Longitudinal biomarkers predicting death of hospitalized patients for SARS-COV-2 infection: a joint analysis with competing risks
Alexandra Lavalley-Morelle(1), Xavier Lescure(1,2), Nathan Peiffer-Smadja(1,2), Simon Gressens(2), Alexandre Lahens(2), Bérénice Souhail((2), Agathe-Julie Bounhol(2), France Mentré(1,3), Jimmy Mullaert(1,3)
(1) Université Paris Cité, IAME, Inserm, France, (2) Department of Infectious and Tropical Diseases, AP-HP, Bichat-Claude Bernard University Hospital, F-75018 Paris, France, (3) Department of Epidemiology, Biostatistics and Clinical Research, AP-HP, Bichat-Claude Bernard University Hospital, F-75018 Paris, France
Introduction
During the covid-19 pandemic, a large number of clinical prognostic scores have been proposed and evaluated for hospitalized patients, exclusively relying on variables available at admission1. However, capturing data collected from the longitudinal follow-up of patients during hospitalization can be of interest to improve prediction accuracy. A joint modeling approach can provide individual dynamic predictions that take the full history of longitudinal measurements into account [1,2]. The objective is to assess the added value of routine biological follow-up with respect to existing baseline scores, in order to predict the risk of in-hospital death in COVID-19 patients.
Methods
Patients diagnosed with COVID-19 and hospitalized in the infectious disease department of an academic hospital in Paris, France (Bichat) between January and July 2020 are considered for the analysis. The primary outcome is time until in-hospital death, whereas hospital discharge is treated as a competing event. All the results of available biological exams during hospital stay are collected. Firstly, each biomarker is modelled by parametric linear or non-linear mixed-effects model jointly estimated with a parametric competing risk model involving subdistribution hazards. The survival model is adjusted on the value of the 4C score [3] (including age, gender, comorbidities, and baseline urea and CRP measurement) and involves a coefficient linking the current value of the biomarker value to the hazard. Estimation is performed using the SAEM algorithm [4] implemented in Monolix 2020R1. Secondly, for biomarkers satisfying quality control (adequacy of the fit and parameter estimation for both submodels), the link coefficient between the biomarker and the risk of death is tested using Wald test. Biomarkers with p-value below 0.05 are considered for the subsequent multivariable analysis. Thirdly, a multivariable joint model combining biomarkers from different physiological areas (arterial blood gas, blood count, inflammation markers) is constructed using a forward selection approach based on the global Wald test of the link between the various biomarkers and the risk of death. For predictions, we consider 3 landmark times at 3, 6 and 9 days after patient admission and horizon times until 30 days. We then derive the time-dependent AUCs with 95% confidence intervals [5] from the baseline model (competing risk model which only includes 4C score as a covariate) and from our multivariable model.
Results
327 patients and 59 biomarkers are considered in the analysis. Median 4C score is 6 (IQR : 4 – 9). 46 patients (14%) died during hospitalization 30 days after their admission while 238 (73%) were discharged. The 4C score, already has a strong effect on in-hospital death (exp(β)=1.43 95%CI [1.30;1.58]). After joint estimation, 36 biomarkers respond to the quality control criteria with 26 biomarkers significantly associated with the score-adjusted instantaneous risk of death. The multivariable joint model includes CO2 arterial pressure and C-reactive protein, whose longitudinal evolution are significantly associated with both risks of death and discharge. The AUC at day 30 is higher when considering the joint model compared to the baseline model only for landmark times of 6 and 9 days. For instance, for landmark time = 9 and horizon time = 30, AUC = 0.64, 95%-CI [0.55,0.74] and AUC = 0.84, 95% CI [0.75,0.92] for the baseline and the joint model, respectively. For landmark time 3, the difference of AUC between the two models is very low, as few longitudinal information is available before day 3.
Discussion
We demonstrated the added-value of longitudinal biological follow-up and the joint modeling approach for improving prognosis predictions. The originality of the work relies on (i) the statistical approach combining a (possibly non-linear) longitudinal model jointly estimated with a parametric subdistribution model to derive individual dynamic predictions considering hospital discharge as a competing event, and (ii) the use of real-life hospital data to collect massive data on biological examinations. Such a tool could help clinicians in complex decisions such as therapeutic escalation or limitation of care, in particular when the follow-up is sufficient and should be evaluated on an external data set.
References:
[1] D. Rizopoulos. Joint models for longitudinal and time-to-event data: with applications in R. Chapman & Hall / CRC biostatistics series. CRC Press, Boca Raton, Fla., 2012
[2] S. Desmée, F. Mentré, C. Veyrat-Follet, B. Sébastien, and J. Guedj. Nonlinear joint models for individual dynamic prediction of risk of death using Hamiltonian Monte Carlo: application to metastatic prostate cancer. BMC Medical Research Methodology, 17(1):105, 2017
[3] S.R. Knight, A. Ho, R. Pius, I. Buchan et al. Risk stratification of patients admitted to hospital with covid-19 using the ISARIC WHO Clinical Characterisation Protocol: development and validation of the 4C Mortality Score, BMJ 370:m3339, 2020
[4] B. Delyon, M. Lavielle, and E. Moulines. Convergence of a stochastic approximation version of EM algorithm. The Annals of Statistics, 27:94, 1999.
[5] P. Blanche, C. Proust-Lima, L. Loubère, C. Berr, JF. Dartigues, and H. Jacqmin-Gadda. Quantifying and comparing dynamic predictive accuracy of joint models for longitudinal marker and time-to-event in presence of censoring and competing risks. Biometrics, 71(1):102–113, 2015
