Authors' Response

Abstract

To the Editor: We offer the following clarification of our methods in response to the critique of Soliman and Carlson, justifying interpretation of our results. Tables 1 and 2 show national inpatient cost estimates for Crohn disease (CD) and ulcerative colitis (UC), obtained directly from the Kids’ Inpatient Database without additional statistical analysis (1). Reported frequencies and means require no caution. Before estimating the CD and UC regression models for predicting hospitalization cost (Table 3), we followed standard preestimation protocol to determine whether ordinary-least-squares assumptions were met after logarithmically transforming cost. Residual plots confirmed that assuming homoscedastic, normally distributed errors was not unreasonable. Without evidence to suggest the need for a different statistical approach, and taking seriously the conclusion of Manning and Mullahy (2) that neither ordinary-least-squares nor the generalized linear model trumps the other for all situations, we did not embrace a generalized linear model framework. To interpret the estimated regression coefficients in 2006 dollars, we first found the cost for the reference case, for which all binary variables had a value of “0,” and the one continuous variable, length of stay (LOS), assumed its mean value. The cost for the reference group was found by exponentiating the following sum (call it “S”): the estimated intercept + (the estimated coefficient on LOS × the mean value for LOS). The marginal cost from a patient or hospital characteristic (an independent variable) was found by subtracting the cost for the reference group from the cost with that characteristic, found by exponentiating (S + the estimated coefficient on the characteristic). See the Appendix to Berry et al (3), for a numerical example, and Tundia et al (4), for interpretation of estimated coefficients from a log-cost-ratio-dependent-variable model. Alternatively, estimated coefficients in a semilog model can be interpreted as percentages, for example, 0.05 would suggest that a 1-unit change in the independent variable, all else constant, leads to a 5% increase in cost (5).