Abstract
Traditional methods for the analysis of failure time data are often employed in the analysis of waiting times of transient states from multistate models. However, such methods can exhibit bias when waiting times among model states are dependent, even when censoring is random. Furthermore, right-censoring can occur prior to entry into the transient state of interest, preventing the observation of transitions from the state and providing another potential source of bias. We introduce a nonparametric linear hazards model for waiting times from multistate models, analogous to Aalen’s linear hazards model for failure time data, where proper estimation can be carried out via reweighting, a method flexible enough to incorporate general forms of induced and other dependent censoring. We illustrate the approximate unbiasedness of the proposed regression coefficient estimators through a simulation study, while also demonstrating the bias arising from traditional Aalen’s linear hazards model estimators obtained from correlated waiting time data. Theoretical results for the parameter estimators are provided. The reweighted estimators are used in the analysis of two data sets, to identify predictors of ambulatory recovery in a data set of spinal cord injury patients receiving activity-based rehabilitation and to identify prognostic indicators for patients receiving bone marrow transplant.
Highlights
The motivating example for this article is a data set of 273 patients with incomplete spinal cord injury (SCI) participating in a national activity-based rehabilitation program [1, 2]
The achievement of these benchmarks provides an example of a multistate model, a five state model with states (1) patient unable to walk, (2) patient able to walk no faster than 0.44 m/s, (3) patient able to walk no faster than 0.7 m/s, (4) patient able to walk no faster than 1.2 m/s, (5) patient able to walk faster than 1.2 m/s (Figure 1)
Similar phenomena were observed under simulation models 1 and 3, the results of which can be found in the supplemental materials associated with this manuscript [17]
Summary
The motivating example for this article is a data set of 273 patients with incomplete spinal cord injury (SCI) participating in a national activity-based rehabilitation program [1, 2]. Walking speed is among the measures of function collected on these patients, and there are several clinical benchmarks – 0.44 m/s represents the minimum walking speed associated with the ability to walk in the community, 0.7 m/s separates those who require assistive walking devices from those who do not, and 1.2 m/s approximately defines the speed required to cross a street at a stoplight [3] The achievement of these benchmarks provides an example of a multistate model, a five state model with states (1) patient unable to walk, (2) patient able to walk no faster than 0.44 m/s, (3) patient able to walk no faster than 0.7 m/s, (4) patient able to walk no faster than 1.2 m/s, (5) patient able to walk faster than 1.2 m/s (Figure 1). Clinicians in the rehabilitation program have been interested in identifying prognostic indicators of the amount of time it takes ambulatory patients to achieve this goal
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