Multivariate Joint Modeling of Repeated Measurements and Time-to-Event: An Application to the Canadian Registry for Pulmonary Fibrosis Cohort Study

Background: Joint models for multiple longitudinal outcomes and survival data have recently gained considerable attention as collecting data on various longitudinal outcomes in clinical studies has become increasingly common. The Canadian Registry for Pulmonary Fibrosis (CARE-PF) cohort study collected data for rheumatoid arthritis-associated interstitial lung disease (RA-ILD) patients with several longitudinal outcomes like forced vital capacity percent-predicted (FVC) and diffusing capacity for carbon monoxide percent-predicted (DLCO). Applying these multiple longitudinal data in a unified model (multivariate joint model) will reveal new insights about the RA-ILD. \n\nObjectives: The purposes of this study were to investigate the association between longitudinal outcomes of FVC and DLCO with survival outcome time-to-death or transplant and to check if the rates of changes for longitudinal outcomes, FVC, and DLCO differ between two High-resolution computed tomography (HRCT) pattern: a non-specific interstitial pneumonia (NSIP) pattern and a usual interstitial pneumonia (UIP) pattern. Furthermore, this study focused on exploring the mean differences between FVC and DLCO longitudinal outcomes among different covariates and identifying the factors associated with survival outcome time-to-death or transplant. \n\nMethods and Materials: This study utilized the interstitial lung disease (ILD) patients' data from the CARE-PF cohort. Multivariable linear mixed effect models were used to compare the rates of change in FVC and DLCO among the patients from NSIP and UIP patterns. Univariate and multivariate joint models were used to analyze the connection between longitudinal outcomes (FVC and DLCO) and survival outcome time-to-death or transplant. Kaplan-Meier analysis, univariable and multivariable Cox regression models, and univariate and multivariate joint models were utilized to explore mortality risk factors among RA-ILD patients. \n\nResults: A total of 142 RA-ILD patients were included in this study, with an average age of 63.91 (±9.91) years. The results of the multivariate joint model indicate a significant slope difference of FVC and a significant slope difference of DLCO for the patients from the NSIP and UIP pattern, and the values were 1.25 and 1.34, respectively. A significantly higher decline of FVC and DLCO was found among the RA-ILD patients with a UIP pattern compared to the RA-ILD patients with NSIP pattern. Again, the variable age of the patients and treatment were significantly associated with the FVC. One year increase in age at the baseline was responsible for an increase in the FVC by 0.42. The FVC was decreased by 6.09 for the patients utilizing the treatment compared to those not.\nMoreover, the variable ever smoked was significantly associated with the DLCO. The DLCO was decreased by 7.62 for the patients who had a smoking history compared to the patients who had no smoking history. From the univariable Cox Regression analysis, it was found that the variable age, sex, high-resolution computed tomography (HRCT) pattern, and ever-smoked were significantly associated with the time-to-death or transplant. However, the multivariate joint model indicated that age, sex, HRCT pattern, ever-smoked, and treatment were not significantly associated with the time-to-death or transplant. The univariate joint model revealed that one unit increase in FVC was responsible for a 5% decrease in death or transplant after controlling the effect of other covariates.\nMoreover, one unit increase in DLCO was responsible for a 9% decrease in death or transplant, controlling the effect of other covariates. However, the multivariate joint modeling revealed that only one longitudinal outcome, DLCO, was significantly related to the survival outcome of time-to-death or transplant. The results of the multivariate joint model indicated that the FVC and the DLCO for patients from a UIP pattern significantly decreased by 2 and 2.87 per year, respectively.\n\nConclusion: The longitudinal outcome of the DLCO was significantly associated with the survival outcome of time-to-death or transplant. For patients with a UIP pattern, the longitudinal outcome of FVC significantly decreased per year. Additionally, there was a significant deviation in the slope of FVC among the patients from NSIP and UIP patterns. For the longitudinal outcome of DLCO, both UIP and NSIP patients experienced a significant yearly decrease, with a significant slope difference between the two patterns. RA-ILD patients with a UIP pattern showed a significantly greater decline in FVC and DLCO than those with NSIP pattern. Patient age was significantly related to FVC. The mean FVC was significantly lower in RA-ILD patients receiving treatment compared to those who were not taking any treatment. Moreover, the DLCO was significantly lower among patients with a smoking history.

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