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Advance Access publication November 6, 2006 Antiviral Effects on Influenza Viral Transmission and Pathogenicity:Observations from Household-based Trials M. Elizabeth Halloran1,2, Frederick G. Hayden3, Yang Yang1, Ira M. Longini, Jr.1,2, and ArnoldS. Monto4 1 Program in Biostatistics and Biomathematics, Fred Hutchinson Cancer Research Center, Seattle, WA.
2 Department of Biostatistics, School of Public Health and Community Medicine, University of Washington, Seattle, WA.
3 Department of Internal Medicine, University of Virginia, Charlottesville, VA.
4 Department of Epidemiology, University of Michigan School of Public Health, Ann Arbor, MI.
Received for publication April 12, 2006; accepted for publication June 5, 2006.
Four household-based, randomized clinical trials, two each of zanamivir and oseltamivir, were designed primar- ily to estimate the effect of postexposure prophylaxis on preventing influenza illness in household contacts.
However, the effect of influenza antivirals on infectiousness as well as on the ability of the virus to cause disease—the pathogenicity—have important public health consequences. The authors show how such studies can provideestimates of pathogenicity, antiviral efficacy for pathogenicity, and the antiviral effect on infectiousness. Analysis ofthe four studies confirmed the high prophylactic efficacy against illness of both zanamivir (75%, 95% confidenceinterval (CI): 54, 86) and oseltamivir (81%, 95% CI: 35, 94). The effect on reducing infectiousness was 19% (95%CI: ÿ160, 75) for zanamivir and 80% (95% CI: 43, 93) for oseltamivir. Pathogenicity in controls ranged from 44%(95% CI: 33, 55) to 66% (95% CI: 48, 72). Efficacy in reducing pathogenicity for zanamivir was 52% (95% CI: 19,72) and 56% (95% CI: 14, 77) in the two studies; for oseltamivir, it was 56% (95% CI: 10, 73) and 79% (95% CI: 45,92). Studies of influenza antivirals in transmission units would be improved if randomization schemes were usedthat allow estimation of the antiviral effect on infectiousness from individual studies.
antiviral agents; disease transmission; family characteristics; influenza, human; randomized controlled trials;treatment outcome Abbreviations: AVEI, antiviral efficacy for infectiousness; AVEId, antiviral efficacy for infectiousness as measured by clinicaldisease outcome in the exposed contact; AVEIi, antiviral efficacy for infectiousness as measured by infection outcome in theexposed contact; AVEP, antiviral efficacy for pathogenicity, AVES, antiviral efficacy for susceptibility; AVESd, antiviral efficacy forsusceptibility as measured by clinical disease outcome in the exposed contact; AVESi, antiviral efficacy for susceptibility asmeasured by infection outcome in the exposed contact; AVET, total antiviral efficacy; AVETd, total antiviral efficacy as measuredby clinical disease outcome in the exposed contact; AVETi, total antiviral efficacy as measured by infection outcome in theexposed contact; Osel I, clinical trial of oseltamivir conducted by Hayden et al. (3); Osel II, clinical trial of oseltamivir conductedby Welliver et al. (4); SAR, secondary attack rate; Zan I, clinical trial of zanamivir conducted by Hayden et al. (1); Zan II, clinicaltrial of zanamivir conducted by Monto et al. (2).
Prevention of influenza in family contacts is recognized demic influenza. The two drugs zanamivir and oseltamivir as a means of reducing spread of influenza within commu- are potent and selective inhibitors of influenza A and B vi- nities and may be an important aspect of intervention in pan- rus neuraminidases. Two household-based randomized trials Reprint requests to Dr. M. Elizabeth Halloran, Fred Hutchinson Cancer Research Center, 1100 Fairview Avenue N, LE-400, Seattle,WA 98109-1024 (e-mail: halloran@fhcrc.org).
Effects of Influenza Antiviral Agents in Households Some characteristics of the four studies as reported in the four papers estimating the effect of postexposure prophylaxis on preventing influenza illness in household contacts * Number of study centers not available.
y PCR, polymerase chain reaction; HAI, hemaglutination-inhibition antibody.
z Includes only those households with laboratory-confirmed index cases.
each of zanamivir (1, 2) and oseltamivir (3, 4) were con- the two studies for each drug can we estimate the effect ducted. The studies showed substantial protection of house- hold contacts against influenza illness with postexposure In this paper, we reanalyze the two studies of zanamivir prophylaxis by either zanamivir or oseltamivir.
and the two studies of oseltamivir. We discuss the design Recent mathematical modeling (5–8) has shown that the and analysis of household studies to estimate the different public health effectiveness of targeted antiviral prophylaxis effects of interest as well as the pathogenicity.
against pandemic influenza depends on more than just theprotective effect against influenza. It also depends on howwell the drug reduces the ability of an influenza case to trans- mit as well as how much it reduces the pathogenicity—theability of the virus to cause disease in an infected person.
During a pandemic, symptomatic cases rather than asymp-tomatic infections would likely be ascertained. The number Table 1 summarizes some characteristics of the four stud- of courses of antivirals required for targeted antiviral pro- ies. Other aspects are discussed below and in the original phylaxis will be heavily influenced by the probability of an infection becoming a case of disease. In addition, becauseasymptomatic infections will likely be less infectious than symptomatic cases, the overall intensity of the epidemic willdepend on the pathogenicity. Although estimates of patho- All four studies were household-based, multicenter, ran- genicity and the effect of antiviral prophylaxis on pathoge- domized, controlled trials, where treatment was randomized nicity can be obtained from each study, none of the studies by household (cluster randomized design). Households with reported these estimates directly. None of the four studies a suspected case of influenza illness were enrolled as a whole was designed to allow estimation of the antiviral effect on in each study. Assignment of the index case to treatment or infectiousness of treated individuals. Only by combining control varied across the studies, resulting in differences in the effect measures estimated in each study. Ages for eligi- Zanamivir. Zan I (Hayden et al. (1)): Presence of at least bility of index cases and contacts also varied across studies two signs and symptoms—tympanic temperature 37.8°C, feverishness, cough, headache, sore throat, myalgia; in con- Zanamivir. Zan I (Hayden et al. (1)): Randomized, double- tacts, at least two were required in at least three consecu- blind, placebo-controlled trial. Households were randomized to the study drug (zanamivir) or placebo. Index cases and eli- Zan II (Monto et al. (2)): Presence of at least two signs gible contacts within a household all received either the drug and symptoms—(tympanic temperature 37.8°C and/or fe- or placebo. Children less than age 5 years did not receive the verishness counted as one), cough, headache, sore throat, Zan II (Monto et al. (2)): Randomized, double-blind, placebo-controlled trial. Households were randomized for el- igible contacts to receive either the study drug (zanamivir) Osel II (Welliver et al. (4)): Oral temperature 37.2°C or placebo. Index cases did not receive antiviral therapy.
and at least one respiratory symptom (cough, nasal conges- Children less than age 5 years did not receive the study drug.
tion, or sore throat), and at least one constitutional symp- tom (headache, aches/pains, chills/sweats, fatigue) occurring open-label trial. Households were randomized for eligible contacts to receive either antiviral postexposure prophylaxis The period for inclusion of secondary cases in the original or antiviral treatment when illness developed (expectant analyses varied across the studies. Let day 1 be the day of treatment). All index cases received study drug (oseltamivir) ascertainment or treatment begun in the index case. In the treatment for 5 days. Children less than age 1 year were ex- zanamivir studies, Zan I (1) included cases within day 1 to 14 of the index case, and Zan II (2) used cases within day 1 Osel II (Welliver et al. (4)): Randomized, double-blind, to 11 days after the index case. In the oseltamivir studies, placebo-controlled trial. Households were randomized for Osel I (3) included cases within day 1 to 10 of the index eligible contacts to receive the study drug (oseltamivir) or case, and Osel II (4) included cases within day 1 to 7 in- placebo. Index cases did not receive antiviral therapy. Chil- dren less than age 12 years were excluded from participatingas contacts but could be (untreated) index cases.
By design, in both oseltamivir studies, treatment and/or prophylaxis began within 48 hours of the onset of symptoms in the index case, while, in both zanamivir studies, it began efficacy parameters of interest, each of which can be based within 36 hours of the onset of symptoms in the index case.
on either influenza illness or influenza infection. As in theinitial analyses, our primary interest is the endpoint of Determination of influenza infection and laboratory-confirmed influenza illness. We differentiate the efficacy measure based on the two different outcomes in theeligible contacts by using a subscript d to denote laboratory- In all four studies, the primary endpoint for the household confirmed influenza illness, and i to denote laboratory- contacts was laboratory-confirmed clinical influenza illness.
confirmed influenza infection. All index cases in this A secondary endpoint was laboratory-confirmed influenza analysis had laboratory-confirmed influenza illness.
infection, whether symptomatic or asymptomatic. All four The first efficacy measure is the protective effect of anti- studies performed extensive laboratory testing of the en- viral prophylaxis in the household contacts of infected index rolled index cases and their contacts. Swabs for cultures cases, AVES. When the outcome in the contact is clinical were conducted on all index cases as soon after ascertain- influenza illness, we denote it as AVESd. When the outcome ment as possible. In both oseltamivir studies, household is infection, we denote it as AVESi. The second measure is contacts were cultured at the same time as the index case.
the efficacy of reducing the infectiousness of an index case Another measure of influenza infection was a greater than for a contact, denoted AVEI. We distinguish AVEId and fourfold increase in hemaglutination-inhibition antibody ti- AVEIi when the outcome in the contact is influenza illness ter between serology at baseline and in serum during con- or influenza infection. The third measure is the combined valescence. This measure was determined for all index cases effect if both the index case and the contact take antivirals and contacts. In individual studies, additional cultures and se- compared with if neither takes antivirals, the total antiviral rology were performed when contacts developed symptoms.
efficacy AVET, where we again distinguish AVETd and The two zanamivir studies also used reverse-transcriptase polymerase chain reaction. Because contacts were tested for The fourth effect is the effect of an antiviral drug on influenza infection regardless of whether they had symp- reducing the ability of the virus to cause disease in an in- toms, it was possible to estimate pathogenicity from the fected person, the pathogenicity. A measure for pathogenic- ity is the probability of developing symptomatic illness if Contacts were supposed to complete diary cards once or a person becomes infected ((9), p. 55). We estimate patho- twice daily for 14 days or more, depending on the study, genicity by using data on the contacts only. We denote path- with details of symptoms and temperature. The definitions ogenicity as P and the efficacy against pathogenicity as of symptomatic influenza cases varied across the four stud- AVEP. The relations among the efficacy measures are shown ies, although they were similar in the two zanamivir studies.
Effects of Influenza Antiviral Agents in Households Estimable antiviral efficacies* from each of the four studies alone and when combinedy * AVES, antiviral efficacy for susceptibility; SAR, secondary attack rate; AVEI, antiviral efficacy for infectiousness; y Primary analysis based on laboratory-confirmed influenza illness; secondary analyses based on laboratory- Estimating AVES, AVEI, and AVET. The secondary attack the index case receives control and the eligible contacts re- rate, SARjk, is the proportion of eligible contacts of prophy- ceive antiviral drug. From the appropriate SARjk’s, we can laxis status k who develop the outcome of interest when estimate the first three antiviral efficacies as follows: exposed to an index case of treatment status j. The subscriptsj and k take on the value 1 for antiviral drug and 0 for control Antiviral efficacies for zanamivir and oseltamivir from the four published papers estimating the effect of postexposure prophylaxis on preventing influenza illness in household contacts*,y * Some estimates reported in the original papers have been rounded to two significant digits.
y Numbers are from only those families with laboratory-confirmed index cases.
z AVE, antiviral efficacy; CI, confidence interval; AVET, total antiviral efficacy; SAR, secondary attack rate; AVETd, total antiviral efficacy as measured by clinical disease outcome in the exposed contact; AVETi, total antiviral efficacy as measured by infection outcome in the exposedcontact; AVES, antiviral efficacy for susceptibility; AVESd, antiviral efficacy for susceptibility as measured by clinical disease outcome in theexposed contact; AVESi, antiviral efficacy for susceptibility as measured by infection outcome in the exposed contact.
§ Number with laboratory-confirmed influenza in a contact divided by total number.
{ Numbers or estimates were derived from information in the paper.
# Excluding contacts culture positive at baseline.
Zanamivir I, Hayden et al. (1)
Oseltamivir I, Hayden et al. (3)
Zanamivir II, Monto et al. (2)
Oseltamivir II, Welliver et al. (4)
Distribution of the number of secondary cases of influenza in contacts by day since ascertainment of the index case according to antiviral agent status of the index cases and contacts.
None of the studies alone provides information enabling must use an estimate of SAR11 from Zan I (1) and of SAR01 from Zan II (2) (left side of equation 2). To estimate AVEI SAR00 from Osel II (4) (right side of equation 2). Similarly, Each of these efficacies can be based on laboratory- to estimate AVET for oseltamivir, one must use SAR11 from confirmed influenza illness or simply laboratory-confirmed Osel I and SAR00 from Osel II. It is generally not advisable to combine estimates from separate studies in this simple Table 2 provides an overview of the efficacy estimates way. However, without doing so, we would not be able to that can be obtained from each study or from combinations obtain the estimates at all. It illustrates the importance of of the studies. The primary outcome in both oseltamivir improving study design in the future. Approximate confi- studies and in Zan II (2) was reduction in influenza illness dence limits were based on the Wald method ((10), p. 240).
in the individual eligible contacts, AVESd. The Zan II and Estimating pathogenicity and AVEP. Pathogenicity P is Osel II (4) studies had similar designs from which SAR00, estimated as the (number of symptomatic influenza infec- SAR01, and hence AVES as on the left side of equation 1 are tions in the contacts)/(number of influenza infections in the estimable. In Osel I (3), SAR10, SAR11, and hence AVES as contacts). The antiviral efficacy for pathogenicity, AVEP, is on the right side of equation 1 are estimable. In Zan I (1), the no: of symptomatic infected antiviral contacts primary outcome was based on reduction of the proportion of households with at least one case of influenza illness no: of symptomatic infected control contacts rather than reduction in the SAR, so it does not correspondto any of these measures. However, in terms of our efficacies of interest, SAR00, SAR11, and thus AVET in equation 3 are All four original papers provide information on the number of contacts with laboratory-confirmed influenza infection as Effects of Influenza Antiviral Agents in Households Antiviral efficacies for zanamivir based on the analyses in this paper * AVE, antiviral efficacy; CI, confidence interval; AVES, antiviral efficacy for susceptibility; SAR, secondary attack rate; AVESd, antiviral efficacy for susceptibility as measured by clinical disease outcome in the exposed contact;AVESi, antiviral efficacy for susceptibility as measured by infection outcome in the exposed contact; AVEI, antiviralefficacy for infectiousness; AVEId, antiviral efficacy for infectiousness as measured by clinical disease outcome inthe exposed contact; AVEIi, antiviral efficacy for infectiousness as measured by infection outcome in the exposedcontact; AVET, total antiviral efficacy; AVETd, total antiviral efficacy as measured by clinical disease outcome in theexposed contact; AVETi, total antiviral efficacy as measured by infection outcome in the exposed contact.
y Number with laboratory-confirmed influenza in a contact divided by total number.
well as the number with laboratory-confirmed influenza ill- Asymptomatic infections presented a problem because ness. Thus, we can estimate the pathogenicity and AVEP we did not have their infection onset times. Asymptomatic from numbers contained in the published papers. We did cases in each treatment status group are allocated to within not have information to estimate separate pathogenicities or after the period according to the distribution of symptom- atic cases within and after the period. (Refer to the Appen-dix for details.) For the zanamivir studies, we estimated AVET from Zan I (1) and AVES from Zan II (2). Using SAR11 from Zan I and To analyze the original data from the four studies, we SAR01 from Zan II, we estimated AVEI given that the con- made an effort to standardize the inclusion criteria for any tacts were treated. For the oseltamivir studies, AVES given particular estimate. We present two periods in which con- that the index case was not treated was estimated from Osel tacts are regarded as secondary cases. Let day 1 be the as- II (4) alone, and AVES given that the index case was treated certainment day of the index case. The two periods are day 1 was estimated from Osel I (3) alone. We estimated AVEI by to 7 and day 2 to 7. Thus, we use the longest period available using SAR00 from Osel II and SAR10 from Osel I. We esti- for all studies in the original four analyses. Contacts with mated AVET by using SAR00 from Osel II and SAR11 from a positive day 1 culture were excluded from the analysis of the oseltamivir studies. Day 1 cultures were not available inthe zanamivir studies. For the period from day 2 to 7, in-fected contacts with symptom onset on day 1 are excluded from the analysis. Only those households with index caseswith laboratory-confirmed influenza were included. For both Table 3 contains estimates of AVES and AVET either re- zanamivir studies, we used the case definition for contacts as ported directly in the four papers or estimated from numbers reported in Zan II (2). For the oseltamivir studies, we used reported in the four papers. The results in table 3 are based the case definition as reported in each paper. Further exclu- on households with index cases with laboratory-confirmed sion criteria can be found in the Appendix.
influenza illness. The AVESd of both oseltamivir and zanamivir Antiviral efficacies for oseltamivir based on the analyses in this paper * AVE, antiviral efficacy; CI, confidence interval; AVES, antiviral efficacy for susceptibility; SAR, secondary attack rate; AVESd, antiviral efficacy for susceptibility as measured by clinical disease outcome in the exposed contact;AVESi, antiviral efficacy for susceptibility as measured by infection outcome in the exposed contact; AVEI, antiviralefficacy for infectiousness; AVEId, antiviral efficacy for infectiousness as measured by clinical disease outcome inthe exposed contact; AVEIi, antiviral efficacy for infectiousness as measured by infection outcome in the exposedcontact; AVET, total antiviral efficacy; AVETd, total antiviral efficacy as measured by clinical disease outcome in theexposed contact; AVETi, total antiviral efficacy as measured by infection outcome in the exposed contact.
y Number with laboratory-confirmed influenza in a contact divided by total number.
is quite high. The corresponding AVETd of zanamivir is also cantly different from 0. The AVETd is also quite high at 91 quite high. Protection against influenza infection, AVESi, is lower than against influenza illness, AVESd.
Table 6 shows estimates of pathogenicity and AVEP based Figure 1 shows the distribution of the day of onset of on numbers contained in the original four papers. The var- symptoms in the laboratory-confirmed secondary cases for iability in the estimates of pathogenicity and AVEP could be the 14 days after ascertainment of the index case. Tables 4 due to variability in the influenza subtypes, the age eligibil- and 5 contain our reanalysis of the zanamivir and oseltamivir ity of the contacts, the case definitions, or other differences data sets. The numbers contributing to each estimate dif- fer from those in the original papers because of exclusionsdescribed in the Materials and Methods section and theAppendix. For zanamivir (table 4), the estimates of AVES and AVET are similar to those in the original papers. Theestimates of AVEI for zanamivir are not significantly dif- In this paper, we have compared the design of four ran- ferent from 0, although the confidence intervals are quite domized clinical studies of influenza antiviral agents. We wide. For oseltamivir (table 5), our estimates of AVES are systematically showed the relation among the different mea- also consistent with the estimates in the original papers. The sures of antiviral efficacy and that the four studies, although estimate of AVEId is high at 80 percent (95 percent confi- similar in many respects, provide information for three dif- dence interval: 43, 93), although the AVEIi is not signifi- ferent efficacy measures. We also showed that none of these Effects of Influenza Antiviral Agents in Households Estimates of pathogenicity, P, and the efficacy of antiviral prophylaxis to reduce pathogenicity, * In the two zanamivir studies (1, 2) and in the Osel II study (4), the numbers include all infected contacts, including from houses with index cases not laboratory confirmed with influenza.
y In the Osel I study (3), numbers include infected contacts from households with laboratory-confirmed index z Numbers are taken from the published papers, but estimates of pathogenicity, P, and AVEP are not in the { Number with laboratory-confirmed illness divided by number with laboratory-confirmed infection.
# Not excluding contacts culture positive at baseline.
four studies alone allows estimation of the effect of antiviral on transmission. Since both drugs exhibit good prophylac- treatment on infectiousness. If randomization were by in- tic efficacy against symptomatic influenza, either would be dividual rather than by household, then it would be possible useful as part of an intervention strategy against pandemic to estimate all of the effects of interest from one study alone.
influenza if efficacy were the only consideration and the Our reanalysis of the four studies gave results for the efficacy against the pandemic strain were similar to that estimates of AVES and AVET similar to those in the original papers. We additionally estimated AVEI for both drugs Some of the limitations of our analysis are inherent in the and AVET for zanamivir. Prophylactic protection of both limitations of the original studies. To be able to estimate the zanamivir and oseltamivir against symptomatic influenza effect of treatment on transmission, AVEI, within one study, is quite good, about 75–85 percent. The efficacy in reducing index cases would need to be individually randomized to pathogenicity is in the 45–60 percent range. Although the ef- treatment separately from their contacts (11), which did not ficacy of oseltamivir on infectiousness of the treated cases is occur in any of these four studies. Our analysis is based on significant and that of zanamivir is not, we warn against over- the simple SAR. However, other statistical methods (11) interpreting these results. The numbers are small, and we are consider further chains of transmission within households combining estimates from two studies in both instances.
and the possibility of infection from outside the household, AVEI is not so important, when AVES is high, as is the case and they include joint estimation of AVES, AVEI, and AVET.
here. One might speculate that oral oseltamivir and in- Extension of these methods could include estimating the haled zanamivir could have different effects on secondary duration of the infectious period (12) and allow for asymp- transmission of virus due to differences in reductions in tomatic infections. The analysis could also estimate the ef- upper respiratory viral levels and possibly symptoms. Oral fect of prophylaxis on reducing infectiousness (11), whereas oseltamivir may reduce viral levels in the nose, whereas in- here we have estimated just the effect of treatment on re- haled zanamivir does not. Inhaled zanamivir does reduce ducing infectiousness. We expect the efficacy of prophylaxis pharyngeal levels of virus, but, to our knowledge, studies of in reducing infectiousness in breakthrough cases to be neither drug have been conducted on their effects on tracheo- greater than that of treatment. Such methods could also in- bronchial levels of virus. Both modalities reduce cough, but corporate model-based methods for random effects across inhaled zanamivir does not reduce significantly the nasal households (13) and the possibility of postinfection selec- symptoms of influenza. Consequently, if infectious droplets tion bias when estimating pathogenicity and AVEP (14).
and aerosols produced from the nose are important in virus Because these results are for households only, trials in other transmission, oseltamivir might have an advantage. This ad- settings such as schools, homes for elderly, and workplaces vantage might not apply to a pandemic virus if replication would also be useful as part of pandemic planning.
occurred in different parts of the respiratory tract.
Randomized field trials of influenza antiviral agents are With these drugs, the combined effect if both the index large and expensive. Simple remedies such as discordant case and contact receive a drug compared with if neither randomization within households and powering studies to does, measured by AVET, is high and is likely dominated by determine AVEI would allow estimation of all the impor- the prophylactic protection rather than the treatment effect tant effects. Comparability of studies would be improved by standardized case definitions, eligibility criteria, and dura- 14. Hudgens MG, Halloran ME. Causal vaccine effects on binary tion of follow-up. We hope that this paper illustrates the im- postinfection outcomes. J Am Stat Assoc 2006;101:51–64.
portance of better planning of field studies to answer therelevant scientific and public health questions of interest.
In the Zan I (1) zanamivir study, all contacts aged less This research was partially supported by National Insti- than 5 years were excluded because they were not treated.
tute of Allergy and Infectious Diseases grant R01-AI32042 All households with index cases aged less than 5 years were and National Institute of General Medical Sciences MIDAS also excluded because the index cases were not treated as well. In Zan II (2), all contacts aged less than 5 years were The authors are grateful to Roche (Basel, Switzerland) excluded because they were not treated. When we estimated and GlaxoSmithKline (Middlesex, United Kingdom) for al- S from Zan II alone, households with index cases aged less than 5 years were included because all index cases were M. E. H. and I. M. L. were ad hoc consultants with Roche not treated by design. When we estimated AVE after writing this paper. A. S. M. received research support both studies, these households were excluded; otherwise, the and as an ad hoc consultant to Roche and GlaxoSmithKline.
two studies are not comparable and cannot be used together.
F. G. H. received a lecture honorarium from Roche and In the Osel II (4) study, there were no data for any eligible contacts aged less than 12 years, which was specified by thedesign. However, there were about 38 index cases aged lessthan 12 years. We did not exclude the households with theseindex cases aged less than 12 years in estimating AVE Osel II alone because all index cases were not treated by 1. Hayden FG, Gubareva LV, Monto AS, et al. Inhaled zanamivir design. In Osel I (3), contacts aged less than 1 year and for the prevention of influenza in families. N Engl J Med households with index cases aged less than 1 year were excluded when we estimated AVES from this study alone 2. Monto AS, Pichichero ME, Blanckenberg SJ, et al. Zanamivir because all subjects aged less than 1 year were not treated by prophylaxis: an effective strategy for the prevention of influ- design. There was one index case aged less than 1 year who enza types A and B within households. J Infect Dis 2002;186: was not treated, and that household was excluded at the data-cleaning step because laboratory results were not avail- 3. Hayden FG, Belshe R, Villanueva C, et al. Management of able for all family members. When we estimated AVE influenza in households: a prospective, randomized compari- son of oseltamivir treatment with or without postexposure T by using both Osel I and Osel II, contacts aged less prophylaxis. J Infect Dis 2004;189:440–9.
than12 years were excluded from Osel I, and households 4. Welliver R, Monto AS, Carewicz O, et al. Effectiveness of with index cases aged less than 1 year were excluded from oseltamivir in preventing influenza in household contacts: both studies to minimize the factors that make the two stud- a randomized controlled trial. JAMA 2001;285:748–54.
5. Longini IM Jr, Halloran ME, Nizam A, et al. Containing pandemic influenza with antiviral agents. Am J Epidemiol2004;159:623–33.
6. Longini IM Jr, Nizam A, Xu S, et al. Containing pandemic influenza at the source. Science 2005;309:1083–7.
One can assume that the antiviral effects on susceptibility 7. Ferguson NM, Cummings DA, Fraser C, et al. Strategies for and infectiousness contribute independently and multiplica- mitigating an influenza pandemic. Nature 2006;442:448–52.
8. Germann TC, Kadau K, Longini IM Jr, et al. Mitigation strat- T. Here, if there is a large difference between egies for pandemic influenza in the United States. Proc Natl S and AVET, then AVEI would account for this. For- mally, under this assumption, AVET ¼ 1 – (1 – AVES) 9. Fox JP, Hall CE, Elveback LR. Epidemiology: man and dis- (1 – AVEI). For oseltamivir, under this assumption, using ease. New York, NY: MacMillan Publishing, 1970.
AVESd ¼ 0.81 from Osel I (3) and AVEId ¼ 0.80, the esti- 10. Rothman KJ, Greenland S, eds. Modern epidemiology. 2nd ed.
mated AVETd would be 0.98, higher than the AVETd ¼ 0.91 Philadelphia, PA: Lippincott-Raven, 1998.
point estimate based on the data. It would be even higher 11. Yang Y, Longini IM Jr, Halloran ME. Design and evaluation if based on AVESd ¼ 0.91 from Osel II (4). Alternatively, of prophylactic interventions using infectious disease inci- one could assume that the AVESd interacts with AVEId in dence data from close contact groups. Appl Stat 2006;55: 12. Cauchemez S, Carrat F, Viboud C, et al. A Bayesian MCMC Id effect, especially when AVESd is high. Given the low numbers and the wide confidence intervals in these stud- approach to study transmission of influenza: application tohousehold longitudinal data. Stat Med 2004;23:3469–87.
ies, however, it is not possible to differentiate the indepen- 13. Halloran ME, Pre´ziosi MP, Chu H. Estimating vaccine ef- dence from the interaction hypothesis. Similar calculations ficacy from secondary attack rates. J Am Stat Assoc 2003;98: can be made for zanamivir from table 4, where the estimates of AVEId are low. When using the day 2 to 7 intervals, based Effects of Influenza Antiviral Agents in Households on the independence assumption, AVETd ¼ 0.79, thus lower group ‘‘00’’ from Osel II (4) to estimate AVET. After ex- compared with 0.87 based directly on the data. Again, the cluding contacts and households according to our inclusion/ numbers are too low to differentiate the two hypotheses.
exclusion criteria, in group ‘‘11’’ of Osel I, there were only Similar relations exist between influenza infection, influ- two symptomatic infections, both in the period of day 1 to 7, enza disease, pathogenicity, and the corresponding efficacies.
while there were 20 asymptomatic infections during the 10- The probability of influenza disease equals the probability day follow-up period. Assigning all 20 asymptomatic infec- of influenza infection multiplied by the probability of dis- tions to the period up to day 7 seems unreasonable.
ease given infection (pathogenicity). Furthermore, AVESd ¼ To estimate p, we first obtain prior knowledge about p 1 – (1 – AVESi)(1 – AVEP). These relations follow directly from all symptomatic cases in an individual study. Let by definition without further assumptions. Taking as an ex- ample Zan II (2), from tables 3 and 6, we obtain AVESd ¼ prior distribution for p proportional to pNsym ð1 ÿ pÞMsym : 1 – (1 – 0.55)(1 – 0.52) ¼ 0.78, which, as expected, is close Given p, the sampling distribution of the data is proportional to the estimate of AVESd ¼ 0.80 in table 3.
for group ‘‘uv.’’ The posterior density for One problem with all four studies, since we use only part total number of secondary infections for group ‘‘uv’’ is es- of the initial follow-up period of the studies, is how to allo- cate asymptomatic infections to the exposure period for asymptomatic infections in the group. For example, in Osel calculating SARs. We used a simple Bayesian technique.
I (3), after exclusions for estimating AVES, 19 symptomatic All asymptomatic infections are assumed infected within infections occurred within the secondary exposure period or after the period under consideration. Let p be the proba- and seven after the period. The prior ratio is 19:7. In group bility that an infected contact occurs in the secondary ‘‘11,’’ the ratio is 3:1. Then, the posterior ratio is (19 þ 3): infection period. We assume that p is the same for symp- (7 þ 1) for the ‘‘11’’ group. The posterior mode is given by tomatic and asymptomatic infections. Given p, we observe (19 þ 3)/(19 þ 3 þ 7 þ 1) ¼ 0.73—very close to 0.75 if we that nsym symptomatic infections occur in the secondary use only the ratio 3:1 of symptomatic cases. The Bayesian exposure period and msym after the period for the group method makes a difference when there are 0’s. As mentioned ‘‘00’’ with untreated index case and control contact. Simi- above, when we estimated AVET for oseltamivir, after nec- larly define nsym and msym for other groups ‘‘uv.’’ We assume essary exclusions, the ‘‘11’’ group in Osel I has two symp- a binomial sampling model. If nsym > 0 and msym > 0; we tomatic infections in the secondary period and 0 after that.
may simply assign asymptomatic cases to the period accord- When the prior ratio 19:7 from the whole Osel I study is ing to the ratio nsym : msym: However, if a drug is highly used, we have a posterior ratio (19 þ 2):(7 þ 0), and the efficacious against pathogenicity, there may be many more posterior mode is 21/28 ¼ 0.75. Consequently, we have 15 asymptomatic than symptomatic infections. For example, instead of 20 asymptomatic infections assigned to the sec- we use group ‘‘11’’ from Osel I (3) in combination with

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