Correlated bivariate continuous and binary outcomes: issues and applications

Structured testing of genetic association with mixed clinical outcomes

Genetic factors play a fundamental role in disease development. Studying the genetic association with clinical outcomes is critical for understanding disease biology and devising novel treatment targets. However, the frequencies of genetic variations are often low, making it difficult to examine the variants one-by-one. Moreover, the clinical outcomes are complex, including patients' survival time and other binary or continuous outcomes such as recurrences and lymph node count, and how to effectively analyze genetic association with these outcomes remains unclear. In this article, we proposed a structured test statistic for testing genetic association with mixed types of survival, binary, and continuous outcomes. The structured testing incorporates known biological information of variants while allowing for their heterogeneous effects and is a powerful strategy for analyzing infrequent genetic factors. Simulation studies show that the proposed test statistic has correct type I error and is highly effective in detecting significant genetic variants. We applied our approach to a uterine corpus endometrial carcinoma study and identified several genetic pathways associated with the clinical outcomes.

Incorporating Data from Multiple Endpoints in the Analysis of Clinical Trials: Example from RSV Vaccines

BACKGROUND

To meet regulatory approval, interventions must demonstrate efficacy against a primary outcome in randomized clinical trials. However, when there are multiple clinically relevant outcomes, selecting a single primary outcome is challenging. Incorporating data from multiple outcomes may increase statistical power in clinical trials. We examined methods for analyzing data on multiple endpoints, inspired by real-world trials of interventions against respiratory syncytial virus (RSV).

METHOD

We developed a novel permutation test representing a weighted average of individual outcome test statistics ( wavP ) to evaluate intervention efficacy in a multiple endpoint analysis. We compared the power and type I error rate of this approach to the Bonferroni correction ( bonfT ) and the minP permutation test. We evaluated the different approaches using simulated data from three hypothetical trials varying the intervention efficacy, correlation, and incidence of the outcomes, and data from a real-world RSV clinical trial.

RESULTS

When the vaccine efficacy against different outcomes was similar, wavP yielded higher power than bonfT and minP ; in some scenarios the improvement in power was substantial. In settings where vaccine efficacy was notably larger against one endpoint compared with the others, all three methods had similar power. We developed an R package, PERmutation basEd ANalysis of mulTiple Endpoints (PERMEATE), to guide the selection of the most appropriate method for analyzing multiple endpoints in clinical trials.

CONCLUSIONS

Analyzing multiple endpoints using a weighted permutation method can increase power, whereas controlling the type I error rate compared with established methods under conditions mirroring real-world RSV clinical trials.

Multilevel joint frailty model for hierarchically clustered binary and survival data

Hierarchical data arise when observations are clustered into groups. Multilevel models are practically useful in these settings, but these models are elusive in the context of hierarchical data with mixed multivariate outcomes. In this article, we consider binary and survival outcomes and assume the hierarchical structure is induced by clustering of both outcomes within patients and clustering of patients within hospitals which frequently occur in multicenter studies. We introduce a multilevel joint frailty model that analyzes the outcomes simultaneously to jointly estimate their regression parameters and explicitly model within-patient correlation between the outcomes and within-hospital correlation separately for each outcome. Estimation is facilitated by a computationally efficient residual maximum likelihood method that further predicts cluster-specific frailties for both outcomes and circumvents the formidable challenges induced by multidimensional integration that complicates the underlying likelihood. The performance of the model and estimation procedure is investigated via extensive simulation studies. The practical utility of the model is illustrated through simultaneous modeling of disease-free survival and binary endpoint of platelet recovery in a multicenter allogeneic bone marrow transplantation dataset that motivates this study.

Simultaneous modeling of multivariate heterogeneous responses and heteroskedasticity via a two-stage composite likelihood

Multivariate heterogeneous responses and heteroskedasticity have attracted increasing attention in recent years. In genome-wide association studies, effective simultaneous modeling of multiple phenotypes would improve statistical power and interpretability. However, a flexible common modeling system for heterogeneous data types can pose computational difficulties. Here we build upon a previous method for multivariate probit estimation using a two-stage composite likelihood that exhibits favorable computational time while retaining attractive parameter estimation properties. We extend this approach to incorporate multivariate responses of heterogeneous data types (binary and continuous), and possible heteroskedasticity. Although the approach has wide applications, it would be particularly useful for genomics, precision medicine, or individual biomedical prediction. Using a genomics example, we explore statistical power and confirm that the approach performs well for hypothesis testing and coverage percentages under a wide variety of settings. The approach has the potential to better leverage genomics data and provide interpretable inference for pleiotropy, in which a locus is associated with multiple traits.

Two-stage multivariate Mendelian randomization on multiple outcomes with mixed distributions

In clinical research, it is important to study whether certain clinical factors or exposures have causal effects on clinical and patient-reported outcomes such as toxicities, quality of life, and self-reported symptoms, which can help improve patient care. Usually, such outcomes are recorded as multiple variables with different distributions. Mendelian randomization (MR) is a commonly used technique for causal inference with the help of genetic instrumental variables to deal with observed and unobserved confounders. Nevertheless, the current methodology of MR for multiple outcomes only focuses on one outcome at a time, meaning that it does not consider the correlation structure of multiple outcomes, which may lead to a loss of statistical power. In situations with multiple outcomes of interest, especially when there are mixed correlated outcomes with different distributions, it is much more desirable to jointly analyze them with a multivariate approach. Some multivariate methods have been proposed to model mixed outcomes; however, they do not incorporate instrumental variables and cannot handle unmeasured confounders. To overcome the above challenges, we propose a two-stage multivariate Mendelian randomization method (MRMO) that can perform multivariate analysis of mixed outcomes using genetic instrumental variables. We demonstrate that our proposed MRMO algorithm can gain power over the existing univariate MR method through simulation studies and a clinical application on a randomized Phase III clinical trial study on colorectal cancer patients.

Partially linear Bayesian modeling of longitudinal rank and time-to-event data using accelerated failure time model with application to brain tumor data

Joint modeling of longitudinal rank and time-to-event data with random effects model using a Bayesian approach is presented. Accelerated failure time (AFT) models can be used for the analysis of time-to-event data to estimate the effects of covariates on acceleration/deceleration of the survival time. The parametric AFT models require determining the event time distribution. So, we suppose that the time variable is modeled with Weibull AFT distribution. In many real-life applications, it is difficult to determine the appropriate distribution. To avoid this restriction, several semiparametric AFT models were proposed, containing spline-based model. So, we propose a flexible extension of the accelerated failure time model. Furthermore, the usual joint linear model, a joint partially linear model, is also considered containing the nonlinear effect of time on the longitudinal rank responses and nonlinear and time-dependent effects of covariates on the hazard. Also, a Bayesian approach that yields Bayesian estimates of the model's parameters is used. Some simulation studies are conducted to estimate parameters of the considered models. The model is applied to a real brain tumor patient's data set that underwent surgery. The results of analyzing data are presented to represent the method.

Bivariate quantitative Bayesian LASSO for detecting association of rare haplotypes with two correlated continuous phenotypes

In genetic association studies, the multivariate analysis of correlated phenotypes offers statistical and biological advantages compared to analyzing one phenotype at a time. The joint analysis utilizes additional information contained in the correlation and avoids multiple testing. It also provides an opportunity to investigate and understand shared genetic mechanisms of multiple phenotypes. Bivariate logistic Bayesian LASSO (LBL) was proposed earlier to detect rare haplotypes associated with two binary phenotypes or one binary and one continuous phenotype jointly. There is currently no haplotype association test available that can handle multiple continuous phenotypes. In this study, by employing the framework of bivariate LBL, we propose bivariate quantitative Bayesian LASSO (QBL) to detect rare haplotypes associated with two continuous phenotypes. Bivariate QBL removes unassociated haplotypes by regularizing the regression coefficients and utilizing a latent variable to model correlation between two phenotypes. We carry out extensive simulations to investigate the performance of bivariate QBL and compare it with that of a standard (univariate) haplotype association test, Haplo.score (applied twice to two phenotypes individually). Bivariate QBL performs better than Haplo.score in all simulations with varying degrees of power gain. We analyze Genetic Analysis Workshop 19 exome sequencing data on systolic and diastolic blood pressures and detect several rare haplotypes associated with the two phenotypes.

Incorporating data from multiple endpoints in the analysis of clinical trials: example from RSV vaccines

Background

To achieve licensure, interventions typically must demonstrate efficacy against a primary outcome in a randomized clinical trial. However, selecting a single primary outcome a priori is challenging. Incorporating data from multiple and related outcomes might help to increase statistical power in clinical trials. Inspired by real-world clinical trials of interventions against respiratory syncytial virus (RSV), we examined methods for analyzing data on multiple endpoints.

Method

We simulated data from three different populations in which the efficacy of the intervention and the correlation among outcomes varied. We developed a novel permutation-based approach that represents a weighted average of individual outcome test statistics ( varP ) to evaluate intervention efficacy in a multiple endpoint analysis. We compared the power and type I error rate of this approach to two alternative methods: the Bonferroni correction ( bonfT ) and another permutation-based approach that uses the minimum P-value across all test statistics ( minP ).

Results

When the vaccine efficacy against different outcomes was similar, VarP yielded higher power than bonfT and minP; in some scenarios the improvement in power was substantial. In settings where vaccine efficacy was notably larger against one endpoint compared to the others, all three methods had similar power.

Conclusions

Analyzing multiple endpoints using a weighted permutation method can increase power while controlling the type I error rate in settings where outcomes share similar characteristics, like RSV outcomes. We developed an R package, PERMEATE , to guide selection of the most appropriate method for analyzing multiple endpoints in clinical trials.

Joint analysis of PK and immunogenicity outcomes using factorization model - a powerful approach for PK similarity study

Biological products, whether they are innovator products or biosimilars, can incite an immunogenic response ensuing in the development of anti-drug antibodies (ADA). The presence of ADA’s often affects the drug clearance, resulting in an increase in the variability of pharmacokinetic (PK) analysis and challenges in the design and analysis of PK similarity studies. Immunogenic response is a complex process which may be manifested by product and non-product-related factors. Potential imbalances in non-product-related factors between treatment groups may lead to differences in antibodies formation and thus in PK outcome. The current standard statistical approaches dismiss any associations between immunogenicity and PK outcomes. However, we consider PK and immunogenicity as the two correlated outcomes of the study treatment. In this research, we propose a factorization model for the simultaneous analysis of PK parameters (normal variable after taking log-transformation) and immunogenic response subgroup (binary variable). The central principle of the factorization model is to describe the likelihood function as the product of the marginal distribution of one outcome and the conditional distribution of the second outcome given the previous one. Factorization model captures the additional information contained in the correlation between the outcomes, it is more efficient than models that ignore potential dependencies between the outcomes. In our context, factorization model accounts for variability in PK data by considering the influence of immunogenicity. Based on our simulation studies, the factorization model provides more accurate and efficient estimates of the treatment effect in the PK data by taking into account the impact of immunogenicity. These findings are supported by two PK similarity clinical studies with a highly immunogenic biologic.

Accelerating Sustainable Development Goals for South African adolescents from high HIV prevalence areas: a longitudinal path analysis

BACKGROUND

Adolescents experience a multitude of vulnerabilities which need to be addressed in order to achieve the Sustainable Development Goals (SDGs). In sub-Saharan Africa, adolescents experience high burden of HIV, violence exposure, poverty, and poor mental and physical health. This study aimed to identify interventions and circumstances associated with three or more targets ("accelerators") within multiple SDGs relating to HIV-affected adolescents and examine cumulative effects on outcomes.

METHODS

Prospective longitudinal data from 3401 adolescents from randomly selected census enumeration areas in two provinces with > 30% HIV prevalence carried out in 2010/11 and 2011/12 were used to examine six hypothesized accelerators (positive parenting, parental monitoring, free schooling, teacher support, food sufficiency and HIV-negative/asymptomatic caregiver) targeting twelve outcomes across four SDGs, using a multivariate (multiple outcome) path model with correlated outcomes controlling for outcome at baseline and socio-demographics. The study corrected for multiple-hypothesis testing and tested measurement invariance across sex. Percentage predicted probabilities of occurrence of the outcome in the presence of the significant accelerators were also calculated.

RESULTS

Sample mean age was 13.7 years at baseline, 56.6% were female. Positive parenting, parental monitoring, food sufficiency and AIDS-free caregiver were variously associated with reductions on ten outcomes. The model was gender invariant. AIDS-free caregiver was associated with the largest reductions. Combinations of accelerators resulted in a percentage reduction of risk of up to 40%.

CONCLUSION

Positive parenting, parental monitoring, food sufficiency and AIDS-free caregivers by themselves and in combination improve adolescent outcomes across ten SDG targets. These could translate to the corresponding real-world interventions parenting programmes, cash transfers and universal access to antiretroviral treatment, which when provided together, may help governments in sub-Saharan Africa more economically to reach their SDG targets.

Detecting rare haplotype association with two correlated phenotypes of binary and continuous types

Multiple correlated traits/phenotypes are often collected in genetic association studies and they may share a common genetic mechanism. Joint analysis of correlated phenotypes has well-known advantages over one-at-a-time analysis including gain in power and better understanding of genetic etiology. However, when the phenotypes are of discordant types such as binary and continuous, the joint modeling is more challenging. Another research area of current interest is discovery of rare genetic variants. Currently there is no method available for detecting association of rare (or common) haplotypes with multiple discordant phenotypes jointly. Our goal is to fill this gap specifically for two discordant phenotypes. We consider a rare haplotype association method for a binary phenotype, logistic Bayesian LASSO (univariate LBL) and its extension for two correlated binary phenotypes (bivariate LBL-2B). Under this framework, we propose a haplotype association test with binary and continuous phenotypes jointly (bivariate LBL-BC). Specifically, we use a latent variable to induce correlation between the two phenotypes. We carry out extensive simulations to investigate bivariate LBL-BC and compare it with univariate LBL and bivariate LBL-2B. In most settings, bivariate LBL-BC performs the best. In only two situations, bivariate LBL-BC has similar performance-when the two phenotypes are (1) weakly or not correlated and the target haplotype affects the binary phenotype only and (2) strongly positively correlated and the target haplotype affects both phenotypes in positive direction. Finally, we apply the method to a data set on lung cancer and nicotine dependence and detect several haplotypes including a rare one.

A comparison of methods for analysing multiple outcome measures in randomised controlled trials using a simulation study

Multiple primary outcomes are sometimes collected and analysed in randomised controlled trials (RCTs), and are used in favour of a single outcome. By collecting multiple primary outcomes, it is possible to fully evaluate the effect that an intervention has for a given disease process. A simple approach to analysing multiple outcomes is to consider each outcome separately, however, this approach does not account for any pairwise correlations between the outcomes. Any cases with missing values must be ignored, unless an additional imputation step is performed. Alternatively, multivariate methods that explicitly model the pairwise correlations between the outcomes may be more efficient when some of the outcomes have missing values. In this paper, we present an overview of relevant methods that can be used to analyse multiple outcome measures in RCTs, including methods based on multivariate multilevel (MM) models. We perform simulation studies to evaluate the bias in the estimates of the intervention effects and the power of detecting true intervention effects observed when using selected methods. Different simulation scenarios were constructed by varying the number of outcomes, the type of outcomes, the degree of correlations between the outcomes and the proportions and mechanisms of missing data. We compare multivariate methods to univariate methods with and without multiple imputation. When there are strong correlations between the outcome measures (ρ > .4), our simulation studies suggest that there are small power gains when using the MM model when compared to analysing the outcome measures separately. In contrast, when there are weak correlations (ρ < .4), the power is reduced when using univariate methods with multiple imputation when compared to analysing the outcome measures separately.

Clinical prediction models to predict the risk of multiple binary outcomes: a comparison of approaches

Clinical prediction models (CPMs) can predict clinically relevant outcomes or events. Typically, prognostic CPMs are derived to predict the risk of a single future outcome. However, there are many medical applications where two or more outcomes are of interest, meaning this should be more widely reflected in CPMs so they can accurately estimate the joint risk of multiple outcomes simultaneously. A potentially naïve approach to multi-outcome risk prediction is to derive a CPM for each outcome separately, then multiply the predicted risks. This approach is only valid if the outcomes are conditionally independent given the covariates, and it fails to exploit the potential relationships between the outcomes. This paper outlines several approaches that could be used to develop CPMs for multiple binary outcomes. We consider four methods, ranging in complexity and conditional independence assumptions: namely, probabilistic classifier chain, multinomial logistic regression, multivariate logistic regression, and a Bayesian probit model. These are compared with methods that rely on conditional independence: separate univariate CPMs and stacked regression. Employing a simulation study and real-world example, we illustrate that CPMs for joint risk prediction of multiple outcomes should only be derived using methods that model the residual correlation between outcomes. In such a situation, our results suggest that probabilistic classification chains, multinomial logistic regression or the Bayesian probit model are all appropriate choices. We call into question the development of CPMs for each outcome in isolation when multiple correlated or structurally related outcomes are of interest and recommend more multivariate approaches to risk prediction.

Joint penalized spline modeling of multivariate longitudinal data, with application to HIV-1 RNA load levels and CD4 cell counts

Motivated by the need to jointly model the longitudinal trajectories of HIV viral load levels and CD4 counts during the primary infection stage, we propose a joint penalized spline modeling approach that can be used to model the repeated measurements from multiple biomarkers of various types (eg, continuous, binary) simultaneously. This approach allows for flexible trajectories for each marker, accounts for potentially time-varying correlation between markers, and is robust to misspecification of knots. Despite its advantages, the application of multivariate penalized spline models, especially when biomarkers may be of different data types, has been limited in part due to its seemingly complexity in implementation. To overcome this, we describe a procedure that transforms the multivariate setting to the univariate one, and then makes use of the generalized linear mixed effect model representation of a penalized spline model to facilitate its implementation with standard statistical software. We performed simulation studies to evaluate the validity and efficiency through joint modeling of correlated biomarkers measured longitudinally compared to the univariate modeling approach. We applied this modeling approach to longitudinal HIV-1 RNA load and CD4 count data from Southern African cohorts to estimate features of the joint distributions such as the correlation and the proportion of subjects with high viral load levels and high CD4 cell counts over time.

Multivariate Mixed Response Model with Pairwise Composite-Likelihood Method

In clinical research, study outcomes usually consist of various patients’ information corresponding to the treatment. To have a better understanding of the effects of different treatments, one often needs to analyze multiple clinical outcomes simultaneously, while the data are usually mixed with both continuous and discrete variables. We propose the multivariate mixed response model to implement statistical inference based on the conditional grouped continuous model through a pairwise composite-likelihood approach. It can simplify the multivariate model by dealing with three types of bivariate models and incorporating the asymptotical properties of the composite likelihood via the Godambe information. We demonstrate the validity and the statistic power of the multivariate mixed response model through simulation studies and clinical applications. This composite-likelihood method is advantageous for statistical inference on correlated multivariate mixed outcomes.

Pharmacokinetic/pharmacodynamic data extrapolation models for improved pediatric efficacy and toxicity estimation, with application to secondary hyperparathyroidism

In most drug development settings, the regulatory approval process is accompanied by extensive studies performed to understand the drug's pharmacokinetic (PK) and pharmacodynamic (PD) properties. In this article, we attempt to utilize the rich PK/PD data to inform the borrowing of information from adults during pediatric drug development. In pediatric settings, it is especially crucial that we are parsimonious with the patients recruited for experimentation. We illustrate our approaches in the context of clinical trials of cinacalcet for treating secondary hyperparathyroidism in pediatric and adult patients with chronic kidney disease, where we model both parathyroid hormone (efficacy endpoint) and corrected calcium levels (safety endpoint). We use population PK/PD modeling of the cinacalcet data to quantitatively assess the similarity between adults and children, and use this information in various hierarchical Bayesian adult borrowing rules whose statistical properties can then be evaluated. In particular, we simulate the bias and mean square error performance of our approaches in settings where borrowing is and is not warranted to inform guidelines for the future use of our methods.

Marginal analysis of multiple outcomes with informative cluster size

In surveillance studies of periodontal disease, the relationship between disease and other health and socioeconomic conditions is of key interest. To determine whether a patient has periodontal disease, multiple clinical measurements (eg, clinical attachment loss, alveolar bone loss, and tooth mobility) are taken at the tooth-level. Researchers often create a composite outcome from these measurements or analyze each outcome separately. Moreover, patients have varying number of teeth, with those who are more prone to the disease having fewer teeth compared to those with good oral health. Such dependence between the outcome of interest and cluster size (number of teeth) is called informative cluster size and results obtained from fitting conventional marginal models can be biased. We propose a novel method to jointly analyze multiple correlated binary outcomes for clustered data with informative cluster size using the class of generalized estimating equations (GEE) with cluster-specific weights. We compare our proposed multivariate outcome cluster-weighted GEE results to those from the convectional GEE using the baseline data from Veterans Affairs Dental Longitudinal Study. In an extensive simulation study, we show that our proposed method yields estimates with minimal relative biases and excellent coverage probabilities.

Do Textbooks Matter for Reading Comprehension? A Study in Flemish Primary Education

This study assessed whether textbooks affect academic performance and engagement in reading comprehension in primary education in Flanders (Belgium). The data of the Progress in International Reading Literacy Study 2016 and a reassessment of this study in 2018 were used to describe students’ learning progress in reading comprehension and evolution in engagement between the fourth and sixth grade. The sample consisted of 3051 students in 98 schools. The averages of students’ learning progress and engagement were compared for five textbooks by using multilevel autoregression model and multilevel change score models. Contrasts between textbooks in average learning progress and engagement were also estimated. To control for differences between student populations that are educated with the different textbooks, we controlled for student’s socioeconomic status, language and initial academic performance in fourth grade at the student- and school-level. The main hypotheses were that textbooks affect learning progress and reading engagement. This was based on the literature and prior (mainly) cross-sectional research which describe textbooks as playing an important role in the curriculum that is taught to students on a daily basis. The results of both models showed that textbooks do not affect student’s average learning progress in reading comprehension and evolution in engagement between the fourth grade and sixth grade in Flanders. Hence, the hypotheses were rejected.

Bivariate logistic Bayesian LASSO for detecting rare haplotype association with two correlated phenotypes

In genetic association studies, joint modeling of related traits/phenotypes can utilize the correlation between them and thereby provide more power and uncover additional information about genetic etiology. Moreover, detecting rare genetic variants are of current scientific interest as a key to missing heritability. Logistic Bayesian LASSO (LBL) has been proposed recently to detect rare haplotype variants using case-control data, that is, a single binary phenotype. As there is currently no haplotype association method that can handle multiple binary phenotypes, we extend LBL to fill this gap. We develop a bivariate model by using a latent variable to induce correlation between the two outcomes. We carry out extensive simulations to investigate the bivariate LBL and compare with the univariate LBL. The bivariate LBL performs better or similar to the univariate LBL in most settings. It has the highest gain in power when a haplotype is associated with both traits and it affects at least one trait in a direction opposite to the direction of the correlation between the traits. We analyze two data sets-Genetic Analysis Workshop 19 sequence data on systolic and diastolic blood pressures and a genome-wide association data set on lung cancer and smoking and detect several associated rare haplotypes.

Simultaneous inference for multiple marginal generalized estimating equation models

Motivated by small-sample studies in ophthalmology and dermatology, we study the problem of simultaneous inference for multiple endpoints in the presence of repeated observations. We propose a framework in which a generalized estimating equation model is fit for each endpoint marginally, taking into account dependencies within the same subject. The asymptotic joint normality of the stacked vector of marginal estimating equations is used to derive Wald-type simultaneous confidence intervals and hypothesis tests for multiple linear contrasts of regression coefficients of the multiple marginal models. The small sample performance of this approach is improved by a bias adjustment to the estimate of the joint covariance matrix of the regression coefficients from multiple models. As a further small sample improvement a multivariate t-distribution with appropriate degrees of freedom is specified as reference distribution. In addition, a generalized score test based on the stacked estimating equations is derived. Simulation results show strong control of the family-wise type I error rate for these methods even with small sample sizes and increased power compared to a Bonferroni-Holm multiplicity adjustment. Thus, the proposed methods are suitable to efficiently use the information from repeated observations of multiple endpoints in small-sample studies.

A Bayesian approach for individual-level drug benefit-risk assessment

In existing benefit-risk assessment (BRA) methods, benefit and risk criteria are usually identified and defined separately based on aggregated clinical data and therefore ignore the individual-level differences as well as the association among the criteria. We proposed a Bayesian multicriteria decision-making method for BRA of drugs using individual-level data. We used a multidimensional latent trait model to account for the heterogeneity of treatment effects with latent variables introducing the dependencies among outcomes. We then applied the stochastic multicriteria acceptability analysis approach for BRA incorporating imprecise and heterogeneous patient preference information. We adopted an efficient Markov chain Monte Carlo algorithm when implementing the proposed method. We applied our method to a case study to illustrate how individual-level benefit-risk profiles could inform decision-making.

A framework for conducting economic evaluations alongside natural experiments

Internationally, policy makers are increasingly focussed on reducing the detrimental consequences and rising costs associated with unhealthy diets, inactivity, smoking, alcohol and other risk factors on the health of their populations. This has led to an increase in the demand for evidence-based, cost-effective Population Health Interventions (PHIs) to reverse this trend. Given that research designs such as randomised controlled trials (RCTs) are often not suited to the evaluation of PHIs, Natural Experiments (NEs) are now frequently being used as a design to evaluate such complex, preventive PHIs. However, current guidance for economic evaluation focusses on RCT designs and therefore does not address the specific challenges of NE designs. Using such guidance can lead to sub-optimal design, data collection and analysis for NEs, leading to bias in the estimated effectiveness and cost-effectiveness of the PHI. As a consequence, there is a growing recognition of the need to identify a robust methodological framework for the design and conducting of economic evaluations alongside such NEs. This paper outlines the challenges inherent to the design and conduct of economic evaluations of PHIs alongside NEs, providing a comprehensive framework and outlining a research agenda in this area.

PCA-Based Multiple-Trait GWAS Analysis: A Powerful Model for Exploring Pleiotropy

Principal component analysis (PCA) is a potential approach that can be applied in multiple-trait genome-wide association studies (GWAS) to explore pleiotropy, as well as increase the power of quantitative trait loci (QTL) detection. In this study, the relationship of test single nucleotide polymorphisms (SNPs) was determined between single-trait GWAS and PCA-based GWAS. We found that the estimated pleiotropic quantitative trait nucleotides (QTNs) β * ^ were in most cases larger than the single-trait model estimations ( β 1 ^ and β 2 ^ ). Analysis using the simulated data showed that PCA-based multiple-trait GWAS has improved statistical power for detecting QTL compared to single-trait GWAS. For the minor allele frequency (MAF), when the MAF of QTNs was greater than 0.2, the PCA-based model had a significant advantage in detecting the pleiotropic QTNs, but when its MAF was reduced from 0.2 to 0, the advantage began to disappear. In addition, as the linkage disequilibrium (LD) of the pleiotropic QTNs decreased, its detection ability declined in the co-localization effect model. Furthermore, on the real data of 1141 Simmental cattle, we applied the PCA model to the multiple-trait GWAS analysis and identified a QTL that was consistent with a candidate gene, MCHR2, which was associated with presoma muscle development in cattle. In summary, PCA-based multiple-trait GWAS is an efficient model for exploring pleiotropic QTNs in quantitative traits.

Methods for the analysis of multiple endpoints in small populations: A review

While current guidelines generally recommend single endpoints for primary analyses of confirmatory clinical trials, it is recognized that certain settings require inference on multiple endpoints for comprehensive conclusions on treatment effects. Furthermore, combining treatment effect estimates from several outcome measures can increase the statistical power of tests. Such an efficient use of resources is of special relevance for trials in small populations. This paper reviews approaches based on a combination of test statistics or measurements across endpoints as well as multiple testing procedures that allow for confirmatory conclusions on individual endpoints. We especially focus on feasibility in trials with small sample sizes and do not solely rely on asymptotic considerations. A systematic literature search in the Scopus database, supplemented by a manual search, was performed to identify research papers on analysis methods for multiple endpoints with relevance to small populations. The identified methods were grouped into approaches that combine endpoints into a single measure to increase the power of statistical tests and methods to investigate differential treatment effects in several individual endpoints by multiple testing.

Evaluating therapeutic effect on WOMAC subscales in osteoarthritis RCTs: When model choice matters

RATIONALE, AIMS, AND OBJECTIVES

The study aimed at developing a method for modelling the Western Ontario and McMaster Universities index (WOMAC), accounting for correlation between its subscales and for heterogeneity of treatment effect (HTE), using data from 2 twin trials on knee osteoarthritis.

METHOD

Two randomized, double-blind, placebo-controlled clinical trials (twin trials). Studies aimed at investigating the effectiveness of a pharmacological treatment on clinical outcomes of knee osteoarthritis, measured using WOMAC index. To take into account that the WOMAC subscales are correlated and skewed, we proposed and compared multivariate gamma and Gaussian approaches with latent variable capturing correlation between outcomes. Besides the latent term, the interaction between the latent term and treatment, accounting for HTE, was further estimated.

RESULTS

Modelling the subscales by using a gamma approach accounting for skewness of data, we found out different results compared with Gaussian models. The main difference regarded the latent variable interacting with treatment (accounting for unobserved heterogeneity), which is not significant for the Gaussian approach (P value = .102) and significant in the gamma model (P value < .002). Thus, indicating that unobserved covariates affect treatment's performance. Additionally, plotting the observed and the estimated values of WOMAC index of the Gaussian and gamma models, we showed that, compared with the Gaussian, the gamma one best fits the data, especially among poor responders.

CONCLUSION

Multivariate gamma approach accounting for correlation between outcomes and for HTE has been demonstrated to be more suitable to model WOMAC subscales and to provide more information on effect of therapy.

Testing Association between Mixed Type Outcomes and Covariates Jointly by the Use of a Latent Variable

Multiple outcomes are often collected simultaneously in biomedical fields in order to identify whether a continuous response and an ordinal response are associated with some covariates simultaneously. Here we propose a joint statistical model by the use of a latent variable underlying the ordinal response. Asymptotic results are obtained and a jointly test is proposed for testing the continuous response and the ordinal response are associated with some covariates simultaneously. Extensive simulations and real data analysis results indicate more efficient performances of the proposed method than that of the combined p-values method.

Keeping Children Safe: a multicentre programme of research to increase the evidence base for preventing unintentional injuries in the home in the under-fives

Background

Unintentional injuries among 0- to 4-year-olds are a major public health problem incurring substantial NHS, individual and societal costs. However, evidence on the effectiveness and cost-effectiveness of preventative interventions is lacking.

Aim

To increase the evidence base for thermal injury, falls and poisoning prevention for the under-fives.

Methods

Six work streams comprising five multicentre case–control studies assessing risk and protective factors, a study measuring quality of life and injury costs, national surveys of children’s centres, interviews with children’s centre staff and parents, a systematic review of barriers to, and facilitators of, prevention and systematic overviews, meta-analyses and decision analyses of home safety interventions. Evidence from these studies informed the design of an injury prevention briefing (IPB) for children’s centres for preventing fire-related injuries and implementation support (training and facilitation). This was evaluated by a three-arm cluster randomised controlled trial comparing IPB and support (IPB+), IPB only (no support) and usual care. The primary outcome was parent-reported possession of a fire escape plan. Evidence from all work streams subsequently informed the design of an IPB for preventing thermal injuries, falls and poisoning.

Results

Modifiable risk factors for falls, poisoning and scalds were found. Most injured children and their families incurred small to moderate health-care and non-health-care costs, with a few incurring more substantial costs. Meta-analyses and decision analyses found that home safety interventions increased the use of smoke alarms and stair gates, promoted safe hot tap water temperatures, fire escape planning and storage of medicines and household products, and reduced baby walker use. Generally, more intensive interventions were the most effective, but these were not always the most cost-effective interventions. Children’s centre and parental barriers to, and facilitators of, injury prevention were identified. Children’s centres were interested in preventing injuries, and believed that they could prevent them, but few had an evidence-based strategic approach and they needed support to develop this. The IPB was implemented by children’s centres in both intervention arms, with greater implementation in the IPB+ arm. Compared with usual care, more IPB+ arm families received advice on key safety messages, and more families in each intervention arm attended fire safety sessions. The intervention did not increase the prevalence of fire escape plans [adjusted odds ratio (AOR) IPB only vs. usual care 0.93, 95% confidence interval (CI) 0.58 to 1.49; AOR IPB+ vs. usual care 1.41, 95% CI 0.91 to 2.20] but did increase the proportion of families reporting more fire escape behaviours (AOR IPB only vs. usual care 2.56, 95% CI 1.38 to 4.76; AOR IPB+ vs. usual care 1.78, 95% CI 1.01 to 3.15). IPB-only families were less likely to report match play by children (AOR 0.27, 95% CI 0.08 to 0.94) and reported more bedtime fire safety routines (AOR for a 1-unit increase in the number of routines 1.59, 95% CI 1.09 to 2.31) than usual-care families. The IPB-only intervention was less costly and marginally more effective than usual care. The IPB+ intervention was more costly and marginally more effective than usual care.

Limitations

Our case–control studies demonstrate associations between modifiable risk factors and injuries but not causality. Some injury cost estimates are imprecise because of small numbers. Systematic reviews and meta-analyses were limited by the quality of the included studies, the small numbers of studies reporting outcomes and significant heterogeneity, partly explained by differences in interventions. Network meta-analysis (NMA) categorised interventions more finely, but some variation remained. Decision analyses are likely to underestimate cost-effectiveness for a number of reasons. IPB implementation varied between children’s centres. Greater implementation may have resulted in changes in more fire safety behaviours.

Conclusions

Our studies provide new evidence about the effectiveness of, as well as economic evaluation of, home safety interventions. Evidence-based resources for preventing thermal injuries, falls and scalds were developed. Providing such resources to children’s centres increases their injury prevention activity and some parental safety behaviours.

Future work

Further randomised controlled trials, meta-analyses and NMAs are needed to evaluate the effectiveness and cost-effectiveness of home safety interventions. Further work is required to measure NHS, family and societal costs and utility decrements for childhood home injuries and to evaluate complex multicomponent interventions such as home safety schemes using a single analytical model.

Trial registration

Current Controlled Trials ISRCTN65067450 and ClinicalTrials.gov NCT01452191.

Funding

The National Institute for Health Research (NIHR) Programme Grants for Applied Research programme and will be published in full inProgramme Grants for Applied Research; Vol. 5, No. 14. See the NIHR Journals Library website for further project information.

Autoregressive and cross-lagged model for bivariate non-commensurate outcomes

Autoregressive and cross-lagged models have been widely used to understand the relationship between bivariate commensurate outcomes in social and behavioral sciences, but not much work has been carried out in modeling bivariate non-commensurate (e.g., mixed binary and continuous) outcomes simultaneously. We develop a likelihood-based methodology combining ordinary autoregressive and cross-lagged models with a shared subject-specific random effect in the mixed-model framework to model two correlated longitudinal non-commensurate outcomes. The estimates of the cross-lagged and the autoregressive effects from our model are shown to be consistent with smaller mean-squared error than the estimates from the univariate generalized linear models. Inclusion of the subject-specific random effects in the proposed model accounts for between-subject variability arising from the omitted and/or unobservable, but possibly explanatory, subject-level predictors. Our model is not restricted to the case with equal number of events per subject, and it can be extended to different types of bivariate outcomes. We apply our model to an ecological momentary assessment study with complex dependence and sampling data structures. Specifically, we study the dependence between the condom use and sexual satisfaction based on the data reported in a longitudinal study of sexually transmitted infections. We find negative cross-lagged effect between these two outcomes and positive autoregressive effect within each outcome. Copyright © 2017 John Wiley & Sons, Ltd.

Identifying Pleiotropic Genes in Genome-Wide Association Studies for Multivariate Phenotypes with Mixed Measurement Scales

We propose a multivariate genome-wide association test for mixed continuous, binary, and ordinal phenotypes. A latent response model is used to estimate the correlation between phenotypes with different measurement scales so that the empirical distribution of the Fisher’s combination statistic under the null hypothesis is estimated efficiently. The simulation study shows that our proposed correlation estimation methods have high levels of accuracy. More importantly, our approach conservatively estimates the variance of the test statistic so that the type I error rate is controlled. The simulation also shows that the proposed test maintains the power at the level very close to that of the ideal analysis based on known latent phenotypes while controlling the type I error. In contrast, conventional approaches–dichotomizing all observed phenotypes or treating them as continuous variables–could either reduce the power or employ a linear regression model unfit for the data. Furthermore, the statistical analysis on the database of the Study of Addiction: Genetics and Environment (SAGE) demonstrates that conducting a multivariate test on multiple phenotypes can increase the power of identifying markers that may not be, otherwise, chosen using marginal tests. The proposed method also offers a new approach to analyzing the Fagerström Test for Nicotine Dependence as multivariate phenotypes in genome-wide association studies.

A Hybrid ANN-GA Model to Prediction of Bivariate Binary Responses: Application to Joint Prediction of Occurrence of Heart Block and Death in Patients with Myocardial Infarction

BACKGROUND

In medical studies, when the joint prediction about occurrence of two events should be anticipated, a statistical bivariate model is used. Due to the limitations of usual statistical models, other methods such as Artificial Neural Network (ANN) and hybrid models could be used. In this paper, we propose a hybrid Artificial Neural Network-Genetic Algorithm (ANN-GA) model to prediction the occurrence of heart block and death in myocardial infarction (MI) patients simultaneously.

METHODS

For fitting and comparing the models, 263 new patients with definite diagnosis of MI hospitalized in Cardiology Ward of Hajar Hospital, Shahrekord, Iran, from March, 2014 to March, 2016 were enrolled. Occurrence of heart block and death were employed as bivariate binary outcomes. Bivariate Logistic Regression (BLR), ANN and hybrid ANN-GA models were fitted to data. Prediction accuracy was used to compare the models. The codes were written in Matlab 2013a and Zelig package in R3.2.2.

RESULTS

The prediction accuracy of BLR, ANN and hybrid ANN-GA models was obtained 77.7%, 83.69% and 93.85% for the training and 78.48%, 84.81% and 96.2% for the test data, respectively. In both training and test data set, hybrid ANN-GA model had better accuracy.

CONCLUSIONS

ANN model could be a suitable alternative for modeling and predicting bivariate binary responses when the presuppositions of statistical models are not met in actual data. In addition, using optimization methods, such as hybrid ANN-GA model, could improve precision of ANN model.

An efficient genome-wide association test for mixed binary and continuous phenotypes with applications to substance abuse research

We propose a new genome-wide association test for mixed binary and continuous phenotypes that uses an efficient numerical method to estimate the empirical distribution of the Fisher's combination statistic under the null hypothesis. Our simulation study shows that the proposed method controls the type I error rate and also maintains its power at the level of the permutation method. More importantly, the computational efficiency of the proposed method is much higher than the one of the permutation method. The simulation results also indicate that the power of the test increases when the genetic effect increases, the minor allele frequency increases, and the correlation between responses decreases. The statistical analysis on the database of the Study of Addiction: Genetics and Environment demonstrates that the proposed method combining multiple phenotypes can increase the power of identifying markers that may not be, otherwise, chosen using marginal tests.

Assessing factors related to waist circumference and obesity: application of a latent variable model

Background. Because the use of BMI (Body Mass Index) alone as a measure of adiposity has been criticized, in the present study our aim was to fit a latent variable model to simultaneously examine the factors that affect waist circumference (continuous outcome) and obesity (binary outcome) among Iranian adults. Methods. Data included 18,990 Iranian individuals aged 20–65 years that are derived from the third National Survey of Noncommunicable Diseases Risk Factors in Iran. Using latent variable model, we estimated the relation of two correlated responses (waist circumference and obesity) with independent variables including age, gender, PR (Place of Residence), PA (physical activity), smoking status, SBP (Systolic Blood Pressure), DBP (Diastolic Blood Pressure), CHOL (cholesterol), FBG (Fasting Blood Glucose), diabetes, and FHD (family history of diabetes). Results. All variables were related to both obesity and waist circumference (WC). Older age, female sex, being an urban resident, physical inactivity, nonsmoking, hypertension, hypercholesterolemia, hyperglycemia, diabetes, and having family history of diabetes were significant risk factors that increased WC and obesity. Conclusions. Findings from this study of Iranian adult settings offer more insights into factors associated with high WC and high prevalence of obesity in this population.

Multivariate Generalized Linear Mixed Models With Random Intercepts To Analyze Cardiovascular Risk Markers in Type-1 Diabetic Patients

Statistical approaches tailored to analyzing longitudinal data that have multiple outcomes with different distributions are scarce. This paucity is due to the non-availability of multivariate distributions that jointly model outcomes with different distributions other than the multivariate normal. A plethora of research has been done on the specific combination of binary-Gaussian bivariate outcomes but a more general approach that allows other mixtures of distributions for multiple longitudinal outcomes has not been thoroughly demonstrated and examined. Here we study a multivariate generalized linear mixed models approach that jointly models multiple longitudinal outcomes with different combinations of distributions and incorporates the correlations between the various outcomes through separate yet correlated random intercepts. Every outcome is linked to the set of covariates through a proper link function that allows the incorporation and joint modelling of different distributions. A novel application was demonstrated on a cohort study of Type 1 diabetic patients to jointly model a mix of longitudinal cardiovascular outcomes and to explore for the first time the effect of glycemic control treatment, plasma prekallikrein biomarker, gender and age on cardiovascular risk factors collectively.

Mendelian Randomization versus Path Models: Making Causal Inferences in Genetic Epidemiology

OBJECTIVE

The term Mendelian randomization is popular in the current literature. The first aim of this work is to describe the idea of Mendelian randomization studies and the assumptions required for drawing valid conclusions. The second aim is to contrast Mendelian randomization and path modeling when different 'omics' levels are considered jointly.

METHODS

We define Mendelian randomization as introduced by Katan in 1986, and review its crucial assumptions. We introduce path models as the relevant additional component to the current use of Mendelian randomization studies in 'omics'. Real data examples for the association between lipid levels and coronary artery disease illustrate the use of path models.

RESULTS

Numerous assumptions underlie Mendelian randomization, and they are difficult to be fulfilled in applications. Path models are suitable for investigating causality, and they should not be mixed up with the term Mendelian randomization. In many applications, path modeling would be the appropriate analysis in addition to a simple Mendelian randomization analysis.

CONCLUSIONS

Mendelian randomization and path models use different concepts for causal inference. Path modeling but not simple Mendelian randomization analysis is well suited to study causality with different levels of 'omics' data.

Modeling of multivariate longitudinal phenotypes in family genetic studies with Bayesian multiplicity adjustment

Genetic studies often collect data on multiple traits. Most genetic association analyses, however, consider traits separately and ignore potential correlation among traits, partially because of difficulties in statistical modeling of multivariate outcomes. When multiple traits are measured in a pedigree longitudinally, additional challenges arise because in addition to correlation between traits, a trait is often correlated with its own measures over time and with measurements of other family members. We developed a Bayesian model for analysis of bivariate quantitative traits measured longitudinally in family genetic studies. For a given trait, family-specific and subject-specific random effects account for correlation among family members and repeated measures, respectively. Correlation between traits is introduced by incorporating multivariate random effects and allowing time-specific trait residuals to correlate as in seemingly unrelated regressions. The proposed model can examine multiple single-nucleotide variations simultaneously, as well as incorporate familyspecific, subject-specific, or time-varying covariates. Bayesian multiplicity technique is used to effectively control false positives. Genetic Analysis Workshop 18 simulated data illustrate the proposed approach's applicability in modeling longitudinal multivariate outcomes in family genetic association studies.