To the Editor:
The usual designs to assess the relationship between exposure and outcome are cohort studies, resulting in relative risks (RRs), and case-control studies, resulting in odds ratios (ORs). Traditionally case-control studies are preferred when events are rare, and cohort studies when exposures are uncommon. When both events and exposures are rare, there is a particular challenge. In such settings, the case- population approach might be of help.
Case-population studies compare exposure in cases and in the general population.1,2 This design requires exhaustive or representative collation of cases of interest in a given territory and a measure of exposure to the exposure of interest in the territory’s population. Denominator is person-time,2 or number of exposed subjects.3 The metric is the case-population ratio, the ratio of exposure in cases and in the general population.
The case-population ratio is perpendicular to the RR: rather than the ratio of case rates among exposed and unexposed, it is the ratio of exposure rates among cases and population. In the usual two-by-two table (Table), where a is the number of exposed cases, b the number of exposed noncases, c the number of unexposed cases, and d the number of unexposed noncases, RR is (a/a+b)/(c/c+d), OR is a/c/b/d (or ad/bc), and case-population ratio is (a/a+c)/((a+b)/(a+b+c+d)). The analysis population may come from a representative population sample with a known sampling rate or from representative samples with unknown sampling rates (eg, the UK Clinical Practice Research Datalink). In that case, case-population ratio could be expressed as (a/(a+c))/((e/e+f)), wheree and f are the exposed and unexposed in the sample, which may or not include the cases.
If cases are rare, case-population ratio can be simplified to ad/bc/((1−Pexp)/(1−Cexp)), where Pexp is the population exposure to the drug of interest (b/b+d), and Cexp is the case exposure to the drug of interest (a/a+c). The smaller the population and case exposures, the better case-population ratio (CPR) approximates the OR. The OR estimates the RR when the event is rare, so the lower the exposure in cases and in the general population, and the rarer the event, the better the CPR approximates the real RR of the association of exposure and event.
We built a table of CPR for various RR and population exposures (eTable, https://links.lww.com/EDE/A718). When population exposure is below 1%, the difference between case-population ratio and actual OR or RR is less than 1%. Above 1%, CPR underestimates RR above 1 and overestimates RR below 1.
We tested this in a case-population study of liver transplantation in Europe for which drug utilization was the exposure of interest.3–5 In this study with exhaustive case identification, and full description of the country’s drug utilization over the same period and in the same population of patients, we computed the actual RR3 and derived the OR, case-population ratio, and confidence intervals. We tested the predictive value of case-population ratio for OR and RR, which conformed to predicted values (eAppendix, https://links.lww.com/EDE/A718).
This method provides a solution to the problem of very rare event/very rare exposure: the rarer the exposure and the event rate, the better the case-population ratio approximates the actual RR. This might be useful in circumstances where the relative exposures of cases and population are known, but the exact number of exposed and unexposed patients is unknown. In this situation, though RR or OR cannot be calculated, the case-population ratio can provide an estimate of OR and RR.
This approach could be applied on an ongoing basis with a continuous surveillance of representative cases of interest of very rare and serious events and a representative sample of the population to measure exposure.
INSERM U657 & CIC-P0005, Univ Bordeaux, Bordeaux, France, [email protected]
Sinem Ezgi Gulmez
INSERM CIC-P0005, Univ Bordeaux, Bordeaux, France
INSERM CIC-P0005, ADERA, Bordeaux, France
INSERM U657, Bordeaux, France
CHU de Montpellier, Montpellier, France
INSERM U657, Rouen, France
1. Capellà D, Laporte JR, Vidal X, et al. European network for the case-population surveillance of rare diseases (Euronet). A prospective feasibility study. Eur J Clin Pharmacol. 1998;53:299–302
2. Théophile H, Laporte JR, Moore N, Martin KL, Bégaud B. The case-population study design: an analysis of its application in pharmacovigilance. Drug Saf. 2011;34:861–868
3. Moore N, Gulmez SE, Larrey D, et al. Choice of the denominator in case population studies: event rates for registration for liver transplantation after exposure to NSAIDs in the SALT study in France. Pharmacoepidemiol Drug Saf. 2013;22:160–167
4. Gulmez SE, Larrey D, Pageaux GP, et al. Methodology for a multinational case-popu lation study on liver toxicity risks with NSAIDs: the Study of Acute Liver Transplant (SALT). Eur J Clin Pharmacol. 2013;69:605–616
5. Gulmez SE, Larrey D, Pageaux GP, et al. Transplantation for acute liver failure in patients exposed to NSAIDs or paracetamol (acetaminophen): the multinational case-population SALT study. Drug Saf. 2013;36:135–144