The Effects of Physician Supply on the Early Detection of Rectal Cancer

Multivariate Analysis

We examined the relationship between physician supply and the odds of late-stage diagnosis using multiple logistic regression. Potential confounding variables were modeled in a similar fashion in all logistic models: age (as a continuous variable), level of education (3 indicator variables), level of income (4 indicator variables), insurance payer (7 indicator variables), race-ethnicity (3 indicator variables), sex, comorbidity (single ordinal variable), and marital status (4 indicator variables).

In the first step of our analysis, we contrasted the effects of the supplies of primary care physicians and specialty physicians by including their county-level measures in the logistic model described above. We chose county-level supply measures as the relevant variable for several reasons. We anticipated most patients would be willing to travel some distance to receive specialty care. Also, we considered ZIP code clusters too small an area to adequately measure access to specialty care, especially in urban areas where they are closely spaced. In addition, several Florida health care programs that affect primary and specialty care access are structured and financed at the county level.

We adjusted primary care and specialty physician supplies simultaneously so that effects of primary care supply were adjusted for specialty supply, and vice versa. In addition to examining their main effects, we also examined whether there was a statistical interaction between primary care and specialty care effects. Because specialty physician supply was likely to be correlated with community characteristics, we also stratified analyses by urban or nonurban residence and by high (above the median) versus low (below the median) socioeconomic area of residence.

In the second step of our analysis, we contrasted the effects of individual primary care specialty supplies (family/general practice, general internal medicine, obstetrics/gynecology) by including measures of their supply at the ZIP code cluster level in the logistic model. We chose ZIP code cluster measures of physician supply for this part of the analysis in accordance with the belief that the choice between an internist, family physician, or gynecologist as a patient’s primary care physician would be most likely influenced by the availability of these physicians at the local level rather than at the regional level. We also simultaneously controlled the effects of individual supplies of primary care physicians and adjusted for overall physician supply in ZIP code clusters.

To allow for nonlinear relationships, we created indicator variables by percentiles of physician supply in all logistic models.⁵² Cases in the lowest 10th percentile of physician supply were designated as the referent group, and 9 indicator variables were created corresponding to each 10-percentile increase in physician supply (n = approximately 900 patients per group). Relationships were then examined by graphing the 9 corresponding odds ratios.^53-55 Linear relationships between physician supply and the odds of late-stage diagnosis were subsequently tested in logistic models using the chi-square likelihood ratio test.⁵²

Because all patients residing in the same county are assigned the same measure of physician supply, there may be correlation of error terms. Clustering by county could lead to underestimation of standard errors in logistic models.⁵⁶ To examine this possibility we reestimated parameters and their errors using the method of generalized estimating equations, which controls for clustered or correlated data.^57,58

For odds ratios that were significant, we estimated the number and percentage of late-stage colorectal cancers that could be attributed to the existing physician supply. We first used methods described by Zhang and Yu⁵⁹ to estimate the corresponding risk ratios from the odds ratios derived from logistic models, then used established methods to derive attributable percentages and numbers from the risk ratios.⁵³

Results

The study population consisted of the 8933 Florida residents who were diagnosed with colorectal cancer in 1994 for whom stage at diagnosis was known Table 1. Table 2 shows the local and regional physician supply for subjects’ places of residence. At the county level, the supply of specialty physicians was more than twice that of primary care physicians. At the local level family/general practice and internal medicine physicians made up the majority of the primary care physicians in patients’ ZIP code clusters.

Figure 1 shows the relationship between total physician supply at the county level and the odds of late-stage diagnosis. Odds ratios are relative to cases in the lowest 10th percentile of total physician supply. There was no apparent relationship, either linear or nonlinear, between increasing physician supply and the odds of late-stage diagnosis (c2 for linear trend = 0.11; P = .74).

Figure 2 shows the separate relationships of primary care and non–primary-care physician supplies with stage at diagnosis. Controlling for specialty physician supply, the effects of primary care physician supply were linear (c2 = 7.34; P = .007). For each 10-percentile increase in primary care physician supply, the odds of late-stage diagnosis decreased by 5% (adjusted odds ratio [OR] = 0.95, 95% confidence interval [CI], 0.92 - 0.99). Controlling for primary care physician supply, the effects of specialty physician supply were also linear (c2 = 7.66, P = .006). For each 10-percentile increase in specialty physician supply, the odds of late-stage diagnosis increased by 5% (adjusted OR = 1.05; 95% CI, 1.02 - 1.09). There was no statistical interaction between the effects of primary care and specialty physician supplies (OR = 0.998; P = .49).