Dose-Response: An International Journal: Volume 3, Issue 3
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2005-30-09
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Dose-Response Vol 3, no 4, Cover
(2005-12-01)
Dose-Response Vol 3, no 4, Table of Contents
(2005-12-01)
STATISTICAL CHALLENGES IN EVALUATING DOSE-RESPONSE USING EPIDEMIOLOGICAL DATA
(2005-12-01) Mundt, Kenneth A
THE EFFECT OF RANDOM ERROR IN EXPOSURE MEASUREMENT UPON THE SHAPE OF THE EXPOSURE RESPONSE
(2005-12-01) Crump, Kenny S
Although statistical analyses of epidemiological data usually treat the exposure variable as being known without error, estimated exposures in epidemiological studies often involve considerable uncertainty. This paper investigates the theoretical effect of random errors in exposure measurement upon the observed shape of the exposure response. The model utilized assumes that true exposures are log-normally distributed, and multiplicative measurement errors are also log-normally distributed and independent of the true exposures. Under these conditions it is shown that whenever the true exposure response is proportional to exposure to a power r, the observed exposure response is proportional to exposure to a power K, where K < r. This implies that the observed exposure response exaggerates risk, and by arbitrarily large amounts, at sufficiently small exposures. It also follows that a truly linear exposure response will appear to be supra-linear—i.e., a linear function of exposure raised to the K-th power, where K is less than 1.0. These conclusions hold generally under the stated log-normal assumptions whenever there is any amount of measurement error, including, in particular, when the measurement error is unbiased either in the natural or log scales. Equations are provided that express the observed exposure response in terms of the parameters of the underlying log-normal distribution. A limited investigation suggests that these conclusions do not depend upon the log-normal assumptions, but hold more widely. Because of this problem, in addition to other problems in exposure measurement, shapes of exposure responses derived empirically from epidemiological data should be treated very cautiously. In particular, one should be cautious in concluding that the true exposure response is supra-linear on the basis of an observed supra-linear form.
A GRAPHICAL METHOD TO EVALUATE EXPOSURE-RESPONSE RELATIONSHIPS IN EPIDEMIOLOGIC STUDIES USING STANDARDIZED MORTALITY OR MORBIDITY RATIOS
(2005-12-01) van Wijngaarden, Edwin
In occupational epidemiology, exposure-response analyses play an important role in the evaluation of the etiologic relevance of chemical and physical exposures. The standardized mortality or morbidity ratio (SMR) has been commonly used in occupational cohort studies. Statistical approaches to evaluate exposure-response patterns using SMRs have mostly been limited to analyses in which the exposure under investigation is categorized. Here, a graphical method for evaluating exposure-response patterns is presented based on SMR estimates across moving exposure windows. This method is demonstrated using the results of two hypothetical cohort studies. The proposed approach may be useful for graphical exploration of exposure-response trends in situations where the number of observed cases is small.