Epidemiologists have used secondary attack rates (SARs) to estimate the protective effects of vaccination since the 1930s. SARs can also be used to estimate the effect of vaccination on reducing infectiousness in breakthrough cases. The conventional SAR approach has been to pool the denominators and numerators across transmission units, then to use a confidence interval for a simple relative risk. We demonstrate appropriate model-based methods to estimate vaccine efficacy (VE) from SARs using generalized estimating equations taking correlation within transmission units into account. The model-based procedures require transformation of the parameter estimates to the SAR scale to obtain vaccine efficacy estimates. Appropriate confidence intervals are then based on the bootstrap, with resampling done by transmission unit. We show that the usual confidence intervals are too narrow. We estimated the effect of pertussis vaccination on person-to-person transmission. The results show that pertussis vaccination reduces the ability of a breakthrough clinical case to produce other clinical cases. The methods can be used in evaluating VE for susceptibility and infectiousness from SARs in other infectious diseases.
Bibliographical noteFunding Information:
M. Elizabeth HlloranaisPfreo, sMarse-ioiPerPrzrrieéisoVissigitin Instruc,tandoHaraoiCt isha douctoral cadidate,n Dpartmente of Biostatistics, Rollins School of Public Health, Emory Univey, Atlantrsa, CAit30322 (E-mil: email@example.com). Prézisiois also from the Niakhar Project, Institut de Rheeherpoccur le Développenmt, Dakaer, Senegal. This reasrceh was partially supported by National Institutes of Health grant R01-AI32042. Préziosi waalsospartially supported by the French Ministry of Foreign Aafi(grrfntasLvisier),aotehSign-eolPignacr Foundation (subvention), and AvisePnteuar (cotsnsultancy fees). Data collceontwis Ž nanacebydInstitut de Recerhecpouhr le Développemt andeAvnntisePsatr. Theeauuthors are grtea-ful to the Niakhar Projteteam,cin particular Francois Simondon, head of the pertussisclinicatrials,l andMichelGarenneandPeterA,inaitiatobrsoyfp-er tussis surveillance in the area; and to Coumba Tore uKane and Souleymae n Mboup (UitynCheiikhvAteaDnrpsDi,koa, aSrenegal), and Nicole Guiso and IsaIbtene(mIlnlteuaPstta,iPstaFerruiaisrncn,hcoabeofri)gigl,lcoea surveillance for the pertussis trials. They also thank BrdlayeEfron for enlightening discussions on bootstrap conŽ dence intervals.
- Generalized estimating equations
- Hierarchical models
- Random effects models
- Secondary attack rate