Time-to-Event Analysis with Unknown Time Origins via Longitudinal Biomarker Registration

In observational studies, the time origin of interest for time-to-event analysis is often unknown, such as the time of disease onset. Existing approaches to estimating the time origins are commonly built on extrapolating a parametric longitudinal model, which rely on rigid assumptions that can lead to biased inferences. In this paper, we introduce a flexible semiparametric curve registration model. It assumes the longitudinal trajectories follow a flexible common shape function with person-specific disease progression pattern characterized by a random curve registration function, which is further used to model the unknown time origin as a random start time. This random time is used as a link to jointly model the longitudinal and survival data where the unknown time origins are integrated out in the joint likelihood function, which facilitates unbiased and consistent estimation. Since the disease progression pattern naturally predicts time-to-event, we further propose a new functional survival model using the registration function as a predictor of the time-to-event. The asymptotic consistency and semiparametric efficiency of the proposed models are proved. Simulation studies and two real data applications demonstrate the effectiveness of this new approach.

Joint modelling of longitudinal 3MS scores and the risk of mortality among cognitively impaired individuals

Background

Modified Mini-Mental State Examination (3MS) is an instrument administered by trained personnel to examine levels of participants’ cognitive function. However, the association between changes in scores over time and the risk of death (mortality) is not known. The aims of this study are to examine the association between 3MS scores and mortality via cognitive impairment among older women and to determine individuals’ risk of changes in scores to better predict their survival and mortality rates.

Methods

We propose a Bayesian joint modelling approach to determine mortality due to cognitive impairment via repeated measures of 3MS scores trajectories over a 21-year follow-up period. Data for this study are taken from the Osteoporotic Fracture longitudinal study among women aged 65+ which started in 1986–88.

Results

The standard relative risk model from the analyses with a baseline 3MS score after adjusting for all the significant covariates demonstrates that, every unit decrease in a 3MS score corresponds to a non-significant 1.059 increase risk of mortality with a 95% CI of (0.981, 1.143), while the extended model results in a significant 0.09% increased risk in mortality. The joint modelling approach found a strong association between the 3MS scores and the risk of mortality, such that, every unit decrease in 3MS scores results in a 1.135 (13%) increased risk of death via cognitive impairment with a 95% CI of (1.056, 1.215).

Conclusion

It has been demonstrated that a decrease in 3MS results has a significant increase risk of mortality due to cognitive impairment via joint modelling, but insignificant when considered under the standard relative risk approach.