American Journal of EPIDEMIOLOGYcourses.washington.edu/b578a/readings/halloran1997.pdf · attack rate, SAR,-,, defined as the proportion of sus-ceptibles with covariate status j making

Volume 146

Number 10

November 15, 1997

American Journal of

EPIDEMIOLOGYCopyright © 1997 by The Johns Hopkins University

School of Hygiene and Public Health

Sponsored by the Society for Epidemlologic Research

REVIEWS AND COMMENTARY

Study Designs for Evaluating Different Efficacy and EffectivenessAspects of Vaccines

M. Elizabeth Halloran,1 Claudio J. Struchiner,2 and Ira M. Longini, Jr.1

Vaccine efficacy and effectiveness (VE) are generally measured as 1 minus some measure of relative risk(RR) in the vaccinated group compared with the unvaccinated group (VE = 1 - RR). In designing a study toevaluate vaccination, the type of effect and the question of interest determine the appropriate choice ofcomparison population and parameter. Possible questions of interest include that of the biologic effect ofvaccination on susceptibility, on infectiousness, or on progression to disease in individuals. The indirecteffects, total effects, and overall public health benefits of widespread vaccination of individuals within thecontext of a vaccination program might also be of primary concern. The change in behavior induced by beliefin the protective effects of vaccination might influence the estimates of these effects or might itself be ofinterest. In this paper, the authors present a framework of study designs that relates the scientific question ofinterest to the choice of comparison groups, the unit of observation, the level of information available foranalysis, and the parameter of effect. Am J Epidemiol 1997; 146:789-803.

clinical trials; communicable diseases; community trials; vaccine efficacy; vaccines

Vaccine efficacy and effectiveness (VE) are gener-ally measured as 1 minus some measure of relativerisk (RR) in the vaccinated group compared with theunvaccinated group:

VE = 1 - RR. (1)

Vaccination can produce several different kinds ofeffects, both at the individual level and at the popula-tion level, and the groups in the comparisons could becomposed of individuals, populations, or communi-ties. Vaccination can induce a biologically protective

Received for publication November 12, 1996, and In final formJune 27, 1997.

Abbreviations: Cl, cumulative incidence; IR, incidence rate; PH,proportional hazards; RR, relative risk; SAR, secondary attack rate;VE, vaccine efficacy/effectiveness.

1 Department of Biostatistlcs, Rollins School of Public Health,Emory University, Atlanta, GA.

2 Escola Nacional de Saude Publica, Fundacao Oswaldo Cruz,Rio de Janeiro, RJ 21041, Brazil.

Reprint requests to Dr. M. Elizabeth Halloran, Rollins School ofPublic Health, Emory University, 1518 Clifton Road NE, Atlanta, GA30322.

response in a vaccinated individual or reduce the de-gree or duration of infectiousness. Widespread vacci-nation in a population can reduce transmission andproduce indirect effects, even in individuals who werenot vaccinated. Vaccinated people might change theirrate of making contacts with potentially infectioussources, and thereby counterbalance the biologic pro-tective effects or alter the overall public health benefitsof vaccination. In designing a study for evaluating theeffects of vaccination, the question of interest guidesthe choice of unit of observation, comparison groups,parameter of effect, and level of information required.

In this paper, we present a systematic overview(table 1) of study designs for evaluating various effectsof vaccination and vaccination programs based on thechoice of comparison groups, the unit of observation,the choice of parameter, and the level of informationrequired. The expression VE = 1 — RR is of the formof the prevented fraction in the exposed, and thusbelongs to the family of parameters of attributable, orprevented, risk. We take as our point of departure the

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Study Designs for Different Aspects of Vaccines 791

review by Greenland and Robins (1, 2) of the family ofparameters of attributable or prevented risk, whichprimarily pertained to noninfectious diseases. The twomain parameters in this family that Greenland andRobins considered are the prevented hazard fraction,based on the incidence or hazard rate ratio, and theprevented fraction, based on the cumulative incidenceratio with the unit of observation being the individual.These two parameters have their analogies in the fam-ily of vaccine efficacy and effectiveness parameters.However, because of the dependent happenings (3)and the indirect effects of intervention in infectiousdiseases, several more measures are relevant for esti-mating the various prevented risk vaccine efficacy andeffectiveness parameters.

In the conceptual framework we present, we expandthe family of prevented risk parameters discussed byGreenland and Robins in two dimensions. In the firstdimension, we add the transmission probability orsecondary attack rate, a parameter that conditions onactual exposure to infection, to the incidence or hazardand cumulative incidence (4), parameters that do notcondition on exposure to infection. The transmissionprobability is fundamental to infectious disease epide-miology. We also show that in this direction, thefamily of vaccine efficacy parameters form a hierarchyordered by the amount of information required fortheir estimation. In the second dimension, to estimatethe indirect and overall effects of widespread vaccina-tion, we enrich the choice of comparison populationsby comparing different populations or communities inthe study designs for dependent happenings (5, 6). Inthese studies, the community or a subpopulation of thecommunity becomes the main unit of comparison.

We also discuss the behavioral and exposure effica-cies of interventions which often occur throughchanges in the rates and types of contacts with poten-tially infective sources (7). We emphasize that a studycan be designed to evaluate several different types ofeffects at the same time. We also emphasize the im-portance of distinguishing risk factors for exposure toinfection from risk factors for susceptibility. Theseconcepts and study designs are applicable to risk fac-tors and interventions other than vaccination againstinfectious diseases. We have found this conceptualframework useful to us in ordering our own thoughtsand in discussions with other colleagues on evaluatingvaccine effects. We present it here in the hope that itwill provide a basis for further developments in therational and complex design of vaccine evaluation.

BIOLOGIC EFFICACY

Figure 1 illustrates transmission between an infec-tious source and a susceptible person who are making

parasite

;infectjqus; \ ; : ; : ; ; ; : ; : ; ; : : _ ( susceptible1

h 0 S { . . . . ] . . . . . . : : : . . . . . » • I h o s t ,

contact

Transmission probability depends on- infectious host- susceptible host- contact definition- parasite

FIGURE 1. Schematic diagram of transmission of an infectiousagent as an infectious host makes contact with a susceptible host.

contact with one another. The transmission probabil-ity, Pij, is the probability that, conditional upon acontact between an infective source with covariatestatus i and a susceptible host with covariate status j ,successful transfer and establishment of the infectiousagent will occur. A related concept is the secondaryattack rate, SAR,-,, defined as the proportion of sus-ceptibles with covariate status j making contact withan infectious person of covariate status i who becomeinfected. The probability of transmission depends onthe characteristics of the infective source i, the infec-tious agent, the susceptible host j , and the type anddefinition of contact. For example, if 0 and 1 denoteunvaccinated and vaccinated status, respectively, thenp0} denotes the transmission probability per contactfrom an unvaccinated infective person to a vaccinateduninfected person. Similarly, SAR10 denotes the sec-ondary attack rate from a vaccinated infective to theunvaccinated susceptibles with whom they make con-tact. The biologic effects of vaccination of an individ-ual can reduce 1) the probability of infection given aspecified exposure to an infectious agent, 2) the pro-gression to, degree, or duration of disease, once theindividual becomes infected, and/or 3) the degree orduration of infectiousness for other individuals. Weconsider estimation of the different types of effectsbelow.

VACCINE EFFECT ON SUSCEPTIBILITY (VEs)

The first question of interest is how vaccinationprotects individuals against either infection or disease.In table 1, the vaccine efficacy measures for how wellthe vaccine reduces susceptibility, VES, are given inthe third column. The top row contains the conditionalparameters, such as the transmission probability orsecondary attack rate. The bottom rows contain theunconditional parameters incidence (hazard) rate andcumulative incidence (attack rate). Under the assump-tion of equal exposure to the infectious agent inthe vaccinated and unvaccinated groups (8), valid

Am J Epldemiot Vot. 146, No. 10, 1997

792 Halloran et al.

estimates of VE5 are obtained from VES = 1 —|7?(vaccinated people)/7?(unvaccinated people)], whereR denotes one of the measures of risk. We show belowthat the conditional and unconditional parameters forma hierarchy requiring different levels of informationabout the transmission system. They are also differ-ently affected by potential sources of bias. Interpreta-tion of the estimated VE5 as the level of biologicprotection conferred by the vaccine is generally com-plicated, as discussed briefly below and elsewhere.

Transmission probability or secondary attack rate

An epidemiologic measure of the biologically pro-tective effect of vaccination is the reduction in theprobability of infection or disease conditional on acertain level of exposure to the infectious agent, givena certain type of contact. Thus, in the absence ofcontrolled challenge experiments, the first choice forepidemiologically estimating the biologic protectiveeffect of vaccination is based on the transmissionprobability ratio, or any similar parameter that condi-tions on actual contact between an infectious sourceand a susceptible person. The concept of a "contact" isvery broad and must be defined in each particularstudy. In a study of sexually transmitted disease, thecontact could be defined per sex act or per partnership.In a study of pertussis, a contact could be defined asattending school on the same day as an infectiousperson or as living in the same household during theentire period of infectiousness of a case. The mode oftransmission of a parasite determines which types ofcontacts are potentially infectious.

The transmission probability is estimated in twomain ways. The first method, called the secondaryattack rate (9-12) or case-contact rate method, hasbeen used to estimate vaccine efficacy since the per-tussis vaccine trials were carried out in the 1930s (13).The vaccine efficacy measure is based on the SARA inthe vaccinated susceptibles who were exposed to in-fection compared with the SAR 0 in unvaccinated sus-ceptibles who had a similar exposure, where the dot inthe subscript can denote any vaccine status for theinfective or an average across the population. Second-ary attack rate studies are commonly used for directlytransmitted infectious agents with high transmissionprobabilities, such as measles, chickenpox, mumps,pertussis, and tuberculosis. Another method of esti-mating the transmission probability is based on thebinomial model. In this case, we observe susceptiblepeople, count the number of contacts they make withinfectives, and count the number of these susceptiblepeople who become infected. The binomial model iscommonly used in studies with low transmission prob-

abilities, such as studies of human immunodeficiencyvirus, in which susceptibles often make more than onecontact before becoming infected. The ascertainmentof the susceptibles or infectives can occur prospec-tively or retrospectively, depending on the design ofthe study.

Let p 0 and p , denote the probability of transmissionto unvaccinated and vaccinated susceptibles, respec-tively. Analogously, let S A R 0 and SAR , denote thesecondary attack rates for unvaccinated and vaccinatedsusceptibles, respectively. The dot denotes the infec-tious contacts, which are assumed to be equal for thevaccinated and unvaccinated susceptibles. VESj},based on the transmission probability or secondaryattack rate, is estimated from

p.x _ SAR.,f P.o S A R Q

/vaccinated infections

\ vaccinated exposures

unvaccinated infections \

unvaccinated exposures/

Estimating vaccine efficacy from the transmissionprobability ratios requires information on who is in-fectious and when, and on whom they contact andhow. Because this method generally requires the mostinformation, Rhodes et al. (14) call the conditionalmeasure a level I parameter (table 1, top row).

Hierarchy of VES parameters

Gathering information on exposure to infection andon contacts between infective and susceptible peoplein a vaccine study is often expensive, difficult, or evenimpossible. Thus, quite often vaccine efficacy studiesrely on time-to-infection or time-to-disease data orsimply on final value data. The analysis may be strat-ified according to variables believed to correlate withexposure to infection. If time-to-event data are col-lected, VES can be estimated from the incidence orhazard rate ratio; Rhodes et al. (14) called this level IIinformation. For the Cox proportional hazards model(15), a special hazard rate ratio that assumes the samebaseline hazard in both the vaccinated and unvacci-nated groups is used. Then only the ordering of theevents is needed; this is called level HI information. Ifonly final value data, called level IV data, are col-lected, VE5 is based on the cumulative incidence orattack rate ratio.

The transmission probability, incidence rate, andcumulative incidence have a fundamental relation toone another because of the dependent happening struc-

Am J Epidemiol Vol. 146, No. 10, 1997


ture of infectious diseases. The incidence rate andcumulative incidence can be thought of as functions ofthe underlying transmission process, even if we do notmeasure the components. The components include therate of contacts in the population, the probability thata contact between an infective and a susceptible willresult in transmission, and the probability that anycontact a susceptible makes is with an infectioussource. Quite simply, the number of infection eventsper person-time equals the number of contacts per unitof time X the transmission probability per infectiouscontact X the probability that the contact is infectious.If c0 is the baseline contact rate, p 0 is the averagetransmission probability from an infectious person toan unvaccinated susceptible person, and P0{i) is the

prevalence of infection in people with whom the un-vaccinated people make contact at time t, the hazardAo(r) or incidence rate IRQCO

m m e unvaccinatedpopulation can be expressed as Xî) = ERQCO =c0poP0(t). The term P0(t) could also represent theprobability that an environmental exposure is contam-inated with the infectious agent, such as cholera bac-teria in drinking water. In the vaccinated group, theincidence IRj(0 or hazard rate Ax(r) of infection is theproduct of the contact rate in the vaccinated group, c,,the average transmission probability from an infec-tious person to a vaccinated susceptible, pA, and P^t),the prevalence of infection in people with whom thevaccinated people make contact at time t: A,(f) =

If the contact rates in the two groups are equal and the prevalences of infection and infectiousness in the groupswith whom they mix are equal, perhaps through randomization, then vaccine efficacy based on the incidenceVESJR(r) or hazard rate ratio VE5 A(f) can be thought of as

y-gvaccinated events/person-time

unvaccinated events/person-time

\\{t) CiP\Pi(t)

Pa

Generally, simple cancellation of the contact rates and the prevalence of infection is not possible because ofheterogeneities in the vaccinated and unvaccinated groups. Therefore, estimation of vaccine efficacy fromtime-to-event data would not generally yield the same estimate as that based on the transmission probability. Theestimated epidemiologic efficacy often differs from the biologic efficacy measure of interest. However, it isuseful to think of the transmission probability and incidence rates as intrinsically related to each other. In the Coxproportional hazards model (PH), the estimate is based on the partial likelihood and requires data on the orderof events, VEPH = 1 — ePt, where e&' would be estimated by the hazard ratio (14).

Similarly, the cumulative incidence, Cl(T), at some time T is a function of the hazard rate during the follow-upperiod, and thus also a function of the transmission probability, contact rate, and prevalence of infection in thecontacts.

VEs,a(7) = 1 -vaccinated infection events/persons-at-risk

unvaccinated infection events/persons-at-risk CIQ(T) 1 — exp(—/J

Even though the cumulative incidence estimate is a sort of black-box estimator, it is useful in vaccine studies tothink about the underlying transmission system that would produce the observed final values.

Example

It is possible to combine different levels of information within the same study by the use of appropriateprobability models or by collection of different levels of data. Sometimes both a conditional and an unconditionalestimate of vaccine efficacy are given from the analysis of a single study. For those study subjects who had aputative exposure to the infectious agent, the conditional estimate is given. The unconditional estimate using alleligible study subjects is also provided. An early example is the study of pertussis vaccine carried out in the 1930s(13), which reported both the proportion of people exposed to infection who developed pertussis and the numberof cases per person-time. The vaccinated and control groups had 1,815 and 2,397 children, respectively, whocontributed 4,575 and 2,268 person-years at risk, respectively. There were 52 cases in the vaccinated group and348 cases in the control group, so

52 cases/2,268 person-years

348 cases/2,307 person-years= 0.85. (2)


794 Halloran et al.

The study also had information on children who had been exposed to pertussis within their own households. Inthe vaccinated group, 29 of 83 exposed children developed pertussis, while 143 of 160 exposed children in theunvaccinated group developed pertussis. Thus,

•p

29 cases/83 vaccinated exposed_

143 cases/160 unvaccinated exposed

= 0.61. (3)

Fine et al. (12) review several studies of pertussis vaccines and discuss some possible biologic reasons fordiffering values of the conditional estimates versus the unconditional estimates.

Example

Greenwood and Yule (8) used the cumulative incidence, or attack rates, in studying the efficacy of typhoidvaccination among troops in the early part of the 20th century. In one of their studies, use of the attack rates wascomplicated because vaccine continued to be administered to the troops until the end of the study. Thus, thedenominators for the vaccinated and unvaccinated groups were changing over the course of the study. Greenwoqdand Yule provided two analyses, one assuming that all of the denominators were based on the vaccinated andunvaccinated groups at the beginning of the study and the other based on who was vaccinated or unvaccinatedat the end of the study. Here we show the analysis using denominators based on the beginning of the study.Greenwood and Yule had 56 cases of typhoid in 10,378 vaccinated soldiers and 272 cases in 8,936 unvaccinatedsoldiers. The estimated efficacy based on these numbers is

56 cases/10,378 at risk

272 cases/8,936 at risk= 0.82. (4)

Example

We compare the conditional estimators with theunconditional estimators in a simple example. Con-sider a 1-year, randomized, double-blinded, placebo-controlled trial with 5,000 people each in the vacci-nated and unvaccinated arms of the study. Supposethat the incidence rate in the unvaccinated group is 2.0percent, and that the vaccine reduces susceptibility toinfection equally and multiplicatively in all vaccinatedpersons by 0.50. Ignoring indirect effects, and assum-ing only one contact per person (16), after 1 year theexpected data would be those shown in table 2. After1 year (t = 1), the estimated efficacy is

50/5,0001) 1 050

If we were able to identify all contacts with infectives,as in the hypothetical study shown in table 3, we couldestimate vaccine efficacy using the transmission prob-ability. Under randomization and double-blinding, weassume that the number of potentially infective con-

TABLE 2. Expected data from a study collecting informationon person-time at risk*

StatusNo. of

participantsNo. of

infections Time (years)

VaccinatedUnvaccinated

5,0005,000

50100

• The incidence rate In the unvaccinated group is 2.0 percent peryear.

tacts in each group is the same. The estimated vaccineefficacy based on the transmission probability wouldbe

50/1,000

' 0 5 0

Complex considerations

We chose this simple example to demonstrate therelations among the different levels of parameters.Generally things are not this simple. By conditioningon contacts with infectives, comparison of the trans-mission probabilities to vaccinated susceptibles versusunvaccinated susceptibles is the most likely of thevaccine efficacy measures to give meaningful infor-mation about the biologic protective effect of the vac-cine. Estimates of vaccine efficacy based on the inci-dence rate ratio or cumulative incidence ratio can beinterpreted under certain assumptions about equal ex-posure to infection in the comparison groups (8), howthe vaccine works, and the distribution of its effects inthe population (16-20). Even under the assumption of

TABLE 3. Expected data from a study collecting informationon number of exposures to an infectious agent

StatusNo. of

participants

No. ofexposures to

Infection

No. ofinfections

Time(years)


5,0005,000

1,0001,000

50100



equal exposure to infection in the vaccinated and un-vaccinated groups, VE5A and VESCI can give verybiased estimates of the effect of vaccination on thetransmission probability (17, 19-21).

Several complicating factors in the evaluation ofvaccine efficacy go beyond the four levels of infor-mation and their respective parameters presented here.Some vaccines made of live, attenuated infectiousagents can spread from the vaccinees to people whohave not been vaccinated, a phenomenon referred toas "contagious treatment" (6). If the vaccine virusspreads to a substantial number of unvaccinated studysubjects, the efficacy of the vaccine could be under-estimated.

Another complicating factor is how to interprettime-varying vaccine efficacy estimates. Vaccine effi-cacy estimates can vary over time because of hetero-geneity in susceptibility, rates of exposure to infec-tious agents, or the protection conferred by the vaccine(17, 19, 20). They could also vary because the efficacyof the vaccine actually wanes over time (22). Theefficacy could also increase with time if the level ofefficacy depends on boosting by natural infection (6).Common to all of these effects is the fact that they canbe captured only if time-to-event data are available.Although heterogeneities can be taken into accountwith frailty models (19, 20) and waning can be esti-mated with parametric or nonparametric models (22),designing studies to estimate changes in efficacy dueto natural boosting remains a challenge. Another openchallenge is that of distinguishing among the possiblecauses of time-varying estimates. The overall, long-term effects of vaccination in a population depend onthese characteristics (23-25), so study designs andmethods of analysis for evaluating them are importantareas for further development.

Practical choice of estimators

The amount of information gathered—that is, fromthe most (level I) to the least (level TV)—will bedetermined by many practical considerations that wecannot consider in detail here. The choice of estima-tors can be driven by the type and duration of thestudy. Postlicensure evaluation of a vaccine after anacute outbreak of an infectious agent often must becarried out using only information on whether peoplebecame infected or developed the disease during theperiod of the outbreak, since time-to-event or exposuredata are not available. In this case, estimation of vac-cine efficacy will be based on the cumulative inci-dence, or attack rates. If time-to-event data were avail-able, relative incidence rates or relative hazards couldbe used. If the study occurred over a longer period oftime, with the risk set also changing over time, then

the relative incidence or relative hazard rates would bea more appropriate choice for the dynamic cohort thatwould be under observation.

CONTACT RATES AND EXPOSURE EFFICACY

Knowledge of being vaccinated could alter the con-tact rate of a vaccinated person or the contact patternin a vaccinated population. With interventions otherthan vaccines, the primary goal of an intervention maybe change in exposure to infection. "Contact rate ef-ficacy" is the relative change in the contact rates dueto an intervention. "Exposure efficacy" or "behaviorefficacy" is the relative increase or decrease in the riskof infection or disease due to the change in exposure tothe infectious agent, depending on the outcome mea-sure chosen (7). For example, if we consider the com-ponents of the hazard rate as discussed above, changesin exposure to the infectious agent can occur in the rateof contact, in the prevalence of infection in the contactgroups, or in the transmission probability through achange in the type of contact. In nonrandomized orobservational studies, the vaccinated and unvaccinatedgroups often differ in their exposure to infection with-out changing their behavior. Unequal exposure to in-fection in the two comparison groups can bias esti-mates of the efficacy measures of interest. Althoughvaccine efficacy estimates based on the transmissionprobability require more information than those basedon the unconditional parameters, they are less sensi-tive to bias from unequal exposure to infection in thetwo groups.

Example (continued)

Continuing the example from above, suppose thatthe study were randomized but not blinded and that thevaccinated individuals all doubled their rate of contactby a factor of 2, so that c, = 2c0. The expected datafrom such a study are shown in table 4. After 1 year(t = 1), the unconditional estimated efficacy would be

100/5,000i) * a

TABLE 4. Expected data In an unblinded, randomized studyIn which all vaccinated Individuals double their contacts by afactor of 2 after randomization

StatusNo. of

participants

No. ofexposures to

infection

No. ofInfections

Time(years)


5,0005,000

2,0001,000

100100


796 Halloran et al.

The efficacy estimate based on the number of infec-tions conditional on the number of exposures to infec-tion would be

100/2,000

= l ~TooTIôo = 0 5 ° -Using the unconditional estimates, with no knowledgeof the change in exposure to infection, we wouldbelieve the protective effect of the vaccine to be zero,while, using the conditional estimates, we correctlyestimate the protective efficacy to be 0.50. A similarresult would occur if vaccinated people made contactwith people who were more infectious or with groupsin which the prevalence of infection was twice as high.Such a result would also occur if the vaccinated peoplechanged the type of contact they made to one that hada higher baseline transmission probability.

The combined effect of the change in exposure toinfection and the biologic protective effect of the vac-cine is an important public health measure of interest.Indeed, an increase in the contact rate or other sourceof increased exposure to infection could outweigh anybiologic protection conferred by the vaccine. Thus, abiologically protective vaccine could have detrimentalpublic health effects. Whether the biologic protectiveefficacy or overall efficacy for an individual is ofinterest depends on the question underlying the study.The study design must be chosen to ensure that thequestion or questions of interest will be answered. Ingeneral, it is important to differentiate risk factors forexposure to infection from risk factors for biologicsusceptibility. Stratification by surrogates for amountof exposure to infection could help to reduce potential

bias in unconditional estimators.It is possible to design studies to examine several

questions at the same time and to estimate more thanone parameter from the data. In the last example, if thenumber of exposures to infection were ascertained,then both VE5^ and VE5 x could be estimated, givingan estimate of both the biologic protective efficacy andthe effect of the combined reduction in susceptibilitywith increased exposure.

VACCINE EFFECT ON INFECTIOUSNESS (VE;)

The biologic effect of the vaccine in reducing infec-tiousness, VE/, can be estimated epidemiologically bycomparing the per-contact transmission probabilityfrom vaccinated people who become infected with thetransmission probability from unvaccinated peoplewho become infected. In contrast to VE5, which isestimated using either conditional or unconditionalparameters, VE, can generally be estimated only usingconditional measures such as the transmission proba-bility or the secondary attack rate (4, 26-28). Toestimate the biologic effect of the vaccine in reducinginfectiousness (4), the relative risk comparison groupsare defined according to the vaccination status of theinfectious person contacting the susceptible person. Intable 1, the VE7 estimate is shown in the secondcolumn of the top row of conditional parameters. Forcompleteness, the third column of parameters containsthe estimate of the combined effects of the vaccine inreducing the transmission probability if both the in-fectious person and the susceptible person in the con-tact are vaccinated (VEr).

Example

Suppose that the goal of a study were to estimate the efficacy of a pertussis vaccine in reducing susceptibilityand infectiousness. In addition to the number of potentially infectious contacts and the vaccine status of theexposed susceptibles, we also record the vaccine status of the infectious contact, possibly the primary case in thehousehold. The data from such a hypothetical study are shown in table 5. For example, there are 44 infectionsin vaccinated people who had a total of 800 exposures to unvaccinated infective people. The estimate of SARîs 44/800. The effect of the vaccine in reducing susceptibility and infectiousness and the combined effects on bothare estimated by

VES . , = 1 -SARo,

SARQO

44/800

88/800

SAR,

SAR 10

6/200

12/200= 0.50;

SAR10 _ 12/200 _ SAR,, _ 6/200 _

SARQO 88/800 SARo, 44/800

SAR,, _ 6/200 _

SARQO 88/800



TABLE 5. Expected data from a study using the household secondary attack rate to estimate both vaccine efficacy forsusceptibility (VEg) and vaccine efficacy for Infectiousness (VEJ

Status No. ofparticipants

5,000

5,000

Infectiouscontact

VaccinatedUnvaccinatedVaccinatedUnvaccinated

No. of exposuresto infection

No. ofInfections

Time (years)

Vaccinated

Unvaccinated

200800200800

6441288

This is interpreted to mean that vaccination reduces the per-contact susceptibility by 0.50 and reduces infec-tiousness (once a vaccinee becomes infected) by 0.45 percent, and the combined reduction in susceptibility andinfectiousness reduces the transmission probability by 0.73.

Generally, contact information is required to estimate the effect of the vaccine in reducing infectiousness. Bymaking strong modeling assumptions, Longini et al. (29) suggest a method for estimating the effect of the vaccineon infectiousness using time-to-event data from studies in multiple populations.

Effect on progression (VEP)

Evaluation of the effect of prophylactic vaccinationon progression to disease, VEp, requires comparisonof morbidity in vaccinated people who have becomeinfected with that in infected unvaccinated people.Estimation of the effect of vaccination on progressionwould generally require observation of the infectedindividuals over time. Problems of interval censoringare important, because often the time of infectionwould not be observed accurately.

INDIRECT AND TOTAL EFFECTS (VEIM AND VEIIS)

While the parameters in the third column of table 1provide estimates of the protective efficacy for indi-viduals and the conditional parameters in the top rowalso provide estimates of the effect of the vaccine oninfectiousness, none of these parameters produceestimates of the indirect or overall public health effectsof vaccination in a population under dependent hap-penings (5, 6). The effects of a vaccination programcould be quite different for people not receiving avaccine than for those who receive the vaccine. Thepopulation-level effects of vaccination depend on thecoverage and distribution of the vaccine, as well as onhow the different groups mix with each other. Theseeffects could result from the biologic effects as well asthe behavioral effects of vaccination. The overall pub-lic health effects of a vaccination program depend onthe effects in both the vaccinated people and the un-vaccinated. Thus, it is important to differentiate amongthree main types of population-level effects. The indi-rect effects are the population-level effects of wide-spread vaccination on people not receiving the vac-cine. The combination of the population-level effectsof widespread vaccination in the individuals receivingthe vaccine we call the total effects of vaccination andthe vaccination program. The overall public health

effects of the vaccination program depend on theweighted average of indirect effects on the individualsnot receiving the intervention and the total effect onthe individuals receiving the intervention.

To emphasize the difference between indirect andtotal effects, we consider a study in which change inaverage age at infection is an outcome measure ofinterest. Assume that the vaccine reduces the proba-bility of becoming infected upon exposure to an in-fectious agent but does not completely protect againstinfection. Widespread vaccination would reduce thelevel of transmission and result in an increase in theaverage age at first infection for both the unvaccinatedindividuals and the vaccinated individuals. The in-crease in average age at first infection would be evengreater in those who were vaccinated than in thosewho were not, however, since they would need to beexposed to infection more often, on average, to be-come infected than those people who did not getvaccinated. Thus, the indirect effect of the vaccinationprogram would be less than the total effect of thevaccination program. The distinction between thesetwo types of effects is not made often enough. Theoverall change in age of infection would be a weightedaverage of the increase in the two groups. Even if theoverall benefits of vaccination in a population arepositive, subgroups of the population may actuallysuffer; thus, such distinctions must be made.

The indirect, total, and overall effects are definedwithin the context of a particular intervention programin a population. A vaccination program or otherkind of intervention program depends on the level ofcoverage and distribution of the vaccine or otherintervention within the population. To estimate theindirect, total, or overall effects of vaccination, weneed to compare different populations or communitieswith and without the intervention program, or withdiffering types of intervention programs. The three


798 Halloran et al.

different kinds of population-level effects—indirect,total, and overall—motivate three types of study de-signs depending on the choice of comparison popula-tions. In the expression VE = 1 — RR, the estimate ofrelative risk is derived from comparing different pop-ulations. Together with the study designs for individ-ual effects presented above, these are the four studydesigns for dependent happenings (5, 6) (figure 2). Intable 1, the study designs for population-level effectsare shown in the right three columns and include studydesigns HA, EfB, and III from figure 2. The parametersdiscussed above are study designs of type I, shown inthe third column of the table.

Since the population-level effects of interest aredefined within the context of a particular interventionprogram, the unit of inference is the population, andseveral populations might be included in the study.The issues raised are similar to those in communitytrials of interventions against noninfectious diseases. Itis important in designing such studies that the popu-lations or communities chosen as the unit of observa-tion be separated as much as possible in every way thatis relevant for transmission of the infection understudy. The separation could be geographic, cultural, ortemporal. We could compare neighboring villages,different cities, or child-care centers with differentlevels and distributions of vaccination. If there istransmission-relevant mixing among the populationunits, this could bias the estimates of effectiveness.One population could be the preintervention popula-tion while the other population was the postinterven-tion population, raising problems of historical con-trols. Studies comparing interventions in differentpopulations can be done either as part of phase mtrials or as part of postlicensure surveillance. Increas-ing interest is being shown in evaluation of potentialindirect and overall effects of vaccination strategiesbefore licensure.

To illustrate the choice of comparison populationsor subpopulations for estimation of the three differenteffects, assume for simplicity as in figure 2 that thereare two populations, A and B. Assume that a vaccina-tion program is implemented in population A so thatsome, but not necessarily all, of the individuals arevaccinated. No one is vaccinated in population B. Toestimate the indirect effects of the vaccination pro-gram, we compare the average outcome in the indi-

POPULATION A POPULATION B

DESIGN moverall

DESIGN ]direct

DESIGN Haindirect

DESIGN libdirect + Indirect

FIGURE 2. Types of effects of vaccination and different studydesigns for their evaluation based on choice of comparison popu-lations. Populations A and B are separated In every way relevant totransmission dynamics. In population A, some but not necessarilyall of the people are vaccinated. In population B, no one Is vacci-nated. (Adapted from Halloran and Struchiner (6)).

viduals who did not receive the vaccine in the vacci-nated population A with the average outcome inunvaccinated individuals in population B. These arestudy designs of type HA, represented by the fourthcolumn in table 1. For estimation of the total effect ofvaccination, the average outcome in vaccinated peoplein population A is compared with the average outcomeof un vaccinated people in population B. This is rep-resented in the fifth column of table 1. Somewhatmore formal definitions of the indirect and total effectsare provided elsewhere (4). The effect parameters aredistinguished by the subscript specifying the studydesign and the measure of relative risk. For example,an estimate of the indirect effect of vaccination basedon the cumulative incidence at some time T is denoted

Subpopulations of the communities could also becompared. For example, the populations could be fur-ther stratified by age, sex, receipt of behavioral inter-ventions, or any other risk factor of interest. For avalid comparison, the analogous subpopulation fromeach community must be included.

Example

As an example, consider using the hazard rate ratio as the measure of the indirect and total effects of thevaccination program. Let AO, Al, and SO denote the unvaccinated and vaccinated people in population A and theunvaccinated people in population B, respectively, and let c, p, and P(t) be the contact rate, transmissionprobability, and prevalence, as defined above. Suppose that the estimated hazard rates in the unvaccinated andvaccinated portions of population A at some time t are \A0(t) = 0.08 and \Al(t) = 0.06, respectively, and the



estimated hazard rate in the unvaccinated population B is A^f) = 0.12. Then the estimated indirect and totaleffects of the vaccination program in population A on the incidence rate compared with no program in populationB would be:

Indirect: 1

= 1 - A«,(0

WOA«,(O

1

= 1= 1 -

cMpMPAl(t)

0.08012

0.06Ol2 = 0.50.

These expressions show that the indirect or total effects result not only from the change in the transmissionprobability induced by the direct biologic effects of the vaccination but also from the change induced by theindirect effects. Vaccination would be expected to reduce the prevalence of infective persons in population A.However, mixing patterns might change because of belief in the protective effect of the vaccine. The prevalenceof infection in the contacts of vaccinated people in population A, PA1(t), might be higher than the prevalence ofinfectives among the contacts of the unvaccinated people in population A, PA0(i). Similarly, the contact ratesmight change in the people who are vaccinated. Thus, the estimated indirect and total effects based on theunconditional parameters can summarize several different consequences of vaccination beyond the biologicconsequences.

Note that conducting a trial that includes severaldifferent populations or communities does not pre-clude studying the efficacy of the vaccines withinpopulations. A phase HI vaccine trial can be designedto answer several questions at the same time. Random-ization within a population can be used to answerefficacy questions, while comparison across popula-tions can be used to evaluate the indirect and overalleffects of vaccination. Consider a study of vaccinationin several populations designed to measure the indirectand overall effects of vaccination with different levelsof coverage in each population. Within each popula-tion, a comparison can be made of the vaccinatedportions of the population with the unvaccinated. Ifinformation is gathered within the populations on ac-tual contacts, the effect of the vaccine on infectious-ness as well as on susceptibility could be evaluated.The most important consideration in designing a vac-cine study is to be clear about the effect(s) or ques-tion^) of interest and the level of information that canbe gathered. Then the parameter of interest and thecomparison populations should be chosen to providethe effect measures of interest.

In the preceding example, within population A, wecould have been conducting a randomized phase HIvaccine trial and used the relative hazards in the vac-cinated and unvaccinated portions of the population toestimate vaccine efficacy, assuming that the exposureto infection in the two groups remained equal afterrandomization:

VESA(O - 1 - T—rr - 1 - (0.6/0.8) = 0.25.A/oW


Although the direct protective efficacy is only 0.25,the combined effect of vaccination and the distributionof vaccinations in the population produces the totalprotective effect relative to the unvaccinated popula-tion of 0.50.

Comparison with prevented fractions innoninfectious diseases

The unconditional vaccine effect parameters dis-cussed above are analogous to the family of preventedfraction parameters discussed by Greenland andRobins (1, 2), with some essential differences. In thework of Greenland and Robins, the prevented fractionin the exposed is estimated by comparing the cumu-lative incidence in the exposed individuals with thecumulative incidence in the unexposed individuals in astudy design similar to study design I with level IVinformation. The unexposed group is supposed to rep-resent what would have happened to the exposedgroup had it not been exposed. The number of pre-vented cases in the exposed can be estimated from theprevented fraction based on the cumulative incidence,if it is known how many people were exposed. Asimilar argument can be made for the prevented hazardfraction, though the number of cases prevented is notso easily estimated. Under dependent happenings,however, in study design I, in population A, for ex-ample, the number of cases in the unvaccinated indi-viduals does not represent the number of cases thatwould have occurred in the unvaccinated individualshad the vaccination program not been implemented. Ifvaccination is widespread enough, the cumulative in-cidence in the unvaccinated group will usually belower in the presence of the vaccination program than

800 Halloran et al.

it would be if no one had been vaccinated. Thus, theestimated number of cases prevented generally willunderestimate the actual number of cases prevented inthe vaccinated group if this figure is calculated usingmethods designed for noninfectious diseases, as instudy design I and in Greenland and Robins (1, 2).

The comparison needs to be made between the cu-mulative incidence in the vaccinated group and whatthe cumulative incidence would have been in the un-vaccinated group if no vaccination program had beenin place, as in study design HB. A similar argumentapplies to estimation of the prevented hazard fraction.Thus, the conceptual framework of the table goesbeyond simply extending the family of parametersdiscussed by Greenland and Robins (1, 2) in twodimensions; it also helps to clarify the similarities anddifferences between the families of prevented fractionparameters in infectious diseases versus noninfectiousdiseases.

Reduction in individual infectiousness versusindirect effects

There is an important difference between estimatingthe reduction in individual infectiousness based on thetransmission probability and estimating the indirecteffects based on unconditional parameters such ashazard rates or cumulative incidence. The uncondi-tional indirect effect in study design HA results fromthe decrease in the exposure to the infectious agent,because 1) fewer people are infected due to reducedtransmission and 2) those vaccinated people who be-come infected might be less infectious. The reductionin infectiousness as estimated using the per-contactreduction in transmission probability does not takeinto account the lack of infectiousness in people whodid not become infected at all because of vaccination.We cannot know who would have become infectedwithout the vaccination program. Thus, with the trans-mission probability, we obtain a truncated estimate ofthe reduction in infectiousness, while the indirect ef-fect estimate takes decreased exposure to the infec-tious agent for a combination of reasons into account.

OVERALL EFFECTIVENESS OF VACCINATIONPROGRAMS (VEIH)

Considering further the study designs for dependenthappenings (figure 2), the overall public health benefitof a vaccination program in a population comparedwith no vaccination is the weighted average of theoutcomes in the vaccinated and unvaccinated personsat risk in population A compared with the outcomes inpersons at risk in population B. The overall effectdepends on the fraction/that is vaccinated in popula-

tion A. These study designs of type HI are representedby the sixth column in table 1. Suppose, in die aboveexample where kA1(t) = 0.06 and \A0(t) = 0.08, that75 percent of the people are vaccinated. The overallestimated incidence in population A would be 0.065.The overall public health effectiveness of the vaccina-tion program in reducing the incidence of infection is

= 1 -(0.065/0.12) = 0.46.

The estimated overall effect lies between the indirect(HA) and total (HB) effects of the vaccination pro-gram. Halloran and Struchiner (6) discuss the studydesigns for dependent happenings in more detail.

Note that it would be possible to estimate the overallincidence in population A without having to establishwho or what fraction had been vaccinated or estimat-ing the indirect or total effects in the vaccinated andunvaccinated subpopulations. Evaluation of the over-all effects of a vaccination program in a populationdoes not necessarily depend on the mixing patternswithin the population, if just the effectiveness in theentire population is of interest. However, the actualoverall effectiveness of a program will depend heavilyon the mixing patterns and the allocation of the vac-cine among the different groups. Generally, targetingvaccination to high-transmission groups will have agreater effect. In addition, if one of the measures ofinterest during a vaccine trial is the overall effective-ness of vaccination, the design of the trial could de-pend on the mixing patterns and the ultimate questionof interest. For example, suppose a trial is designed toestimate the efficacy of a vaccine in preschool-agechildren but the overall effects of the vaccination arealso to be evaluated. If most transmission occursamong school-age children and from school-age chil-dren to preschool-age children, then, to evaluate themaximum overall effects or to understand the long-term potential overall effects of vaccination, theschool-age children might need to be vaccinated eventhough they are not part of the efficacy trial. If mosttransmission occurs among preschool-age children,this would not be important. On the other hand, vac-cination of either the school-age children or thepreschool-age children might reduce the number ofevents substantially, impairing evaluation of the effi-cacy. This and many other tradeoffs must be madewhen designing trials to answer more than one ques-tion at a time. Disentangling the direct effects from theindirect effects of vaccines will not always be straight-forward.



Example

Monto et al. (30) estimated both the protective ef-ficacy and the overall effect of an influenza vaccina-tion program. They vaccinated 85 percent of theschool-age children in Tecumseh, Michigan, againstHong Kong influenza just before the epidemic of1968. The 10-week epidemic period was November17, 1968, to January 26, 1969. The weekly meaninfluenza illness rates in vaccinated and unvaccinatedchildren were 0.072 and 0.090, respectively. Thisyields an approximate estimate of vaccine efficacy of0.20 (i.e., VE5 ~ 1 - (0.072/0.090) = 0.20), which israther low. The overall influenza illness attack rate inTecumseh for the epidemic period was 0.14, while theadjusted overall influenza attack rate in unvaccinated,neighboring Adrian, Michigan, was 0.42 for the sameperiod. Using the methods of study design HI, theoverall effectiveness of vaccinating 85 percent ofTecumseh's schoolchildren is estimated to have been0.67.

The use of study designs similar to design in, com-paring the overall effects of interventions across pop-ulations, has been common in infectious disease epi-demiology for a long time, but it is becoming morewidespread with the integration of more current epi-demiologic and statistical methods (31-33). Hayes etal. (34) discuss matching on communities for the ran-domization and analysis scheme. A design similar tothat of study design EH is being used currently in acholera vaccine effectiveness trial in more than 20communities (J. Clemens, National Institutes ofHealth, personal communication, 1997) by dividingeach community in half geographically and vaccinat-ing all of the individuals in just one half. A similardesign will soon be used in community trials of influ-enza vaccines in matched day-care centers. Evaluationof malaria transmission-blocking vaccines that haveonly indirect effects in humans will require evaluationcomparing separate populations. Many of the lessonsfrom group-randomized designs will be applicable,with special consideration of the dependence of eventsin infectious diseases. Study designs HA and HB,which examine the effects in the vaccinated or unvac-cinated subpopulations, have been less common.Hopefully they will become an integral part of vaccineevaluation as investigators become more aware of thedifferences among the population-level effects in thedifferent groups and combine efficacy and effective-ness evaluation in the same study.

Basic reproductive number <

Another important parameter of infectious diseaseepidemiology is the basic reproductive number, RQ.

Am J Epidemiol Vof. U&, No. W, 1997

With microparasitic infectious agents, such as viruses,bacteria, and small parasites, the RQ is the number ofnew infectives produced by one infectious person in acompletely susceptible population during his or herperiod of infectiousness (35). Similar to the hazardrate, it can be thought of as the product of severalcomponents of the transmission system, including thetransmission probability, the rate of contact, and theduration of infectiousness. The duration of infectious-ness in the expression for Ro replaces the prevalence ofinfectives in the expression for the hazard rate. Al-though it is not included in table 1, Ro is important inunderstanding the population dynamics of an infec-tious agent and the public health effects of interven-tion. Since a vaccinated person has only a fraction ofthe transmission probability and possibly a shorterduration of infectiousness, a vaccinated person wouldnot be transmission-dynamically equivalent to a na-ively susceptible person. The fractional contribution ofa vaccinated person to RQ compared with the contri-bution of an unvaccinated individual is called the"naive susceptible equivalent" (25). The biologic ef-fect of the vaccine can reduce either the transmissionprobability per contact or the duration of infectious-ness. Thus, estimates of the effect of vaccination oninfectiousness, susceptibility, or changes in the dura-tion of infectiousness could provide some informationon the effect of vaccination on Ro. For example, ifeveryone in a population were vaccinated and thereduction in susceptibility were 0.50, the reduction ininfectiousness were 0.30, and the reduction in theduration of infectiousness were 0.60, a vaccinatedperson would be the naive susceptible equivalent of0.09 of an unvaccinated person. The reproductivenumber in the vaccinated population would be 0.09times the original RQ. A vaccine effectiveness measurecan also be based on 1 minus the relative basic repro-ductive numbers in two groups, depending on thechoice of comparison populations.

SUMMARY

We have presented a systematic framework of studydesigns for evaluating different effects of vaccinationand vaccination programs depending on the choice ofcomparison groups and parameter of effect (table 1).We have found this framework useful in organizingour own thoughts and in discussions with other col-leagues in designing studies to evaluate vaccination.We hope that others find it useful and that it cancontribute to more clarity in the design and analysis ofstudies of the effects of vaccination on individuals andin populations. Although there are several similaritiesto the family of prevented risk parameters discussedby Greenland and Robins (1, 2), the dependent hap-

802 Halloran et al.

pening structure of infectious diseases adds more lev-els and types of parameters.

In the third column of table 1, the aim of the studiesis to estimate the protective efficacy of vaccination inindividuals. This column is divided into two parts,with the amount of information required for estimationincreasing from bottom to top (14). This column pro-vides an overview of what is estimable based on thetype of data collected in the study. The lower partcontains vaccine efficacy based on the unconditionalparameters incidence rate ratio (VE5 m), hazard rateratio (VE5 x), and cumulative incidence ratio (VE5 CI),which do not require information on actual exposure toinfection. These are study designs of type I. If expo-sure to infection is not equal in the two comparisongroups, these designs estimate the combined effects ofunequal exposure and the direct biologic protectiveeffects of vaccination. The top row represents theconditional parameters, such as the transmission prob-ability or secondary attack rate. While the third col-umn represents the design needed to estimate the vac-cine's effect on susceptibility, VESp, the fourth andfifth columns represent designs for the effect on in-fectiousness, VEy p, and the combined effects on thetwo, VEj-p, respectively.

To measure the indirect, total, or overall publichealth effects of widespread vaccination, it is neces-sary to compare the effects of vaccination programs indifferent populations on the parameters of interest.The choice of subpopulations within the different pop-ulations determines whether one is measuring the in-direct effects, VEj^ (study design IIA), the total ef-fects, VEy^ (study design KB), or the overall effectsVE m (study design HI) of the vaccination program.We have emphasized that studies can be designed toanswer more than one question at a time.

The fundamental relation between the aspects ofexposure to infection and susceptibility to the rate ofevents clarifies the difference between biologic as-pects of the transmission process and the contact as-pects. The hierarchy of parameters also provides aframework for thinking about vaccine efficacy studiesbased on different parameters, especially the condi-tional versus unconditional parameters, as a missing-data or errors-in-variables problem (4, 7, 36).

We have not discussed vaccine efficacy based ondifference parameters here. These were considered byGreenwood and Yule (8) as early as 1915. Differenceestimates depend on the absolute incidence in theunvaccinated group, and provide more evidence of thepossible public health relevance of vaccines, evenwhen measured within a single population. Table 1could be entirely rewritten for difference parameters.The parameters listed in table 1 are not exhaustive, but

they represent several of the commonly used mea-sures. Many other outcome measures could be used toestimate the effects of a vaccine or a vaccinationprogram. These include average age of first infectionand time-to-event as in accelerated failure time mod-els, both of which are related to the hazard rate.Case-control studies are represented by the frameworkshown here whenever the odds ratio estimator is anapproximation of one of the relative risk parameters oftable 1.

Increased attention is being given to the design andanalysis of vaccine evaluation studies, both pre- andpostlicensure. This framework should prove useful inproviding a wider and more precise vocabulary forexpressing the various kinds of effects being measuredand the types of studies needed to estimate the vacci-nation effects of interest.

ACKNOWLEDGMENTS

This work was partially supported by National Institute ofAllergy and Infectious Diseases FIRST Award R29-AI31057 and grant RO1-AI32042. Dr. C. I. Struchiner waspartially supported by the Brazilian Research Council(CNPq).

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