Multivariate joint model under competing risks to predict death of hospitalized patients for SARS-CoV-2 infection

During the coronavirus disease 2019 (COVID-19) pandemic, several clinical prognostic scores have been proposed and evaluated in hospitalized patients, relying on variables available at admission. However, capturing data collected from the longitudinal follow-up of patients during hospitalization may improve prediction accuracy of a clinical outcome. To answer this question, 327 patients diagnosed with COVID-19 and hospitalized in an academic French hospital between January and July 2020 are included in the analysis. Up to 59 biomarkers were measured from the patient admission to the time to death or discharge from hospital. We consider a joint model with multiple linear or nonlinear mixed-effects models for biomarkers evolution, and a competing risks model involving subdistribution hazard functions for the risks of death and discharge. The links are modeled by shared random effects, and the selection of the biomarkers is mainly based on the significance of the link between the longitudinal and survival parts. Three biomarkers are retained: the blood neutrophil counts, the arterial pH, and the C-reactive protein. The predictive performances of the model are evaluated with the time-dependent area under the curve (AUC) for different landmark and horizon times, and compared with those obtained from a baseline model that considers only information available at admission. The joint modeling approach helps to improve predictions when sufficient information is available. For landmark 6 days and horizon of 30 days, we obtain AUC [95% CI] 0.73 [0.65, 0.81] and 0.81 [0.73, 0.89] for the baseline and joint model, respectively (p = 0.04). Statistical inference is validated through a simulation study.

Developing a clinical-environmental-genotypic prognostic index for relapsing-onset multiple sclerosis and clinically isolated syndrome

Our inability to reliably predict disease outcomes in multiple sclerosis remains an issue for clinicians and clinical trialists. This study aims to create, from available clinical, genetic and environmental factors; a clinical–environmental–genotypic prognostic index to predict the probability of new relapses and disability worsening. The analyses cohort included prospectively assessed multiple sclerosis cases (N = 253) with 2858 repeated observations measured over 10 years. N = 219 had been diagnosed as relapsing-onset, while N = 34 remained as clinically isolated syndrome by the 10th-year review. Genotype data were available for 199 genetic variants associated with multiple sclerosis risk. Penalized Cox regression models were used to select potential genetic variants and predict risk for relapses and/or worsening of disability. Multivariable Cox regression models with backward elimination were then used to construct clinical–environmental, genetic and clinical–environmental–genotypic prognostic index, respectively. Robust time-course predictions were obtained by Landmarking. To validate our models, Weibull calibration models were used, and the Chi-square statistics, Harrell’s C-index and pseudo-R² were used to compare models. The predictive performance at diagnosis was evaluated using the Kullback–Leibler and Brier (dynamic) prediction error (reduction) curves. The combined index (clinical–environmental–genotypic) predicted a quadratic time-dynamic disease course in terms of worsening (HR = 2.74, CI: 2.00–3.76; pseudo-R²=0.64; C-index = 0.76), relapses (HR = 2.16, CI: 1.74–2.68; pseudo-R² = 0.91; C-index = 0.85), or both (HR = 3.32, CI: 1.88–5.86; pseudo-R² = 0.72; C-index = 0.77). The Kullback–Leibler and Brier curves suggested that for short-term prognosis (≤5 years from diagnosis), the clinical–environmental components of disease were more relevant, whereas the genetic components reduced the prediction errors only in the long-term (≥5 years from diagnosis). The combined components performed slightly better than the individual ones, although their prognostic sensitivities were largely modulated by the clinical–environmental components. We have created a clinical–environmental–genotypic prognostic index using relevant clinical, environmental, and genetic predictors, and obtained robust dynamic predictions for the probability of developing new relapses and worsening of symptoms in multiple sclerosis. Our prognostic index provides reliable information that is relevant for long-term prognostication and may be used as a selection criterion and risk stratification tool for clinical trials. Further work to investigate component interactions is required and to validate the index in independent data sets.

Reflections on modern methods: Dynamic prediction using joint models of longitudinal and time-to-event data

Individualized prediction is a hallmark of clinical medicine and decision making. However, most existing prediction models rely on biomarkers and clinical outcomes available at a single time. This is in contrast to how health states progress and how physicians deliver care, which relies on progressively updating a prognosis based on available information. With the use of joint models of longitudinal and survival data, it is possible to dynamically adjust individual predictions regarding patient prognosis. This article aims to introduce the reader to the development of dynamic risk predictions and to provide the necessary resources to support their implementation and assessment, such as adaptable R code, and the theory behind the methodology. Furthermore, measures to assess the predictive performance of the derived predictions and extensions that could improve the predictions are presented. We illustrate personalized predictions using an online dataset consisting of patients with chronic liver disease (primary biliary cirrhosis).

Individualized dynamic prediction of survival with the presence of intermediate events

Often, in follow-up studies, patients experience intermediate events, such as reinterventions or adverse events, which directly affect the shapes of their longitudinal profiles. Our work is motivated by two studies in which such intermediate events have been recorded during follow-up. In both studies, we are interested in the change of the longitudinal evolutions after the occurrence of the intermediate event and in utilizing this information to improve the accuracy of dynamic prediction of their risk. To achieve so, we propose a flexible joint modeling framework for longitudinal and time-to-event data, which includes features of the intermediate event as time-varying covariates in both the longitudinal and survival submodels. We consider a set of joint models that postulate different effects of the intermediate event in the longitudinal profile and the risk of the clinical endpoint, with different formulations for the association structure while allowing its functional form to change after the occurrence of the intermediate event. Based on these models, we derive dynamic predictions of conditional survival probabilities which are adaptive to different scenarios with respect to the occurrence of the intermediate event. We evaluate the predictive accuracy of these predictions with a simulation study using the time-dependent area under the receiver operating characteristic curve and the expected prediction error adjusted to our setting. The results suggest that accounting for the changes in the longitudinal profiles and the instantaneous risk for the clinical endpoint is important, and improves the accuracy of the dynamic predictions.

Prediction of Survival With Long-Term Disease Progression in Most Common Spinocerebellar Ataxia

BACKGROUND

Spinocerebellar ataxias are rare dominantly inherited neurodegenerative diseases that lead to severe disability and premature death.

OBJECTIVE

To quantify the impact of disease progression measured by the Scale for the Assessment and Rating of Ataxia on survival, and to identify different profiles of disease progression and survival.

METHODS

Four hundred sixty-two spinocerebellar ataxia patients from the EUROSCA prospective cohort study, suffering from spinocerebellar ataxia type 1, spinocerebellar ataxia type 2, spinocerebellar ataxia type 3, and spinocerebellar ataxia type 6, and who had at least two measurements of Scale for the Assessment and Rating of Ataxia score, were analyzed. Outcomes were change over time in Scale for the Assessment and Rating of Ataxia score and time to death. Joint model was used to analyze disease progression and survival.

RESULTS

Disease progression was the strongest predictor for death in all genotypes: An increase of 1 standard deviation in total Scale for the Assessment and Rating of Ataxia score increased the risk of death by 1.28 times (95% confidence interval: 1.18-1.38) for patients with spinocerebellar ataxia type 1; 1.19 times (1.12-1.26) for spinocerebellar ataxia type 2; 1.30 times (1.19-1.42) for spinocerebellar ataxia type 3; and 1.26 times (1.11-1.43) for spinocerebellar ataxia type 6. Three subgroups of disease progression and survival were identified for patients with spinocerebellar ataxia type 1: "severe" (n = 13; 12%), "intermediate" (n = 31; 29%), and "moderate" (n = 62; 58%). Patients in the severe group were more severely affected at baseline with higher Scale for the Assessment and Rating of Ataxia scores and frequency of nonataxia signs compared to those in the other groups.

CONCLUSION

Rapid ataxia progression is associated with poor survival of the most common spinocerebellar ataxia. Theses current results have implications for the design of future interventional studies of spinocerebellar ataxia. © 2019 International Parkinson and Movement Disorder Society.

Individualized dynamic prediction of prostate cancer recurrence with and without the initiation of a second treatment: Development and validation

With the emergence of rich information on biomarkers after treatments, new types of prognostic tools are being developed: dynamic prognostic tools that can be updated at each new biomarker measurement. Such predictions are of interest in oncology where after an initial treatment, patients are monitored with repeated biomarker data. However, in such setting, patients may receive second treatments to slow down the progression of the disease. This paper aims to develop and validate dynamic individual predictions that allow the possibility of a new treatment in order to help understand the benefit of initiating new treatments during the monitoring period. The prediction of the event in the next x years is done under two scenarios: (1) the patient initiates immediately a second treatment, (2) the patient does not initiate any treatment in the next x years. Predictions are derived from shared random-effect models. Applied to prostate cancer data, different specifications for the dependence between the prostate-specific antigen repeated measures, the initiation of a second treatment (hormonal therapy), and the risk of clinical recurrence are investigated and compared. The predictive accuracy of the dynamic predictions is evaluated with two measures (Brier score and prognostic cross-entropy) for which approximated cross-validated estimators are proposed.