PROGRAMA PARA CONTROLAR EL ATMEGA 164P

There are a few comments to be made regarding potential limitations of our investigations. Many of these issues should be subject of future activities, but are beyond the scope of this work.

Firstly, the exposure-disease model accounting for errors in exposure would require further modification if the potential correlation of radon exposure with the binary variables in the model (categories of years since quitting smoking, indicator for smoking of other products or asbestos exposure) were accounted for or if even misclassification in these variables was considered. Secondly, detailed investigations regarding the performance of the regression calibration method and the method by Reeves are necessary. The performance of the regression calibration method particularly for large Berkson errors, also allowing for heteroscedasticity, are currently investigated by Küchenhoff et al. (in preparation)

Thirdly, the size of error in packyears and the non-differentiality of this error could be challenged. In fact, the sparcity of literature on error in assessing smoking variables via questionnaire is astonishing, but possibly due to the fact, that the risks from smoking are most prominent even without sophisticated methods. One recent work by Caraballo et al. (2001) comparing self-reported cigarette smoking with measured serum cotinine levels conclude that self-reports appear to be a very good indicator of actual smoking status. Additionally, the optimal treatment of zero exposure, particularly in lognormal distributions, not only with

regard to measurement error correction is subject of concern (Greenland and Poole, 1995). Modelling packyears with imputation of 0.05 packyears for non-smokers would result in wrong answers due to the inflated exposure variance. Modelling packyears+1 seemed to work well, but more detailed investigations would be helpful. Additionally, the size of error in radon exposure could not be estimated from the German radon study data and the supplied additional external data was not completely satisfactory. However, in an assessment process as complex as measuring radon exposure, it is extremely difficult to pinpoint an estimate, and a sensitivity analysis varying error size of a plausible range seemed to be most sensible.

Further, mixed error structures, that is multiplicative error in one predictor and additive error in another predictor can theoretically be accounted for by various correction methods. However, applications have so far not implemented such complex models. Applying the regression calibration method or the method by Reeves et al. would be problematic. Also, interaction between the predictors and the impact of errors in the predictors on the interaction need to be considered. Finally, only one of the sources of residual confounding was extensively explored, namely the impact of the error in assessing the confounding variable. However, further analysis regarding the German radon studies is necessary to grasp the full dimension of this issue.

5 SUMMARY

Case-control studies on lung cancer and residential radon exposure had been conducted in Germany. Relative risk estimates from primary analysis were now subject to accounting for uncertainties in radon exposure and in the most potent confounder smoking. The regression calibration method and an approximate maximum likelihood method were applied. The differentiation between classical error (from assessing radon exposure or packyears) or Berkson error (from using radon exposure instead of alpha dose, from using packyears instead of inhaled dose of smoking carcinogens) was of major importance in this analysis.

Estimates of relative lung cancer risk due to radon exposure were found to be higher after accounting for multiplicative classical error in radon exposure and packyears. Outliers in the data strongly influence risk estimates, but their impact is reduced, if classical error is accounted for. In one study, the influence of one outlier explained the particularly large risk- increasing impact of error correction. But also residual confounding due to adjusting for imprecisely measured packyears deflated the risk estimate in this study. It is interesting that the small correlation between radon exposure and packyears had this notable effect. On the other hand, classical errors in packyears had no large impact in the radon-prone study areas. Further, Berkson error did not induce substantial bias on the radon risk estimates, but possibly decreased the power to detect existing effects and inflated the confidence intervals.

It was concluded that such an analysis was extremely valuable to understand the impact of uncertainties in the risk factor of primary interest on the risk estimate under study and the potential for residual confounding by assessment errors in the smoking variable. Note that assuming some error in the risk factors is more realistic than assuming no error. With regard to study design, study regions with no correlation between the variable of primary interest and potential confounders are preferable.

However, the exact magnitude of the error could not be estimated based on the available data. Further investigations regarding residual confounding due to model mis-specification and latent smoking-related variables are necessary to grasp the full dimension of an important issue in epidemiology, i.e. the role of the outstanding confounder smoking for estimating small risks.

6

In Deutschland waren Fall-Kontroll-Studien zu Lungenkrebs und Radon in Innenräumen durchgeführt worden. In der Schätzung des relativen Lungenkrebsrisikos wurden nun Unsicherheiten in der Radonexposition und im stärksten potentiellen „Confounder“ Rauchen berücksichtigt. Hierbei wurden die Methode der Regressionscalibrierung und eine approximative „Maximum Likelihood“ Methode angewandt. Die Unterscheidung zwischen klassischem Fehler (durch Erhebung der Radonexposition oder der Packungsjahre) und Berkson-Fehler (durch Verwendung von Radonexposition als Surrogat für Alpha-Dosis oder von Packungsjahren als Surrogat für Lungendosis durch inhalierte Karzinogene im Rauch) war von besonderer Bedeutung in dieser Analyse.

Die Risikoschätzer waren höher, wenn multiplikative klassische Messfehler in der Erhebung der Radonexposition und der Packungsjahre berücksichtigt wurden. Ausreißer in den Daten haben einen starken Einfluß auf Risikoschätzer, welcher jedoch durch Berücksichtigung klassischer Fehler reduziert wird. In einer Studie erklärte der Einfluß eines Ausreißers den besonders starken das Risiko erhöhenden Effekt der Fehlerkorrektur. Aber auch „Residual Confounding“ durch Adjustierung für ungenau erhobene Packungsjahre verringerte das beobachtete Risiko in dieser Studie. Es ist interessant, dass sich die kleine Korrelation zwischen Radonexposition und den Packungsjahren so stark auswirkte. In höher mit Radon belasteten Studiengebieten hatten klassische Fehler in den Packungsjahren keinen großen Effekt. Ferner bewirkte der Berkson-Fehler keine nennenswerte Verzerrung der Risikoschätzer, aber schmälerte die „Power“, um existierende Effekte zu erkennen. Diese Analyse war extrem nützlich, um die Auswirkung von Messfehlern im primären Risikofaktor auf das zu untersuchende Risiko und das Potential von „Residual Confounding“ durch Fehler in der Rauchvariablen zu verstehen. Man halte sich vor Augen, dass die Annahme irgendeines Fehlers in den Risikofaktoren realistischer ist als die Annahme keines Fehlers. Bezüglich des Studiendesigns, ist eine Studienregion, wo die Primärexposition nicht mit dem potentiellen „Confounder“ korreliert ist, vorzuziehen.

Die genaue Fehlergröße konnte jedoch nicht aus den zur Verfügung stehenden Daten geschätzt werden. Außerdem sind weitere Untersuchungen hinsichtlich des „Residual Confounding“ durch Modell-Fehlspezifikation und latente Rauchvariable notwendig, um das volle Ausmaß eines wichtigen Punktes in der Epidemiologie zu verstehen, nämlich die Rolle des herausragenden „Confounder“ Rauchen für die Schätzung kleiner Risiken.

7 A GUIDE TO DEFINITIONS AND ABBREVIATIONS