trials, with features such as treatment or subgroup selection, typically associated with phase II trials. They promise to increase the efficiency of development programmes of new drugs, for example, in terms of sample size and/or development time. It is well acknowledged that adaptive designs are more involved from a logistical perspective and require more upfront planning, often in the form of extensive simulation studies, than conventional approaches. Here, we present a framework for adaptive treatment and subgroup selection using the same notation, which links the somewhat disparate literature on treatment selection on one side and on subgroup selection on the other. Furthermore, we introduce a flexible and efficient simulation model that serves both designs. As primary endpoints often take a long time to observe, interim analyses are frequently informed by early outcomes. Therefore, all methods presented accommodate interim analyses informed by either the primary outcome or an early outcome. The R package asd, previously developed to simulate designs with treatment selection, was extended to include subgroup selection (so-called adaptive enrichment designs). Here, we describe the functionality of the R package asd and use it to present some worked-up examples motivated by clinical trials in chronic obstructive pulmonary disease and oncology. The examples both illustrate various features of the R package and provide insights into the operating characteristics of adaptive seamless studies.

On the relation between the cause-specific hazard and the subdistribution rate for competing risks data: The Fine-Gray model revisited.

Abstract: The Fine-Gray proportional subdistribution hazards model has been puzzling many people since its introduction. The main reason for the uneasy feeling is that the approach considers individuals still at risk for an event of cause 1 after they fell victim to the competing risk of cause 2. The subdistribution hazard and the extended risk sets, where subjects who failed of the competing risk remain in the risk set, are generally perceived as unnatural . One could say it is somewhat of a riddle why the Fine-Gray approach yields valid inference. To take away these uneasy feelings, we explore the link between the Fine-Gray and cause-specific approaches in more detail. We introduce the reduction factor as representing the proportion of subjects in the Fine-Gray risk set that has not yet experienced a competing event. In the presence of covariates, the dependence of the reduction factor on a covariate gives information on how the effect of the covariate on the cause-specific hazard and the subdistribution hazard relate. We discuss estimation and modeling of the reduction factor, and show how they can be used in various ways to estimate cumulative incidences, given the covariates. Methods are illustrated on data of the European Society for Blood and Marrow Transplantation.

Multiple imputation methods for handling incomplete longitudinal and clustered data where the target analysis is a linear mixed effects model

Abstract: Multiple imputation (MI) is increasingly popular for handling multivariate missing data. Two general approaches are available in standard computer packages: MI based on the posterior distribution of incomplete variables under a multivariate (joint) model, and fully conditional specification (FCS), which imputes missing values using univariate conditional distributions for each incomplete variable given all the others, cycling iteratively through the univariate imputation models. In the context of longitudinal or clustered data, it is not clear whether these approaches result in consistent estimates of regression coefficient and variance component parameters when the analysis model of interest is a linear mixed effects model (LMM) that includes both random intercepts and slopes with either covariates or both covariates and outcome contain missing information. In the current paper, we compared the performance of seven different MI methods for handling missing values in longitudinal and clustered data in the context of fitting LMMs with both random intercepts and slopes. We study the theoretical compatibility between specific imputation models fitted under each of these approaches and the LMM, and also conduct simulation studies in both the longitudinal and clustered data settings. Simulations were motivated by analyses of the association between body mass index (BMI) and quality of life (QoL) in the Longitudinal Study of Australian Children (LSAC). Our findings showed that the relative performance of MI methods vary according to whether the incomplete covariate has fixed or random effects and whether there is missingnesss in the outcome variable. We showed that compatible imputation and analysis models resulted in consistent estimation of both regression parameters and variance components via simulation. We illustrate our findings with the analysis of LSAC data.

Extensions of the probabilistic ranking metrics of competing treatments in network meta-analysis to reflect clinically important relative differences on many outcomes.

Abstract: One of the key features of network meta-analysis is ranking of interventions according to outcomes of interest. Ranking metrics are prone to misinterpretation because of two limitations associated with the current ranking methods. First, differences in relative treatment effects might not be clinically important and this is not reflected in the ranking metrics. Second, there are no established methods to include several health outcomes in the ranking assessments. To address these two issues, we extended the P-score method to allow for multiple outcomes and modified it to measure the mean extent of certainty that a treatment is better than the competing treatments by a certain amount, for example, the minimum clinical important difference. We suggest to present the tradeoff between beneficial and harmful outcomes allowing stakeholders to consider how much adverse effect they are willing to tolerate for specific gains in efficacy. We used a published network of 212 trials comparing 15 antipsychotics and placebo using a random effects network meta-analysis model, focusing on three outcomes; reduction in symptoms of schizophrenia in a standardized scale, all-cause discontinuation, and weight gain.

Estimating treatment effects with partially observed covariates using outcome regression with missing indicators

Abstract: Missing data is a common issue in research using observational studies to investigate the effect of treatments on health outcomes. When missingness occurs only in the covariates, a simple approach is to use missing indicators to handle the partially observed covariates. The missing indicator approach has been criticized for giving biased results in outcome regression. However, recent papers have suggested that the missing indicator approach can provide unbiased results in propensity score analysis under certain assumptions. We consider assumptions under which the missing indicator approach can provide valid inferences, namely, (1) no unmeasured confounding within missingness patterns; either (2a) covariate values of patients with missing data were conditionally independent of treatment or (2b) these values were conditionally independent of outcome; and (3) the outcome model is correctly specified: specifically, the true outcome model does not include interactions between missing indicators and fully observed covariates. We prove that, under the assumptions above, the missing indicator approach with outcome regression can provide unbiased estimates of the average treatment effect. We use a simulation study to investigate the extent of bias in estimates of the treatment effect when the assumptions are violated and we illustrate our findings using data from electronic health records. In conclusion, the missing indicator approach can provide valid inferences for outcome regression, but the plausibility of its assumptions must first be considered carefully.

On the interpretation of the hazard ratio in Cox regression.

Abstract: We argue that the term "relative risk" should not be used as a synonym for "hazard ratio" and encourage to use the probabilistic index as an alternative effect measure for Cox regression. The probabilistic index is the probability that the event time of an exposed or treated subject exceeds the event time of an unexposed or untreated subject conditional on the other covariates. It arises as a well known and simple transformation of the hazard ratio and nicely reveals the interpretational limitations. We demonstrate how the probabilistic index can be obtained using the R-package Publish.

An approach to model clustered survival data with dependent censoring.

Abstract: In this study we introduce a likelihood-based method, via the Weibull and piecewise exponential distributions, capable of accommodating the dependence between failure and censoring times. The methodology is developed for the analysis of clustered survival data and it assumes that failure and censoring times are mutually independent conditional on a latent frailty. The dependent censoring mechanism is accounted through the frailty effect and this is accomplished by means of a key parameter accommodating the correlation between failure and censored observations. The full specification of the likelihood in our work simplifies the inference procedures with respect to Huang and Wolfe since it reduces the computation burden of working with the profile likelihood. In addition, the assumptions made for the baseline distributions lead to models with continuous survival functions. In order to carry out inferences, we devise a Monte Carlo EM algorithm. The performance of the proposed models is investigated through a simulation study. Finally, we explore a real application involving patients from the Dialysis Outcomes and Practice Patterns Study observed between 1996 and 2015.

False discovery rate control for multiple testing based on discrete p-values

Abstract: For multiple testing based on discrete p-values, we propose a false discovery rate (FDR) procedure "BH+" with proven conservativeness. BH+ is at least as powerful as the BH (i.e., Benjamini-Hochberg) procedure when they are applied to superuniform p-values. Further, when applied to mid-p-values, BH+ can be more powerful than it is applied to conventional p-values. An easily verifiable necessary and sufficient condition for this is provided. BH+ is perhaps the first conservative FDR procedure applicable to mid-p-values and to p-values with general distributions. It is applied to multiple testing based on discrete p-values in a methylation study, an HIV study and a clinical safety study, where it makes considerably more discoveries than the BH procedure. In addition, we propose an adaptive version of the BH+ procedure, prove its conservativeness under certain conditions, and provide evidence on its excellent performance via simulation studies.

Comparison of random‐effects meta‐analysis models for the relative risk in the case of rare events: A simulation study

Abstract: Pooling the relative risk (RR) across studies investigating rare events, for example, adverse events, via meta-analytical methods still presents a challenge to researchers. The main reason for this is the high probability of observing no events in treatment or control group or both, resulting in an undefined log RR (the basis of standard meta-analysis). Other technical challenges ensue, for example, the violation of normality assumptions, or bias due to exclusion of studies and application of continuity corrections, leading to poor performance of standard approaches. In the present simulation study, we compared three recently proposed alternative models (random-effects [RE] Poisson regression, RE zero-inflated Poisson [ZIP] regression, binomial regression) to the standard methods in conjunction with different continuity corrections and to different versions of beta-binomial regression. Based on our investigation of the models' performance in 162 different simulation settings informed by meta-analyses from the Cochrane database and distinguished by different underlying true effects, degrees of between-study heterogeneity, numbers of primary studies, group size ratios, and baseline risks, we recommend the use of the RE Poisson regression model. The beta-binomial model recommended by Kuss (2015) also performed well. Decent performance was also exhibited by the ZIP models, but they also had considerable convergence issues. We stress that these recommendations are only valid for meta-analyses with larger numbers of primary studies. All models are applied to data from two Cochrane reviews to illustrate differences between and issues of the models. Limitations as well as practical implications and recommendations are discussed; a flowchart summarizing recommendations is provided.

A Bayesian basket trial design that borrows information across strata based on the similarity between the posterior distributions of the response probability.

Abstract: Basket trials simultaneously evaluate the effect of one or more drugs on a defined biomarker, genetic alteration, or molecular target in a variety of disease subtypes, often called strata. A conventional approach for analyzing such trials is an independent analysis of each of the strata. This analysis is inefficient as it lacks the power to detect the effect of drugs in each stratum. To address these issues, various designs for basket trials have been proposed, centering on designs using Bayesian hierarchical models. In this article, we propose a novel Bayesian basket trial design that incorporates predictive sample size determination, early termination for inefficacy and efficacy, and the borrowing of information across strata. The borrowing of information is based on the similarity between the posterior distributions of the response probability. In general, Bayesian hierarchical models have many distributional assumptions along with multiple parameters. By contrast, our method has prior distributions for response probability and two parameters for similarity of distributions. The proposed design is easier to implement and less computationally demanding than other Bayesian basket designs. Through a simulation with various scenarios, our proposed design is compared with other designs including one that does not borrow information and one that uses a Bayesian hierarchical model.

Multilevel regression and poststratification as a modeling approach for estimating population quantities in large population health studies: A simulation study

Abstract: There are now a growing number of applications of multilevel regression and poststratification (MRP) in population health and epidemiological studies. MRP uses multilevel regression to model individual survey responses as a function of demographic and geographic covariates. Estimated mean outcome values for each demographic-geographic respondent subtype are then weighted by the proportions of each subtype in the population to produce an overall population-level estimate. We recently reported an extensive case study of a large nationwide survey and found that MRP performed favorably compared to conventional survey sampling weights for the estimation of population descriptive quantities in a highly selected sample. In this study, we aimed to evaluate, by way of a simulation experiment, both the accuracy and precision of MRP versus survey sampling weights in the context of large population health studies. While much of the research into MRP has been focused on U.S. political and social science, we considered an alternative population structure of smaller size and with notably fewer geographic subsets. We explored the impact on MRP performance of sample size, model misspecification, interactions, and the addition of a geographic-level covariate. MRP was found to achieve generally superior performance in both accuracy and precision at both the national and state levels. Results were generally robust to model misspecification, and MRP performance was further improved by the inclusion of a geographic-level covariate. These findings offer further evidence that MRP provides a promising analytic approach for addressing participation bias in the estimation of population descriptive quantities from large-scale health surveys and cohort studies.

Validation of discrete time-to-event prediction models in the presence of competing risks.

Abstract: Clinical prediction models play a key role in risk stratification, therapy assignment and many other fields of medical decision making. Before they can enter clinical practice, their usefulness has to be demonstrated using systematic validation. Methods to assess their predictive performance have been proposed for continuous, binary, and time-to-event outcomes, but the literature on validation methods for discrete time-to-event models with competing risks is sparse. The present paper tries to fill this gap and proposes new methodology to quantify discrimination, calibration, and prediction error (PE) for discrete time-to-event outcomes in the presence of competing risks. In our case study, the goal was to predict the risk of ventilator-associated pneumonia (VAP) attributed to Pseudomonas aeruginosa in intensive care units (ICUs). Competing events are extubation, death, and VAP due to other bacteria. The aim of this application is to validate complex prediction models developed in previous work on more recently available validation data. Keywords: area under the curve; calibration slope; competing events; discrete time-to-event model; dynamic prediction models; prediction error; validation.

A weighted FDR procedure under discrete and heterogeneous null distributions.

Abstract: Multiple testing (MT) with false discovery rate (FDR) control has been widely conducted in the "discrete paradigm" where p-values have discrete and heterogeneous null distributions. However, in this scenario existing FDR procedures often lose some power and may yield unreliable inference, and for this scenario there does not seem to be an FDR procedure that partitions hypotheses into groups, employs data-adaptive weights and is nonasymptotically conservative. We propose a weighted p-value-based FDR procedure, "weighted FDR (wFDR) procedure" for short, for MT in the discrete paradigm that efficiently adapts to both heterogeneity and discreteness of p-value distributions. We theoretically justify the nonasymptotic conservativeness of the wFDR procedure under independence, and show via simulation studies that, for MT based on p-values of binomial test or Fisher's exact test, it is more powerful than six other procedures. The wFDR procedure is applied to two examples based on discrete data, a drug safety study, and a differential methylation study, where it makes more discoveries than two existing methods.

On the estimation of average treatment effects with right-censored time to event outcome and competing risks.

Abstract: We are interested in the estimation of average treatment effects based on right-censored data of an observational study. We focus on causal inference of differences between t-year absolute event risks in a situation with competing risks. We derive doubly robust estimation equations and implement estimators for the nuisance parameters based on working regression models for the outcome, censoring, and treatment distribution conditional on auxiliary baseline covariates. We use the functional delta method to show that these estimators are regular asymptotically linear estimators and estimate their variances based on estimates of their influence functions. In empirical studies, we assess the robustness of the estimators and the coverage of confidence intervals. The methods are further illustrated using data from a Danish registry study.

Sampling uncertainty versus method uncertainty: A general framework with applications to omics biomarker selection.

Abstract: Uncertainty is a crucial issue in statistics which can be considered from different points of view. One type of uncertainty, typically referred to as sampling uncertainty, arises through the variability of results obtained when the same analysis strategy is applied to different samples. Another type of uncertainty arises through the variability of results obtained when using the same sample but different analysis strategies addressing the same research question. We denote this latter type of uncertainty as method uncertainty. It results from all the choices to be made for an analysis, for example, decisions related to data preparation, method choice, or model selection. In medical sciences, a large part of omics research is focused on the identification of molecular biomarkers, which can either be performed through ranking or by selection from among a large number of candidates. In this paper, we introduce a general resampling-based framework to quantify and compare sampling and method uncertainty. For illustration, we apply this framework to different scenarios related to the selection and ranking of omics biomarkers in the context of acute myeloid leukemia: variable selection in multivariable regression using different types of omics markers, the ranking of biomarkers according to their predictive performance, and the identification of differentially expressed genes from RNA-seq data. For all three scenarios, our findings suggest highly unstable results when the same analysis strategy is applied to two independent samples, indicating high sampling uncertainty and a comparatively smaller, but non-negligible method uncertainty, which strongly depends on the methods being~compared.

Dynamic prediction: A challenge for biostatisticians, but greatly needed by patients, physicians and the public

Abstract: Prognosis is usually expressed in terms of the probability that a patient will or will not have experienced an event of interest t years after diagnosis of a disease. This quantity, however, is of little informative value for a patient who is still event-free after a number of years. Such a patient would be much more interested in the conditional probability of being event-free in the upcoming t years, given that he/she did not experience the event in the s years after diagnosis, called "conditional survival." It is the simplest form of a dynamic prediction and can be dealt with using straightforward extensions of standard time-to-event analyses in clinical cohort studies. For a healthy individual, a related problem with further complications is the so-called "age-conditional probability of developing cancer" in the next t years. Here, the competing risk of dying from other diseases has to be taken into account. For both situations, the hazard function provides the central dynamic concept, which can be further extended in a natural way to build dynamic prediction models that incorporate both baseline and time-dependent characteristics. Such models are able to exploit the most current information accumulating over time in order to accurately predict the further course or development of a disease. In this article, the biostatistical challenges as well as the relevance and importance of dynamic prediction are illustrated using studies of multiple myeloma, a hematologic malignancy with a formerly rather poor prognosis which has improved over the last few years.

A two-phase Bayesian methodology for the analysis of binary phenotypes in genome-wide association studies.

Abstract: Recent advances in sequencing and genotyping technologies are contributing to a data revolution in genome-wide association studies that is characterized by the challenging large p small n problem in statistics. That is, given these advances, many such studies now consider evaluating an extremely large number of genetic markers (p) genotyped on a small number of subjects (n). Given the dimension of the data, a joint analysis of the markers is often fraught with many challenges, while a marginal analysis is not sufficient. To overcome these obstacles, herein, we propose a Bayesian two-phase methodology that can be used to jointly relate genetic markers to binary traits while controlling for confounding. The first phase of our approach makes use of a marginal scan to identify a reduced set of candidate markers that are then evaluated jointly via a hierarchical model in the second phase. Final marker selection is accomplished through identifying a sparse estimator via a novel and computationally efficient maximum a posteriori estimation technique. We evaluate the performance of the proposed approach through extensive numerical studies, and consider a genome-wide application involving colorectal cancer.

Flexible parametric model for survival data subject to dependent censoring.

Abstract: When modeling survival data, it is common to assume that the (log-transformed) survival time (T) is conditionally independent of the (log-transformed) censoring time (C) given a set of covariates. There are numerous situations in which this assumption is not realistic, and a number of correction procedures have been developed for different models. However, in most cases, either some prior knowledge about the association between T and C is required, or some auxiliary information or data is/are supposed to be available. When this is not the case, the application of many existing methods turns out to be limited. The goal of this paper is to overcome this problem by developing a flexible parametric model, that is a type of transformed linear model. We show that the association between T and C is identifiable in this model. The performance of the proposed method is investigated both in an asymptotic way and through finite sample simulations. We also develop a formal goodness-of-fit test approach to assess the quality of the fitted model. Finally, the approach is applied to data coming from a study on liver transplants.

Marginal variable screening for survival endpoints

Abstract: When performing survival analysis in very high dimensions, it is often required to reduce the number of covariates using preliminary screening. During the last years, a large number of variable screening methods for the survival context have been developed. However, guidance is missing for choosing an appropriate method in practice. The aim of this work is to provide an overview of marginal variable screening methods for survival and develop recommendations for their use. For this purpose, a literature review is given, offering a comprehensive and structured introduction to the topic. In addition, a novel screening procedure based on distance correlation and martingale residuals is proposed, which is particularly useful in detecting nonmonotone associations. For evaluating the performance of the discussed approaches, a simulation study is conducted, comparing the true positive rates of competing variable screening methods in different settings. A real data example on mantle cell lymphoma is provided.

Allometric analysis using the multivariate shifted exponential normal distribution.

Abstract: In allometric studies, the joint distribution of the log-transformed morphometric variables is typically elliptical and with heavy tails. To account for these peculiarities, we introduce the multivariate shifted exponential normal (MSEN) distribution , an elliptical heavy-tailed generalization of the multivariate normal (MN). The MSEN belongs to the family of MN scale mixtures (MNSMs) by choosing a convenient shifted exponential as mixing distribution. The probability density function of the MSEN has a simple closed-form characterized by only one additional parameter, with respect to the nested MN, governing the tail weight. The first four moments exist and the excess kurtosis can assume any positive value. The membership to the family of MNSMs allows us a simple computation of the maximum likelihood (ML) estimates of the parameters via the expectation-maximization (EM) algorithm; advantageously, the M-step is computationally simplified by closed-form updates of all the parameters. We also evaluate the existence of the ML estimates. Since the parameter governing the tail weight is estimated from the data, robust estimates of the mean vector of the nested MN distribution are automatically obtained by downweighting; we show this aspect theoretically but also by means of a simulation study. We fit the MSEN distribution to multivariate allometric data where we show its usefulness also in comparison with other well-established multivariate elliptical distributions.

Parametric modal regression with varying precision

Abstract: In this paper, we propose a simple parametric modal linear regression model where the response variable is gamma distributed using a new parameterization of this distribution that is indexed by mode and precision parameters, that is, in this new regression model, the modal and precision responses are related to a linear predictor through a link function and the linear predictor involves covariates and unknown regression parameters. The main advantage of our new parameterization is the straightforward interpretation of the regression coefficients in terms of the mode of the positive response variable, as is usual in the context of generalized linear models, and direct inference in parametric mode regression based on the likelihood paradigm. Furthermore, we discuss residuals and influence diagnostic tools. A Monte Carlo experiment is conducted to evaluate the performances of these estimators in finite samples with a discussion of the results. Finally, we illustrate the usefulness of the new model by two applications, to biology and demography.

Multiple imputation in the presence of an incomplete binary variable created from an underlying continuous variable.

Abstract: Multiple imputation (MI) is used to handle missing at random (MAR) data Despite warnings from statisticians, continuous variables are often recoded into binary variables With MI it is important that the imputation and analysis models are compatible; variables should be imputed in the same form they appear in the analysis model With an encoded binary variable more accurate imputations may be obtained by imputing the underlying continuous variable We conducted a simulation study to explore how best to impute a binary variable that was created from an underlying continuous variable We generated a completely observed continuous outcome associated with an incomplete binary covariate that is a categorized version of an underlying continuous covariate, and an auxiliary variable associated with the underlying continuous covariate We simulated data with several sample sizes, and set 25% and 50% of data in the covariate to MAR dependent on the outcome and the auxiliary variable We compared the performance of five different imputation methods: (a) Imputation of the binary variable using logistic regression; (b) imputation of the continuous variable using linear regression, then categorizing into the binary variable; (c, d) imputation of both the continuous and binary variables using fully conditional specification (FCS) and multivariate normal imputation; (e) substantive-model compatible (SMC) FCS Bias and standard errors were large when the continuous variable only was imputed The other methods performed adequately Imputation of both the binary and continuous variables using FCS often encountered mathematical difficulties We recommend the SMC-FCS method as it performed best in our simulation studies

Construction and assessment of prediction rules for binary outcome in the presence of missing predictor data using multiple imputation and cross-validation: Methodological approach and data-based evaluation.

Abstract: We investigate calibration and assessment of predictive rules when missing values are present in the predictors. Our paper has two key objectives. The first is to investigate how the calibration of the prediction rule can be combined with use of multiple imputation to account for missing predictor observations. The second objective is to propose such methods that can be implemented with current multiple imputation software, while allowing for unbiased predictive assessment through validation on new observations for which outcome is not yet available. We commence with a review of the methodological foundations of multiple imputation as a model estimation approach as opposed to a purely algorithmic description. We specifically contrast application of multiple imputation for parameter (effect) estimation with predictive calibration. Based on this review, two approaches are formulated, of which the second utilizes application of the classical Rubin's rules for parameter estimation, while the first approach averages probabilities from models fitted on single imputations to directly approximate the predictive density for future observations. We present implementations using current software that allow for validation and estimation of performance measures by cross-validation, as well as imputation of missing data in predictors on the future data where outcome is missing by definition. To simplify, we restrict discussion to binary outcome and logistic regression throughout. Method performance is verified through application on two real data sets. Accuracy (Brier score) and variance of predicted probabilities are investigated. Results show substantial reductions in variation of calibrated probabilities when using the first approach.

Approaches for missing covariate data in logistic regression with MNAR sensitivity analyses.

Abstract: Data with missing covariate values but fully observed binary outcomes are an important subset of the missing data challenge. Common approaches are complete case analysis (CCA) and multiple imputation (MI). While CCA relies on missing completely at random (MCAR), MI usually relies on a missing at random (MAR) assumption to produce unbiased results. For MI involving logistic regression models, it is also important to consider several missing not at random (MNAR) conditions under which CCA is asymptotically unbiased and, as we show, MI is also valid in some cases. We use a data application and simulation study to compare the performance of several machine learning and parametric MI methods under a fully conditional specification framework (MI-FCS). Our simulation includes five scenarios involving MCAR, MAR, and MNAR under predictable and nonpredictable conditions, where "predictable" indicates missingness is not associated with the outcome. We build on previous results in the literature to show MI and CCA can both produce unbiased results under more conditions than some analysts may realize. When both approaches were valid, we found that MI-FCS was at least as good as CCA in terms of estimated bias and coverage, and was superior when missingness involved a categorical covariate. We also demonstrate how MNAR sensitivity analysis can build confidence that unbiased results were obtained, including under MNAR-predictable, when CCA and MI are both valid. Since the missingness mechanism cannot be identified from observed data, investigators should compare results from MI and CCA when both are plausibly valid, followed by MNAR sensitivity analysis.

Developing risk models for multicenter data using standard logistic regression produced suboptimal predictions: A simulation study

Abstract: Although multicenter data are common, many prediction model studies ignore this during model development. The objective of this study is to evaluate the predictive performance of regression methods for developing clinical risk prediction models using multicenter data, and provide guidelines for practice. We compared the predictive performance of standard logistic regression, generalized estimating equations, random intercept logistic regression, and fixed effects logistic regression. First, we presented a case study on the diagnosis of ovarian cancer. Subsequently, a simulation study investigated the performance of the different models as a function of the amount of clustering, development sample size, distribution of center-specific intercepts, the presence of a center-predictor interaction, and the presence of a dependency between center effects and predictors. The results showed that when sample sizes were sufficiently large, conditional models yielded calibrated predictions, whereas marginal models yielded miscalibrated predictions. Small sample sizes led to overfitting and unreliable predictions. This miscalibration was worse with more heavily clustered data. Calibration of random intercept logistic regression was better than that of standard logistic regression even when center-specific intercepts were not normally distributed, a center-predictor interaction was present, center effects and predictors were dependent, or when the model was applied in a new center. Therefore, to make reliable predictions in a specific center, we recommend random intercept logistic regression.

Distribution‐free simultaneous tests for location–scale and Lehmann alternative in two‐sample problem

Abstract: The paper deals with the classical two-sample testing problem for the equality of two populations, one of the most fundamental problems in biomedical experiments and case-control studies. The most familiar alternatives are the difference in location parameters or the difference in scale parameters or in both the parameters of the population density. All the tests designed for classical location or scale or location-scale alternatives assume that there is no change in the shape of the distribution. Some authors also consider the Lehmann-type alternative that addresses the change in shape. Two-sample tests under Lehmann alternative assume that the location and scale parameters are invariant. In real life, when a shift in the distribution occurs, one or more of the location, scale, and shape parameters may change simultaneously. We refer to change of one or more of the three parameters as a versatile alternative. Noting the dearth of literature for the equality two populations against such versatile alternative, we introduce two distribution-free tests based on the Euclidean and Mahalanobis distance. We obtain the asymptotic distributions of the two test statistics and study asymptotic power. We also discuss approximating p-values of the proposed tests in real applications with small samples. We compare the power performance of the two tests with several popular existing distribution-free tests against various fixed alternatives using Monte Carlo. We provide two illustrations based on biomedical experiments. Unlike existing tests which are suitable only in certain situations, proposed tests offer very good power in almost all types of shifts.