Article

# Case Definition and Design Sensitivity

Journal of the American Statistical Association (Impact Factor: 1.98). 12/2013; 108(504):1457-1468. DOI: 10.1080/01621459.2013.820660

Source: PubMed

**ABSTRACT**

In a case-referent study, cases of disease are compared to non-cases with respect to their antecedent exposure to a treatment in an effort to determine whether exposure causes some cases of the disease. Because exposure is not randomly assigned in the population, as it would be if the population were a vast randomized trial, exposed and unexposed subjects may differ prior to exposure with respect to covariates that may or may not have been measured. After controlling for measured pre-exposure differences, for instance by matching, a sensitivity analysis asks about the magnitude of bias from unmeasured covariates that would need to be present to alter the conclusions of a study that presumed matching for observed covariates removes all bias. The definition of a case of disease affects sensitivity to unmeasured bias. We explore this issue using: (i) an asymptotic tool, the design sensitivity, (ii) a simulation for finite samples, and (iii) an example. Under favorable circumstances, a narrower case definition can yield an increase in the design sensitivity, and hence an increase in the power of a sensitivity analysis. Also, we discuss an adaptive method that seeks to discover the best case definition from the data at hand while controlling for multiple testing. An implementation in R is available as SensitivityCaseControl.

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**ABSTRACT:**A common practice with ordered doses of treatment and ordered responses, perhaps recorded in a contingency table with ordered rows and columns, is to cut or remove a cross from the table, leaving the outer corners-that is, the high-versus-low dose, high-versus-low response corners-and from these corners to compute a risk or odds ratio. This little remarked but common practice seems to be motivated by the oldest and most familiar method of sensitivity analysis in observational studies, proposed by Cornfield et al. (1959), which says that to explain a population risk ratio purely as bias from an unobserved binary covariate, the prevalence ratio of the covariate must exceed the risk ratio. Quite often, the largest risk ratio, hence the one least sensitive to bias by this standard, is derived from the corners of the ordered table with the central cross removed. Obviously, the corners use only a portion of the data, so a focus on the corners has consequences for the standard error as well as for bias, but sampling variability was not a consideration in this early and familiar form of sensitivity analysis, where point estimates replaced population parameters. Here, this cross-cut analysis is examined with the aid of design sensitivity and the power of a sensitivity analysis. © 2015, The International Biometric Society.Biometrics 08/2015; DOI:10.1111/biom.12373 · 1.57 Impact Factor

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