Letters

Income distribution, socioeconomic status, and self rated health in US

Authors ignored data in their study

Authors' reply

Authors ignored data in their study

EDITORI take issue with Kennedy et al's conclusion that the frequently observed association between income inequality and health is not an artefact of an omitted relation between individual income and individual health.¹ They had only limited information on individual incomes in their study. Furthermore, they ignored some of the income and inequality data that they did have available. Consequently, their conclusion that income inequality exerts an independent effect on individual health is inappropriate.

The authors controlled for individual income by using survey data on household income and controlling for household size. Their income data were categorical and so were necessarily measured with error. The top category was for households with incomes of $50 000 (17.3% of the sample). Without explanation the authors combined this category with the category of households with an income of $35 000 to <$50 000 (another 15% of the sample). The authors also retained observations on people for whom income data were missing (12.6% of the sample). Thus 44.9% of their sample had missing data or the highest incomes in the study.

The authors also analysed subsamples of their data stratified by income. However, they combined several income categories in each subsample and failed to control for this. Finally, they ignored additional information by using only a four category measure of income inequality even though they had available a continuous measure of it (the Gini coefficient).

Despite these measurement issues, the authors show that the relative risk associated with residence in a state with high income inequality falls by about one third when controls for individual income are added to the logistic regression. This suggests that if the authors had more complete data on individual incomes the association between inequality and health might be further mitigated; the apparent association might even disappear completely, which is the opposite of what the authors conclude from their analysis.

By choosing to ignore relevant information Kennedy et al have added to the ambiguity in their findings and unnecessarily undermined the value of their analysis.

Jeffrey Milyo, Postdoctoral fellow. 
Health Policy Program, Yale University, New Haven, CT 06511, USA jmilyo{at}tufts.edu

Authors' reply

EDITORMilyo's main criticism is that we did not adequately address the statistical artefact issue as our estimates of the effects of individual income on health used household income categories rather than a continuous measure of household income. Our study was limited to the income data available to us. Measurement of household income in a telephone survey requires a balance between precision and loss of information to non-response. It is now standard survey practice to ask for income by category to minimise non-response, as the loss of precision is not considered to have any substantive impact on estimates. We did not ignore information; it was simply unavailable.

We acknowledge that using categorical instead of continuous individual household income information may have hindered our ability to rule out completely the residual confounding effect of individual household income on health. This, though, is unlikely to have affected our results.

Milyo expresses concerns about our having collapsed the top two income categories and included cases for which income data were missing, suggesting again that we ignored these issues. Although we did not clarify this in the paper, we included the observations of people who refused to answer the income question to avoid losing the information that this group could contribute to the estimates of the odds ratios for the demographic, risk factor, and household composition control variables. The relation between self reported health and household income flattened out after $35 000, and for ease of interpretation we combined the $35 000 to <$50  and $50 000 income categories as they did not differ substantively. We made these decisions after checking whether dropping people with missing income and combining the top two income categories affected the results; they did not.

A final concern of Milyo is that use of the Gini coefficient as a categorical rather than a continuous variable ignores important information. After determining that the loss of information made little difference to our conclusion we presented our findings in terms of Gini categories rather than in terms of a continuous Gini measure to make the results understandable to a broad audience. For most readers, the change in an odds ratio associated with a 1 unit change in the Gini coefficient has no intuitive meaning.

We do not see a need to qualify our original conclusion. The relation between income inequality and self reported health is robust. Even after we controlled for factors such as individual household income (though not as perfectly measured as might be), race, smoking, obesity, and educationall of which may be in the causal pathway between inequality and poor healththe relation remained significant.

Bruce P Kennedy, Deputy director. 
Ichiro Kawachi, Associate professor. 
Roberta Glass, Research specialist. 
Deborah Prothrow-Stith, Professor. 
Harvard School of Public Health, Boston, MA 02115, USA