Participants who are randomized to treatment but have no post-baseline data pose a unique challenge. These participants need to be included to preserve randomization. Because there is no information about the outcome or the intercurrent event(s) that led to missing data, an estimand of interest, and the focus of this study, is a hypothetical strategy to estimate what would have been observed if participants had not discontinued. Various imputation-based and likelihood-based analyses were compared in simulated and real clinical trial data. Models that used baseline as a covariate or constrained baseline values to be equal yielded similar results and had greater power than an unconstrained analysis that fit baseline as a response. Assigning change to the first post-baseline visit as 0 and applying an analysis with baseline as a covariate controlled Type I error at the nominal level and had power equal to or greater than other methods. Treatment contrasts were not biased when the reason for missing all post-baseline data was random or treatment related. Within-group bias occurred with outcome-related missingness of all post-baseline data, but the bias was nearly equal in the two arms, leading to unbiased treatment contrasts. Bias occurred when missing all post-baseline data was related to treatment and outcome. Given the idiosyncratic nature of clinical trials, no universally best analytic approach exists for dealing with participants that have a baseline but no post-baseline data. Analysts can choose among the methods to tailor an approach to the situation at hand.

Respiratory infections remain a major global health burden, causing substantial morbidity and mortality worldwide. The responsible viruses circulate concurrently, potentially affecting each other’s dynamics, yet the extent and direction of such interactions remain poorly understood. Characterising these cross-pathogen effects at the population level is essential for elucidating transmission dynamics and guiding mitigation strategies. Using incidence data from a participatory syndromic surveillance system with multiplex PCR (polymerase chain reaction) confirmation of specific pathogens, we applied complementary statistical approaches, including multivariate regression, endemic–epidemic, and distributed-lag models, to characterise immediate and delayed associations among seven major respiratory diseases. We show that these pathogens form a connected system of temporal associations in which some pairs, such as SARS-CoV-2 and human seasonal coronaviruses, exhibit positive associations in their temporal incidence patterns, primarily from SARS-CoV-2 to human seasonal coronaviruses, whereas others, such as influenza and rhinovirus or parainfluenza virus show negative associations in circulation dynamics. Associations were often directional rather than reciprocal: for instance, rhinovirus was negatively associated with subsequent human seasonal coronaviruses, whereas the reverse pattern was not observed, while positive bidirectional associations between human metapneumovirus and parainfluenza virus were observed in several models. Temporal association patterns were largely consistent across analytical frameworks, suggesting persistent co-circulation dynamics among the studied respiratory viruses. By integrating multiple analytic frameworks, our study provides a comprehensive, data-driven view of patterns of co-circulation and statistical association among respiratory viruses, offering crucial insights for improved epidemic forecasting and mitigation strategies.

Taper models are widely used to estimate log assortments and, consequently, forest yield from inventory data. However, for Pinus taeda, few studies have employed mixed-effects taper models that explicitly account for the hierarchical structure of forestry data and heterogeneity of variances. This study addresses this gap by developing and evaluating mixed-effects taper models based on modified versions of Kozak’s (1969) equation. The models incorporate random effects at the farm/forest region, stand, and tree levels and allow for different variance structures, enabling them to capture the heterogeneity commonly observed in P. taeda stands. Diagnostic procedures using least confounded residuals were applied to assess model adequacy. Compared with traditional fixed-effects taper models, the selected mixed-effects model achieved superior performance, including reduced bias, improved fit across stem sections, and better predictive accuracy. Additionally, in Appendices, we provide a tutorial outlining the computational procedures in R software for statistical modeling of data related to this species within the mixed-effects model framework.

Height–diameter models are widely used to estimate tree height from diameter at breast height (DBH) and play a crucial role in forest inventories by reducing fieldwork effort. However, statistical challenges such as nonlinearity, heteroscedasticity, nonnormality, and outliers can compromise model accuracy. To address these issues, this study proposes a generalization of Scolforo’s height‒diameter model (Scolforo, 1998), which incorporates random effects to improve flexibility and fit. With observational data from Eucalyptus urograndis plantations, we present a step-by-step framework for model fitting, inference, and validation. Our approach considers hierarchical structures and variability across stands to improve predictive performance. To rigorously assess model adequacy, we conducted a simulation study under various scenarios, evaluating goodness-of-fit with deviance, randomized quantile residuals, and least-confounded residuals. These diagnostics identify misspecification and enable robust parameter estimation. Additionally, we provide a detailed tutorial (Appendix B) for implementing the model in R that encompasses (i) inference for fixed and random effects, (ii) local influence analysis to detect sensitive observations, and (iii) residual-based diagnostics adapted to mixed models. Our results reveal the adaptability of the model to complex data structures while maintaining interpretability. The proposed framework provides forest researchers a reliable tool for height prediction that combines theoretical rigor and practical applicability. The accompanying R tutorial increases reproducibility and facilitates the integration of the framework into forest inventory workflows.

BACKGROUND AND OBJECTIVE:In clinical trials, surrogate endpoints are often used instead of true endpoints due to practical convenience, time efficiency, and reduced sample size requirements. To determine if a surrogate endpoint can effectively replace a true endpoint, a meta-analytic approach is often employed, evaluating the surrogate endpoint at both the individual and trial levels. Ideally, both surrogacy levels should be sufficiently high to consider the surrogate endpoint a valid replacement for purposes such as accelerated regulatory approval. We aimed to provide an R implementation for surrogacy evaluation of categorical, survival, or continuous surrogate endpoints for a survival true endpoint. METHODS:In settings where the true endpoint is a time-to-event variable and the surrogate endpoint is continuous, categorical, or also a time-to-event endpoint, the meta-analytic approach to evaluate surrogacy is based on a two-stage approach. In the first stage, a copula model is employed and a measure for individual level surrogacy is estimated. In the second stage, the estimates of the treatment effects are used to compute a measure for trial-level surrogacy. At this step, measurement error can be taken into account via weights or via a model. RESULTS:The R package Surrogate provides functions that implement the two-stage approach for various settings. For all settings, models incorporating Clayton, Plackett and Hougaard copulas are available. Additionally, the functions allow for adjustments for measurement error. We demonstrate their use across these settings by applying them to various datasets. CONCLUSION:We demonstrate how the R package Surrogate can be used to evaluate categorical, survival, or continuous surrogate endpoints for a survival true endpoint.

Identifying factors that affect the vulnerability of areas to COVID-19 infection is essential, as it helps to identify the locations or risk groups that require additional attention. While connectivity among regions is a crucial driver in the epidemic growth, it is also observed that differences amongst locations in the regions exist, with some locations impacted much more or much less when compared to the surrounding region. We aim to develop a statistical model for assessment of localities’ vulnerability to COVID-19 based on risk factors, which also accounts for the regional settlement of the virus. In this cross-sectional ecological study, to determine the local vulnerability to COVID-19 in small areas (Belgian statistical sector level) as compared to in the larger neighborhood (municipality level), we propose a model with the mean incidence decomposed into a local vulnerability component and a regional outbreak component. This is illustrated by analyzing the vulnerability of the Flemish and Brussels regions in Belgium during the second and third waves of the COVID-19 pandemic, from September 2020 to May 2021. We investigate three groups of risk factors: socio-demographic, socio-economic, and environmental factors. As data are incomplete, a sensitivity analysis is undertaken to check the stability of model estimates. Results for the period September to December 2020 show that sectors with a higher median income and a larger proportion of non-Belgian residents were less vulnerable to COVID-19, while sectors with a higher proportion of pensioners, a lower education level, and/or a higher black carbon level had a higher vulnerability. We present a simple yet efficient tool to identify areas with an increased vulnerability to COVID-19 in an outbreak setting. This can be helpful for policymakers to develop targeted public health interventions with localized lockdowns, enhanced testing and vaccination, and to plan resource allocations.

This paper discusses some statistical aspects of the UK Covid-19 pandemic response, focussing particularly on cases where we believe that a statistically questionable approach or presentation has had a substantial impact on public perception, or government policy, or both. We discuss the presentation of statistics relating to Covid risk, and the risk of the response measures, arguing that biases tended to operate in opposite directions, overplaying Covid risk and underplaying the response risks. We also discuss some issues around the presentation of life loss data, excess deaths, and the use of case data. The consequences of neglect of most individual variability from epidemic models, alongside the consequences of some other statistically important omissions, are also covered. Finally, the evidence that full stay-at-home lockdowns were necessary to reverse waves of infection is examined, with new analyses provided for several European countries.

Alzheimer’s disease (AD) is a heterogeneous neurodegenerative disease driven by pathological depositions of proteins that accumulate over decades. Compelling genetic and neurobiological evidence suggests that amyloid accumulation in the brain initiates and drives early-stage AD. Measurement of fibrillar amyloid has been pivotal to the development and approval of disease-slowing treatments. Various biomarkers of AD pathophysiology provide evidence of target engagement and downstream effects on disease progression, and their use as surrogate endpoints may help identify and expeditiously bring new treatments to patients. In clinical trials, a surrogate endpoint serves as a substitute for a direct measurement of a patient’s clinical status, and its use can provide ethical, logistical, and economic advantages. Establishing biomarkers as surrogate endpoints involves evaluating scientific evidence through diverse statistical approaches to demonstrate their predictivity of clinical benefit. This article evaluated evidence supporting amyloid β plaque reduction as a surrogate endpoint in symptomatic AD by exploring regulatory considerations and guidelines for surrogate endpoints, examining the amyloid hypothesis and the current therapeutic landscape in AD, and presenting supporting evidence of surrogate endpoints from a recent clinical development program of AD.

Oral health in older adults is often poor, with a high prevalence of caries, periodontal disease, and tooth loss. As dental care utilization declines with age, while contact with general practitioners (GPs) increases, GPs could play an important role in preventive oral care, by detecting oral care needs and initiating preventive actions. To compare oral health assessment outcomes between GP trainees (GPTs) and dentists (benchmark), 58 adults aged 65 years or older were independently assessed by GPTs and dentists on the same day using the nine-item Oral Health Screener (OHS), covering both self-reported and observational items. Percent agreement, kappa statistics, and generalized linear mixed models (GLMM) were used to assess inter-rater reliability. GPTs showed high agreement with dentists for self-reported items (89.7-94.8%; kappa: 0.75-0.96; GLMM correlations with covariate adjustment: 0.93-1.00), moderate to strong agreement for denture hygiene assessment (88.2%; κ = 0.72; corr.=0.87) and gum condition (84.5%; κ = 0.57; corr.=0.87), but low agreement for observational items including teeth (69.1%; κ = 0.29; corr.=0.58), tongue (84.5%; κ = 0.23; corr.=0.26), soft tissues (75.9%; κ = 0.15; corr.=0.15), and oral hygiene (61.4%; κ = 0.21; corr.=0.18). These findings indicate that GPTs can reliably assess patient-reported oral health items but show substantial variability in evaluating clinical signs. These findings highlight the potential of GPs to identify oral health problems while underscoring the need for targeted training to enhance their observational skills.

In progressive diseases such as Alzheimer's, treatments that slow progression should start early to preserve higher levels of functioning for a longer period. In corresponding clinical trials, treatment effects are usually expressed as mean differences on a clinical scale at fixed time points. Early in the disease course, however, these mean differences may appear small but may nonetheless correspond to an important slowing of disease progression. This complicates the appreciation of the relevance of observed treatment effects. We introduce a class of target parameters that quantify treatment effects on the time scale in longitudinal studies; for instance, in terms of time saved or percentage slowing of progression. We focus on data from randomized trials where the target parameters are identified under regularity assumptions. These target parameters remain well defined if treatment was not randomized, but additional untestable assumptions are required for identification. We propose general two-step estimators. In the first step, the data can be analyzed with standard methods for longitudinal data and standard software can thus be used. In the second step, summary statistics from the first step are used for inferences about the target parameters. The second step has been implemented in the TCT R package. We study the asymptotic properties and efficiency of these two-step estimators, and evaluate them in an extensive simulation study. These estimators are used in a phase 2/3 clinical trial for Alzheimer's disease, leading to important additional insights into the treatment effect.

In many studies, multiple longitudinal outcomes are collected, and interest lies in studying the association between these outcomes. Joint modeling is then required, but full likelihood estimation becomes infeasible as the number of outcomes increases. To address this, the pairwise-fitting approach was developed. However, the robustness of this pseudo-likelihood-based approach under missing at random (MAR) remains unclear. We investigate the impact of MAR dropout on the pairwise-fitting approach through a case and simulation study and compare the results to full likelihood estimation. In the simulation study, we simulate three continuous longitudinal outcomes so that full likelihood estimation remains computationally feasible, allowing a comparison with the pairwise fitting approach. Various settings are examined, including random intercept and random intercept-and-slope models, in which we vary the standard deviation of the error terms and the degree of correlation between random effects. Our results show that bias remains limited in random intercept models and in most random intercept-and-slope models. However, when the standard deviation of the error terms becomes large compared to that of the random effects, some bias appears in the covariances between the random effects of the outcomes not driving dropout. This bias is mitigated using multiple imputation. As a case study, we analyzed data from a schizophrenia study using both full likelihood and pseudo-likelihood approaches and compared the results.

Skeletal muscle is a plastic tissue that undergoes structural changes during childhood. Previous studies assumed a simple linear muscle growth function with respect to age, but longitudinal data are needed to check this assumption, and to develop both parameter‐ and muscle‐specific growth trajectories. Both muscle quantity and quality are related to muscle function, indicating the importance of normal muscle development to participate in daily life activities. In children with altered muscle growth, such as those with neurological or neuromuscular disorders, norm‐reference data are crucial to improve understanding of abnormal muscle development in relation to age and to optimize age‐specific therapeutic interventions. The overall aim of the current prospective study was to create an extensive longitudinal normative database on muscle morphology and composition of the medial gastrocnemius and semitendinosus muscle in typically developing (TD) children, aged 4 months to 12 years old, hereby developing muscle‐ and parameter‐specific norm‐reference trajectories. Muscle morphology, that is, muscle belly length (ML), tendon length (TL), muscle‐tendon unit length (MTUL), muscle volume (MV) and cross‐sectional area (CSA), and muscle composition, that is, echo‐intensity (EI), were assessed using three‐dimensional freehand ultrasound. Muscle morphology was also normalized to body height, body weight or the product of body height and weight. It was hypothesized that absolute morphological parameters increase gradually with increasing age, following a simple straight linear growth pattern, while normalized morphological parameters were expected to remain stable over time. Mixed‐effect models were fitted to estimate muscle‐ and parameter‐specific trajectories with respect to age. Linear mixed‐effect models (LMM) and non‐linear mixed‐effect models (non‐LMM) were compared using the Akaike information criterion, with a lower value indicating a better model fit. Data were collected from 59 TD children (median age [interquartile range]: 5.92 [1.33–8.97] years; boys/girls: 29/30; 3–8 repeated measurements) for the medial gastrocnemius, totaling 230 measurements, and from 55 TD children (median age [interquartile range]: 5.95 [1.57–8.63] years; boys/girls: 26/29; 3–7 repeated measurements) for the semitendinosus, totaling 207 measurements. The current results revealed that for the absolute morphological parameters of the medial gastrocnemius, the longitudinal trajectory of MTUL showed a piecewise trajectory with a significant breakpoint ( p < 0.0001) at the age of 2.16 years influenced by ML growth, and another at the age of 6.91 years influenced by TL growth. CSA and MV showed comparable trajectories, with trajectory changes around ages 2 and 10 years. For the semitendinosus, TL and CSA increased linearly with age, whereas ML was best fitted by an LMM with a quadratic function, with an inflection point around the age of 7 years. MV displayed a piecewise trajectory with a significant breakpoint ( p < 0.0001) at 4.53 years. The normalized parameters of both muscles showed a more complex pattern than the expected straight horizontal trajectory. Non‐LMM with one significant breakpoint ( p < 0.0001) showed the best fit for EI of both muscles, but only small changes in relation to age were seen. Our results demonstrated that changes in muscle parameters according to age cannot be explained by merely a simple straight linear trajectory and highlighted the importance of muscle‐ and parameter‐specific models.

The identification of highly influential animals in the estimation of model parameters is fundamental to understanding individual variation in lactation patterns and to identifying unique profiles, helping the researcher to gain insight into the phenomenon under investigation. In this study, we analyzed the lactation curves of 30 Saanen goats using a nonlinear mixed-effects model derived from Wood's lactation model and applied a local influence diagnostic tool to detect animals that may disproportionately affect parameter estimates. The data comes from an unbalanced experiment designed to study the effect of cumulative stress on the average weekly milk production. The diagnostic of local influence enabled the identification of some animals with an unusual profile. Through the parameters of the fitted model, we identified that the treatment effect was not statistically significant during the experimental week, but negatively affected milk production throughout the lactation period.

In clinical trials, surrogate endpoints, that are more cost-effective, occur earlier, or are more frequently measured, are sometimes used to replace costly, late, or rare true endpoints. Regulatory authorities typically require thorough evaluation and validation to accept these surrogate endpoints as reliable substitutes. To this end, the meta-analytic framework is considered a very viable approach to validate surrogates at both trial and individual levels. However, this framework requires data from multiple trials or centers, posing challenges when data sharing is not feasible. In this article, we propose a federated data analysis approach that allows organizations to maintain control over their datasets while still enabling surrogate validation through meta-analytic techniques. In this approach, there is no longer a need for raw data sharing. Instead, independent analyses are conducted at each organization. Thereafter, the results of these independent analyses are aggregated at a central analysis hub and the metrics for surrogate evaluation are extracted. We apply this approach to simulated and real clinical data, demonstrating how this federated approach can overcome data-sharing constraints and validate surrogate endpoints in decentralized settings.

Children with Duchenne muscular dystrophy (DMD) present with progressive gait pathology due to progressive muscle weakness and contractures. However, the associations between specific muscle impairments and specific gait features have never been quantified. Therefore, the aim of this longitudinal observational cohort study was to investigate the longitudinal interaction between progressive muscle impairments and progressive gait pathology in growing boys with DMD. Thirty-one boys with DMD (aged 4.6–16.4 years) were repeatedly measured between 2015 and 2022, resulting in a total dataset of 152 observations. Fixed dynamometry, goniometry and 3D gait analysis were used to assess lower limb muscle weakness, passive range of motion and gait. Joint random-effect models between gait and muscle outcomes were fitted. The correlation between the random intercepts (ra) and random slopes (rb) indicated the relationship between the initial values and progression rates over time of two outcomes, respectively. Specific muscle impairments were related to specific gait features, both in terms of initial values (ra=0.470–0.757; p < 0.029) and progression rates (rb=0.547–0.812; p < 0.024). Decreased hip extension strength was associated with increased maximal posterior trunk angle (rb=-0.588; p = 0.0004), increased maximal anterior pelvic tilt angle (ra=-0.543; p = 0.0040 and rb=-0.812; p < 0.0001), and reduced maximal hip extension moment (ra=0.536; p = 0.0289). Decreased hip abduction strength was associated with increased step width (ra=-0.549; p = 0.0021) and increased maximal internal foot progression angle (rb=-0.547; p = 0.0117). Decreased knee extension strength was associated with reduced maximal knee extension moment (ra=0.702; p < 0.0001), reduced maximal knee power absorption (ra=0.757; p < 0.0001), and reduced dorsiflexion angle at initial contact (rb=0.684; p = 0.0237). Decreased dorsiflexion range of motion was associated with reduced dorsiflexion angle at initial contact (ra=0.732; p < 0.0001 and rb=0.627; p = 0.0202) and reduced maximal dorsiflexion angle in swing (ra=0.663; p < 0.0001). This is the first study that objectively quantified the longitudinal interaction between muscle impairments and gait features, providing valuable insights into the underlying mechanisms of pathological gait in DMD. The observed associations highlight the importance of targeted clinical assessments. These findings offer a foundation for optimizing rehabilitation strategies, orthotic management, and orthopedic interventions, ultimately improving clinical decision-making and enhancing mobility outcomes in children with DMD.

Aims/Purpose: Challenges in modeling rates of visual field (VF) progression relate to flooring effects and sensitivity to inclusion criteria like follow‐up (FU) duration. We explored the relationship between VF progression and age, disease severity, and FU duration in primary open angle glaucoma (POAG).Methods: Mean Deviation (MD) of 655 POAG eyes of 424 patients from the UZ Leuven Glaucoma Clinic with at least 5 VFs and 2 years of follow‐up were used. Baseline severity was defined as Above 0 (≥0dB), mild ( < 0 and ≥‐6dB), moderate ( < ‐6 and ≥‐12dB), advanced ( < ‐12 and ≥‐15dB), and severe ( < ‐15dB) disease. Linear mixed models and changepoint detection were used. Sensitivity analysis of modeled progression rates within each severity group was done by varying maximally included duration of FU.Results: MD progression rates per year were ‐0.34dB (p < 0.001) for Above 0, ‐0.49dB (p < 0.001) for mild, ‐0.49dB (p < 0.001) for moderate, ‐0.26dB (p = 0.009) for advanced, and +0.1dB (p = 0.317) for severe POAG. Random effects correlation between baseline MD and progression rates was 0.36. The fixed effects for age and test related learning effect were non‐significant (p = 0.65) and ‐0.21 (p = 0.004) respectively. The correlation between the implied slope and baseline age was ‐0.26. Changepoint analysis showed that group level progression estimates stabilized when minimum FU times were at least 2.17, 1.99, 2.18, and 4.56 years for mild, moderate, advanced and severe POAG respectively.Conclusions: Older patients progress faster across severity levels and a significant learning effect is present when excluding patients with severe POAG. Excluding patients with a baseline MD above 0dB, the modeled average MD change is similar between mild and moderate POAG. Less progression is observed in advanced and no progression in severe POAG, consistent with the flooring effect. In mild and moderate POAG patients progression estimates converged after a minimum FU of at least 2 years.

In empirical studies, multiple outcomes are often measured repeatedly over time, and interest frequently lies in studying the association between these longitudinal outcomes and a time-to-event outcome. Therefore, shared-parameter joint models for longitudinal and time-to-event outcomes have been developed. However, while such joint models in theory also allow for multiple longitudinal outcomes, they are often restricted to a limited number of outcomes due to computational complexity when fitting the models. To address this problem, we propose a new joint model, which is based on correlated instead of shared random effects, and for which a pairwise-modelling strategy can be used. In this approach, the longitudinal outcomes are modelled with (generalized) linear mixed models and the survival outcome with a Weibull proportional hazards frailty model. Instead of fitting the full joint model, this approach involves fitting all possible bivariate models, and inference is based on pseudo-likelihood theory. The main advantage of our approach is that there is no restriction on the number of longitudinally measured outcomes that are jointly modelled with the time-to-event outcome.

BACKGROUND:Recent studies suggest that fast and deep inspirations against either low or high external loads may provide patients with weaning difficulties with a training stimulus during inspiratory muscle training (IMT). However, the relationship between external IMT load, reflected by changes in airway pressure swings (ΔPaw), and total inspiratory effort, measured by oesophageal pressure swings (ΔPes), remains unexplored. Additionally, the association between ΔPes, ΔPaw, and inspiratory muscle activations remains unclear. OBJECTIVES:The ai of this study was to compare ΔPes and ΔPaw and their relationship with inspiratory muscle activation in patients with weaning difficulties during different breathing conditions. METHODS:ΔPes and scalene, sternocleidomastoid, and parasternal intercostal muscles activation were recorded during the following conditions: 1) (proportional) pressure support ventilation; 2) unsupported spontaneous breathing; 3) low-load IMT (load: <10% maximal inspiratory pressure, PImax = 3 cmH2O) executed with slow and deep inspirations (low-load slow) and 4) low-load IMT (load: <10% maximal inspiratory pressure, PImax = 3 cmH2O) executed with fast deep inspirations (low-load fast); and 5) high-load IMT (load ∼ 30% PImax) executed with fast and deep inspirations. ΔPaw, end-inspiratory lung volume, and peak inspiratory flow were recorded during conditions 2-5. Variables were compared across conditions using mixed-model analysis. Spearman's rank correlations were calculated between inspiratory muscle activations and both ΔPes and ΔPaw. RESULTS:Five patients (age: 68 ± 1 y; 20% male; PImax: 37 ± 7 cmH2O [59 ± 23% predicted]; forced vital capacity: 0.66 ± 0.16 L [21 ± 6% predicted]) were included in the study. ΔPes values were 3-4 times larger than ΔPaw values during unsupported spontaneous breathing and IMT conditions. ΔPes, sternocleidomastoid activation, end-inspiratory lung volume, and peak inspiratory flow were larger during low-load fast IMT than during low-load slow IMT and unsupported spontaneous breathing but were similar between low-load fast and high-load IMTs. Inspiratory muscle activations correlated weakly to moderately with ΔPaw and moderately with ΔPes. CONCLUSIONS:In five patients with weaning difficulties, low-load fast IMT provided a training stimulus similar to high-load IMT. Both yielded significantly higher training stimulus than low-load slow IMT and unsupported spontaneous breathing. These results should be considered in future trials comparing IMT with sham conditions. CLINICAL TRIAL REGISTRATION NUMBERS:NCT03240263 and NCT04658498.

In many biomedical studies multiple responses are collected over time, which results in highdimensional longitudinal data. It is often of interest to model the continuous and binary responses jointly, which can be done with joint generalized mixed models in which the association is modelled through random effects. Investigating the association between the responses is often limited to scrutinizing the correlations between the latent random effects. In this article, this approach is extended by deriving closed-form formulas for the manifest correlations (and corresponding standard errors), which reflects the correlation between the observed responses as observed. In addition, the marginal joint model is constructed, from which predictions of subvectors of one response conditional on subvectors of other response(s) and potentially a subvector of the history of the response can be derived. Corresponding prediction and confidence intervals are constructed. Two case studies are discussed, in which further pseudo-likelihood methodology is applied to reduce the computational complexity.