Subject-specific Random Effects Research Articles

Causal inference using multivariate generalized linear mixed-effects models.

Dynamic prediction of causal effects under different treatment regimens is an essential problem in precision medicine. It is challenging because the actual mechanisms of treatment assignment and effects are unknown in observational studies. We propose a multivariate generalized linear mixed-effects model and a Bayesian g-computation algorithm to calculate the posterior distribution of subgroup-specific intervention benefits of dynamic treatment regimes. Unmeasured time-invariant factors are included as subject-specific random effects in the assumed joint distribution of outcomes, time-varying confounders, and treatment assignments. We identify a sequential ignorability assumption conditional on treatment assignment heterogeneity, that is, analogous to balancing the latent treatment preference due to unmeasured time-invariant factors. We present a simulation study to assess the proposed method's performance. The method is applied to observational clinical data to investigate the efficacy of continuously using mycophenolate in different subgroups of scleroderma patients.

Bayesian modeling of the impact of antibiotic resistance on the efficiency of MRSA decolonization.

Methicillin-resistant Staphylococcus aureus (MRSA) is a major cause of morbidity and mortality. Colonization by MRSA increases the risk of infection and transmission, underscoring the importance of decolonization efforts. However, success of these decolonization protocols varies, raising the possibility that some MRSA strains may be more persistent than others. Here, we studied how the persistence of MRSA colonization correlates with genomic presence of antibiotic resistance genes. Our analysis using a Bayesian mixed effects survival model found that genetic determinants of high-level resistance to mupirocin was strongly associated with failure of the decolonization protocol. However, we did not see a similar effect with genetic resistance to chlorhexidine or other antibiotics. Including strain-specific random effects improved the predictive performance, indicating that some strain characteristics other than resistance also contributed to persistence. Study subject-specific random effects did not improve the model. Our results highlight the need to consider the properties of the colonizing MRSA strain when deciding which treatments to include in the decolonization protocol.

Bayesian joint models for multi-regional clinical trials.

In recent years, multi-regional clinical trials (MRCTs) have increased in popularity in the pharmaceutical industry due to their ability to accelerate the global drug development process. To address potential challenges with MRCTs, the International Council for Harmonisation released the E17 guidance document which suggests the use of statistical methods that utilize information borrowing across regions if regional sample sizes are small. We develop an approach that allows for information borrowing via Bayesian model averaging in the context of a joint analysis of survival and longitudinal data from MRCTs. In this novel application of joint models to MRCTs, we use Laplace's method to integrate over subject-specific random effects and to approximate posterior distributions for region-specific treatment effects on the time-to-event outcome. Through simulation studies, we demonstrate that the joint modeling approach can result in an increased rejection rate when testing the global treatment effect compared with methods that analyze survival data alone. We then apply the proposed approach to data from a cardiovascular outcomes MRCT.

Characterization of direct and/or indirect genetic associations for multiple traits in longitudinal studies of disease progression.

When quantitative longitudinal traits are risk factors for disease progression and subject to random biological variation, joint model analysis of time-to-event and longitudinal traits can effectively identify direct and/or indirect genetic association of single nucleotide polymorphisms (SNPs) with time-to-event. We present a joint model that integrates: (1) a multivariate linear mixed model describing trajectories of multiple longitudinal traits as a function of time, SNP effects, and subject-specific random effects and (2) a frailty Cox survival model that depends on SNPs, longitudinal trajectory effects, and subject-specific frailty accounting for dependence among multiple time-to-event traits. Motivated by complex genetic architecture of type 1 diabetes complications (T1DC) observed in the Diabetes Control and Complications Trial (DCCT), we implement a 2-stage approach to inference with bootstrap joint covariance estimation and develop a hypothesis testing procedure to classify direct and/or indirect SNP association with each time-to-event trait. By realistic simulation study, we show that joint modeling of 2 time-to-T1DC (retinopathy and nephropathy) and 2 longitudinal risk factors (HbA1c and systolic blood pressure) reduces estimation bias in genetic effects and improves classification accuracy of direct and/or indirect SNP associations, compared to methods that ignore within-subject risk factor variability and dependence among longitudinal and time-to-event traits. Through DCCT data analysis, we demonstrate feasibility for candidate SNP modeling and quantify effects of sample size and Winner's curse bias on classification for 2 SNPs identified as having indirect associations with time-to-T1DC traits. Joint analysis of multiple longitudinal and multiple time-to-event traits provides insight into complex traits architecture.

Gaps in Cystic Fibrosis Care Are Associated with Reduced Lung Function in the U.S. Cystic Fibrosis Foundation Patient Registry.

Rationale: Cystic fibrosis (CF) is a genetic disease leading to progressive lung function loss and early mortality. Many clinical and demographic variables are associated with lung function decline, but little is known about the effects of prolonged periods of missed care. Objectives: To determine if missed care in the Cystic Fibrosis Foundation Patient Registry (CFFPR) is associated with decreased lung function at follow-up visits. Methods: Deidentified CFFPR data for 2004-2016 were analyzed, with the exposure of interest being ⩾12-month gap in CFFPR data. We modeled percentage predicted forced expiratory volume in 1 second using longitudinal semiparametric modeling with natural cubic splines for age (knots at quantiles) and with subject-specific random effects, adjusted for sex and CFTR (cysticfibrosis transmembrane conductance regulator) genotype, race, and ethnicity and included time-varying covariates for gaps in care, insurance type, underweight body mass index, CF-related diabetes status, and chronic infections. Results: A total of 24,328 individuals with 1,082,899 encounters in the CFFPR met inclusion criteria. In the cohort, 8,413 (35%) individuals had at least a single ⩾12-month episode of discontinuity, whereas 15,915 (65%) had continuous care. Of the encounters preceded by a 12-month gap, 75.8% occurred in patients 18 years and older. Compared with those with continuous care, those with a discontinuous care episode had a lower follow-up percentage predicted forced expiratory volume in 1 second at the index visit (-0.81%; 95% confidence interval, -1.00, -0.61) after adjustment for other variables. The magnitude of this difference was much greater (-2.1%; 95% confidence interval, -1.5, -2.7) in young adult F508del homozygotes. Conclusions: There was a high rate of ⩾12-month gap in care, especially in adults, documented in the CFFPR. Discontinuous care identified in the CFFPR was strongly associated with decreased lung function, especially in adolescents and young adults homozygous for the F508del CFTR mutation. This may have implications for identifying and treating people with lengthy gaps in care and may have implications for CFF care recommendations.

PS-P04-10: IMPACT OF BLOOD PRESSURE VARIABILITY ON THE RISK OF STROKE AND PREMATURE DEATH

Objective: Visit-to-visit blood pressure variability (BPV) has been identified in several recent studies as a risk factor for stroke, independently of the level of BP. If true, this finding could help to identify patients at higher risk of stroke and to develop new preventive strategies. However, studies on BPV are exposed to important methodological challenges including conditioning on the future, which violates the assumption of the Cox model, using endogenous variables like the expected BP and its variance, and not handling properly the measurement error. Our objective was to address these issues by designing a joint model with heterogeneous variance for the repeated measures of BP, allowing us to analyze the association between BPV and the risk of stroke and the competing risk of death. Design and Method: We used data from PROGRESS (Perindopril Protection against Stroke Study), a placebo-controlled BP-lowering randomized trial for the prevention of stroke recurrence in 6105 patients with a previous history of stroke or TIA. During 5 years of follow-up, BP was measured 12 times, and 727 strokes and 438 non-stroke deaths were observed. We designed an innovative and dedicated joint model combining a linear mixed model, including a subject-specific random effect for the residual variance and two proportional hazard models for the two competing risks of stroke and death. In this model, the risk of each event may depend on the current value and current slope of the individual expected trajectory of BP as well as the intra-subject residual variance. Results: In separate analysis of each arm of the trial, we found that the risk of stroke increased with the current level of BP (HR = 1.13 per 5 mmHg, 95%CI = [1.08; 1.17], p-value < 0.001) but was not associated with its intra-individual variability (HR = 0.89, 95%CI = [0.71; 1.12], p-value = 0.317). Conversely, the risk of non-stroke death increased with the intra-individual variability of BP (HR = 1.43, 95%CI = [1.08; 1.88], p-value = 0.011) but not with its current level (HR = 1.03, 95%CI = [0.97; 1.09], p-value = 0.317). Results were similar on the complete sample adjusting for the randomized treatment. Conclusion: Using appropriate modeling accounting for measurement error and limiting selection and other potential biases, we found a differential effect of expected BP and BPV on the risk of stroke and of death. These results, if confirmed and enlarged to other populations, would have important consequences to design efficient and individualized preventive strategies.

Bayesian Multi-level Mixed-effects Model for Influenza Dynamics

Abstract Influenza A viruses (IAV) are the only influenza viruses known to cause flu pandemics. Understanding the evolution of different sub-types of IAV on their natural hosts is important for preventing and controlling the virus. We propose a mechanism-based Bayesian multi-level mixed-effects model for characterising influenza viral dynamics, described by a set of ordinary differential equations (ODE). Both strain-specific and subject-specific random effects are included for the ODE parameters. Our models can characterise the common features in the population while taking into account the variations among individuals. The random effects selection is conducted at strain level through re-parameterising the covariance parameters of the corresponding random effect distribution. Our method does not need to solve ODE directly. We demonstrate that the posterior computation can proceed via a simple and efficient Markov chain Monte Carlo algorithm. The methods are illustrated using simulated data and a real data from a study relating virus load estimates from influenza infections in ducks.

A Joint Model Considering Measurement Errors for Optimally Identifying Tumor Mutation Burden Threshold.

Tumor mutation burden (TMB) is a recognized stratification biomarker for immunotherapy. Nevertheless, the general TMB-high threshold is unstandardized due to severe clinical controversies, with the underlying cause being inconsistency between multiple assessment criteria and imprecision of the TMB value. The existing methods for determining TMB thresholds all consider only a single dimension of clinical benefit and ignore the interference of the TMB error. Our research aims to determine the TMB threshold optimally based on multifaceted clinical efficacies accounting for measurement errors. We report a multi-endpoint joint model as a generalized method for inferring the TMB thresholds, facilitating consistent statistical inference using an iterative numerical estimation procedure considering mis-specified covariates. The model optimizes the division by combining objective response rate and time-to-event outcomes, which may be interrelated due to some shared traits. We augment previous works by enabling subject-specific random effects to govern the communication among distinct endpoints. Our simulations show that the proposed model has advantages over the standard model in terms of precision and stability in parameter estimation and threshold determination. To validate the feasibility of the proposed thresholds, we pool a cohort of 73 patients with non-small-cell lung cancer and 64 patients with nasopharyngeal carcinoma who underwent anti-PD-(L)1 treatment, as well as validation cohorts of 943 patients. Analyses revealed that our approach could grant clinicians a holistic efficacy assessment, culminating in a robust determination of the TMB screening threshold for superior patients. Our methodology has the potential to yield innovative insights into therapeutic selection and support precision immuno-oncology.

Without Commitment to an Ontology, There Could Be No Causal Inference.

Without Commitment to an Ontology, There Could Be No Causal Inference.

Static home-based versus dynamic mobility-based assessments of exposure to urban green space

There is growing interest in urban green space exposure estimated dynamically by accounting for individuals’ mobility during daily life. We aimed to explore if daily green space exposure estimates based on individuals’ mobility substantially differ from static home-based exposure estimates, and to examine potential effect modification by personal (sex and work status) and temporal (weekends versus weekdays) characteristics. To assess the association between daily exposure to urban green space, we used home address and time-activity data collected from 1911 participants in western New York, US, using their GPS-enabled mobile phones. We abstracted both individuals’ home address based (home-based) and daily time activity based (mobility-based) green space exposures from the Normalized Difference Vegetation Index (NDVI). Then, we assessed the association between mobility-based and home-based exposure estimates using linear mixed effect regression models with subject-specific random effects. We also explored whether this effect was modified by individual-level characteristics, including work status and sex, as well as whether assessments took place on weekdays versus weekends. We found that daily dynamic exposure to urban green space based on individuals’ mobility was not substantially different from static exposure estimates based on one’s residence, but that there were statistically significant effect modifiers. Specifically, the correspondence between mobility-based and home-based exposure to green space was relatively lower for employed compared to unemployed participants, whereas their correspondence during weekends increased compared to weekdays. Our findings suggest that there is a strong correspondence between mobility-based and home-based exposure to urban green space, but that their associations are modified by personal and temporal characteristics. Further research is needed to confirm our finding for general population in other settings, such as different seasons and other regions.

Comparison of statistical methods for the analysis of recurrent adverse events in the presence of non-proportional hazards and unobserved heterogeneity: a simulation study

BackgroundIn preventive drug trials such as intermittent preventive treatment for malaria prevention during pregnancy (IPTp), where there is repeated treatment administration, recurrence of adverse events (AEs) is expected. Challenges in modelling the risk of the AEs include accounting for time-to-AE and within-patient-correlation, beyond the conventional methods. The correlation comes from two sources; (a) individual patient unobserved heterogeneity (i.e. frailty) and (b) the dependence between AEs characterised by time-dependent treatment effects. Potential AE-dependence can be modelled via time-dependent treatment effects, event-specific baseline and event-specific random effect, while heterogeneity can be modelled via subject-specific random effect. Methods that can improve the estimation of both the unobserved heterogeneity and treatment effects can be useful in understanding the evolution of risk of AEs, especially in preventive trials where time-dependent treatment effect is expected.MethodsUsing both a simulation study and the Chloroquine for Malaria in Pregnancy (NCT01443130) trial data to demonstrate the application of the models, we investigated whether the lognormal shared frailty models with restricted cubic splines and non-proportional hazards (LSF-NPH) assumption can improve estimates for both frailty variance and treatment effect compared to the conventional inverse Gaussian shared frailty model with proportional hazard (ISF-PH), in the presence of time-dependent treatment effects and unobserved patient heterogeneity. We assessed the bias, precision gain and coverage probability of 95% confidence interval of the frailty variance estimates for the models under varying known unobserved heterogeneity, sample sizes and time-dependent effects.ResultsThe ISF-PH model provided a better coverage probability of 95% confidence interval, less bias and less precise frailty variance estimates compared to the LSF-NPH models. The LSF-NPH models yielded unbiased hazard ratio estimates at the expense of imprecision and high mean square error compared to the ISF-PH model.ConclusionThe choice of the shared frailty model for the recurrent AEs analysis should be driven by the study objective. Using the LSF-NPH models is appropriate if unbiased hazard ratio estimation is of primary interest in the presence of time-dependent treatment effects. However, ISF-PH model is appropriate if unbiased frailty variance estimation is of primary interest.Trial registrationClinicalTrials.gov; NCT01443130

Craniofacial growth and SITAR growth curve analysis.

SITAR (SuperImposition by Translation And Rotation) is a shape invariant growth curve model that effectively summarizes somatic growth in puberty. To apply the SITAR model to longitudinal mandibular growth data to clarify its suitability to facial growth analysis. 2D-cephalometric data on two mandibular measurements (AP: articulare-pogonion; CP: condylion-pogonion) were selected from the Denver Growth Study, consisting of longitudinal records (age range: 7.9-19.0 years) of females (sample size N: 21; number of radiographs n: 154) and males (N: 18; n: 137). The SITAR mixed effects model estimated, for each measurement and gender separately, a mean growth curve versus chronological age, along with mean age at peak velocity (APV) and peak velocity (PV), plus subject-specific random effects for PV and mean size. The models were also fitted versus Greulich-Pyle bone age. In males, mean APV occurred at 14.6 years (AP) and 14.4 years (CP), with mean PV 3.1 mm/year (AP) and 3.3 mm/year (CP). In females, APV occurred at 11.6 years (AP and CP), with mean PV 2.3 mm/year (AP) and 2.4 mm/year (CP). The models explained 95-96 per cent of the cross-sectional variance for males and 92-93 per cent for females. The random effects demonstrated standard deviations (SDs) in size of 5.6 mm for males and 3.9 mm for females, and SDs for PV between 0.3 and 0.5 mm/year. The bone age results were similar. The SITAR model is a useful tool to analyse epidemiological craniofacial growth based on cephalometric data and provides an array of information on pubertal mandibular growth and its variance in a concise manner.

A Small Area Estimation Method for Investigating the Relationship between Public Perception of Drug Problems with Neighborhood Prognostics: Trends in London between 2012 and 2019.

The correlation of the public’s perception of drug problems with neighborhood characteristics has rarely been studied. The aim of this study was to investigate factors that correlate with public perceptions in London boroughs using the Mayor’s Office for Policing and Crime (MOPAC) Public Attitude Survey between 2012 and 2019. A subject-specific random effect deploying a Generalized Linear Mixed Model (GLMM) using an Adaptive Gaussian Quadrature method with 10 integration points was applied. To obtain time trends across inner and outer London areas, the GLMM was fitted using a Restricted Marginal Pseudo Likelihood method. The perception of drug problems increased with statistical significance in 17 out of 32 London boroughs between 2012 and 2019. These boroughs were geographically clustered across the north of London. Levels of deprivation, as measured by the English Index of Multiple Deprivation, as well as the percentage of local population who were non-UK-born and recorded vehicle crime rates were shown to be positively associated with the public’s perception of drug problems. Conversely, recorded burglary rate was negatively associated with the public’s perception of drug problems in their area. The public are influenced in their perception of drug problems by neighborhood factors including deprivation and visible manifestations of antisocial behavior.

Measuring the Attenuation in a Subject-specific Random Effect with Paired Data

This paper is motivated by an investigation into the growth of pigs, which studied among other things the effect of short–term feed with drawal on live weight. This treatment was thought to reduce the variability in the weights of the pigs. We represent this reduction as an attenuation in an animal–specific random effect. Given data on each pig before and after treatment, we consider the problems of testing for a treatment effect and measuring the strength of the effect, if significant. These problems are related to those of testing the homogeneity of correlated variances, and re gression with errors in variables. We compare three different estimates of the attenuation factor using data on the live weights of pigs, and by simulation.

Joint modelling of longitudinal response and time-to-event data using conditional distributions: a Bayesian perspective

Over the last 20 or more years a lot of clinical applications and methodological development in the area of joint models of longitudinal and time-to-event outcomes have come up. In these studies, patients are followed until an event, such as death, occurs. In most of the work, using subject-specific random-effects as frailty, the dependency of these two processes has been established. In this article, we propose a new joint model that consists of a linear mixed-effects model for longitudinal data and an accelerated failure time model for the time-to-event data. These two sub-models are linked via a latent random process. This model will capture the dependency of the time-to-event on the longitudinal measurements more directly. Using standard priors, a Bayesian method has been developed for estimation. All computations are implemented using OpenBUGS. Our proposed method is evaluated by a simulation study, which compares the conditional model with a joint model with local independence by way of calibration. Data on Duchenne muscular dystrophy (DMD) syndrome and a set of data in AIDS patients have been analysed.

Nonparametric Bayesian functional two-part random effects model for longitudinal semicontinuous data analysis.

Longitudinal semicontinuous data, characterized by repeated measures of a large portion of zeros and continuous positive values, are frequently encountered in many applications including biomedical, epidemiological, and social science studies. Two-part random effects models (TPREM) have been used to investigate the association between such longitudinal semicontinuous data and covariates accounting for the within-subject correlation. The existing TPREM is, however, limited to incorporate a functional covariate, which is often available in a longitudinal study. Moreover, the existing TPREM typically assumes the normality of subject-specific random effects, which can be easily violated when there exists a subgroup structure. In this article, we propose a nonparametric Bayesian functional TPREM to assess the relationship between the longitudinal semicontinuous outcome and various types of covariates including a functional covariate. The proposed model also relaxes the normality assumption for the random effects through a Dirichlet process mixture of normals, which allows for identifying an underlying subgroup structure. The methodology is illustrated through an application to social insurance expenditure data collected by the Korean Welfare Panel Study and a simulation study.

Modeling form factors for sal (Shorea robusta Gaertn.) using tree and stand measures, and random effects

Form factor (FF) is widely used for the correct estimation of tree volume. Few FF models have been developed and applied to the volume estimation, however, they have failed to account for the influence of important tree and stand characteristics on the FF variations. We aimed to incorporate the effects of these characteristics into the FF models for sal (Shorea robusta Gaertn.) trees in Nepal. A comprehensive data set representative to wide variations of tree size, crown architecture, stem form, stand density, site productivity, and environmental condition was used for the purpose. We evaluated various tree and stand measures characterized by the meaningful biological explanation as predictors in the FF models. The unstructured random component accounting for the subject-specific (diameter class-specific) random effects was included into the FF model through the application of the mixed-effects modeling. Among several predictor variables evaluated, tree height (HEIGHT), crown index (ratio of crown depth to crown diameter, CI), relative diameter (ratio of the subject tree DBH to quadratic mean DBH, Dq), and basal area proportion of the species of interest (BAPRO) significantly contributed to the FF variations. The FF models described the substantial proportion of the FF variations. There was an increased FF with increasing HEIGHT and BAPRO, but decreased FF with increasing Dq and CI. The FF was influenced significantly differently by different covariate predictors with the biggest influence of Dq followed by CI, HEIGHT, and BAPRO. Calibration of the mixed-effects FF models with the random effects estimated from the complimentary FF of four sample trees per DBH class could provide the highest prediction accuracy. Inclusion of tree- and stand-level measures, and subject-specific random effects into the FF models could significantly increase the FF prediction accuracy and increase the biological robustness of the models.

Mixed location scale hidden Markov model for the analysis of intensive longitudinal data

Hidden Markov models (HMM) presents an attractive analytical framework for capturing the state-switching process for auto-correlated data. These models have been extended to longitudinal data setting where simultaneous multiple processes are observed by including subject specific random effects. However, application of HMMs for intensive longitudinal data, where each subject gets measured intensively over relatively short period of time, has not been widely studied. In this paper, we extend the mixed hidden Markov model and allow subject heterogeneity with respect to the mean and within subject variance by including subject random effects in both perspectives. We focus on the application of this model to intensive longitudinal studies in psychological and behavioral research where individual’s latent states and state-switching process are of interest. Models are estimated using forward–backward algorithm via Bayesian sampling approach. Advantages over regular HMM and mixed HMM that only accounts for the subjects’ mean heterogeneity are illustrated through a series of simulation studies. Finally, models are applied to an adolescent mood study data set and results show that the proposed mixed location scale HMM achieves better model fit and more interpretative mood state identification in terms of state specific covariate effects compared to regular HMM and mixed HMM.

New Approaches for Variable Selection in Longitudinal Studies: An Application to Genetic Association Studies and Bone Loss

We study the problem of variable selection in the context of longitudinal studies by linear mixed effect models when the dimensionality of predictors subject to selection is high. We consider a fully Bayesian formulation of the problem with spike-and-slab a prior distributions which is an appealing solution, however, we find it computationally demanding. As an alternative, we propose a general penalized log-likelihood framework based on marginalized observation equation and a heterogeneous error term. The parameters of the model are estimated by a block wise coordinate gradient descent algorithm. Given the formulation of the considered linear mixed effect models as random slope and intercept models, we consider yet another variable selection procedure which is more ad hoc but has an advantage of computational speed. The procedure consists of two steps and is based on assessing the significance of co-variates from biased predictors of subject-specific random effects. We study the impact of this mis-specification on the accuracy of variable selection. We demonstrate the applicability of the proposed frameworks by studying the association between single nucleotide polymorphisms and bone loss that contributes to the development of osteopenia and osteoporosis in post-menopausal women and aged men and is a strong risk factor for bones fractures and its related mortality. The data is obtained from the longitudinal Dubbo Osteoporosis Epidemiology Study.

Growth Trajectories in Genetic Subtypes of Prader-Willi Syndrome.

Prader–Willi syndrome (PWS) is a rare disorder caused by the loss of expression of genes on the paternal copy of chromosome 15q11-13. The main molecular subtypes of PWS are the deletion of 15q11-13 and non-deletion, and differences in neurobehavioral phenotype are recognized between the subtypes. This study aimed to investigate growth trajectories in PWS and associations between PWS subtype (deletion vs. non-deletion) and height, weight and body mass index (BMI). Growth data were available for 125 individuals with PWS (63 males, 62 females), of which 72 (57.6%) had the deletion subtype. There was a median of 28 observations per individual (range 2–85), producing 3565 data points distributed from birth to 18 years of age. Linear mixed models with cubic splines, subject-specific random effects and an autoregressive correlation structure were used to model the longitudinal growth data whilst accounting for the nature of repeated measures. Height was similar for males in both PWS subtypes, with non-deletion females being shorter than deletion females for older ages. Weight and BMI were estimated to be higher in the deletion subtype compared to the non-deletion subtype, with the size of difference increasing with advancing age for weight. These results suggest that individuals with deletion PWS are more prone to obesity.