To the Editor:
I read with interest the recent article by Chen et al1 on the prediction of daily whole-body vibration exposure by observable driving-related variables, and the application of the predicted exposure levels in a logistic regression model for low back pain. They found an odds ratio of 3.7 (confidence interval = 1.1–12.2) associated with an increment of daily vibration exposure by each m2/s4-hour, which they interpreted as support for the construct validity of the exposure prediction rule.
However, I have some concerns regarding the precision of this estimate and its interpretation. First, the simple substitution of the predicted exposure levels in the disease model did not allow for the uncertainty of the prediction. The confidence interval given in the paper is too narrow and must be corrected by taking into account the estimation error of the prediction model. This problem is similar to the correction of confidence intervals for relative risk estimates in the case of calibrated exposure measurements.2,3 In both problems, standard errors of the parameter estimates in the disease model cannot be produced by standard analytical packages; rather, special routines are necessary to consider the estimation error in the preceding step of regression analysis. The delta method4 is a mathematical approach that has been successfully applied in epidemiology. Alternatively, the corrected confidence interval can be determined by the bootstrap method.5 I expect that the confidence intervals of the exposure effect reported by Chen and colleagues would widen after correction for prediction error, perhaps affecting the interpretation.
Secondly, the size of the effect of the predicted exposure on risk of low back pain (even after correction) does not prove the construct validity of the prediction rule. For example, in the extreme case in which all predictors of vibration exposure are also predictors of low back pain, the constructed exposure prediction rule will show a strong association with the risk of low back pain regardless of the prediction error. Thus, it is necessary to compare the model fit of the proposed disease model using the predicted vibration level with the fit of other competitive models that also incorporate all the driving-related variables.
In summary, I appreciate the low relative prediction error in predicting unknown vibration levels by driving-related variables, but I have doubts about the correct use of predicted exposure levels in evaluating the effect of whole-body vibration on low back pain.
Department of Epidemiology; German Institute of Human Nutrition; Nuthetal, Germany; firstname.lastname@example.org
1. Chen JC, Chang WR, Shih TS, et al. Using “exposure prediction rules” for exposure assessment: an example on whole-body vibration in taxi drivers. Epidemiology
2. Rosner B, Willett WC, Spiegelman D. Correction of logistic regression relative risk estimates and confidence intervals for systematic within-person measurement error. Stat Med
3. Rosner B, Spiegelman D, Willett WC. Correction of logistic regression relative risk estimates and confidence intervals for measurement error: the case of multiple covariates measured with error. Am J Epidemiol
4. Rao CR. Linear statistical inference and its application
ed. New York: John Wiley and Sons; 1973.
5. Rosner B, Gore R. Measurement error correction in nutritional epidemiology based on individual foods, with application to the relation of diet to breast cancer. Am J Epidemiol