Confidence Interval Estimates of Impact Numbers for a Cross-sectional Sampling Scheme
Keywords: impact numbers, effect measures, cross-sectional sampling, confidence interval, delta method
Background: Impact numbers reflect the number of people specific to a population among whom one outcome is attributable to the exposure of a risk factor. Impact numbers could add a new dimension in a public health research because of their interpretational simplicities. While the estimates of impact numbers and of their confidence interval estimates are investigated for cohort and case control studies, these numbers are not yet been documented adequately for a cross-sectional study. Aim: To review existing literature of impact numbers and provide methods of constructing confidence interval estimates of these numbers under a cross-sectional sampling scheme. Methods: Four impact numbers, namely, population impact number (PIN), exposure impact number (EIN), case impact number (CIN) and exposed case impact number (ECIN) will be considered. Because these numbers are defined as the reciprocals of some standard effect measures, the confidence interval estimates of these numbers will be constructed using the principle of inverting and exchanging the confidence interval estimates of the corresponding effect measures. As an alternative, we also consider confidence interval estimates using delta method and compare performances of the two methods in terms of the confidence lengths. Example: The estimates of impact numbers are considered for a cross-sectional study, with 220+ (mg%) of serum cholesterol (SC) as a risk factor of coronary heart disease (CHD). The PIN estimate of 29.4 (95% CI: 20.4, 52.6) means that for every 29 to 30 people in the population, on average one case is attributable to SC. With exposure is of concern, EIN of 16.7 (95% CI: 11.63, 29.41) means that for every 16 to 17 people with SC of 220+ (mg%), on average one case is attributable to SC. The CIN of 2.04 (95% CI: 1.984, 2.092) implies that for every 2 people who developed CHD, on average one case is attributable to SC. When exposed case is of concern, ECIN of 1.58 (95% CI: 1.233, 2.188) implies that for every 1 to 2 people with SC of 220+ (mg%) who developed CHD, on average one case is attributable to SC. Conclusion: Impact numbers complemented with corresponding confidence interval estimates are easily understood by researchers, policy makers, health care providers and consumers for their interpretational simplicities. Because these numbers are defined on different populations, researchers could use all or any of them depending on their research interest and objective.