Statistics in Medicine: Calculating confidence intervals for relative risks (odds ratios) and standardised ratios and rates

Abstract

Gardner and Alunan explained the rationale for using estimation and confidence intervals in making inferences from analytical studies and described their calculation for means or proportions and their differences.1 In this paper we present methods for calculating confidence intervals for other common statistics obtained from medical investigations. The techniques for obtaining confidence intervals for estimates of relative risk are described. These can come either from an incidence study, where, for example, the frequency of a congenital malformation at birth is compared in two defined groups of mothers, or from a case-control study, where a group of patients with the disease of interest (the cases) is compared with another group of people without the disease (the controls). The methods of obtaining confidence intervals for standardised disease ratios and rates in studies of incidence, prevalence, and mortality are described. Such rates and ratios are commonly calculated to enable appropriate comparisons to be made between study groups after adjustment for confounding factors like age and sex. The most frequently used standardised indices are the standardised incidence ratio (SIR) and the standardised mortality ratio (SMR). A worked example is included for each method. The calculations have been carried out to full arithmetical precision, as is recom? mended practice,2 although intermediate steps are shown as rounded results. Some of the methods given in this paper are large sample approximations and are not reliable for studies with fewer than about 20 cases. Appropriate design principles for these types of study have to be adhered to since confidence intervals convey only the effects of sampling variation on the precision of the estimated statistics and cannot control for other errors such as biases due to the selection of inappropriate controls or in the methods of collecting the data.