Application of multivariate joint modeling of longitudinal biomarkers and time-to-event data to a rare kidney stone cohort.

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Time-dependent Cox proportional hazards regression is a popular statistical method used in kidney disease research to evaluate associations between biomarkers collected serially over time with progression to kidney failure. Typically, biomarkers of interest are considered time-dependent covariates being updated at each new measurement using last observation carried forward (LOCF). Recently, joint modeling has emerged as a flexible alternative for multivariate longitudinal and time-to-event data. This study describes and demonstrates multivariate joint modeling using as an example the association of serial biomarkers (plasma oxalate [POX] and urinary oxalate [UOX]) and kidney function among patients with primary hyperoxaluria in the Rare Kidney Stone Consortium Registry. Time-to-kidney failure was regressed on serially measured biomarkers in two ways: time-dependent LOCF Cox proportional hazards regression and multivariate joint models. In time-dependent LOCF Cox regression, higher POX was associated with increased risk of kidney failure (HR = 2.20 per doubling, 95% CI = [1.38-3.51], p < 0.001) whereas UOX was not (HR = 1.08 per doubling, [0.66-1.77], p = 0.77). In multivariate joint models, estimates suggest higher UOX may be associated with lower risk of kidney failure (HR = 0.42 per doubling [0.15-1.04], p = 0.066), though not statistically significant, since impaired urinary excretion of oxalate may reflect worsening kidney function. Multivariate joint modeling is more flexible than LOCF and may better reflect biological plausibility since biomarkers are not steady-state values between measurements. While LOCF is preferred to naïve methods not accounting for changes in biomarkers over time, results may not accurately reflect flexible relationships that can be captured with multivariate joint modeling.