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Statistical Methods in Medical Research (2008)

Nonparametric estimation of state occupation, entry and

exit times with multistate current status data

Ling Lan and Somnath Datta

somnath.datta_AT_louisville.edu

www.louisville.edu/~s0datt03

www.louisville.edu/~l0lan001

Department of Bioinformatics & Biostatistics

University of Louisville, KY, USA

As a type of multivariate survival data, multistate models have a wide range of applications, notably in cancer and infectious disease progression studies. In this paper, we revisit the problem of estimation of state occupation, entry and exit times in a multistate model where various estimators have been proposed in the past under a variety of parametric and nonparametric assumptions. We focus on two nonparametric approaches, one using a product limit formula as recently proposed in Datta and Sundaram (2006, Biometrics) and a new approach using a fractional risk set calculation followed by a subtraction formula to calculate the state occupation probability of a transient state. A numerical comparison between the two methods is presented using simulation studies. We illustrate the two methods using two cancer data sets extracted from the SEER cancer registry.

Tables and Figures of L₁ Distances in a Five-state Semi-Markov Model

Lognormal state waiting times

Uniform censoring (Table & Figure)

Weibull censoring (Table & Figure)

Weibull state waiting times

Uniform censoring (Table & Figure)

Weibull censoring (Table & Figure)

Tables and Figures of L₁ Distances in a Four-state Markov Tracking Model

Lognormal state waiting times

Uniform censoring (Table & Figure)

Weibull censoring (Table & Figure)

Weibull state waiting times

Uniform censoring (Table & Figure)

Weibull censoring (Table & Figure)