Low power? Use two-dimensional confidence regions as a graphical method for depicting uncertainty

Prospective studies of rare outcomes, such as HIV seroconversion or obsessive-compulsive disorder, can often result in small sample sizes with limited power for detecting associations. For this reason, it is useful to develop graphical procedures that enable researchers to depict uncertainty around parameter estimates and examine the direction of association when statistical power is low. Classical procedures include the reporting of confidence intervals, which typically are derived from asymptotic normality of parameters estimated using large samples. In this paper, we present a likelihood-based procedure for the estimation of the confidence region of two parameters from a conditional logistic regression of a nested case-control study with a relatively small number of cases. Graphical depiction of the confidence regions provides an easily comprehensible procedure to quantify the uncertainty of the estimation based on small samples.