A joint normal-ordinal (probit) model for ordinal and continuous longitudinal data.

In biomedical studies, continuous and ordinal longitudinal variables are frequently encountered. In many of these studies it is of interest to estimate the effect of one of these longitudinal variables on the other. Time-dependent covariates have, however, several limitations; they can, for example, not be included when the data is not collected at fixed intervals. The issues can be circumvented by implementing joint models, where two or more longitudinal variables are treated as a response and modeled with a correlated random effect. Next, by conditioning on these response(s), we can study the effect of one or more longitudinal variables on another. We propose a normal-ordinal(probit) joint model. First, we derive closed-form formulas to estimate the model-based correlations between the responses on their original scale. In addition, we derive the marginal model, where the interpretation is no longer conditional on the random effects. As a consequence, we can make predictions for a subvector of one response conditional on the other response and potentially a subvector of the history of the response. Next, we extend the approach to a high-dimensional case with more than two ordinal and/or continuous longitudinal variables. The methodology is applied to a case study where, among others, a longitudinal ordinal response is predicted with a longitudinal continuous variable.

An observational cohort study examined the change point of kidney function stabilization in the initial period after transplantation.

Baseline kidney function following kidney transplantation is often used in research and clinical decision-making yet is not well defined. Here, a method to determine baseline function was proposed and validated on three single-center retrospective cohorts consisting of 922 patients from Belgium (main cohort) and two validation cohorts of 987 patients from the Netherlands and 519 patients from Germany. For each transplant, a segmented regression model was fitted on the estimated glomerular filtration rate (eGFR) evolution during the first-year post-transplantation. This yielded estimates for change point timing, rate of eGFR change before and after change point and eGFR value at change point, now considered the "baseline function". Associations of eGFR evolution with recipient/donor characteristics and the graft failure rate were assessed with linear regression and Cox regression respectively. The change point occurred on average at an eGFR value of 43.7±14.6 mL/min/1.73m2, at a median time of 6.5 days post-transplantation. Despite significant associations with several baseline donor-recipient characteristics (particularly, donor type; living vs deceased), the predictive value of these characteristics for eGFR value and timing of the change point was limited. This followed from a large heterogeneity within eGFR trajectories, which in turn indicated that favorable levels of kidney function could be reached despite a suboptimal initial evolution. Segmented regression consistently provided a good fit to early eGFR evolution, and its estimate of the change point can be a useful reference value in future analyses. Thus, our study shows that baseline kidney function after transplantation is heterogeneous and partly related to pretransplant donor characteristics.

A competing risks model to estimate the risk of graft failure and patient death after kidney transplantation using continuous donor-recipient age combinations.

Graft failure and recipient death with functioning graft are important competing outcomes after kidney transplantation. Risk prediction models typically censor for the competing outcome thereby overestimating the cumulative incidence. The magnitude of this overestimation is not well described in real-world transplant data. This retrospective cohort study analyzed data from the European Collaborative Transplant Study (n = 125 250) and from the American Scientific Registry of Transplant Recipients (n = 190 258). Separate cause-specific hazard models using donor and recipient age as continuous predictors were developed for graft failure and recipient death. The hazard of graft failure increased quadratically with increasing donor age and decreased decaying with increasing recipient age. The hazard of recipient death increased linearly with increasing donor and recipient age. The cumulative incidence overestimation due to competing risk-censoring was largest in high-risk populations for both outcomes (old donors/recipients), sometimes amounting to 8.4 and 18.8 percentage points for graft failure and recipient death, respectively. In our illustrative model for posttransplant risk prediction, the absolute risk of graft failure and death is overestimated when censoring for the competing event, mainly in older donors and recipients. Prediction models for absolute risks should treat graft failure and death as competing events.

Incidence, prevalence, and co-occurrence of autoimmune disorders over time and by age, sex, and socioeconomic status: a population-based cohort study of 22 million individuals in the UK.

BACKGROUND: A rise in the incidence of some autoimmune disorders has been described. However, contemporary estimates of the overall incidence of autoimmune diseases and trends over time are scarce and inconsistent. We aimed to investigate the incidence and prevalence of 19 of the most common autoimmune diseases in the UK, assess trends over time, and by sex, age, socioeconomic status, season, and region, and we examine rates of co-occurrence among autoimmune diseases. METHODS: In this UK population-based study, we used linked primary and secondary electronic health records from the Clinical Practice Research Datalink (CPRD), a cohort that is representative of the UK population in terms of age and sex and ethnicity. Eligible participants were men and women (no age restriction) with acceptable records, approved for Hospital Episodes Statistics and Office of National Statistics linkage, and registered with their general practice for at least 12 months during the study period. We calculated age and sex standardised incidence and prevalence of 19 autoimmune disorders from 2000 to 2019 and used negative binomial regression models to investigate temporal trends and variation by age, sex, socioeconomic status, season of onset, and geographical region in England. To characterise co-occurrence of autoimmune diseases, we calculated incidence rate ratios (IRRs), comparing incidence rates of comorbid autoimmune disease among individuals with a first (index) autoimmune disease with incidence rates in the general population, using negative binomial regression models, adjusted for age and sex. FINDINGS: Among the 22 009 375 individuals included in the study, 978 872 had a new diagnosis of at least one autoimmune disease between Jan 1, 2000, and June 30, 2019 (mean age 54·0 years [SD 21·4]). 625 879 (63·9%) of these diagnosed individuals were female and 352 993 (36·1%) were male. Over the study period, age and sex standardised incidence rates of any autoimmune diseases increased (IRR 2017-19 vs 2000-02 1·04 [95% CI 1·00-1·09]). The largest increases were seen in coeliac disease (2·19 [2·05-2·35]), Sjogren's syndrome (2·09 [1·84-2·37]), and Graves' disease (2·07 [1·92-2·22]); pernicious anaemia (0·79 [0·72-0·86]) and Hashimoto's thyroiditis (0·81 [0·75-0·86]) significantly decreased in incidence. Together, the 19 autoimmune disorders examined affected 10·2% of the population over the study period (1 912 200 [13·1%] women and 668 264 [7·4%] men). A socioeconomic gradient was evident across several diseases, including pernicious anaemia (most vs least deprived area IRR 1·72 [1·64-1·81]), rheumatoid arthritis (1·52 [1·45-1·59]), Graves' disease (1·36 [1·30-1·43]), and systemic lupus erythematosus (1·35 [1·25-1·46]). Seasonal variations were observed for childhood-onset type 1 diabetes (more commonly diagnosed in winter) and vitiligo (more commonly diagnosed in summer), and regional variations were observed for a range of conditions. Autoimmune disorders were commonly associated with each other, particularly Sjögren's syndrome, systemic lupus erythematosus, and systemic sclerosis. Individuals with childhood-onset type 1 diabetes also had significantly higher rates of Addison's disease (IRR 26·5 [95% CI 17·3-40·7]), coeliac disease (28·4 [25·2-32·0]), and thyroid disease (Hashimoto's thyroiditis 13·3 [11·8-14·9] and Graves' disease 6·7 [5·1-8·5]), and multiple sclerosis had a particularly low rate of co-occurrence with other autoimmune diseases. INTERPRETATION: Autoimmune diseases affect approximately one in ten individuals, and their burden continues to increase over time at varying rates across individual diseases. The socioeconomic, seasonal, and regional disparities observed among several autoimmune disorders in our study suggest environmental factors in disease pathogenesis. The inter-relations between autoimmune diseases are commensurate with shared pathogenetic mechanisms or predisposing factors, particularly among connective tissue diseases and among endocrine diseases. FUNDING: Research Foundation Flanders.

An information-theoretic approach for the assessment of a continuous outcome as a surrogate for a binary true endpoint based on causal inference: Application to vaccine evaluation.

Within the causal association paradigm, a method is proposed to assess the validity of a continuous outcome as a surrogate for a binary true endpoint. The methodology is based on a previously introduced information-theoretic definition of surrogacy and has two main steps. In the first step, a new model is proposed to describe the joint distribution of the potential outcomes associated with the putative surrogate and the true endpoint of interest. The identifiability issues inherent to this type of models are handled via sensitivity analysis. In the second step, a metric of surrogacy new to this setting, the so-called individual causal association is presented. The methodology is studied in detail using theoretical considerations, some simulations, and data from a randomized clinical trial evaluating an inactivated quadrivalent influenza vaccine. A user-friendly R package Surrogate is provided to carry out the evaluation exercise.

Assessing the Operational Characteristics of the Individual Causal Association as a Metric of Surrogacy in the Binary Continuous Setting.

In a causal inference framework, a new metric has been proposed to quantify surrogacy for a continuous putative surrogate and a binary true endpoint, based on information theory. The proposed metric, termed the individual causal association (ICA), was quantified using a joint causal inference model for the corresponding potential outcomes. Due to the non-identifiability inherent in this type of models, a sensitivity analysis was introduced to study the behavior of the ICA as a function of the non-identifiable parameters characterizing the aforementioned model. In this scenario, to reduce uncertainty, several plausible yet untestable assumptions like monotonicity, independence, conditional independence or homogeneous variance-covariance, are often incorporated into the analysis. We assess the robustness of the methodology regarding these simplifying assumptions via simulation. The practical implications of the findings are demonstrated in the analysis of a randomized clinical trial evaluating an inactivated quadrivalent influenza vaccine.

Evaluation of a flexible piecewise linear mixed-effects model in the analysis of randomized cross-over trials.

Cross-over designs are commonly used in randomized clinical trials to estimate efficacy of a new treatment. They have received a lot of attention, particularly in connection with regulatory requirements for new drugs. The main advantage of using cross-over designs over conventional parallel designs is increased precision, thanks to within-subject comparisons. In the statistical literature, more recent developments are discussed in the analysis of cross-over trials, in particular regarding repeated measures. A piecewise linear model within the framework of mixed effects has been proposed in the analysis of cross-over trials. In this article, we report on a simulation study comparing performance of a piecewise linear mixed-effects (PLME) model against two commonly cited models-Grizzle's mixed-effects (GME) and Jones & Kenward's mixed-effects (JKME) models-used in the analysis of cross-over trials. Our simulation study tried to mirror real-life situation by deriving true underlying parameters from empirical data. The findings from real-life data confirmed the original hypothesis that high-dose iodine salt have significantly lowering effect on diastolic blood pressure (DBP). We further sought to evaluate the performance of PLME model against GME and JKME models, within univariate modeling framework through a simulation study mimicking a 2 × 2 cross-over design. The fixed-effects, random-effects and residual error parameters used in the simulation process were estimated from DBP data, using a PLME model. The initial results with full specification of random intercept and slope(s), showed that the univariate PLME model performed better than the GME and JKME models in estimation of variance-covariance matrix (G) governing the random effects, allowing satisfactory model convergence during estimation. When a hierarchical view-point is adopted, in the sense that outcomes are specified conditionally upon random effects, the variance-covariance matrix of the random effects must be positive-definite. The PLME model is preferred especially in modeling an increased number of random effects, compared to the GME and JKME models that work equally well with random intercepts only. In some cases, additional random effects could explain much variability in the data, thus improving precision in estimation of the estimands (effect size) parameters.

Pairwise fitting of piecewise mixed models for the joint modeling of multivariate longitudinal outcomes, in a randomized crossover trial.

Many statistical models have been proposed in the literature for the analysis of longitudinal data. One may propose to model two or more correlated longitudinal processes simultaneously, with a goal of understanding their association over time. Joint modeling is then required to carefully study the association structure among the outcomes as well as drawing joint inferences about the different outcomes. In this study, we sought to model the associations among six nutrition outcomes while circumventing the computational challenge posed by their clustered and high-dimensional nature. We analyzed data from a 2 × $\times$ 2 randomized crossover trial conducted in Kenya, to compare the effect of high-dose and low-dose iodine in household salt on systolic blood pressure (SBP) and diastolic blood pressure (DBP) in women of reproductive age and their household matching pair of school-aged children. Two additional outcomes, namely, urinary iodine concentration (UIC) in women and children were measured repeatedly to monitor the amount of iodine excreted through urine. We extended the model proposed by Mwangi et al. (2021, Communications in Statistics: Case Studies, Data Analysis and Applications, 7(3), 413-431) allowing flexible piecewise joint models for six outcomes to depend on separate random effects, which are themselves correlated. This entailed fitting 15 bivariate general linear mixed models and deriving inference for the joint model using pseudo-likelihood theory. We analyzed the outcomes separately and jointly using piecewise linear mixed-effects (PLME) model and further validated the results using current state-of-the-art Jones and Kenward methodology (JKME model) used for analyzing randomized crossover trials. The results indicate that high-dose iodine in salt significantly reduced blood pressure (BP) compared to low-dose iodine in salt. Estimates for the random effects and residual error components showed that SBP and DBP had strong positive correlation, with effect of the random slope indicating that significantly related outcomes are strongly associated in their evolution. There was a moderately strong inverse relationship between evolutions of UIC and BP both in women and children. These findings confirmed the original hypothesis that high-dose iodine salt has significant lowering effect on BP. We further sought to evaluate the performance of our proposed PLME model against the widely used JKME model, within the multivariate joint modeling framework through a simulation study mimicking a 2 × 2 $2\times 2$ crossover design. From our findings, the multivariate joint PLME model performed exceptionally well both in estimation of random-effects matrix (G) and Hessian matrix (H), allowing satisfactory model convergence during estimation. It allowed a more complex fit to the data with both random intercepts and slopes effects compared to the multivariate joint JKME model that allowed for random intercepts only. When a hierarchical viewpoint is adopted, in the sense that outcomes are specified conditionally upon random effects, the variance-covariance matrix of the random effects must be positive definite. In some cases, additional random effects could explain much variability in the data, thus improving precision in estimation of the estimands (effect size) parameters. The key highlight in this evaluation shows that multivariate joint JKME model is a powerful tool especially while fitting mixed models with random intercepts only, in crossover design settings. Addition of random slopes may lead to model complexities in most cases, resulting in unsatisfactory model convergence during estimation. To circumvent convergence pitfalls, extention of JKME model to PLME model allows a more flexible fit to the data (generated from crossover design settings), especially in the multivariate joint modeling framework.

An observational cohort study of histological screening for BK polyomavirus nephropathy following viral replication in plasma.

Systematic screening for BKPyV-DNAemia has been advocated to aid prevention and treatment of polyomavirus associated nephropathy (PyVAN), an important cause of kidney graft failure. The added value of performing a biopsy at time of BKPyV-DNAemia, to distinguish presumptive PyVAN (negative SV40 immunohistochemistry) and proven PyVAN (positive SV40) has not been established. Therefore, we studied an unselected cohort of 950 transplantations, performed between 2008-2017. BKPyV-DNAemia was detected in 250 (26.3%) transplant recipients, and positive SV40 in 91 cases (9.6%). Among 209 patients with a concurrent biopsy at time of first BKPyV-DNAemia, 60 (28.7%) biopsies were SV40 positive. Plasma viral load showed high diagnostic value for concurrent SV40 positivity (ROC-AUC 0.950, 95% confidence interval 0.916-0.978) and the semiquantitatively scored percentage of tubules with evidence of polyomavirus replication (pvl score) (0.979, 0.968-0.988). SV40 positivity was highly unlikely when plasma viral load is below 4 log10 copies/ml (negative predictive value 0.989, 0.979-0.994). In SV40 positive patients, higher plasma BKPyV-DNA load and higher pvl scores were associated with slower viral clearance from the blood (hazard ratio 0.712, 95% confidence interval 0.604-0.839, and 0.327, 0.161-0.668, respectively), whereas the dichotomy positivity/negativity of SV40 immunohistochemistry did not predict viral clearance. Although the pvl score offers some prognostic value for viral clearance on top of plasma viral load, the latter provided good guidance for when a biopsy was unnecessary to exclude PyVAN. Thus, the distinction between presumptive and proven PyVAN, based on SV40 immunohistochemistry, has limited clinical value. Hence, management of BKPyV-DNAemia and immunosuppression reduction should be weighed against the risk of occurrence of rejection, or exacerbation of rejection observed concomitantly.

Autoimmune diseases and cardiovascular risk: a population-based study on 19 autoimmune diseases and 12 cardiovascular diseases in 22 million individuals in the UK.

BACKGROUND: Some autoimmune diseases are associated with an increased risk of cardiovascular disease. We aimed to determine whether or not this is true, and to what extent, for a broad range of autoimmune conditions. METHODS: In this population-based study, we used linked primary and secondary care records from the Clinical Practice Research Datalink (CPRD), GOLD and Aurum datasets, to assemble a cohort of individuals across the UK who were newly diagnosed with any of 19 autoimmune diseases between Jan 1, 2000, and Dec 31, 2017, younger than 80 years at diagnosis, and free of cardiovascular diseases up to 12 months after diagnosis. We also assembled a matched cohort with up to five individuals matched on age, sex, socioeconomic status, region, and calendar year, who were free of autoimmune disease and free of cardiovascular diseases up to 12 months after study entry. Both cohorts were followed up until June 30, 2019. We investigated the incidence of 12 cardiovascular outcomes and used Cox proportional hazards models to examine differences in patients with and without autoimmune diseases. FINDINGS: Of 22 009 375 individuals identified from the CPRD databases, we identified 446 449 eligible individuals with autoimmune diseases and 2 102 830 matched controls. In the autoimmune cohort, mean age at diagnosis was 46·2 years (SD 19·8), and 271 410 (60·8%) were women and 175 039 (39·2%) were men. 68 413 (15·3%) people with and 231 410 (11·0%) without autoimmune diseases developed incident cardiovascular disease during a median of 6·2 years (IQR 2·7-10·8) of follow-up. The incidence rate of cardiovascular disease was 23·3 events per 1000 patient-years among patients with autoimmune disease and 15·0 events per 1000 patient-years among those without an autoimmune disease (hazard ratio [HR] 1·56 [95% CI 1·52-1·59]). An increased risk of cardiovascular disease with autoimmune disease was seen for every individual cardiovascular disease and increased progressively with the number of autoimmune diseases present (one disease: HR 1·41 [95% CI 1·37-1·45]; two diseases: 2·63 [2·49-2·78]); three or more diseases: 3·79 [3·36-4·27]), and in younger age groups (age <45 years: 2·33 [2·16-2·51]; 55-64 years: 1·76 [1·67-1·85]; ≥75 years: 1·30 [1·24-1·36]). Among autoimmune diseases, systemic sclerosis (3·59 [2·81-4·59]), Addison's disease (2·83 [1·96-4·09]), systemic lupus erythematosus (2·82 [2·38-3·33]), and type 1 diabetes (2·36 [2·21-2·52]) had the highest overall cardiovascular risk. INTERPRETATION: These findings warrant targeted cardiovascular prevention measures, in particular in younger patients with autoimmune diseases, and further research into pathophysiological mechanisms underlying these complications. FUNDING: Horizon 2020 Marie Sklodowska-Curie Actions and European Society of Cardiology.

A linear mixed model to estimate COVID-19-induced excess mortality.

The Corona Virus Disease (COVID-19) pandemic has increased mortality in countries worldwide. To evaluate the impact of the pandemic on mortality, the use of excess mortality rather than reported COVID-19 deaths has been suggested. Excess mortality, however, requires estimation of mortality under nonpandemic conditions. Although many methods exist to forecast mortality, they are either complex to apply, require many sources of information, ignore serial correlation, and/or are influenced by historical excess mortality. We propose a linear mixed model that is easy to apply, requires only historical mortality data, allows for serial correlation, and down-weighs the influence of historical excess mortality. Appropriateness of the linear mixed model is evaluated with fit statistics and forecasting accuracy measures for Belgium and the Netherlands. Unlike the commonly used 5-year weekly average, the linear mixed model is forecasting the year-specific mortality, and as a result improves the estimation of excess mortality for Belgium and the Netherlands.

A longitudinal transition imputation model for categorical data applied to a large registry dataset.

Imputation of longitudinal categorical covariates with several waves and many predictors is cumbersome in terms of implausible transitions, colinearity, and overfitting. We designed a simulation study with data obtained from a general practitioners' morbidity registry in Belgium for three waves, with smoking as the longitudinal covariate of interest. We set varying proportions of data on smoking to missing completely at random and missing not at random with proportions of missingness equal to 10%, 30%, 50%, and 70%. This study proposed a 3-stage approach that allows flexibility when imputing time-dependent categorical covariates. First, multiple imputation using fully conditional specification or multiple imputation for the predictor variables was deployed using the wide format such that previous and future information of the same patient was utilized. Second, a joint Markov transition model for initial, forward, backward, and intermittent probabilities was developed for each imputed dataset. Finally, this transition model was used for imputation. We compared the performance of this methodology with an analyses of the complete data and with listwise deletion in terms of bias and root mean square error. Next, we applied this methodology in a clinical case for years 2017 to 2021, where we estimated the effect of several covariates on the pneumococcal vaccination. This methodological framework ensures that the plausibility of transitions is preserved, overfitting and colinearity issues are resolved, and confounders can be utilized. Finally, a companion R package was developed to enable the replication and easy application of this methodology.

A longitudinal perspective on perceived vulnerability to disease during the COVID-19 pandemic in Belgium.

During the coronavirus disease 2019 pandemic, individuals relied heavily on media sources to stay informed about the disease and public health measures. However, differences exist in the type and frequency of news media consumption, which can be linked to their perceived vulnerability to disease. In this longitudinal study, 1000 Flemish (Belgium) individuals were followed from March 2020 until September 2020, focussing on the evolution in perceived vulnerability to disease (i.e. perceived infectability and germ aversion). Media consumption significantly impacts perceived germ aversion; heavy consumers of commercial media reported greater germ aversion than light consumers of these media. The evolution of germ aversion among individuals from March to August depends on their gender, living environment, age and possibility to work from home. Furthermore, the evolution of perceived infectability depends on the age and living environment of the respondent. These findings may interest policy makers and media professionals to anticipate how anxieties regarding contracting an infectious disease evolve over time and how individual characteristics affect this evolution.

Reflections on the concept of optimality of single decision point treatment regimes.

In many areas, applied researchers as well as practitioners have to choose between different solutions for a problem at hand; this calls for optimal decision rules to settle the choices involved. As a key example, one may think of the search for optimal treatment regimes (OTRs) in clinical research, that specify which treatment alternative should be administered to each patient under study. Motivated by the fact that the concept of optimality of decision rules in general and treatment regimes in particular has received so far relatively little attention and discussion, we will present a number of reflections on it, starting from the basics of any optimization problem. Specifically, we will analyze the search space and the to be optimized criterion function underlying the search of single decision point OTRs, along with the many choice aspects that show up in their specification. Special attention is paid to formal characteristics and properties as well as to substantive concerns and hypotheses that may guide these choices. We illustrate with a few empirical examples taken from the literature. Finally, we discuss how the presented reflections may help sharpen statistical thinking about optimality of decision rules for treatment assignment and to facilitate the dialogue between the statistical consultant and the applied researcher in search of an OTR.

Modeling local dependence in latent vector autoregressive models.

We propose a Bayesian latent vector autoregressive (LVAR) model to analyze multivariate longitudinal data of binary and ordinal variables (items) as a function of a small number of continuous latent variables. We focus on the evolution of the latent variables while taking into account the correlation structure of the responses. Often local independence is assumed in this context. Local independence implies that, given the latent variables, the responses are assumed mutually independent cross-sectionally and longitudinally. However, in practice conditioning on the latent variables may not remove the dependence of the responses. We address local dependence by further conditioning on item-specific random effects. A simulation study shows that wrongly assuming local independence may give biased estimates for the regression coefficients of the LVAR process as well as the item-specific parameters. Novel features of our proposal include (i) correcting biased estimates of the model parameters, especially the regression coefficients of the LVAR process, obtained when local dependence is ignored and (ii) measuring the magnitude of local dependence. We applied our model on data obtained from a registry on the elderly population in Belgium. The purpose was to examine the values of oral health information on top of general health information.

Implementing the meta-analytic approach for the evaluation of surrogate endpoints in SAS and R: a word of caution.

The meta-analytic approach has become the gold-standard methodology for the evaluation of surrogate endpoints and several implementations are currently available in SAS and R. The methodology is based on hierarchical models that are numerically demanding and, when the amount of data is limited, maximum likelihood algorithms may not converge or may converge to an ill-conditioned maximum such as a boundary solution. This may produce misleading conclusions and have negative implications for the evaluation of new drugs. In the present work, we explore the use of two distinct functions in R (lme and lmer) and the MIXED procedure in SAS to assess the validity of putative surrogate endpoints in the meta-analytic framework, via simulations and the analysis of a real case study. We describe some problems found with the lmer function in R that led to a poorer performance as compared with the lme function and MIXED procedure.

Latent Ornstein-Uhlenbeck models for Bayesian analysis of multivariate longitudinal categorical responses.

We propose a Bayesian latent Ornstein-Uhlenbeck (OU) model to analyze unbalanced longitudinal data of binary and ordinal variables, which are manifestations of fewer continuous latent variables. We focus on the evolution of such latent variables when they continuously change over time. Existing approaches are limited to data collected at regular time intervals. Our proposal makes use of an OU process for the latent variables to overcome this limitation. We show that assuming real eigenvalues for the drift matrix of the OU process, as is frequently done in practice, can lead to biased estimates and/or misleading inference when the true process is oscillating. In contrast, our proposal allows for both real and complex eigenvalues. We illustrate our proposed model with a motivating dataset, containing patients with amyotrophic lateral sclerosis disease. We were interested in how bulbar, cervical, and lumbar functions evolve over time.

Serial correlation structures in latent linear mixed models for analysis of multivariate longitudinal ordinal responses.

We propose a latent linear mixed model to analyze multivariate longitudinal data of multiple ordinal variables, which are manifestations of fewer continuous latent variables. We focus on the latent level where the effects of observed covariates on the latent variables are of interest. We incorporate serial correlation into the variance component rather than assuming independent residuals. We show that misleading inference may be drawn when misspecifying the variance component. Furthermore, we provide a graphical tool depicting latent empirical semi-variograms to detect serial correlation for latent stationary linear mixed models. We apply our proposed model to examine the treatment effect on patients having the amyotrophic lateral sclerosis disease. The result shows that the treatment can slow down progression of latent cervical and lumbar functions.

The evolution of histological changes suggestive of antibody-mediated injury, in the presence and absence of donor-specific anti-HLA antibodies.

The interplay between donor-specific anti-HLA antibodies (HLA-DSA), histology of active antibody-mediated rejection (aABMRh ), transplant glomerulopathy (cg), and graft failure in kidney transplantation remains insufficiently understood. We performed a single-center cohort study (n = 1000) including 2761 protocol and 833 indication biopsies. Patients with pretransplant HLA-DSA were more prone to develop aABMRh (OR 22.7, 95% CI, 11.8-43.7, P < 0.001), cg (OR 5.76, 95% CI, 1.67-19.8, P = 0.006), and aABMRh/cg (OR 19.5, 95% CI, 10.6-35.9, P < 0.001). The negative impact of pre-transplant HLA-DSA on graft survival (HR 2.12, 95% CI, 1.41-3.20, P < 0.001) was partially mediated through aABMRh and cg occurrence. When adjusted for time-dependent HLA-DSA (HR 4.03, 95% CI, 2.21-7.15, P = 0.002), graft failure was only affected by aABMRh when cg was evident. In HLA-DSA negative patients, aABMRh was associated with impaired graft outcome only when evolving to cg (HR 1.32, 95% CI, 1.07-1.61, P = 0.008). We conclude that the kinetics of HLA-DSA are important to estimate the rate of graft failure, and that histological follow-up is necessary to discover, often subclinical, ABMR and cg. In the absence of HLA-DSA, patients experience similar histological lesions and the evolution to transplant glomerulopathy associates with impaired graft outcome.

Eplet Mismatch Load and De Novo Occurrence of Donor-Specific Anti-HLA Antibodies, Rejection, and Graft Failure after Kidney Transplantation: An Observational Cohort Study.

BACKGROUND: In kidney transplantation, evaluating mismatches of HLA eplets-small patches of surface-exposed amino acids of the HLA molecule-instead of antigen mismatches might offer a better approach to assessing donor-recipient HLA incompatibility and improve risk assessment and prediction of transplant outcomes. METHODS: To evaluate the effect of number of eplet mismatches (mismatch load) on de novo formation of donor-specific HLA antibodies (DSAs) and transplant outcomes, we conducted a cohort study that included consecutive adult kidney recipients transplanted at a single center from March 2004 to February 2013. We performed retrospective high-resolution genotyping of HLA loci of 926 transplant pairs and used the HLAMatchmaker computer algorithm to count HLA eplet mismatches. RESULTS: De novo DSAs occurred in 43 (4.6%) patients. Multivariable analysis showed a significant independent association between antibody-verified eplet mismatch load and de novo DSA occurrence and graft failure, mainly explained by DQ antibody-verified eplet effects. The association with DQ antibody-verified eplet mismatches was linear, without a safe threshold at which de novo DSA did not occur. Odds for T cell- or antibody-mediated rejection increased by 5% and 12%, respectively, per antibody-verified DQ eplet mismatch. CONCLUSIONS: Eplet mismatches in HLA-DQ confer substantial risk for de novo DSA formation, graft rejection, and graft failure after kidney transplantation. Mismatches in other loci seem to have less effect. The results suggest that antibody-verified HLA-DQ eplet mismatch load could be used to guide personalized post-transplant immunosuppression. Adoption of molecular matching for DQA1 and DQB1 alleles could also help to minimize de novo DSA formation and potentially improve transplant outcomes.