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Michael E. Tarter,¹ Michael D. Lock,² and Rose M. Ray³

¹Department of Biomedical and Environmental Health Sciences, University of California, Berkeley, CA 94720 USA
²Becton Dickinson Immunocytometry Systems, San Jose, CA 95131 USA
³Failure Analysis Associates, Menlo Park, CA 94025 USA

Abstract

We introduce a new form of regression that has many applications to environmental studies. For a sequence composed of key variates with prototypic value x, this form differs from the estimation of a location parameter-based curve, µ(x) , a scale parameter-based curve, (x) , or other currently used types of regression. Instead of estimating a curve location, scale, or -quantile parameter, it assumes that there are two or more population subgroups ; for example, consisting of unsensitized and sensitized individuals, respectively. Although within each subgroup the relationships µ(x) or (x) may or may not be horizontal, these relationships are not deemed to be of primary importance. Instead, the mixing parameter P that indexes the proportions of the two subgroups is treated as being related to the key variate value x.

In the sense that its goal is the estimation of a proportion, the new procedure resembles logit regression. But, in terms of the continuous spectrum of values attained by the response variate, the means used to attain its goal are dissimilar from those of logit regression. Specifically, group membership is not known directly but is determined from a proxy continuous variate whose values overlap between groups. Examples are given with simulated and natural data where this new form of regression is applied. We believe that conditional switching regression is a particularly valuable research tool when chemical level x of an induced asthma attack or birthweight x measured in a study of the biomarker cotinine's effect on pregnancy outcomes determines whether an attack or a negative outcome occurs. In these applications it is this binary-valued and yet indirectly measured response, and not the continuously valued attack severity or birthweight deficit variate, that is of primary interest. Key words: birth weight, Fourier series, gestation age, mixture decomposition, nonparametric estimation, nonparametric regression, population components, switching regression. Environ Health Perspect 103:748-755 (1995)

Address correspondence to R.M. Ray, Failure Analysis Associates, PO Box 3015, Menlo Park, CA 94025 USA.

Received 25 August 1994 ; accepted 27 April 1995.