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Abstract

We present a nonparametric method for estimating the conditional future state entry probabilities and distributions of state entry time conditional on a past state visit when data are subject to dependent censorings in a progressive multistate model where Markovianity of the system is not assumed. These estimators are constructed using the competing risk techniques with risk sets consisting of fractional observations and inverse probability of censoring weights. The fractional observations correspond to estimates of the number of persons who ultimately enter a state from which the future state in question can be reached in one step. We then address the corresponding regression problem by combining these marginal estimators with the pseudo-value approach. The performance of our regression scheme is studied using a comprehensive simulation study. An analysis of existing data on graft-versus-host disease for bone marrow transplant individuals is presented using our novel methodology. A second analysis of another well-known data set on burn patients is also included.

Keywords

Nonparametric multistate dependent censoring competing risk fractional weight inverse weight pseudo-value approach

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References

Datta

Satten

. Estimation of integrated transition hazards and stage occupation probabilities for non-Markov systems under dependent censoring. Biometrics 2002; 58: 792–802.

Lan

Datta

. Non-parametric estimation of state occupation, entry and exit times with multistate current status data. Stat Methods Med Res 2010; 19: 147–165.

Klein

Moeschberger

. Survival analysis: Techniques for censored and truncated data, vol. 2. New York: Springer, 2003.

Datta

Satten

. Validity of the Aalen–Johansen estimators of stage occupation probabilities and Nelson–Aalen estimators of integrated transition hazards for non-Markov models. Stat Probab Lett 2001; 55: 403–411.

Datta

Lan

Sundaram

. Nonparametric estimation of waiting time distributions in a Markov model based on current status data. J Stat Plan Inference 2009; 139: 2885–2897.

Datta

Ferguson

. Nonparametric estimation of marginal temporal functionals in a multi-state model. In: Lisnianski A and Frenkel I (eds) Recent advances in system reliability. London: Springer, 2012, pp. 219–235.

Lan

Datta

. Comparison of state occupation, entry, exit and waiting times in two or more groups based on current status data in a multistate model. Stat Med 2010; 29: 906–914.

Satten

Datta

Robins

. Estimating the marginal survival function in the presence of time dependent covariates. Stat Probab Lett 2001; 54: 397–403.

Martinussen

Scheike

. Dynamic regression models for survival data, vol. 1. New York: Springer, 2007.

10.

Andersen

Klein

Rosthøj

. Generalised linear models for correlated pseudo-observations, with applications to multi-state models. Biometrika 2003; 90: 15–27.

11.

Klein

Gerster

Andersen

, et al. SAS and R functions to compute pseudo-values for censored data regression. Comput Methods Programs Biomed 2008; 89: 289–300.

12.

Efron

. Bootstrap methods: Another look at the jackknife. New York: Springer, 1992.

13.

Datta

Satten

. Estimating future stage entry and occupation probabilities in a multistage model based on randomly right-censored data. Stat Probab Lett 2000; 50: 89–95.

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Regression analysis of a future state entry time distribution conditional on a past state occupation in a progressive multistate model

Abstract

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Supplementary Material