A Pearson‐type goodness‐of‐fit test for stationary and time‐continuous Markov regression models

Aguirre-Hernández, Rosalía; Farewell, Vernon T.

doi:10.1002/sim.1152

Cited by 51 publications

(50 citation statements)

References 7 publications

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“…Aguirre-Hernández and Farewell [6] presented what was essentially an extension of Kalbfleish and Lawless's Pearson chi-square method, to cope with the common situation of irregular observation times and continuous covariates. Simulations suggest that the null distribution of this statistic is reasonably well approximated by the analogous χ 2 d−p distribution when there are no continuous covariates and has a slightly inflated mean when continuous covariates are present.…”

Section: Contingency Table Based Methodsmentioning

confidence: 99%

“…The remainder of the chapter considers in more detail some of the existing informal diagnostics for model fit, applying them to the CAV and BOS datasets. Chapter 3 develops existing work by Aguirre-Hernández and Farewell [6] on a general Pearson-type goodness-of-fit test for Markov models. The test is extended to allow application on misclassification hidden Markov models.…”

Section: Contentsmentioning

confidence: 99%

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Model diagnostics for multi-state models

Titman

Sharples

2009

Stat Methods Med Res

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Multi-state models are a popular method of describing medical processes that can be represented as discrete states or stages. They have particular use when the data are panel-observed, meaning they consist of discrete snapshots of disease status at irregular time points which may be unique to each patient. However, due to the difficulty of inference in more complicated cases, strong assumptions such as the Markov property, patient homogeneity and time homogeneity are applied. It is important that the validity of these assumptions is tested. A review of methods for diagnosing model fit for panel-observed continuous-time Markov and misclassification-type hidden Markov models is given, with illustrative application to a dataset on cardiac allograft vasculopathy progression in post-heart transplant patients.

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Section: Contingency Table Based Methodsmentioning

confidence: 99%

Section: Contentsmentioning

confidence: 99%

Model diagnostics for multi-state models

Titman

Sharples

2009

Stat Methods Med Res

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“…A formal goodness-of-fit test for the hypothesis that panel data were generated by a fitted Markov model was developed by Aguirre-Hernandez and Farewell (2002). This test was extended by Titman and Sharples (2008) The null distribution of the statistic is not exactly χ 2 , with a complex form for general panel data (Titman 2009).…”

Section: Formal Goodness-of-fit Testmentioning

confidence: 99%

“…This test was extended by Titman and Sharples (2008) The null distribution of the statistic is not exactly χ 2 , with a complex form for general panel data (Titman 2009). For simpler models without covariates, Aguirre-Hernandez and Farewell (2002) showed by simulation that the χ 2 approximation was adequate. The pearson.msm function provides theoretical upper and (unless there are exact death times) lower bounds for the test p value.…”

Section: Formal Goodness-of-fit Testmentioning

confidence: 99%

Multi-State Models for Panel Data: ThemsmPackage forR

Jackson¹

2011

J. Stat. Soft.

954

1,010

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Panel data are observations of a continuous-time process at arbitrary times, for example, visits to a hospital to diagnose disease status. Multi-state models for such data are generally based on the Markov assumption. This article reviews the range of Markov models and their extensions which can be fitted to panel-observed data, and their implementation in the msm package for R. Transition intensities may vary between individuals, or with piecewise-constant time-dependent covariates, giving an inhomogeneous Markov model. Hidden Markov models can be used for multi-state processes which are misclassified or observed only through a noisy marker. The package is intended to be straightforward to use, flexible and comprehensively documented. Worked examples are given of the use of msm to model chronic disease progression and screening. Assessment of model fit, and potential future developments of the software, are also discussed.Keywords: multi-state models, Markov models, panel data, R, msm.1. Markov multi-state models for panel data DefinitionsA multi-state model describes how an individual moves between a series of states in continuous time. Suppose an individual is in state S(t) at time t. The movement on the discrete state space 1, . . . , R is governed by transition intensities q rs (t, z(t)) : r, s = 1, . . . , R. These may depend on time t, or, more generally, also on a set of individual-level or time-dependent explanatory variables z(t). The intensity represents the instantaneous risk of moving from state r to state s = r: q rs (t, z(t)) = lim δt→0 P(S(t + δt) = s|S(t) = r)/δt.

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“…Aguirre-Hernandez and Farewell (2002) and Titman and Sharples (2010) provide tests for a set of multi-state models, but this set does not include our model. However, Titman and Sharples also review less formal ways of model validation, and we use their basic ideas in the following validation of Model A.…”

Section: Model Validationmentioning

confidence: 99%