Background: In epidemiology it is often required to estimate the association between risk of disease and an explanatory variable (X) which cannot be measured precisely. Instead of X we can observe a mismeasured surrogate variable W, related to X. To ignore the measurement error affecting W may lead to biased estimates of relative risks (RR). Rosner provided a method, belonging to the 'Regression calibration models' class, to correct point and interval estimates of the RR derived from logistic regression in the presence of categorical variables (i.e. quantile scale). Rosner's approach replaces the observed value (W=j) with the expected value of the explanatory variable (X=x) as estimated in a validation study. The final adjusted estimation is given considering the exposure variable on a continuous scale, which is not commonly used by epidemiologists. Objective: To develop a procedure which adjusts the estimates of RR for the effects of misclassification ascribable to measurement error, both for intrinsically discrete variables and continuous variables expressed in a discrete scale. Methods: The properties of the estimates of RR in the situation outlined above were evaluated by a simulation study. Five hundred case-control studies (2,500 cases and 2,500 controls) were generated. The true values (X) of the exposure variable were sampled from a known distribution, and the observed values (W) were obtained by adding a measurement error. The distribution of the exposure variable and that of the error were defined on the basis of the results supplied by a study on the assessment of alcohol intake in Italy. Correction of observed alcohol consumption has been reached with Rosner's procedure and a new proposed method, allowing estimation of true odds ratio for each category of X. Results: The results of this simulation showed that the estimated RR is severely under estimated both in the continuous and in the discrete case, when tile effect of measurement error is ignored. This negative bias appeared to be removed only in part by Rosner's technique. The performance of the method here proposed is still under investigation. Conclusions: The effects of measurement error on the estimates of RR were found to be not negligible, at least when the exposure variable is weakly related to disease. At present, the techniques available to adjust such estimates are far from being satisfactory. References: Rosner B. Measurement error models for ordinal exposure variables measured with error Stat in Med 15:293-303. 1996. Carroll RJ, Ruppert D and Stefanski LA, Measurement error in nonlinear models, Chapman & Hall, London, 1995.

Biased estimates of relative risks and mismeasured exposure variables / M. Ferraroni, M. Mezzetti, A. Decarli, S. Milani. ((Intervento presentato al 15. convegno SCIENTIFIC MEETING OF THE INTERNATIONAL EPIDEMIOLOGICAL ASSOCIATION tenutosi a Firenze nel 1999.

### Biased estimates of relative risks and mismeasured exposure variables

#####
*M. Ferraroni*^{Primo};A. Decarli^{Penultimo};S. Milani^{Ultimo}

^{Primo};A. Decarli

^{Penultimo};S. Milani

^{Ultimo}

##### 1999

#### Abstract

Background: In epidemiology it is often required to estimate the association between risk of disease and an explanatory variable (X) which cannot be measured precisely. Instead of X we can observe a mismeasured surrogate variable W, related to X. To ignore the measurement error affecting W may lead to biased estimates of relative risks (RR). Rosner provided a method, belonging to the 'Regression calibration models' class, to correct point and interval estimates of the RR derived from logistic regression in the presence of categorical variables (i.e. quantile scale). Rosner's approach replaces the observed value (W=j) with the expected value of the explanatory variable (X=x) as estimated in a validation study. The final adjusted estimation is given considering the exposure variable on a continuous scale, which is not commonly used by epidemiologists. Objective: To develop a procedure which adjusts the estimates of RR for the effects of misclassification ascribable to measurement error, both for intrinsically discrete variables and continuous variables expressed in a discrete scale. Methods: The properties of the estimates of RR in the situation outlined above were evaluated by a simulation study. Five hundred case-control studies (2,500 cases and 2,500 controls) were generated. The true values (X) of the exposure variable were sampled from a known distribution, and the observed values (W) were obtained by adding a measurement error. The distribution of the exposure variable and that of the error were defined on the basis of the results supplied by a study on the assessment of alcohol intake in Italy. Correction of observed alcohol consumption has been reached with Rosner's procedure and a new proposed method, allowing estimation of true odds ratio for each category of X. Results: The results of this simulation showed that the estimated RR is severely under estimated both in the continuous and in the discrete case, when tile effect of measurement error is ignored. This negative bias appeared to be removed only in part by Rosner's technique. The performance of the method here proposed is still under investigation. Conclusions: The effects of measurement error on the estimates of RR were found to be not negligible, at least when the exposure variable is weakly related to disease. At present, the techniques available to adjust such estimates are far from being satisfactory. References: Rosner B. Measurement error models for ordinal exposure variables measured with error Stat in Med 15:293-303. 1996. Carroll RJ, Ruppert D and Stefanski LA, Measurement error in nonlinear models, Chapman & Hall, London, 1995.##### Pubblicazioni consigliate

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