Volume 4: No. 4, October 2007
|¶P(y | x)||=f(b)bi|
where f(.) is the probability density function of a standard normal random variable, is the mean of our data vector, and bi is the coefficient on the ith covariate (16). To address concerns about correlations among observations within census tracts, we adjusted the standard errors of our coefficient estimates for clustering within census tracts (15). We used Stata (StataCorp LP, College Station, Texas) for all estimation procedures.
The overall screening rate for women in our sample was 64% for the 2-year study period. Figure 1 shows mammography rates by age group in Hawaii. We found no differences in screening rates among age groups.
Figure 1. Breast cancer screening rates by age group, Hawaii, 2003–2004.
Figure 2 displays the results obtained by estimating a local-linear regression of the mammography dummy on the log of per capita household income. In the figure, we predict the probability of mammography for incomes ranging from the bottom 5th percentile to the top 95th percentile of the earnings distribution. The figure shows a wide disparity in the demand for mammography screening by income. At the lowest end, the probability of obtaining a mammogram is 57.1%, whereas at the highest end, the probability is 67.7%.
Figure 2. Probability of obtaining a mammogram among a sample of women aged 50 to 70 years, for incomes ranging from the 5th percentile to the 95th percentile of the earnings distribution, Hawaii, 2003–2004.
Table 2 presents the results of probit models. In columns 1 and 2 of Table 2, we report the correlation between per capita family income and the probability of obtaining a mammogram without any additional control variables (column 1) and with a set of age dummies (column 2). Both estimates are positive and significant. A 1% increase in per capita family income is associated with an increase in the probability of obtaining a mammogram of 0.001 percentage points. In less infinitesimal terms, calculations based on the estimates in column 2 suggest that movement from the 5th percentile to the 35th percentile of the earnings distribution increases the probability of mammography by 0.0378 percentage points. A similar movement from the 65th percentile to the 95th percentile has an effect of 0.0394 percentage points. As in Figure 1, we do not see any substantial variation in mammography screening among age groups.
Column 3 is identical to column 2 except that we use family income in lieu of per capita family income. We now see that the marginal effect of income is cut by roughly 22.5%. Presumably, the reason for this decrease is that per capita income is a better proxy for the family’s living standards. Thus, we expect less attenuation bias when using per capita family income than when using total family income.
In columns 4 and 5, we control for the member’s morbidity level. Column 4 includes the actual morbidity index, and column 5 includes dummy variables for each morbidity level. We see that the higher morbidity levels as measured are highly correlated with obtaining a mammogram. We also see that the inclusion of morbidity controls does not alter the estimated effect of income.
In column 6 of the table, we include dummy variables indicating the member’s location. The locations are east Hawaii, west Hawaii, Kauai, Lanai, Maui, Molokai, Honolulu, and Oahu other than Honolulu. We see that inclusion of these dummies increases the effect of income by 28.6%. The inclusion of regional dummies identifies the relationship between changes in income and mammography screening within regions of Hawaii. Moreover, the higher coefficient on income associated with the regional dummies suggests a relationship between income and mammography screening within regions of Hawaii.
In column 7, we add a dummy variable indicating whether or not the individual is a member of a health maintenance organization (HMO). The HMO dummy is positive and significant. While holding other factors constant, we see that belonging to an HMO increases the probability of mammography screening by 0.016, which constitutes a 2.5% increase in the mean probability of obtaining a mammogram.
Column 7 also includes a set of race dummies. We see some variation across race. Mammography screening is most common among Chinese women, who are followed by Japanese women. The dummy variable indicating missing race data is negative and significant, suggesting that race data are not missing randomly.
Table 3 provides more details for column 5 of Table 2. We show results only for east Hawaii, Maui, Honolulu, and parts of Oahu other than Honolulu because other regions of the state yielded samples that were too small. Although some regions such as east Hawaii and Maui have reasonable sample sizes, they lack a large number of census tracts, which tend to be concentrated on Oahu. Accordingly, we may still expect imprecise estimates for these regions. Table 3 shows that even within narrowly defined geographic regions, the demand for mammography by income varies, consistent with column 6 of Table 2.
The overall screening rate of 64% in our sample is broadly consistent with other estimates of mammography (2,3). It is important to emphasize, however, that estimates using self-reported data tend to be higher than estimates using insurance or hospital records (2,4).
We document a large disparity in mammography use across the earnings distribution in Hawaii. At the 5th percentile of the earnings distribution, the probability of mammography is 57.1%, and at the 95th percentile, it is 67.7%. We find that a 1% increase in income increases the probability of having a mammogram by 0.001. We emphasize that our measures of family income contain error because they measure only median income in a given census tract. Given the conventional wisdom that classical measurement error will tend to attenuate coefficient estimates, it is reasonable to expect that the true relationship between income and mammography screening is far greater than we have estimated (17). In other words, the real problem is probably far worse than we document.
We estimate a stronger relationship between income and mammography screening than other studies that use multivariate probit analysis (3,11). There are two reasons for the stronger relationship. First, we merged in income by census tract, whereas other studies have used income by zip code (which is coarser) or have used wide income brackets. The second reason for the stronger relationship is that we used income per household member. For both of these reasons, we have a more precise measure of family income, which mitigates the attenuation bias that results from less well-measured income.
The large disparity in mammography across the earnings distribution observed in our study is interesting for two reasons. First, despite having 100% coverage of mammography in our sample, we still see a higher demand for preventive medical care among the rich than among the poor. Income plays a large role in a population where everybody has health insurance and there are no out-of-pocket expenses for obtaining mammograms. While universal health coverage may mitigate socioeconomic disparities in the demand for preventive medicine, as suggested by the Rand Health Insurance Experiment (18), our findings suggest that universal health coverage will not eliminate disparities. Rather, our findings suggest that a gradient in the consumption of prophylactic health care would persist even with universal coverage. Second, we saw that the income gradient exists within narrowly defined geographic regions such as the County of Honolulu, where physical access to medical care providers is not an issue. The observed socioeconomic gradient in the demand for mammography screening does not appear to be the consequence of poorer people residing in areas that are geographically isolated from providers of medical care.
We also determined that higher morbidity levels are highly correlated with obtaining a mammogram. To understand the positive coefficient on the morbidity index in Table 2, it is important to note that many measures of morbidity tend to be highly correlated with the patient’s use of medical services or medical demand (19). Moreover, many studies have also shown that physician recommendation, which is more likely to occur when use of medical services is high, is a strong predictor of mammography screening (3,5,20-22). Given this finding, it is not surprising that the morbidity index is such a strong predictor of mammography screening.
The effect of income was not altered by the inclusion of morbidity controls in Table 2, which is curious, given that a strong correlation between income and health has been documented in virtually every context imaginable (9,10). This result is less surprising, however, when one considers that our morbidity index is probably measuring medical demand, at least to some extent, and that medical demand is a function of both income and health status. Each function tends to affect the demand for medical care in opposing ways. On one hand, because richer people tend to consume more medical services, the inclusion of the morbidity controls should attenuate the effect of income, holding all other factors equal. On the other hand, poorer people tend to be sicker people who, other factors held constant, consume more medical services, thus causing the inclusion of morbidity controls to increase the effect of income. The existence of these two countervailing effects suggests that the inclusion of the morbidity controls would have no net impact on the estimated effect of income.
Belonging to an HMO increased the probability of mammography screening in our study. Differing pecuniary incentives do not explain this finding because there is no cost to the individual for mammography in either the preferred provider organization (PPO) plan or the HMO plan. However, HMO members of the health care plan in this study are required to choose a principal provider for their care and, as part of the health plan’s quality care initiative, principal providers receive lists of patients who do not receive mammograms. This practice is not part of the PPO plan, a difference that is consistent with the commonly held notion that HMOs tend to place a greater emphasis on preventive care than do PPOs. Nevertheless, other studies do not find any relationship between mammography and HMO participation (11).
Finally, our suggestion that race data are not missing randomly (Table 2, column 6) provides an important caveat to researchers who wish to use voluntary questionnaires to make inferences about population relationships.
So, if income gradients in mammography use are not caused by lack of coverage or geographic isolation, then what is responsible for them? We explore some possible explanations below.
Ex ante moral hazard
One possible explanation for our findings is ex ante moral hazard, or the notion that insurance coverage for curative care reduces the incentive for investing in preventive care (23,24). The issue of ex ante moral hazard does not explain our results for several reasons. First, for ex ante moral hazard to be responsible for our results, coverage of curative care would have to differ systematically between rich and poor members, which it does not. Second, although insurance at least partially mitigates the costs of cancer treatment, risks such as increased probability of death due to late detection remain even with comprehensive insurance coverage. Given this information, it is not surprising that evidence of ex ante moral hazard is scant in the literature (23).
Another possible explanation for our results is that poorer people incur a higher time cost for obtaining a mammogram. For example, richer people may have more flexible employment, enabling them to take time off work with little or no effect on their earnings. Poorer people may also tend to have wage-based rather than salaried jobs, meaning that they must forgo valuable work time to see a physician or obtain a mammogram. Moreover, poorer people may rely more heavily on public transportation than do richer people, which would also tend to increase the time cost of obtaining medical care. Indeed, evidence exists that these time costs may be particularly important among Asian Americans (25), of whom there are many in Hawaii. Thus, time costs may be an important mechanism in this study.
A third possible explanation for our results is that poorer members are less informed than richer members about the potential benefits of mammography screening. Although the benefits of early detection are well-documented in the literature, this information may not be disseminated equally across the earnings distribution. Indeed, some evidence suggests that race, which is highly correlated with income, is a significant predictor of attitudes toward the efficacy of screening for breast and cervical cancer (26,27).
Our study has several limitations. First, data are from a single health plan in Hawaii and may not generalize to other settings or populations. Second, we had race information available only on a subset of members who had seen their doctor in the past year. Racial disparities in breast cancer screening for the general population may differ from our results. Third, information on relevant factors such as health beliefs, transportation, and family history of disease was not available. Fourth, we used median income level by census tract rather than an individual’s actual income, which introduces measurement error.
Despite these limitations, our findings suggest that an income gradient exists in the probability of obtaining breast cancer screening, with low-income women being less likely than high-income women to receive screenings. To address this disparity, further research will be needed to identify the reasons for lack of compliance with recommended guidelines. For instance, we could use chart data to determine how often physicians schedule screenings that patients fail to attend. Analyzing barriers to breast cancer screenings from the patient perspective is also of interest.
Corresponding Author: Timothy Halliday, PhD, John A. Burns School of Medicine; University of Hawaii at Manoa, 2424 Maile Way, Saunders Hall 533, Honolulu, HI 96822. Telephone: 808-956-8615. E-mail: email@example.com.
Author Affiliations: Deborah A. Taira, James Davis, Hawaii Medical Service Association (an independent licensee of the Blue Cross and Blue Shield Association) and John A. Burns School of Medicine, Honolulu, Hawaii; Henry Chan, Hawaii Medical Service Association, Honolulu, Hawaii.
Table 1. Sample (N = 46,328) Characteristics, Study on Socioeconomic Disparities in Breast Cancer Screening in Hawaii, 2003–2004
Table 2. Probit Models in Which the Dependent Variable is an Indicator for Having Had a Mammogram, Study on Socioeconomic Disparities in Breast Cancer Screening in Hawaii, 2003–2004a
Table 3. Income Gradients by Region, Study on Socioeconomic Disparities in Breast Cancer Screening in Hawaii, 2003–2004a
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