On power and sample size for studying features of the relative odds of disease

Estimates of sample size and statistical power are essential ingredients in the design of epidemiologic studies. Once an association between disease and exposure has been demonstrated, additional studies are often needed to investigate special features of the relation between exposure, other covariates, and risk of disease. The authors present a general formulation to compute sample size and power for case-control and cohort studies to investigate more complex patterns in the odds ratios, such as to distinguish between two different slopes of linear trend, to distinguish between two possible dose-response relations, or to distinguish different models for the joint effects of two important exposures or of one exposure factor adjusting for another. Such special studies of exposure-response relations may help investigators to distinguish between plausible biologic models and may lead to more realistic models for calculating attributable risk and lifetime disease risk. The sample size formulae are applied to studies of indoor radon exposure and lung cancer and suggest that epidemiologic studies may not be feasible for addressing some issues. For example, if the risk estimates from underground miners' studies are, in truth, not applicable to home exposures and overestimate the gradient of risk from home exposure to radon by, for example, a factor of 2, then enormously large numbers of subjects would be required to detect the difference. Furthermore, if the true interaction between smoking and radon exposure is less than multiplicative, only the largest investigations will have sufficient power to reject additivity. For the simple case of testing for no exposure effect, when exposure is either dichotomous or continuous, these methods yield well-known formulae.