ORIGINAL ARTICLES Index event biasda numerical example

AbstractStudies of determinants of recurrent disease often give unexpected results. In particular, well-established risk factors may seem not tohave much influence on the recurrence risk. Recently, it has been argued that such paradoxical findings may be because of the bias causedby the selection of patients based on the occurrence of an earlier episode of the disease. This bias was referred to as index event bias. Here,we give a theoretical quantitative example of index event bias, showing that, as a result of selection of patients on the basis of previousdisease: (1) risk factors become inversely associated when they are not in the unselected population, and (2) the crude association betweenthe risk factor of interest and disease becomes biased toward the null. 2013 Elsevier Inc. All rights reserved. Keywords: Recurrence; Epidemiologic methods; Bias (epidemiology); Multifactorial causality; Risk factors; Models, theoretical 1. IntroductionMany medical disorders can recur within individuals. Ifthe risk of developing a disorder is increased after its firstoccurrence, previously affected individuals constitute a riskgroup for the disorder and target for prevention. As preven-tion can be accomplished by manipulating causal factors,studies have been devoted to identifying causal factors ofrecurrence and estimating their strength.Such studies often give unexpected results. In particular,factors that have been well established as determinants ofthe first occurrence of a disease may seem not to influencethe risk of recurrence much. For instance, factor V Leidenis an established strong risk factor of first-time venousthrombosis, with reported relative risks (RRs) of up to 80for homozygous individuals vs. noncarriers [1]. However,among patients with a previous thrombotic event, its effectontherecurrenceisnotclear[2].Anotherexampleisthathy-pertension, although increasing the risk of first-time strokeaboutfourfold[3],hasturnedoutasamuchweakerriskfactorforstrokerecurrence,withRRsrangingfrom0.9to1.6[4e8].DahabrehandKent [9] haverecentlyarguedthatsuchpara-doxical findings can be the result of selection of a study popu-lationonthebasisofpreviousoccurrenceofanevent.Becauseof conditioning on this event, an inverse association between(known and unknown) risk factors may arise, when these riskfactors are not mutually associated within the general popula-tion. Asa consequence,the association betweentheindividualriskfactorsandrecurrenceoftheeventwillbebiasedtowardthenull (‘‘index event bias’’). In the example of hypertension andstroke, experimental studies show that the reduction of hyper-tension has strong beneficial effects on stroke recurrence rates[10,11],furtherindicatingthattheapparentweaknessoftheas-sociation in observational studies is indeed a result of bias.Although Dahabreh and Kent make a strong case for in-dex event bias as an explanation of the paradoxical findingsin recurrence risk research, they do not adduce quantitativeexamples to show the mechanism of the bias. In the presentarticle, we will illustrate the operation of the bias by the useof a numerical example.2. Simulation in shortWe present hypothetical data for a study intending tomeasure the association of a particular risk factor with