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 (CTS; n = 125 250) and from the American Scientific Registry of Transplant Recipients (SRTR; 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 post-transplant 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.

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.

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.

A joint penalized spline smoothing model for the number of positive and negative COVID-19 tests.

One of the key tools to understand and reduce the spread of the SARS-CoV-2 virus is testing. The total number of tests, the number of positive tests, the number of negative tests, and the positivity rate are interconnected indicators and vary with time. To better understand the relationship between these indicators, against the background of an evolving pandemic, the association between the number of positive tests and the number of negative tests is studied using a joint modeling approach. All countries in the European Union, Switzerland, the United Kingdom, and Norway are included in the analysis. We propose a joint penalized spline model in which the penalized spline is reparameterized as a linear mixed model. The model allows for flexible trajectories by smoothing the country-specific deviations from the overall penalized spline and accounts for heteroscedasticity by allowing the autocorrelation parameters and residual variances to vary among countries. The association between the number of positive tests and the number of negative tests is derived from the joint distribution for the random intercepts and slopes. The correlation between the random intercepts and the correlation between the random slopes were both positive. This suggests that, when countries increase their testing capacity, both the number of positive tests and negative tests will increase. A significant correlation was found between the random intercepts, but the correlation between the random slopes was not significant due to a wide credible interval.

Gout and incidence of 12 cardiovascular diseases: a case-control study including 152 663 individuals with gout and 709 981 matched controls.

BACKGROUND: Gout, a common crystal arthropathy, is associated with increased risk of cardiovascular disease. We aimed to identify how this risk varies by individual cardiovascular disease across a broad spectrum of conditions. METHODS: In this matched case-control study, we used linked primary and secondary electronic health records from the UK Clinical Practice Research Datalink to assemble a cohort of individuals with a first-time diagnosis of gout between Jan 1, 2000 and Dec 31, 2017, who were aged 80 years or younger at diagnosis, and free of cardiovascular diseases up to 12 months after diagnosis. The control cohort comprised up to five control individuals per patient with gout, matched on age, sex, socioeconomic status, geographical region, and calendar time, randomly selected among individuals free of gout at any time before and during the study period. The cohorts were followed up until June 30, 2019. We investigated the incidence of 12 cardiovascular diseases and used Cox proportional hazards models to examine differences in people with and without gout, overall and by subgroups of sex, age, socioeconomic status, and year of study inclusion. We further adjusted models for known cardiovascular risk factors (blood pressure, BMI, smoking status, cholesterol, type 2 diabetes, chronic kidney disease, and history of hypertension). FINDINGS: We identified 152 663 individuals with gout (mean age 56·2 years [SD 13·3]; 120 324 [78·8%] men and 32 339 [21·2%] women) and 709 981 matched controls (mean age 56·5 years [13·2]; 561 002 [79·0%] men and 148 979 [21·0%] women). Of these individuals, 31 479 (20·6%) with gout and 106 520 (15·0%) without gout developed cardiovascular disease during a median follow-up of 6·5 years (IQR 3·1-10·5). Patients with gout had higher risk of cardiovascular diseases than matched controls (hazard ratio [HR] 1·58 [95% CI 1·52-1·63]). Excess risk of cardiovascular disease in gout was greater in women than men (women: HR 1·88 [1·75-2·02]; men: HR 1·49 [1·43-1·56]), and, among all age groups, was highest in younger individuals (HR in people aged <45 years: 2·22 [1·92-2·57]). Excess risk was observed across all 12 cardiovascular diseases investigated. Patients with gout had higher BMI than matched controls (mean difference 2·90 kg/m2 [95% CI 2·87-2·93]) and higher prevalence of chronic kidney disease, dyslipidaemia, history of hypertension, obesity, and type 2 diabetes. Adjusting for known cardiovascular risk factors attenuated but did not eliminate the excess risk of cardiovascular disease related to gout (adjusted HR 1·31 [1·27-1·36]). INTERPRETATION: Patients with gout had an excess risk of developing a broad range of cardiovascular diseases that extend beyond atherosclerotic diseases and include heart failure, arrhythmias, valve disease, and thromboembolic diseases. Excess risk was highest in women and younger individuals. These findings suggest that strategies to reduce cardiovascular risk in patients with gout need to evolve and be implemented in clinical practice. FUNDING: Research Foundation Flanders.

Trends in cardiovascular disease incidence among 22 million people in the UK over 20 years: population based study.

OBJECTIVE: To investigate the incidence of cardiovascular disease (CVD) overall and by age, sex, and socioeconomic status, and its variation over time, in the UK during 2000-19. DESIGN: Population based study. SETTING: UK. PARTICIPANTS: 1 650 052 individuals registered with a general practice contributing to Clinical Practice Research Datalink and newly diagnosed with at least one CVD from 1 January 2000 to 30 June 2019. MAIN OUTCOME MEASURES: The primary outcome was incident diagnosis of CVD, comprising acute coronary syndrome, aortic aneurysm, aortic stenosis, atrial fibrillation or flutter, chronic ischaemic heart disease, heart failure, peripheral artery disease, second or third degree heart block, stroke (ischaemic, haemorrhagic, and unspecified), and venous thromboembolism (deep vein thrombosis or pulmonary embolism). Disease incidence rates were calculated individually and as a composite outcome of all 10 CVDs combined and were standardised for age and sex using the 2013 European standard population. Negative binomial regression models investigated temporal trends and variation by age, sex, and socioeconomic status. RESULTS: The mean age of the population was 70.5 years and 47.6% (n=784 904) were women. The age and sex standardised incidence of all 10 prespecified CVDs declined by 19% during 2000-19 (incidence rate ratio 2017-19 v 2000-02: 0.80, 95% confidence interval 0.73 to 0.88). The incidence of coronary heart disease and stroke decreased by about 30% (incidence rate ratios for acute coronary syndrome, chronic ischaemic heart disease, and stroke were 0.70 (0.69 to 0.70), 0.67 (0.66 to 0.67), and 0.75 (0.67 to 0.83), respectively). In parallel, an increasing number of diagnoses of cardiac arrhythmias, valve disease, and thromboembolic diseases were observed. As a result, the overall incidence of CVDs across the 10 conditions remained relatively stable from the mid-2000s. Age stratified analyses further showed that the observed decline in coronary heart disease incidence was largely restricted to age groups older than 60 years, with little or no improvement in younger age groups. Trends were generally similar between men and women. A socioeconomic gradient was observed for almost every CVD investigated. The gradient did not decrease over time and was most noticeable for peripheral artery disease (incidence rate ratio most deprived v least deprived: 1.98 (1.87 to 2.09)), acute coronary syndrome (1.55 (1.54 to 1.57)), and heart failure (1.50 (1.41 to 1.59)). CONCLUSIONS: Despite substantial improvements in the prevention of atherosclerotic diseases in the UK, the overall burden of CVDs remained high during 2000-19. For CVDs to decrease further, future prevention strategies might need to consider a broader spectrum of conditions, including arrhythmias, valve diseases, and thromboembolism, and examine the specific needs of younger age groups and socioeconomically deprived populations.