Karsten Drescher

Maximum likelihood estimation of the attributable fraction from logistic models

Bruzzi et al. (1985, American Journal of Epidemiology 122, 904-914) provided a general logistic-model-based estimator of the attributable fraction for case-control data, and Benichou and Gail (1990, Biometrics 46, 991-1003) gave an implicit-delta-method variance formula for this estimator. The Bruzzi et al. estimator is not, however, the maximum likelihood estimator (MLE) based on the model, as it uses the model only to construct the relative risk estimates, and not the covariate-distribution estimate. We here provide maximum likelihood estimators for the attributable fraction in cohort and case-control studies, and their asymptotic variances. The case-control estimator generalizes the estimator of Drescher and Schill (1991, Biometrics 47, 1247-1256). We also present a limited simulation study which confirms earlier work that better small-sample performance is obtained when the confidence interval is centered on the log-transformed point estimator rather than the original point estimator.

Assessment of the Combined Effects of Substances: The Relationship between Concentration Addition and Independent Action

The assessment of the combined effects of substances is usually based on one of two different concepts: concentration addition or independent action. Both concepts are founded on different pharmacological assumptions about sites and modes of actions of substances, but in toxicology and ecotoxicology such knowledge is rare for most chemicals. In order to validate experimental results and to allow for precautious assessments, the quantitative relationships between concentration addition and independent action are therefore of interest. In this paper, we derive for the Weibull, the logistic, and the normal distribution functions the concentrations where the response probability due to concentration addition exceeds that due to independent action and vice versa. This is done (a) by analytically comparing both models for low and high mixture concentrations and (b) by numerically calculating the response probabilities when concentration addition and independent action agree. It is shown that the relationships between the models for joint action depend on the distribution functions, the corresponding slope parameters, and on the mixture concentrations administered.

Attributable risk estimation from case-control data via logistic regression

By fitting an unconditional logistic regression model to unmatched case-control data, an estimate of the joint population attributable risk for the factor included is obtained. This estimate and its asymptotic variance can easily be computed from the intercept parameter and its asymptotic variance. A generalization to the analysis of stratified data with large strata enables the calculation of stratum-specific attributable risks and their variances via stratum-specific intercept parameters. If sampling of cases is independent of strata, an estimate of the summary attributable risk and its asymptotic variance may be obtained as a weighted sum of the stratum-specific attributable risks.

LOGISTIC ANALYSIS OF STUDIES WITH TWO‐STAGE SAMPLING: A COMPARISON OF FOUR APPROACHES

This paper discusses the analysis of two-stage studies where covariates are missing or measured with error at the first stage of sampling and are validated at the second stage in a subsample. Four recently developed approaches, the weighted pseudo-likelihood method of Flanders and Greenland (1991), the pseudo-conditional likelihood methods of Breslow and Cain (1988) and Schill et al. (1993) and the maximum likelihood estimate obtained via the EM-algorithm (Wacholder and Weinberg, 1994) are reviewed, and some connections between them are established. It is shown that, with respect to odds ratio estimation, case-control designs can be analysed as if first-stage sampling had been prospective. The procedures are numerically compared with respect to asymptotic relative efficiency in a missing value setting.

Smoking cessation and nonsmoking intervals: effect of different smoking patterns on lung cancer risk.

A case-control study of lung cancer was conducted in northwestern Germany in 1985–86. The study included 194 lung cancer cases and the same number of hospital controls and population controls who were matched to the cases by sex and age. Personal interviews were conducted by trained interviewers. We report here the effect of different smoking patterns—such as nonsmoking intervals, and time since quitting smoking—on lung cancer risk. Both quitting smoking and having a nonsmoking interval are seen to reduce lung cancer risk significantly. For a nonsmoking interval of three years or more, relative risk (RR)=0.21, 95 percent confidence interval (CI)=0.08–0.52; for quitting smoking for 10 years or more, RR=0.23, CI=0.11–0.48). A dose-response relationship was estimated for cigarette dose, length of nonsmoking interval, and time since stopped smoking.

Methodik von Fall-Kontroll-Studien zur Aufdeckung kleiner Risiken, insbesondere in der Umweltepidemiologie

Zum Nachweis eines Zusammenhanges zwischen Umweltfaktoren, wie z. B. der Luftverschmutzung und der Entstehung chronischer Erkrankungen, wie z. B. des Lungenkrebses, wird in der Epidemiologie haufig die Methodik der Fall-Kontroll-Studie angewendet. Sind diese Umweltrisiken einerseits klein und andererseits mit bekannten und gesicherten Risikofaktoren (wie z. B. dem Rauchen) assoziiert, so ergeben sich eine Reihe methodischer und inhaltlicher Probleme.

Air Pollution as a Risk Factor in Lung Cancer: Some Preliminary Design Considerations

For the question whether air pollution may cause lung cancer to a certain degree a preliminary epidemiologic study design will be described. Sample size estimates based on rather incomplete information and simple statistical models indicated that the study would involve a considerable number of cases and controls. We show that a pilot study is necessary, in order to clarify whether such a study is feasible or whether it goes beyond of what may be answered by an epidemiologic study.

The 2-phase case-control design: an efficient way to use expert-time.

OBJECTIVES The objective of this paper is to show the benefits of using a 2-phase case-control (2PCC) design in identifying dose-response relationships between cumulative occupational exposure as assessed by experts and lung cancer incidence in an actual study. METHODS A population-based case-control study including 246 cases and 531 controls was conducted in an area with high lung cancer rates in Northeast France. Detailed occupational and personal risk factors were obtained in face-to-face interviews. Cumulative expert-based exposure scores were obtained from a subset of 215 cases and 269 controls stratified on smoking and a prior algorithmic exposure score for asbestos, crystalline silica, and polycyclic aromatic hydrocarbons (PAH) in the framework of a 2PCC design. This subset deliberately under-sampled large strata among controls but not among cases. Logistic regression models adapted to 2PCC studies were applied and corresponding computations of attributable fractions and their confidence intervals developed. RESULTS Based on this 2PCC design, statistically significant dose-response relationships were obtained for asbestos, crystalline silica, PAH, and diesel motor exhaust. Simulations within this study showed that 2PCC studies were always more powerful than random samples. CONCLUSION The 2PCC design may be the design of choice when resources allow only a limited number of subjects with a full expert-based exposure assessment.