An Application of Markov Processes to the Study of the Epidemiology of Mental Disease

Marshall, Andrew W.; Goldhamer, Herbert

doi:10.2307/2281101

Cited by 11 publications

(3 citation statements)

References 0 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Much work has also been done on the cohort analysis of patients first admitted in each year-see in particular Brooke (1963) and the papers in Freeman and Farndale (1963). This has given rise to an interesting example of the application of the theory of Markov chains (Marshall and Goldhamer, 1955). Apart from the light this throws on the effects of treatment and the increase in mortality in mental hospital patients, this type of study has great administrative importance.…”

Section: The Distribution Of Mental Disease In Communitiesmentioning

confidence: 99%

Statistical Methods in Psychiatric Research

Morán

1969

Journal of the Royal Statistical Society. Series A (General)

View full text Add to dashboard Cite

Section: The Distribution Of Mental Disease In Communitiesmentioning

confidence: 99%

Statistical Methods in Psychiatric Research

Morán

1969

Journal of the Royal Statistical Society. Series A (General)

View full text Add to dashboard Cite

“…Fix and Neyman also discuss estimation procedures for fitting the parameters in their model. Marshall and Goldhamer, [4], presented several discrete Markov chain models as a framework for the handling of data in connection with the epidemiology of mental disease. Their object was to characterize the age distributions of the mentally ill population.…”

Section: Earlier Modelsmentioning

confidence: 99%

A semi-markov model for clinical trials

Weiss

Zelen

1965

Journal of Applied Probability

View full text Add to dashboard Cite

This paper applies the theory of semi-Markov processes to the construction of a stochastic model for interpreting data obtained from clinical trials. The model characterizes the patient as being in one of a finite number of states at any given time with an arbitrary probability distribution to describe the length of stay in a state. Transitions between states are assumed to be chosen according to a stationary finite Markov chain.Other attempts have been made to develop stochastic models of clinical trials. However, these have all been essentially Markovian with constant transition probabilities which implies that the distribution of time spent during a visit to a state is exponential (or geometric for discrete Markov chains). Markov models need also to assume that the transitions in the state of a patient depend only on absolute time whereas the semi-Markov model assumes that transitions depend on time relative to a patient. Thus the models are applicable to degenerative diseases (cancer, acute leukemia), while Markov models with time dependent transition probabilities are applicable to colds and epidemic diseases. In this paper the Laplace transforms are obtained for (i) probability of being in a state at timet, (ii) probability distribution to reach absorption state and (iii) the probability distribution of the first passage times to go from initial states to transient or absorbing states, transient to transient, and transient to absorbing. The model is applied to a clinical study of acute leukemia in which patients have been treated with methotrexate and 6-mercaptopurine. The agreement between the data and the model is very good.

show abstract

“…Although the models were recognized as an over-simplification of the data, they did highlight many problems facing data analysts wishing to summarize longitudinal data of this type. Other work in this area has been conducted by Marshall & Goldhamer (1955), Eaton (1974), Duncan-Jones (1981) and Dunn & Skuse (1981).…”

Section: Introductionmentioning

confidence: 99%

Patterns of psychiatric diagnosis in general practice: the Second National Morbidity Survey

Dunn

1986

Psychol. Med.

View full text Add to dashboard Cite

SynopsisMultidimensional scaling, in the form of principal coordinates analysis and two-way correspondence analysis, is used to illustrate inter-practice variation in patterns of psychiatric diagnoses provided by data from the longitudinal file of the Second National Morbidity Survey. The results strongly support the view that general practitioners' diagnostic habits should be validated before their records are used to provide data on ‘official’ estimates of psychiatric morbidity. It is recommended that, whatever the quality of the data, large tables of official socio-economic or medical statistics should be supplemented by graphical summaries, as they quite often are in France.

show abstract

An Application of Markov Processes to the Study of the Epidemiology of Mental Disease

Cited by 11 publications

References 0 publications

Statistical Methods in Psychiatric Research

Statistical Methods in Psychiatric Research

A semi-markov model for clinical trials

Patterns of psychiatric diagnosis in general practice: the Second National Morbidity Survey

Contact Info

Product

Resources

About