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Multi-State Markov Model: An Application to Liver Cirrhosis

100%
Grover G., Sreenivas V., Khanna S., Seth D.
Statistics in Transition new series
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2014
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vol. 15
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issue 3
429-442
EN
The control and treatment of chronic diseases is a major public health challenge, particularly for patients suffering from liver disease. In this paper, we propose a frame to estimate survival and death probabilities of the patients suffering from liver cirrhosis and HCC in the presence of competing risks. Database of the admitted patients in a hospital in Delhi has been used for the study. A stochastic illness-death model has been developed describing two liver illness states (Cirrhosis and HCC) and two death states (death due to liver disease and death due to competing risk). Individuals in the study were observed for one year of life at any age xi. The survival and death probabilities of the individuals suffering from liver cirrhosis and HCC have been estimated using the method of maximum likelihood. The probability of staying in the cirrhotic state is estimated to be threefold higher than that of developing HCC (0.64/0.21) in one year of life. The probability of cirrhotic patient moving to HCC state is twice (0.21/0.11) the probability of dying due to liver disease. HCC being the severe stage, the probability of patient dying due to HCC is three times that of cirrhosis. Markov model proves to be a useful tool for analysis of chronic degenerative disease like liver cirrhosis. It can provide in-depth insight for both the researchers and policy makers to resolve complex problems related to liver cirrhosis with irreversible transitions.
2
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Restriction Testing in Binary Choice Model with I(1) Regressors

100%
Grabowski W.
Central European Journal of Economic Modelling and Econometrics
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2009
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issue 4
3
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Estimation of P(X ≤ Y ) for discrete distributions with non-identical support

100%
Mouli Choudhury M., Bhattacharya R., Maiti S. S.
Statistics in Transition new series
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2022
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vol. 23
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issue 3
43-64
EN
The Uniformly Minimum Variance Unbiased (UMVU) and the Maximum Likelihood (ML) estimations of R = P(X ≤ Y ) and the associated variance are considered for independent discrete random variables X and Y. Assuming a discrete uniform distribution for X and the distribution of Y as a member of the discrete one parameter exponential family of distributions, theoretical expressions of such quantities are derived. Similar expressions are obtained when X and Y interchange their roles and both variables are from the discrete uniform distribution. A simulation study is carried out to compare the estimators numerically. A real application based on demand-supply system data is provided.
4
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Finite Mixtures Model Approach to Sensitive Questions in Surveys

88%
Artem S., Rostyslav M.
Statistics in Transition new series
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2011
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vol. 12
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issue 2
331-344
EN
Observations from mixtures of different subpopulations are common in biological and sociological studies. We consider the case, when the observations are taken from a set of groups containing subjects, which belong to different subpopulations. Proportion of each subpopulation in a group is known and can vary from group to group. Our aim is to estimate the means of an observed variable for subjects, which belong to each subpopulation. In this paper we consider the case, when subpopulations are defined by answers on so called “sensitive questions”. We consider some parametric and nonparametric estimates of the subpopulation means, such as weighted means, maximum likelihood and weighted least squares estimates. Finite sample properties of these estimates are analyzed. Mean square errors of the estimates are compared on simulated data. Some asymptotic results are also given.
5
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State-dependent Autoregressive Models with p Lags: Properties, Estimation and Forecasting

75%
Gobbi F., Mulinacci S.
Central European Journal of Economic Modelling and Econometrics
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2022
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issue 1
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