Conditional rate derivation in the presence of intervening variables using a Markov chain
| Autor: | Richard H. Shachtman, John R. Schoenfelder, Carol J. R. Hogue |
|---|---|
| Rok vydání: | 1982 |
| Předmět: |
Risk
Analysis of Variance Distribution (number theory) Markov chain Variable-order Markov model Research methodology Yugoslavia Abortion Induced Management Science and Operations Research Delivery Obstetric Markov Chains Computer Science Applications Outcome and Process Assessment Health Care Pregnancy Statistics Econometrics Humans Female Epidemiologic Methods Incidence (geometry) Mathematics Event (probability theory) |
| Zdroj: | Operations research. 30(6) |
| ISSN: | 0030-364X |
| Popis: | When conducting inferential and epidemiologic studies, researchers are often interested in the distribution of time until the occurrence of some specified event, a form of incidence calculation. Furthermore, this interest often extends to the effects of intervening factors on this distribution. In this paper we impose the assumption that the phenomena being investigated are governed by a stationary Markov chain and review how one may estimate the above distribution. We then introduce and relate two different methods of investigating the effects of intervening factors. In particular, we show how an investigator may evaluate the effect of potential intervention programs. Finally, we demonstrate the proposed methodology using data from a population study.In an effort to determine whether a prespecified response occurs more frequently among those persons who exhibit a certain risk, biological and epidemiological investigations often assess the relationship between risk factors (e.g., personal or demographic variables) and response factors (e.g., development of disease). Researchers frequently will investigate more than the initial risk and response; they will consider intervening variables. 2 ways of incorporating intervening variables--as either subsequent or antecedent factors--are investigated in this discussion. Noting that traditional epidemiological approaches to both methods of intervening variable analysis frequently exert an unreasonable large data demand, it is shown how a Markov chain (MC) may be used to significantly reduce the data requirements. It is assumed that the underlying process is a stationary (time homogeneous) MC. Formal analytic definitions of both types (antecedent and subsequent) of intervening variable analyses are presented, and a relationship is derived between them. It is shown how researchers may conduct both analyses, as well as the ordinary (nonintervening variable) analysis, using functions of the MC transition matrix. All analyses demand only sufficient data either to estimate the transition matrix or to modify an existing matrix; none requires the subgroup specific data required by traditional epidemiologic approaches (e.g., direct incidence measures). To illustrate these concepts, a numerical example is presented using a MC from a study of induced abortion. The MC was submitted to formal goodness of fit tests to verify the Markov property (Shachtman et al.). Alternatively, depending on the application the researcher may prefer to employ structural assumption validation, accept the model as a reasonable approximation to the empirical process under study, or "internally" validate the property by examining functions of the transition matrix and seeing if these functions replicate equivalent empirical distribution functions derived directly from the underlying data. Possibly the most important aspect of this approach is that by developing stochastic models, e.g., Markov chain models, and using these conditional rates, researchers may perform intervening variable analyses as parameterizations of the model used in the nonintervening variable analysis. This permits them to circumvent the estimation of independent distributions for each of the subgroups defined by the intervening variables, offering the potential for a large reduction in data requirements. |
| Databáze: | OpenAIRE |
| Externí odkaz: |
|