Linear Model Framework Research Articles

DC‐bias and temperature included CSWPL model for RF power transistors

AbstractA novel frequency domain behavioral modeling method for gallium‐nitride (GaN) devices is presented in this article. By utilizing a multi‐dimensional polynomial function, the proposed technique interpolates DC‐bias voltage and temperature based on the Canonical section‐wise piecewise linear (CSWPL) model framework. A detailed description of the model's theory is provided. With data from 10‐W GaN devices, the model was implemented in commercial software and validated through both DC and radio frequency (RF) tests. A robust predictive ability is demonstrated by the obtained results, thus proving the accuracy of the developed modeling method. This model is superior to the standard CSWPL model in that it is capable of predicting transistor behavior at different bias voltages and temperatures using a single set of parameters, thereby greatly reducing the complexity of the model and the time required for extraction.

A Tutorial for Deception Detection Analysis or: How I Learned to Stop Aggregating Veracity Judgments and Embraced Signal Detection Theory Mixed Models

Historically, deception detection research has relied on factorial analyses of response accuracy to make inferences. However, this practice overlooks important sources of variability resulting in potentially misleading estimates and may conflate response bias with participants’ underlying sensitivity to detect lies from truths. We showcase an alternative approach using a signal detection theory (SDT) with generalized linear mixed models framework to address these limitations. This SDT approach incorporates individual differences from both judges and senders, which are a principal source of spurious findings in deception research. By avoiding data transformations and aggregations, this methodology outperforms traditional methods and provides more informative and reliable effect estimates. This well-established framework offers researchers a powerful tool for analyzing deception data and advances our understanding of veracity judgments. All code and data are openly available.

Predictive Modeling of Phenotypic Antimicrobial Susceptibility of Selected Beta-Lactam Antimicrobials from Beta-Lactamase Resistance Genes.

The outcome of bacterial infection management relies on prompt diagnosis and effective treatment, but conventional antimicrobial susceptibility testing can be slow and labor-intensive. Therefore, this study aims to predict phenotypic antimicrobial susceptibility of selected beta-lactam antimicrobials in the bacteria of the family Enterobacteriaceae from different beta-lactamase resistance genotypes. Using human datasets extracted from the Antimicrobial Testing Leadership and Surveillance (ATLAS) program conducted by Pfizer and retail meat datasets from the National Antimicrobial Resistance Monitoring System for Enteric Bacteria (NARMS), we used a robust or weighted least square multivariable linear regression modeling framework to explore the relationship between antimicrobial susceptibility data of beta-lactam antimicrobials and different types of beta-lactamase resistance genes. In humans, in the presence of the blaCTX-M-1, blaCTX-M-2, blaCTX-M-8/25, and blaCTX-M-9 groups, MICs of cephalosporins significantly increased by values between 0.34-3.07 μg/mL, however, the MICs of carbapenem significantly decreased by values between 0.81-0.87 μg/mL. In the presence of carbapenemase genes (blaKPC, blaNDM, blaIMP, and blaVIM), the MICs of cephalosporin antimicrobials significantly increased by values between 1.06-5.77 μg/mL, while the MICs of carbapenem antimicrobials significantly increased by values between 5.39-67.38 μg/mL. In retail meat, MIC of ceftriaxone increased significantly in the presence of blaCMY-2, blaCTX-M-1, blaCTX-M-55, blaCTX-M-65, and blaSHV-2 by 55.16 μg/mL, 222.70 μg/mL, 250.81 μg/mL, 204.89 μg/mL, and 31.51 μg/mL respectively. MIC of cefoxitin increased significantly in the presence of blaCTX-M-65 and blaTEM-1 by 1.57 μg/mL and 1.04 μg/mL respectively. In the presence of blaCMY-2, MIC of cefoxitin increased by an average of 8.66 μg/mL over 17 years. Compared to E. coli isolates, MIC of cefoxitin in Salmonella enterica isolates decreased significantly by 0.67 μg/mL. On the other hand, MIC of ceftiofur increased in the presence of blaCTX-M-1, blaCTX-M-65, blaSHV-2, and blaTEM-1 by 8.82 μg/mL, 9.11 μg/mL, 8.18 μg/mL, and 1.04 μg/mL respectively. In the presence of blaCMY-2, MIC of ceftiofur increased by an average of 10.20 μg/mL over 14 years. The ability to predict antimicrobial susceptibility of beta-lactam antimicrobials directly from beta-lactamase resistance genes may help reduce the reliance on routine phenotypic testing with higher turnaround times in diagnostic, therapeutic, and surveillance of antimicrobial-resistant bacteria of the family Enterobacteriaceae.

Behavioural ecology meets oncology: quantifying the recovery of animal behaviour to a transient exposure to a cancer risk factor.

Wildlife is increasingly exposed to sublethal transient cancer risk factors, including mutagenic substances, which activates their anti-cancer defences, promotes tumourigenesis, and may negatively impact populations. Little is known about how exposure to cancer risk factors impacts the behaviour of wildlife. Here, we investigated the effects of a sublethal, short-term exposure to a carcinogen at environmentally relevant concentrations on the activity patterns of wild Girardia tigrina planaria during a two-phase experiment, consisting of a 7-day exposure to cadmium period followed by a 7-day recovery period. To comprehensively explore the effects of the exposure on activity patterns, we employed the double hierarchical generalized linear model framework which explicitly models residual intraindividual variability in addition to the mean and variance of the population. We found that exposed planaria were less active compared to unexposed individuals and were able to recover to pre-exposure activity levels albeit with a reduced variance in activity at the start of the recovery phase. Planaria showing high activity levels were less predictable with larger daily activity variations and higher residual variance. Thus, the shift in behavioural variability induced by an exposure to a cancer risk factor can be quantified using advanced tools from the field of behavioural ecology. This is required to understand how tumourous processes affect the ecology of species.

Methods for meta-analysis and meta-regression of binomial data: concepts and tutorial with Stata command metapreg

BackgroundDespite the widespread interest in meta-analysis of proportions, its rationale, certain theoretical and methodological concepts are poorly understood. The generalized linear models framework is well-established and provides a natural and optimal model for meta-analysis, network meta-analysis, and meta-regression of proportions. Nonetheless, generic methods for meta-analysis of proportions based on the approximation to the normal distribution continue to dominate.MethodsWe developed metapreg, a tool with advanced statistical procedures to perform a meta-analysis, network meta-analysis, and meta-regression of binomial proportions in Stata using binomial, logistic and logistic-normal models. First, we explain the rationale and concepts essential in understanding statistical methods for meta-analysis of binomial proportions and describe the models implemented in metapreg. We then describe and demonstrate the models in metapreg using data from seven published meta-analyses. We also conducted a simulation study to compare the performance of metapreg estimators with the existing estimators of the population-averaged proportion in metaprop and metan under a broad range of conditions including, high over-dispersion and small meta-analysis.Conclusionmetapreg is a flexible, robust and user-friendly tool employing a rigorous approach to evidence synthesis of binomial data that makes the most efficient use of all available data and does not require ad-hoc continuity correction or data imputation. We expect its use to yield higher-quality meta-analysis of binomial proportions.

On Diagnostics in Bell--Touchard Regression Models

The Bell--Touchard regression model for count response variables was introduced recently in the statistical literature. This regression model for counts is, in some aspects, similar to the generalized linear model framework, and the mean response is related to covariates and unknown regression coefficients, which allows for parameter interpretation in terms of the response variable in its original scale. However, diagnostic methods for this class of regression models were not developed. In this paper, we fill this gap and propose a variety of diagnostic tools, such as leverage measures, global influence, normal curvatures of local influence under some perturbation schemes, and Pearson residuals. All diagnostic measures developed are applied in a real data set to analyze the fitted Bell--Touchard regression model in practice.

Multivariate Generalized Linear Mixed Models for Count Data

Univariate regression models have rich literature for counting data. However, this is not the case for multivariate count data. Therefore, we present the Multivariate Generalized Linear Mixed Models framework that deals with a multivariate set of responses, measuring the correlation between them through random effects that follows a multivariate normal distribution. This model is based on a GLMM with a random intercept and the estimation process remains the same as a standard GLMM with random effects integrated out via Laplace approximation. We efficiently implemented this model through the TMB package available in R. We used Poisson, negative binomial (NB), and COM-Poisson distributions. To assess the estimator properties, we conducted a simulation study considering four different sample sizes and three different correlation values for each distribution. We achieved unbiased and consistent estimators for Poisson and NB distributions; for COM-Poisson estimators were consistent, but biased, especially for dispersion, variance, and correlation parameter estimators. These models were applied to two datasets. The first concerns a sample from 30 different sites collected in Australia where the number of times each one of the 41 different ant species was registered; which results in an impressive 820 variance-covariance and 41 dispersion parameters are estimated simultaneously, let alone the regression parameters. The second is from the Australia Health Survey with 5 response variables and 5190 respondents. These datasets can be considered overdispersed by the generalized dispersion index. The COM-Poisson model overcame the other two competitors considering three goodness-of-fit indexes, AIC, BIC, and maximized log-likelihood values. As a result, it estimated parameters with smaller standard errors and a greater number of significant correlation coefficients. Therefore, the proposed model is capable of dealing with multivariate count data, either under- equi- or overdispersed responses, and measuring any kind of correlation between them taking into account the effects of the covariates.

Genetic and brain similarity independently predict childhood anthropometrics and neighborhood socioeconomic conditions

Linking the developing brain with individual differences in clinical and demographic traits is challenging due to the substantial interindividual heterogeneity of brain anatomy and organization. Here we employ an integrative approach that parses individual differences in both cortical thickness and common genetic variants, and assess their effects on a wide set of childhood traits. The approach uses a linear mixed model framework to obtain the unique effects of each type of similarity, as well as their covariance. We employ this approach in a sample of 7760 unrelated children in the ABCD cohort baseline sample (mean age 9.9, 46.8% female). In general, associations between cortical thickness similarity and traits were limited to anthropometrics such as height, weight, and birth weight, as well as a marker of neighborhood socioeconomic conditions. Common genetic variants explained significant proportions of variance across nearly all included outcomes, although estimates were somewhat lower than previous reports. No significant covariance of the effects of genetic and cortical thickness similarity was found. The present findings highlight the connection between anthropometrics as well as neighborhood socioeconomic conditions and the developing brain, which appear to be independent from individual differences in common genetic variants in this population-based sample.

A process‐based water stable isotope mixing model for plant water sourcing

AbstractStable isotopes of hydrogen and oxygen in water are common tools for investigating water uptake apportionment, but many of the existing methods rely on simple linear mixing approaches that do not mechanistically incorporate additional information about site physical properties and conditions. Here, we develop a ‘physically based root water uptake isotope mixing estimation’ model (PRIME) that combines a continuous and parametric probability density function for root water uptake with site physical data in a process‐based linear mixing framework. To demonstrate the application of PRIME, water uptake patterns of boreal forest Pinus banksiana trees were estimated on four dates in 2019. To aid in validation, estimates were compared with that of the Bayesian linear mixing model framework, MixSIAR. The two approaches provided similar results, but due to its continuous and parametric nature, PRIME provided estimates of superior resolution, certainty, and model parsimony. Although both models incorporate additional physical information into their mixing frameworks, PRIME does so in a mechanistic manner, thereby reflecting the relevant hydrological processes more effectively than the purely empirical approach taken by MixSIAR. Furthermore, because PRIME uses a continuous function to describe the predicted uptake pattern, it allows users to quantify water uptake with essentially infinite resolution, through integration over the desired depth ranges. These findings demonstrate the advantages of utilizing a continuous, parametric, and process‐based mixing model to estimate root water uptake apportionment, thus providing a relatively simple yet powerful tool with which to approach plant water sourcing.

Modular Linear Power Flow Model Against Large Fluctuations

The linear power flow model based on an empirical operating point is generally employed in power generation dispatch. However, with the increasing penetration of renewable energy sources (RESs) and frequent topology changes, the expansion of the operating region causes considerable modeling errors in the static linear power flow model. In this paper, the sources of linearization error are thoroughly analyzed, and a modular linear power flow modeling framework is proposed. It is found that the key features that affect the accuracy of linearization are the truncation error and its first derivative. This motivates us to cluster historical scenarios based on selected features. The key approach is to individually select a linear power flow model for power system operating conditions with similar linearization error features. This allows us to derive a refined linear power flow model for each cluster to avoid excessive linearization errors using a uniform linear power flow model. Numerical results for several IEEE and Polish test systems show that the linearization error of the proposed method is reduced up to 52.98% compared to current methods. The results demonstrate that the proposed method can use a small number of linearization segments to deal with topology changes.

A GLM-based zero-inflated generalized Poisson factor model for analyzing microbiome data.

High-throughput sequencing technology facilitates the quantitative analysis of microbial communities, improving the capacity to investigate the associations between the human microbiome and diseases. Our primary motivating application is to explore the association between gut microbes and obesity. The complex characteristics of microbiome data, including high dimensionality, zero inflation, and over-dispersion, pose new statistical challenges for downstream analysis. We propose a GLM-based zero-inflated generalized Poisson factor analysis (GZIGPFA) model to analyze microbiome data with complex characteristics. The GZIGPFA model is based on a zero-inflated generalized Poisson (ZIGP) distribution for modeling microbiome count data. A link function between the generalized Poisson rate and the probability of excess zeros is established within the generalized linear model (GLM) framework. The latent parameters of the GZIGPFA model constitute a low-rank matrix comprising a low-dimensional score matrix and a loading matrix. An alternating maximum likelihood algorithm is employed to estimate the unknown parameters, and cross-validation is utilized to determine the rank of the model in this study. The proposed GZIGPFA model demonstrates superior performance and advantages through comprehensive simulation studies and real data applications.

Modeling basal body temperature data using horseshoe process regression.

Biomedical data often exhibit jumps or abrupt changes. For example, women's basal body temperature may jump at ovulation, menstruation, implantation, and miscarriage. These sudden changes make these data challenging to model: many methods will oversmooth the sharp changes or overfit in response to measurement error. We develop horseshoe process regression (HPR) to address this problem. We define a horseshoe process as a stochastic process in which each increment is horseshoe-distributed. We use the horseshoe process as a nonparametric Bayesian prior for modeling a potentially nonlinear association between an outcome and its continuous predictor, which we implement via Stan and in the R package HPR. We provide guidance and extensions to advance HPR's use in applied practice: we introduce a Bayesian imputation scheme to allow for interpolation at unobserved values of the predictor within the HPR; include additional covariates via a partial linear model framework; and allow for monotonicity constraints. We find that HPR performs well when fitting functions that have sharp changes. We apply HPR to model women's basal body temperatures over the course of the menstrual cycle.

Probing the interplay of biophysical constraints and photosynthesis to model tree growth

Tree growth is a key uncertainty in projections of forest productivity and the global carbon cycle. While global vegetation models commonly represent tree growth as a carbon assimilation (source)-driven process, accumulating evidence points toward widespread non-photosynthetic (sink) limitations. Notably, growth biophysical potential, defined as the upper-limit to tree growth imposed by temperature and turgor constraints on cell division, has been suggested to be a potent driver of observed decoupling between tree growth and photosynthesis. Understanding the interplay between biophysical potential and photosynthesis and how to accommodate it parsimoniously in models remains a challenge.Here, we use a soil-plant-atmosphere continuum model together with a regional network of forest structure and annual, radial tree growth observations extending over three decades to simulate tree photosynthesis and biophysical potential along an aridity gradient and across five tree species in NE Spain. We then apply a linear modelling framework to quantify the relative importance of photosynthesis, biophysical potential and their interactions to predict annual tree growth along the aridity gradient.Overall similar relative importance of photosynthesis and biophysical potential was underlain by strong variations with climate, photosynthesis being more relevant at wet sites and biophysical potential at dry sites. Observed spatial and temporal trends further suggested that tree growth is primarily limited by biophysical potential under dry conditions and that disregarding it could lead to underestimating tree growth decline with increased aridity under climate change.Our results support the idea that biophysical potential is an important component of sink limitations to tree radial growth. Its representation in vegetation models could accommodate spatially and temporally dynamic source-sink limitations on tree growth.

Beyond Exams: Investigating AI Tool Impact on Student Attitudes, Ethical Awareness, and Academic Dishonesty in Online College Assessments

Academic dishonesty in higher education is a growing concern, exacerbated by the increasing use of AI tools in online assessments. This study investigates the relationship between AI tool dependence, ethical awareness, student attitudes, and academic dishonesty among college students. It also explores the moderating effects of demographic factors. Survey data from college students were analyzed using a Generalized Linear Model (GLM) framework for a thorough examination of the complex interplay between the variables while considering the moderating influence of age, gender, type of institution, and technological proficiency. The study reveals that AI tool dependence is prevalent among college students. While students generally hold positive attitudes toward academic integrity, there is variability in the intensity and nature of these attitudes. Moreover, ethical awareness appears limited, highlighting a potential gap between ethical beliefs and behavior. Surprisingly, there is a consistent pattern of positive attitudes toward academic dishonesty. However, these findings are not explored in-depth in this study. Importantly, neither ethical awareness nor student attitudes significantly mediate the relationship between AI tool dependence and academic dishonesty. Demographic factors do not appear to significantly moderate these relationships. In light of these findings, institutions are encouraged to explore the implementation of the AI Dependence Inclusive Course for Transparency Program (AIDICT). This specialized initiative, shaped by the study’s insights, enhances ethical education and raises awareness of the ethical implications associated with AI tool usage.

A multi-dimensional incomplete stepped-wedge trial design to estimate the impact of standards-based audit.

A clinical audit is a low-cost process used for quality improvement in healthcare. Such audits are however infrequently used in resource poor countries, where the need for and potential impact of quality improvement is higher. Sets of standards for use in maternal and newborn care have been established based on internal guidelines and evidence. The before-after design of a clinical audit is prone to bias in the estimation of the impact of conducting a clinical audit. A trial design that would provide an unbiased estimate of the impact of implementing a clinical audit process on the attainment of standards selected (a standards-based audit) was needed. The aim of this paper is to introduce and describe the design of trials we developed to meet this need. A novel randomised stepped-wedge trial design to estimate the impact of conducting standards-based audits is presented. A multi-dimensional incomplete stepped-wedge cluster randomised trial design suitable for estimation of the impact of Standards-based audits on compliance with standard is proposed; two variants are described in detail. A method for sample size estimation is described. Analyses can be performed for the binary outcome using a generalised linear mixed model framework to estimate the impact of the approach on compliance with standards subjected to a standards-based audit; additional terms to consider including in sensitivity analyses are considered. The design presented has the potential to estimate the impact of introducing the standards-based audit process on compliance with standard, while providing participating healthcare providers opportunity to gain experience of implementing the standards-based audit process. The design may be applicable in other areas in which multiple processes are to be studied.

Master statistical analysis plan: attractive targeted sugar bait phase III trials in Kenya, Mali, and Zambia

This manuscript is a master statistical analysis plan for each of three-cluster randomized controlled trials to evaluate the efficacy of attractive targeted sugar baits (ATSB) described in an already published protocol. The master SAP contains an overarching plan for all three trials, which can be adapted to trial-specific circumstances. The primary objective of the trials is to evaluate the efficacy of ATSB in the presence of universal vector control coverage with insecticide-treated nets (ITN) or indoor residual spraying (IRS) after two transmission seasons on clinical malaria incidence as compared with universal vector control coverage with ITN or IRS alone. The primary outcome measure is the incidence rate of clinical malaria, assessed in cohorts aged 12 months to less than 15 years (≥ 5 years to 15 years in Mali) during monthly follow-up visits. The primary unadjusted analysis will be conducted on the intention-to-treat analysis population without adjustment for any anticipated confounding variables. The primary outcome will be analyzed using a multi-level model constructed on a generalized linear model framework with a Poisson likelihood and a log link function. Random intercepts will be included for each study cluster and a fixed effect for study-arm. The analyst will be blinded to study arm assignment. Several secondary outcomes will be analyzed, as well as a pooled analysis (individual patient data meta-analysis) across the three trial sites. Additionally, a standard meta-analysis is expected to be conducted using combined data from all sites.

Bayesian second-order sensitivity of longitudinal inferences to non-ignorability: an application to antidepressant clinical trial data.

Incomplete data is a prevalent complication in longitudinal studies due to individuals' drop-out before intended completion time. Currently available methods via commercial software for analyzing incomplete longitudinal data at best rely on the ignorability of the drop-outs. If the underlying missing mechanism was non-ignorable, potential bias arises in the statistical inferences. To remove the bias when the drop-out is non-ignorable, joint complete-data and drop-out models have been proposed which involve computational difficulties and untestable assumptions. Since the critical ignorability assumption is unverifiable based on the observed part of the sample, some local sensitivity indices have been proposed in the literature. Specifically, Eftekhari Mahabadi (Second-order local sensitivity to non-ignorability in Bayesian inferences. Stat Med 2018;59:55-95) proposed a second-order local sensitivity tool for Bayesian analysis of cross-sectional studies and show its better performance for handling bias compared with the first-order ones. In this paper, we aim to extend this index for the Bayesian sensitivity analysis of normal longitudinal studies with drop-outs. The index is driven based on a selection model for the drop-out mechanism and a Bayesian linear mixed-effect complete-data model. The presented formulas are calculated using the posterior estimation and draws from the simpler ignorable model. The method is illustrated via some simulation studies and sensitivity analysis of a real antidepressant clinical trial data. Overall, the numerical analysis showed that when repeated outcomes are subject to missingness, regression coefficient estimates are nearly approximated well by a linear function in the neighbourhood of MAR model, but there are a considerable amount of second-order sensitivity for the error term and random effect variances in Bayesian linear mixed-effect model framework.

Missing Data Imputation with High-Dimensional Data

Imputation of missing data in high-dimensional datasets with more variables P than samples N, P ≫ N , is hampered by the data dimensionality. For multivariate imputation, the covariance matrix is ill conditioned and cannot be properly estimated. For fully conditional imputation, the regression models for imputation cannot include all the variables. Thus, the high dimension requires special imputation approaches. In this article, we provide an overview and realistic comparisons of imputation approaches for high-dimensional data when applied to a linear mixed modeling (LMM) framework. We examine approaches from three different classes using simulation studies: multiple imputation with penalized regression, multiple imputation with recursive partitioning and predictive mean matching; and multiple imputation with Principal Component Analysis (PCA). We illustrate the methods on a real case study where a multivariate outcome (i.e., an extracted set of correlated biomarkers from human urine samples) was collected and monitored over time and we discuss the proposed methods with more standard imputation techniques that could be applied by ignoring either the multivariate or the longitudinal dimension. Our simulations demonstrate the superiority of the recursive partitioning and predictive mean matching algorithm over the other methods in terms of bias, mean squared error and coverage of the LMM parameter estimates when compared to those obtained from a data analysis without missingness, although it comes at the expense of high computational costs. It is worthwhile reconsidering much faster methodologies like the one relying on PCA.

Bayesian linear mixed model with multiple random effects for prediction analysis on high-dimensional multi-omics data.

Accurate disease risk prediction is an essential step in the modern quest for precision medicine. While high-dimensional multi-omics data have provided unprecedented data resources for prediction studies, their high-dimensionality and complex inter/intra-relationships have posed significant analytical challenges. We proposed a two-step Bayesian linear mixed model framework (TBLMM) for risk prediction analysis on multi-omics data. TBLMM models the predictive effects from multi-omics data using a hybrid of the sparsity regression and linear mixed model with multiple random effects. It can resemble the shape of the true effect size distributions and accounts for non-linear, including interaction effects, among multi-omics data via kernel fusion. It infers its parameters via a computationally efficient variational Bayes algorithm. Through extensive simulation studies and the prediction analyses on the positron emission tomography imaging outcomes using data obtained from the Alzheimer's Disease Neuroimaging Initiative, we have demonstrated that TBLMM can consistently outperform the existing method in predicting the risk of complex traits. The corresponding R package is available on GitHub (https://github.com/YaluWen/TBLMM).

A novel rare variants association test for binary traits in family-based designs via copulas.

With the cost-effectiveness technology in whole-genome sequencing, more sophisticated statistical methods for testing genetic association with both rare and common variants are being investigated to identify the genetic variation between individuals. Several methods which group variants, also called gene-based approaches, are developed. For instance, advanced extensions of the sequence kernel association test, which is a widely used variant-set test, have been proposed for unrelated samples and extended for family data. Family data have been shown to be powerful when analyzing rare variants. However, most of such methods capture familial relatedness using a random effect component within the generalized linear mixed model framework. Therefore, there is a need to develop unified and flexible methods to study the association between a set of genetic variants and a trait, especially for a binary outcome. Copulas are multivariate distribution functions with uniform margins on the interval and they provide suitable models to capture familial dependence structure. In this work, we propose a flexible family-based association test for both rare and common variants in the presence of binary traits. The method, termed novel rare variant association test (NRVAT), uses a marginal logistic model and a Gaussian Copula. The latter is employed to model the dependence between relatives. An analytic score-type test is derived. Through simulations, we show that our method can achieve greater power than existing approaches. The proposed model is applied to investigate the association between schizophrenia and bipolar disorder in a family-based cohort consisting of 17 extended families from Eastern Quebec.