The mix of primary care versus surgical specialist physicians: an examination of gallbladder surgery.

• Author: Jones, Alison S.

beds are a complement to surgical care and may act as a constraint on supply of surgical care.

15. This amounts to estimation of an unweighted linear probability model and represents a substantial cost savings over the more expensive likelihood techniques employed subsequently. A number of sources document the similarity of signs and t-ratios of OLS and both probit and logit coefficients [11; 24; 12; 23; 25].

16. The potential endogeneity of this variable casts some uncertainty on the interpretation of this result.

    1. Introduction

       One important initiative in President Clinton's proposed Health Security Plan is the creation of incentives for physicians to provide primary care. It is believed that reductions in the number of surgical specialists accompanied by increases in the number of primary care physicians will shift the mix of services from more costly inpatient interventions towards less costly outpatient interventions and preventive care. The proposed incentives include shifting federal support for medical education away from specialty care towards primary care as well as increasing Medicare payment rates for primary care physicians [27]. A clearer understanding of the effects of primary care and surgeon supply on demand for surgical procedures is thus a critical element in the health reform debate.

       A positive association between the supply of physicians in an area and the use of physician services is well documented [6; 21; 24]. However, recent studies of ambulatory services have found only weak evidence or no evidence that physician supply is a significant determinant of use of services [13; 20; 22; 28]. Some early studies of the market for surgery used aggregate data and found that surgeon supply is a significant positive determinant of surgery rates [7; 14; 15]. There has been some discussion in the literature regarding the relative advantages of using aggregate versus individual level data to examine this issue.(1) Other researchers [20; 29], using individual level data, did not confirm the findings based on aggregate data. However, Feldman and Sloan [6] note that studies based on individual data could still be subject to omitted variable bias unless a fixed effects specification is used.(2)

       Evidence regarding the relationship between the supply of primary care physicians and surgery rates is also mixed. Some researchers have found evidence that these specialists act as substitutes for surgical specialists suggesting that they may perform surgery or provide alternative non-surgical treatment [7; 14; 20]. However, other studies indicate that primary care specialists function as gatekeepers in determining which patients are good candidates for surgery [3; 5; 8; 19].(3)

       In this study, the role of primary care physicians and general surgeons in the demand for gallbladder procedures is examined using a fixed-effects model and individual level data. This type of procedure was chosen because it has high incidence(4) and is generally viewed as elective.(5) A model developed by Sloan and Feldman [24] is extended to include other area demand characteristics (besides surgeon supply) in the individual consumer's demand equation.

    2. Model

       The point of departure is a consumer maximizing utility defined over perceived level of health (H) and other goods and services (G) . H is determined by the surgical care the consumer purchases (S) and the information that he receives from the surgeon about the benefit of the marginal unit of care purchased (I). Optimal S, [S.sup.*], is derived from the first order maximization conditions as a function of the exogenous variables.

       [S.sup.*] = [S.sup.*](P, X, I) (1)

       where X is a vector of individual consumer demand characteristics and P is a vector of relevant prices. Because primary care physicians may serve as an important source of referrals for surgical procedures or as substitutes for surgical care, the price and availability (as a time price proxy) of these specialists are also included in P. Since I is not observed, an expression for it, [I.sup.*], is derived from a model of surgeon behavior based on Sloan and Feldman [24].

       Physicians are utility maximizers choosing their net income (Y), workload (W) and information provided (I).(6) A linear individual consumer demand curve and one patient characteristic, E, which results in a differential demand response to surgeon information are assumed.(7)

       [Q.sub.Di] = [Alpha] + [Beta]P + [Gamma][X.sub.i] + [Delta][E.sub.i] + [Epsilon]I + [Zeta][E.sub.i]I (2)

       where I represents the surgeon's uniform level of information provided to all patients. The surgeon's market demand curve is just the horizontal sum of individual demand curves in her market. Assuming quasi-concavity of physician utility and substituting the market demand curve, [Q.sub.D], into the surgeon's income equation, the first order conditions are solved for the optimal level of I, [I.sup.*], in terms of the exogenous variables in the model. Assuming a linear functional form for [I.sup.*]:

       [Mathematical Expression Omitted]

       where [Mathematical Expression Omitted] and [Mathematical Expression Omitted] are average area patient characteristics, R is the area population to surgeon ratio, and Z is a vector of exogenous variables from the surgeon's cost function. Substituting [I.sup.*] into the consumer's demand equation for surgical care and assuming a linear relationship gives (8)

       [Mathematical Expression Omitted].

       This equation differs from the S-F model by the addition of the interaction terms and in the inclusion of other area demand characteristics besides the population to surgeon ratio in [I.sup.*]. Estimation of the above empirical model may yield results that are consistent with other theoretical formulations that do not imply a direct effect of surgeon supply on the demand for surgery. For example, the coefficient of the population to surgeon ratio may pick up differences in time price that affect individual levels of demand. Similarly, the coefficients on the interaction term may capture time price interactions with individual characteristics that could influence an individual's valuation of time, such as level of education. It seems likely, however, that time price may be fairly uniform when analysis is restricted to a single high incidence procedure.(9)

    3. Methods

       In the normal linear case, a fixed-effects specification would be estimated when correlation between error terms of observations within the same geographic area arises from omitted area specific variables that are correlated with both outcome and regressors. In a non-linear model such as that used here, the analog of a fixed-effects specification is Chamberlain's [4] conditional likelihood model. When group size is small, conditional likelihood estimation leads to consistent parameter estimates whereas estimation of a fixed-effects maximum likelihood model results in biased coefficients. However, Lord [10] suggested that the bias in the structural parameters is in-significant in the case where the number of observations within the groups approaches infinity at a rate faster than the rate at which the number of groups approaches infinity. Wright and Douglas [30] conducted Monte Carlo studies and found that for N = 500, 20 [less than or equal to] T [less than or equal to] 80, the fixed-effects maximum likelihood estimator is very close to the conditional maximum likelihood estimator and that its distribution is well approximated by standard asymptotic theory. Because the group sizes in the data set used in this study are well in excess of 20 and the number of observations is well in excess of 500, maximum likelihood fixed effects is used to obtain conditional likelihood parameter estimates.

       A fixed effects logit model is employed to obtain consistent estimates of the conditional likelihood parameters and an independent logit specification is used to obtain marginal likelihood estimates. The latter provide rough estimates of the amount of bias that may be present when within group correlation is ignored.

    4. Data

       Variable names and definitions are presented in Table I. Individual characteristics are from the 1976, 1978, 1980 and 1982 National Health Interview Survey (NHIS). In order to reduce the computational costs of the marginal and conditional likelihood analyses, the four year data set was randomly split into two sub-samples of individuals aged 17 to 64. This process resulted in a final analysis file containing 114,216 individuals. Descriptive comparisons of the analysis variables indicated that these sub-samples are comparable.

       Average area surgeon fees for cholecystectomy (GBFEE) were constructed from the HIAA Prevailing Health Care Charges System tapes and deflated by an estimated area cost of living value for the relevant year.(10) Deflated average area primary care physician fees for an office visit (AVGFEE) were constructed from Medicare Part B data. Physician and surgeon supply variables (POPSURG and POPIMGP) are...