Estimation of progression of multi-state chronic disease using the Markov model and prevalence pool concept

BackgroundWe propose a simple new method for estimating progression of a chronic disease with multi-state properties by unifying the prevalence pool concept with the Markov process model.MethodsEstimation of progression rates in the multi-state model is performed using the E-M algorithm. This approach is applied to data on Type 2 diabetes screening.ResultsGood convergence of estimations is demonstrated. In contrast to previous Markov models, the major advantage of our proposed method is that integrating the prevalence pool equation (that the numbers entering the prevalence pool is equal to the number leaving it) into the likelihood function not only simplifies the likelihood function but makes estimation of parameters stable.ConclusionThis approach may be useful in quantifying the progression of a variety of chronic diseases.

[1]  N. Day,et al.  Simplified models of screening for chronic disease: estimation procedures from mass screening programmes. , 1984, Biometrics.

[2]  K. Narayan,et al.  Causes of death and associated factors among patients with non-insulin-dependent diabetes mellitus in Taipei, Taiwan. , 1999, Diabetes research and clinical practice.

[3]  R Brookmeyer,et al.  Estimation of current human immunodeficiency virus incidence rates from a cross-sectional survey using early diagnostic tests. , 1995, American journal of epidemiology.

[4]  F. Alexander,et al.  The natural history of breast carcinoma , 2000, Cancer.

[5]  K. Hsiao,et al.  Community-Based Epidemiological Study on Diabetes in Pu-Li, Taiwan , 1992, Diabetes Care.

[6]  Stephen W. Duffy,et al.  A Markov chain method to estimate the tumour progression rate from preclinical to clinical phase, sensitivity and positive predictive value for mammography in breast cancer screening , 1996 .

[7]  L. Sharples,et al.  Use of the Gibbs sampler to estimate transition rates between grades of coronary disease following cardiac transplantation. , 1993, Statistics in medicine.

[8]  Stephen Wolfram,et al.  Mathematica ® 3.0 Standard Add-on Packages , 1993 .

[9]  N. Welton,et al.  Estimation of Markov Chain Transition Probabilities and Rates from Fully and Partially Observed Data: Uncertainty Propagation, Evidence Synthesis, and Model Calibration , 2005, Medical decision making : an international journal of the Society for Medical Decision Making.

[10]  J D Habbema,et al.  Modelling issues in cancer screening , 1995, Statistical methods in medical research.

[11]  S. Duffy,et al.  Estimating sensitivity and sojourn time in screening for colorectal cancer: a comparison of statistical approaches. , 1998, American journal of epidemiology.

[12]  J. Habbema,et al.  A model‐based analysis of the hip project for breast cancer screening , 1990, International journal of cancer.

[13]  L. Tabár,et al.  Estimation of mean sojourn time in breast cancer screening using a Markov chain model of both entry to and exit from the preclinical detectable phase. , 1995, Statistics in medicine.

[14]  Nicholas T. Longford,et al.  Handling missing data in diaries of alcohol consumption , 2000 .

[15]  J. Kalbfleisch,et al.  The Analysis of Panel Data under a Markov Assumption , 1985 .