Document Type


Degree Name



Dept. of Public Health & Preventive Medicine


Oregon Health & Science University


Slower gait speed has previously been shown to be associated with mortality in aging populations, based on a single measure of gait speed, but repeated measures of gait speed may be more informative. Although an extended Cox model can accommodate a timevarying covariate, the Cox framework has certain limitations in context of endogenous or continuous time-varying covariates or time-varying covariates measured with error.

The joint modeling framework uses a smooth, continuous model of the time-varying covariate that may more accurately represent its true, underlying longitudinal trajectory. The framework also incorporates measurement error of the time-varying covariate and uses a likelihood formulation that is consistent with endogenous covariates (i.e., covariates whose future trajectories after the occurrence of the event of interest are altered by the event). The chief benefits of these improvements, substantiated by simulation study, is that joint models are not subject to underestimation of the effect size and standard error, as may occur in extended Cox models. Also, joint models have less stringent assumptions about missing data mechanisms than linear mixed-effects models, so they can correct bias in longitudinal estimates that may result from non-ignorable missingness.

The objective of this thesis is to estimate the association between longitudinal trajectories of gait speed and survival time and to compare estimates of association from separate models (i.e., mixed-effects models and Cox models) and joint models.

A subset of 877 ambulatory, community-dwelling older men from 2 of the 6 sites in the Osteoporotic Fractures in Men (MrOS) study performed a walking test up to 5 times over a median follow-up time of 7 years and were followed for a median of 11 years for mortality. We modeled the hazard ratio (HR) of gait speed 1) as a baseline measure alone, 2) as a time-varying covariate (extended Cox), and 3) as a longitudinal sub-model using linear mixed-effects with cubic natural splines (joint model). Slower gait speed was associated with mortality in all models. The HR per 0.1 m/s decline in gait speed was 1.08 in the Cox model (95% CI: 1.01 to 1.15); 1.14 (95% CI: 1.05 to 1.22) in the extended Cox model; and 1.25 (95% CI: 1.15 to 1.36) in the best-fitting joint model. Estimates of longitudinal parameters from the linear mixed-effects vs. joint model suggested estimation was not sensitive to missingness assumptions. As expected, the extended Cox model underestimated the effect of longitudinal gait speed on survival time. Estimates of longitudinal parameters were similar across modeling strategy, suggesting that the longitudinal process was not sensitive to missingness assumptions. Contrary to expectation, standard errors for both longitudinal and event parameters were very similar across all modeling strategies. Providers may benefit by considering the increased estimate of the association between gait speed and survival time. Traditional modeling techniques may underestimate the magnitude of this association.




School of Medicine



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