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A measurement-error model for binary and ordinal regression.

Exposure assessment poses special problems in air pollution epidemiology. This paper proposes a probit regression model for binary and ordinal outcomes that uses exposure validation information to develop estimates for the coefficient of the true exposure when only the inaccurate 'surrogate' measure of exposure is available for the individuals in the health study. This method is closely related to recently developed measurement-error methods, and is based on the assumption that the outcome and the surrogate exposure are conditionally independent given the true exposure. A test statistic is proposed for checking this conditional independence assumption when more than one surrogate is available, and an interpretation of the coefficient estimate is provided in the event that the assumption is violated. The methods are applied to an example involving nitrogen dioxide exposure and wheeze in children.