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Utilization of ambulatory care studies: testing the assumptions

1991, Quality and Quantity

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This study examines the implicit assumptions in linear regression models used to predict ambulatory health care utilization, using data from 48,202 patients in the Quebec National Health Plan. Four main hypotheses regarding state transitions in utilization are tested: the dependence on transition rates, the differential effect of predictors based on state transitions, time dependence of transitions, and the non-equilibrium nature of the transition system. Findings indicate that the first three hypotheses cannot be rejected, suggesting that traditional linear regression methods may yield biased estimates in this context.

Quality & Quantity 25: 0 1991 Kluwer Academic 137 137-150, 1991. Publishers. Printed in the Netherlands. Utilization of ambulatory care studies: testing the assumptions FRANCOIS BBLAND Groupe de Recherche Interdisciplinaire en Sank, MontrPal. 2375 Chemin de la C&e Ste-Catherine, 3J 7. Canada Pavilion Marguerite d’ Youville. C.P. 6128. Succ. A, Montreal. Universitk de Qkbec. H3C Abstract. A linear regression procedure is usually used to estimate the effect of a set of predictors on utilization of ambulatory health care. The implicit assumptions embedded in the linear regression model have never been examined. Here, with utilization data of a sample of 48202 patients from the file of the Quebec National Health Plan, four implicit hypotheses embedded in the linear regression model are tested: (I) the transition from the state of utilization to the state of no utilization, and vice-versa, depends on the level of the transition rates, (2) the effect of independent variables depends on the transitions being predicted from or to the state of utilization,(3) the transition is time dependent, and (4) the system of transitions from one state to another is not at equilibrium. The analysis shows that the first three hypotheses cannot be rejected. Thus, the use of the familiar linear regression procedure in this study to estimate the effect of a set of factors on utilization would have yielded biased estimates. Studies of factors that explained or predicted the level of utilization of ambulatory health care have usually imposed implicit constraints of the linear regression model on their data (Andersen and Laake, 1983; Berkanovic et al., 1981; Broyles et al., 1983; Cleary et al., 1982; Diehr et al., 1984; Dutton, 1978; Evashwick et al., 1984; Hershey et al., 1975; Ingham and Miller, 1983; Markides et al., 1985; Rundall and Wheeler, 1979; Sharp et al., 1983; Stoller, 1982; Tanner et al., 1983; Thomas and Penchansky, 1984; Wan, 1982; Wan and Odell, 1981; Wolinsky, 1978; Wolinsky et al., 1983; Wright et al., 1980). Exceptions to this include the Shapiro and Roos paper (Shapiro and Roos, 1985) in which utilization of ambulatory health care over a two-year period, in a sample of elderly, was studied with a logistic model and the Hulka et al. paper (Hulka et al., 1972) where discriminant analysis was used. Other authors have used Probit (Kuder and Levitz, 1985) or Tobit (Link et al., 1982) procedures. Studies which are preoccupied with the evolution of health services utilization have used the regression model with time-period entered as dummy variables (McCall and Way, 1983). The implicit assumptions embedded in the linear regression model have never been examined in the current literature on health services utilization. But when a lagged regression model is used to fit longitudinal data, assumptions are made (1) that the transition rates toward a utilization level at one period of time from another level at a preceding period of time are a linear function of the independent variables and (2) that the transition rates from 138 Frarqois Bkland one level to the other, and from the latter to the former, are equal. When cross-sectional data are used in a regression model, the assumption that the utilization is a system at equilibrium is added to these two assumptions (Coleman, 1981). These assumptions can have far reaching consequences on the estimate of the effect parameters in a model predicting the level of utilization. For example, sociodemographic characteristics, which are defined in most studies as proxies for otherwise excluded cultural, social and psychological factors, may influence the propensity to initiate a visit to a physician, while their influence on follow-up visits could be minimal. Moreover, inasmuch as the propensity to use physicians’ services increases with the use of physicians (Kilpatrick, 1977a,b), effects of predictors of the first visit, after a period in which no visit occured, may differ from the effects of predictors of visits following the first one, even if they are not from the same episode. In a model that does not distinguish between transition toward use and transition toward no use, the effect of a variable will be a weighted average of its effect on both types of transitions. In the best case, the weighted average of the effect of the variable on utilization will be lower than the effect on the transition rates, in the worst case, the variable can be excluded altogether from the equation. The goal of this paper is to assess the effects of the assumptions of the linear regression model on the parameter estimates of four independent variables known to predict utilization of ambulatory care, and to discuss the ability of different assumptions to reflect the process of utilization of ambulatory medical care. The model Let us say that in a period of time, an individual can either be a user or a non-user of a medical service. The probability that he abstains from using is p, the probability that he uses is 1 -p. On the one hand, in a system where an observation is made at two time periods to and t,, an individual being in a state of non-user at to can move to the state of being a user at t, or he can stay in the state of being a non-user. On the other hand, a user of ambulatory medical care at to can move to the status of user at tl or he can still be a user in that period. These movements from one period to the next can be defined by the transition rates qi (i = 0, l), q. being the transition rate from being a non-user to being a user, and q1 being the transition rate from being a user to being a non-user. The transition rate is defined as the ratio of the probability of changing