American Journal of Epidemiology Advance Access originally published online on November 6, 2006
American Journal of Epidemiology 2007 165(2):212-221; doi:10.1093/aje/kwj362
| ||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
ORIGINAL CONTRIBUTIONS |
Antiviral Effects on Influenza Viral Transmission and Pathogenicity: Observations from Household-based Trials
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
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{at}fhcrc.org).
Received for publication April 12, 2006. Accepted for publication June 5, 2006.
 |
ABSTRACT |
|---|
 TOP ABSTRACT INTRODUCTIONMATERIALS AND METHODSRESULTSDISCUSSIONAPPENDIXReferences |
|---|
Four household-based, randomized clinical trials, two each of zanamivir and oseltamivir, were designed primarily 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 provide estimates of pathogenicity, antiviral efficacy for pathogenicity, and the antiviral effect on infectiousness. Analysis of the four studies confirmed the high prophylactic efficacy against illness of both zanamivir (75%, 95% confidence interval (CI): 54, 86) and oseltamivir (81%, 95% CI: 35, 94). The effect on reducing infectiousness was 19% (95% CI: –160, 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 used that 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 clinical disease outcome in the exposed contact; AVEIi, antiviral efficacy for infectiousness as measured by infection outcome in the exposed contact; AVEP, antiviral efficacy for pathogenicity; AVES, antiviral efficacy for susceptibility; 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; AVET, total antiviral efficacy; 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 exposed contact; Osel I, clinical trial of oseltamivir conducted by Hayden et al. (3); Osel II, clinical trial of oseltamivir conducted by Welliver et al. (4); SAR, secondary attack rate; Zan I, clinical trial of zanamivir conducted by Hayden et al. (1); Zan II, clinical trial of zanamivir conducted by Monto et al. (2)
|
INTRODUCTION |
|---|
|
TOPABSTRACTINTRODUCTIONMATERIALS AND METHODSRESULTSDISCUSSIONAPPENDIXReferences |
|---|
Prevention of influenza in family contacts is recognized as a means of reducing spread of influenza within communities and may be an important aspect of intervention in pandemic influenza. The two drugs zanamivir and oseltamivir are potent and selective inhibitors of influenza A and B virus neuraminidases. Two household-based randomized trials each of zanamivir (1, 2) and oseltamivir (3, 4) were conducted. The studies showed substantial protection of household contacts against influenza illness with postexposure prophylaxis by either zanamivir or oseltamivir.
Recent mathematical modeling (5–8) has shown that the public health effectiveness of targeted antiviral prophylaxis against pandemic influenza depends on more than just the protective effect against influenza. It also depends on how well the drug reduces the ability of an influenza case to transmit as well as how much it reduces the pathogenicity—the ability of the virus to cause disease in an infected person. During a pandemic, symptomatic cases rather than asymptomatic infections would likely be ascertained. The number of courses of antivirals required for targeted antiviral prophylaxis will be heavily influenced by the probability of an infection becoming a case of disease. In addition, because asymptomatic infections will likely be less infectious than symptomatic cases, the overall intensity of the epidemic will depend on the pathogenicity. Although estimates of pathogenicity and the effect of antiviral prophylaxis on pathogenicity can be obtained from each study, none of the studies reported these estimates directly. None of the four studies was designed to allow estimation of the antiviral effect on infectiousness of treated individuals. Only by combining the two studies for each drug can we estimate the effect on infectiousness.
In this paper, we reanalyze the two studies of zanamivir and the two studies of oseltamivir. We discuss the design and analysis of household studies to estimate the different effects of interest as well as the pathogenicity.
|
MATERIALS AND METHODS |
|---|
|
TOPABSTRACTINTRODUCTIONMATERIALS AND METHODSRESULTSDISCUSSIONAPPENDIXReferences |
|---|
Description of the studies
Table 1 summarizes some characteristics of the four studies. Other aspects are discussed below and in the original papers (1–4).
|
Study designs
All four studies were household-based, multicenter, randomized, controlled trials, where treatment was randomized by household (cluster randomized design). Households with a suspected case of influenza illness were enrolled as a whole in each study. Assignment of the index case to treatment or control varied across the studies, resulting in differences in the effect measures estimated in each study. Ages for eligibility of index cases and contacts also varied across studies (table 1).
Zanamivir.
Zan I (Hayden et al. (1)): Randomized, double-blind, placebo-controlled trial. Households were randomized to the study drug (zanamivir) or placebo. Index cases and eligible contacts within a household all received either the drug or placebo. Children less than age 5 years did not receive the study drug.
Zan II (Monto et al. (2)): Randomized, double-blind, placebo-controlled trial. Households were randomized for eligible contacts to receive either the study drug (zanamivir) or placebo. Index cases did not receive antiviral therapy. Children less than age 5 years did not receive the study drug.
Oseltamivir.
Osel I (Hayden et al. (3)): Randomized, open-label trial. Households were randomized for eligible contacts to receive either antiviral postexposure prophylaxis or antiviral treatment when illness developed (expectant treatment). All index cases received study drug (oseltamivir) treatment for 5 days. Children less than age 1 year were excluded from participating.
Osel II (Welliver et al. (4)): Randomized, double-blind, placebo-controlled trial. Households were randomized for eligible contacts to receive the study drug (oseltamivir) or placebo. Index cases did not receive antiviral therapy. Children less than age 12 years were excluded from participating as 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 within 36 hours of the onset of symptoms in the index case.
Determination of influenza infection and case definitions
In all four studies, the primary endpoint for the household contacts was laboratory-confirmed clinical influenza illness. A secondary endpoint was laboratory-confirmed influenza infection, whether symptomatic or asymptomatic. All four studies performed extensive laboratory testing of the enrolled index cases and their contacts. Swabs for cultures were conducted on all index cases as soon after ascertainment as possible. In both oseltamivir studies, household contacts were cultured at the same time as the index case. Another measure of influenza infection was a greater than fourfold increase in hemaglutination-inhibition antibody titer between serology at baseline and in serum during convalescence. This measure was determined for all index cases and contacts. In individual studies, additional cultures and serology were performed when contacts developed symptoms. The two zanamivir studies also used reverse-transcriptase polymerase chain reaction. Because contacts were tested for influenza infection regardless of whether they had symptoms, it was possible to estimate pathogenicity from the data.
Contacts were supposed to complete diary cards once or twice daily for 14 days or more, depending on the study, with details of symptoms and temperature. The definitions of symptomatic influenza cases varied across the four studies, although they were similar in the two zanamivir studies.
Zanamivir.
Zan I (Hayden et al. (1)): Presence of at least two signs and symptoms—tympanic temperature 
37.8°C, feverishness, cough, headache, sore throat, myalgia; in contacts, at least two were required in at least three consecutive (half-day) diary entries.
Zan II (Monto et al. (2)): Presence of at least two signs and symptoms—(tympanic temperature 37.8°C and/or feverishness counted as one), cough, headache, sore throat, myalgia.
Oseltamivir.
Osel I (Hayden et al. (3)): Temperature 37.8°C and cough and/or coryza.
Osel II (Welliver et al. (4)): Oral temperature 37.2°C and at least one respiratory symptom (cough, nasal congestion, or sore throat), and at least one constitutional symptom (headache, aches/pains, chills/sweats, fatigue) occurring within a 24-hour period.
The period for inclusion of secondary cases in the original analyses varied across the studies. Let day 1 be the day of ascertainment or treatment begun in the index case. In the 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 to 11 days after the index case. In the oseltamivir studies, Osel I (3) included cases within day 1 to 10 of the index case, and Osel II (4) included cases within day 1 to 7 inclusive of the index case.
Statistical analysis
Efficacy parameters of interest.
To begin, we define three efficacy parameters of interest, each of which can be based on either influenza illness or influenza infection. As in the initial analyses, our primary interest is the endpoint of laboratory-confirmed influenza illness. We differentiate the efficacy measure based on the two different outcomes in the eligible contacts by using a subscript d to denote laboratory-confirmed influenza illness, and i to denote laboratory-confirmed influenza infection. All index cases in this analysis had laboratory-confirmed influenza illness.
The first efficacy measure is the protective effect of antiviral prophylaxis in the household contacts of infected index cases, AVES. When the outcome in the contact is clinical influenza illness, we denote it as AVESd. When the outcome is infection, we denote it as AVESi. The second measure is the efficacy of reducing the infectiousness of an index case for a contact, denoted AVEI. We distinguish AVEId and AVEIi when the outcome in the contact is influenza illness or influenza infection. The third measure is the combined effect if both the index case and the contact take antivirals compared with if neither takes antivirals, the total antiviral efficacy AVET, where we again distinguish AVETd and AVETi.
The fourth effect is the effect of an antiviral drug on reducing the ability of the virus to cause disease in an infected person, the pathogenicity. A measure for pathogenicity is the probability of developing symptomatic illness if a person becomes infected ((9), p. 55). We estimate pathogenicity by using data on the contacts only. We denote pathogenicity as P and the efficacy against pathogenicity as AVEP. The relations among the efficacy measures are shown in the Appendix.
Estimating AVES, AVEI, and AVET.
The secondary attack rate, SARjk, is the proportion of eligible contacts of prophylaxis status k who develop the outcome of interest when exposed to an index case of treatment status j. The subscripts j and k take on the value 1 for antiviral drug and 0 for control or no antiviral. For example, SAR01 denotes the SAR when the index case receives control and the eligible contacts receive antiviral drug. From the appropriate SARjk's, we can estimate the first three antiviral efficacies as follows:
 | (1) |
 | (2) |
 | (3) |
Table 2 provides an overview of the efficacy estimates that can be obtained from each study or from combinations of the studies. The primary outcome in both oseltamivir studies and in Zan II (2) was reduction in influenza illness in the individual eligible contacts, AVESd. The Zan II and Osel II (4) studies had similar designs from which SAR00, SAR01, and hence AVES as on the left side of equation 1 are estimable. In Osel I (3), SAR10, SAR11, and hence AVES as on the right side of equation 1 are estimable. In Zan I (1), the primary outcome was based on reduction of the proportion of households with at least one case of influenza illness rather than reduction in the SAR, so it does not correspond to any of these measures. However, in terms of our efficacies of interest, SAR00, SAR11, and thus AVET in equation 3 are estimable.
|
None of the studies alone provides information enabling estimation of AVEI. To estimate AVEI for zanamivir, one 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 for oseltamivir, one must use SAR10 from Osel I (3) and SAR00 from Osel II (4) (right side of equation 2). Similarly, to estimate AVET for oseltamivir, one must use SAR11 from Osel I and SAR00 from Osel II. It is generally not advisable to combine estimates from separate studies in this simple way. However, without doing so, we would not be able to obtain the estimates at all. It illustrates the importance of improving study design in the future. Approximate confidence limits were based on the Wald method ((10), p. 240).
Estimating pathogenicity and AVEP.
Pathogenicity P is estimated as the (number of symptomatic influenza infections in the contacts)/(number of influenza infections in the contacts). The antiviral efficacy for pathogenicity, AVEP, is
 | (4) |
Reanalysis of the four studies
To analyze the original data from the four studies, we made an effort to standardize the inclusion criteria for any particular estimate. We present two periods in which contacts are regarded as secondary cases. Let day 1 be the ascertainment day of the index case. The two periods are day 1 to 7 and day 2 to 7. Thus, we use the longest period available for all studies in the original four analyses. Contacts with a positive day 1 culture were excluded from the analysis of the oseltamivir studies. Day 1 cultures were not available in the zanamivir studies. For the period from day 2 to 7, infected contacts with symptom onset on day 1 are excluded from the analysis. Only those households with index cases with laboratory-confirmed influenza were included. For both zanamivir studies, we used the case definition for contacts as reported in Zan II (2). For the oseltamivir studies, we used the case definition as reported in each paper. Further exclusion criteria can be found in the Appendix.
Asymptomatic infections presented a problem because we did not have their infection onset times. Asymptomatic cases in each treatment status group are allocated to within or after the period according to the distribution of symptomatic cases within and after the period. (Refer to the Appendix 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 SAR01 from Zan II, we estimated AVEI given that the contacts were treated. For the oseltamivir studies, AVES given that the index case was not treated was estimated from Osel II (4) alone, and AVES given that the index case was treated was estimated from Osel I (3) alone. We estimated AVEI by using SAR00 from Osel II and SAR10 from Osel I. We estimated AVET by using SAR00 from Osel II and SAR11 from Osel I.
|
RESULTS |
|---|
|
TOPABSTRACTINTRODUCTIONMATERIALS AND METHODSRESULTSDISCUSSIONAPPENDIXReferences |
|---|
Table 3 contains estimates of AVES and AVET either reported directly in the four papers or estimated from numbers reported in the four papers. The results in table 3 are based on households with index cases with laboratory-confirmed influenza illness. The AVESd of both oseltamivir and zanamivir is quite high. The corresponding AVETd of zanamivir is also quite high. Protection against influenza infection, AVESi, is lower than against influenza illness, AVESd.
|
Figure 1 shows the distribution of the day of onset of symptoms in the laboratory-confirmed secondary cases for the 14 days after ascertainment of the index case. Tables 4 and 5 contain our reanalysis of the zanamivir and oseltamivir data sets. The numbers contributing to each estimate differ from those in the original papers because of exclusions described in the Materials and Methods section and the Appendix. For zanamivir (table 4), the estimates of AVES and AVET are similar to those in the original papers. The estimates of AVEI for zanamivir are not significantly different from 0, although the confidence intervals are quite wide. For oseltamivir (table 5), our estimates of AVES are also consistent with the estimates in the original papers. The estimate of AVEId is high at 80 percent (95 percent confidence interval: 43, 93), although the AVEIi is not significantly different from 0. The AVETd is also quite high at 91 percent.
|
|
|
Table 6 shows estimates of pathogenicity and AVEP based on numbers contained in the original four papers. The variability in the estimates of pathogenicity and AVEP could be due to variability in the influenza subtypes, the age eligibility of the contacts, the case definitions, or other differences in the studies.
|
|
DISCUSSION |
|---|
|
TOPABSTRACTINTRODUCTIONMATERIALS AND METHODSRESULTSDISCUSSIONAPPENDIXReferences |
|---|
In this paper, we have compared the design of four randomized clinical studies of influenza antiviral agents. We systematically showed the relation among the different measures of antiviral efficacy and that the four studies, although similar in many respects, provide information for three different efficacy measures. We also showed that none of these four studies alone allows estimation of the effect of antiviral treatment on infectiousness. If randomization were by individual rather than by household, then it would be possible to estimate all of the effects of interest from one study alone.
Our reanalysis of the four studies gave results for the estimates of AVES and AVET similar to those in the original papers. We additionally estimated AVEI for both drugs and AVET for zanamivir. Prophylactic protection of both zanamivir and oseltamivir against symptomatic influenza is quite good, about 75–85 percent. The efficacy in reducing pathogenicity is in the 45–60 percent range. Although the efficacy of oseltamivir on infectiousness of the treated cases is significant and that of zanamivir is not, we warn against overinterpreting these results. The numbers are small, and we are combining estimates from two studies in both instances. AVEI is not so important, when AVES is high, as is the case here. One might speculate that oral oseltamivir and inhaled zanamivir could have different effects on secondary transmission of virus due to differences in reductions in upper respiratory viral levels and possibly symptoms. Oral oseltamivir may reduce viral levels in the nose, whereas inhaled zanamivir does not. Inhaled zanamivir does reduce pharyngeal levels of virus, but, to our knowledge, studies of neither drug have been conducted on their effects on tracheobronchial levels of virus. Both modalities reduce cough, but inhaled zanamivir does not reduce significantly the nasal symptoms of influenza. Consequently, if infectious droplets and aerosols produced from the nose are important in virus transmission, oseltamivir might have an advantage. This advantage might not apply to a pandemic virus if replication occurred in different parts of the respiratory tract.
With these drugs, the combined effect if both the index case and contact receive a drug compared with if neither does, measured by AVET, is high and is likely dominated by the prophylactic protection rather than the treatment effect on transmission. Since both drugs exhibit good prophylactic efficacy against symptomatic influenza, either would be useful as part of an intervention strategy against pandemic influenza if efficacy were the only consideration and the efficacy against the pandemic strain were similar to that against the interpandemic strain.
Some of the limitations of our analysis are inherent in the limitations of the original studies. To be able to estimate the effect of treatment on transmission, AVEI, within one study, index cases would need to be individually randomized to treatment separately from their contacts (11), which did not occur in any of these four studies. Our analysis is based on the simple SAR. However, other statistical methods (11) consider further chains of transmission within households and the possibility of infection from outside the household, and they include joint estimation of AVES, AVEI, and AVET. Extension of these methods could include estimating the duration of the infectious period (12) and allow for asymptomatic infections. The analysis could also estimate the effect of prophylaxis on reducing infectiousness (11), whereas here we have estimated just the effect of treatment on reducing infectiousness. We expect the efficacy of prophylaxis in reducing infectiousness in breakthrough cases to be greater than that of treatment. Such methods could also incorporate model-based methods for random effects across households (13) and the possibility of postinfection selection bias when estimating pathogenicity and AVEP (14). Because these results are for households only, trials in other settings such as schools, homes for elderly, and workplaces would also be useful as part of pandemic planning.
Randomized field trials of influenza antiviral agents are large and expensive. Simple remedies such as discordant randomization within households and powering studies to determine AVEI would allow estimation of all the important effects. Comparability of studies would be improved by standardized case definitions, eligibility criteria, and duration of follow-up. We hope that this paper illustrates the importance of better planning of field studies to answer the relevant scientific and public health questions of interest.
|
APPENDIX |
|---|
|
TOPABSTRACTINTRODUCTIONMATERIALS AND METHODSRESULTSDISCUSSIONAPPENDIXReferences |
|---|
Age-based exclusion criteria
In the Zan I (1) zanamivir study, all contacts aged less than 5 years were excluded because they were not treated. All households with index cases aged less than 5 years were also excluded because the index cases were not treated as well. In Zan II (2), all contacts aged less than 5 years were excluded because they were not treated. When we estimated AVES from Zan II alone, households with index cases aged less than 5 years were included because all index cases were not treated by design. When we estimated AVEI by using both studies, these households were excluded; otherwise, the two studies are not comparable and cannot be used together.
In the Osel II (4) study, there were no data for any eligible contacts aged less than 12 years, which was specified by the design. However, there were about 38 index cases aged less than 12 years. We did not exclude the households with these index cases aged less than 12 years in estimating AVES from Osel II alone because all index cases were not treated by design. In Osel I (3), contacts aged less than 1 year and households with index cases aged less than 1 year were excluded when we estimated AVES from this study alone because all subjects aged less than 1 year were not treated by design. There was one index case aged less than 1 year who was not treated, and that household was excluded at the data-cleaning step because laboratory results were not available for all family members. When we estimated AVEI and AVET by using both Osel I and Osel II, contacts aged less than12 years were excluded from Osel I, and households with index cases aged less than 1 year were excluded from both studies to minimize the factors that make the two studies not comparable.
Relations among the efficacy measures
One can assume that the antiviral effects on susceptibility and infectiousness contribute independently and multiplicatively to AVET. Here, if there is a large difference between AVES and AVET, then AVEI would account for this. Formally, under this assumption, AVET = 1 – (1 – AVES)(1 – AVEI). For oseltamivir, under this assumption, using AVESd = 0.81 from Osel I (3) and AVEId = 0.80, the estimated AVETd would be 0.98, higher than the AVETd = 0.91 point estimate based on the data. It would be even higher if based on AVESd = 0.91 from Osel II (4). Alternatively, one could assume that the AVESd interacts with AVEId in a more complex way. It may be that AVESD dominates over the AVEId effect, especially when AVESd is high. Given the low numbers and the wide confidence intervals in these studies, however, it is not possible to differentiate the independence from the interaction hypothesis. Similar calculations can be made for zanamivir from table 4, where the estimates of AVEId are low. When using the day 2 to 7 intervals, based on the independence assumption, AVETd = 0.79, thus lower compared with 0.87 based directly on the data. Again, the numbers are too low to differentiate the two hypotheses.
Similar relations exist between influenza infection, influenza disease, pathogenicity, and the corresponding efficacies. The probability of influenza disease equals the probability of influenza infection multiplied by the probability of disease given infection (pathogenicity). Furthermore, AVESd = 1 – (1 – AVESi)(1 – AVEP). These relations follow directly by definition without further assumptions. Taking as an example Zan II (2), from tables 3 and 6, we obtain AVESd = 1 – (1 – 0.55)(1 – 0.52) = 0.78, which, as expected, is close to the estimate of AVESd = 0.80 in table 3.
Imputing the infection times
One problem with all four studies, since we use only part of the initial follow-up period of the studies, is how to allocate asymptomatic infections to the exposure period for calculating SARs. We used a simple Bayesian technique. All asymptomatic infections are assumed infected within or after the period under consideration. Let p be the probability that an infected contact occurs in the secondary infection period. We assume that p is the same for symptomatic and asymptomatic infections. Given p, we observe that n
symptomatic infections occur in the secondary exposure period and m after the period for the group "00" with untreated index case and control contact. Similarly define n
and m for other groups "uv." We assume a binomial sampling model. If n > 0 and m > 0, we may simply assign asymptomatic cases to the period according to the ratio n:m. However, if a drug is highly efficacious against pathogenicity, there may be many more asymptomatic than symptomatic infections. For example, we use group "11" from Osel I (3) in combination with group "00" from Osel II (4) to estimate AVET. After excluding contacts and households according to our inclusion/exclusion criteria, in group "11" of Osel I, there were only two symptomatic infections, both in the period of day 1 to 7, while there were 20 asymptomatic infections during the 10-day follow-up period. Assigning all 20 asymptomatic infections to the period up to day 7 seems unreasonable.
To estimate p, we first obtain prior knowledge about p from all symptomatic cases in an individual study. Let 
We assume a prior distribution for p proportional to pNsym (1 – p)Msym. Given p, the sampling distribution of the data is proportional to 
for group "uv." The posterior density for p is then proportional to 
and we estimate p by the mode 
Thus, the total number of secondary infections for group "uv" is estimated as 
where t
is the number of asymptomatic infections in the group. For example, in Osel I (3), after exclusions for estimating AVES, 19 symptomatic infections occurred within the secondary exposure period and seven after the period. The prior ratio is 19:7. In group "11," the ratio is 3:1. Then, the posterior ratio is (19 + 3):(7 + 1) for the "11" group. The posterior mode is given by (19 + 3)/(19 + 3 + 7 + 1) = 0.73—very close to 0.75 if we use only the ratio 3:1 of symptomatic cases. The Bayesian method makes a difference when there are 0's. As mentioned above, when we estimated AVET for oseltamivir, after necessary exclusions, the "11" group in Osel I has two symptomatic infections in the secondary period and 0 after that. When the prior ratio 19:7 from the whole Osel I study is used, we have a posterior ratio (19 + 2):(7 + 0), and the posterior mode is 21/28 = 0.75. Consequently, we have 15 instead of 20 asymptomatic infections assigned to the secondary infection period.
|
ACKNOWLEDGMENTS |
|---|
This research was partially supported by National Institute of Allergy and Infectious Diseases grant R01-AI32042 and National Institute of General Medical Sciences MIDAS grant U01-GM070749.
The authors are grateful to Roche (Basel, Switzerland) and GlaxoSmithKline (Middlesex, United Kingdom) for allowing access to the data sets.
M. E. H. and I. M. L. were ad hoc consultants with Roche after writing this paper. A. S. M. received research support and as an ad hoc consultant to Roche and GlaxoSmithKline. F. G. H. received a lecture honorarium from Roche and a small research grant from Roche.
|
References |
|---|
|
TOPABSTRACTINTRODUCTIONMATERIALS AND METHODSRESULTSDISCUSSIONAPPENDIXReferences |
|---|
- Hayden FG, Gubareva LV, Monto AS, et al. (2000) Inhaled zanamivir for the prevention of influenza in families. N Engl J Med 343:1282–9.
[Abstract/Free Full Text] - Monto AS, Pichichero ME, Blanckenberg SJ, et al. (2002) Zanamivir prophylaxis: an effective strategy for the prevention of influenza types A and B within households. J Infect Dis 186:1582–8.[CrossRef][Web of Science][Medline]
- Hayden FG, Belshe R, Villanueva C, et al. (2004) Management of influenza in households: a prospective, randomized comparison of oseltamivir treatment with or without postexposure prophylaxis. J Infect Dis 189:440–9.[CrossRef][Web of Science][Medline]
- Welliver R, Monto AS, Carewicz O, et al. (2001) Effectiveness of oseltamivir in preventing influenza in household contacts: a randomized controlled trial. JAMA 285:748–54.
[Abstract/Free Full Text] - Longini IM Jr, Halloran ME, Nizam A, et al. (2004) Containing pandemic influenza with antiviral agents. Am J Epidemiol 159:623–33.
[Abstract/Free Full Text] - Longini IM Jr, Nizam A, Xu S, et al. (2005) Containing pandemic influenza at the source. Science 309:1083–7.
[Abstract/Free Full Text] - Ferguson NM, Cummings DA, Fraser C, et al. (2006) Strategies for mitigating an influenza pandemic. Nature 442:448–52.[CrossRef][Medline]
- Germann TC, Kadau K, Longini IM Jr,, et al. (2006) Mitigation strategies for pandemic influenza in the United States. Proc Natl Acad Sci U S A 103:5935–40.
[Abstract/Free Full Text] - Fox JP, Hall CE, Elveback LR. (1970) Epidemiology: man and disease. (MacMillan Publishing, New York, NY).
- Rothman KJ. (1998) Greenland S, eds. Modern epidemiology. 2nd ed (Lippincott-Raven, Philadelphia, PA).
- Yang Y, Longini IM Jr, Halloran ME. (2006) Design and evaluation of prophylactic interventions using infectious disease incidence data from close contact groups. Appl Stat 55:317–30.
- Cauchemez S, Carrat F, Viboud C, et al. (2004) A Bayesian MCMC approach to study transmission of influenza: application to household longitudinal data. Stat Med 23:3469–87.[CrossRef][Web of Science][Medline]
- Halloran ME, Préziosi MP, Chu H. (2003) Estimating vaccine efficacy from secondary attack rates. J Am Stat Assoc 98:38–46.[CrossRef]
- Hudgens MG and Halloran ME. (2006) Causal vaccine effects on binary postinfection outcomes. J Am Stat Assoc 101:51–64.[CrossRef]
CiteULike 
Connotea 
Del.icio.us What's this?
This article has been cited by other articles:
|
|
 |
|
  N. E. Basta, D. L. Chao, M. E. Halloran, L. Matrajt, and I. M. Longini Jr Strategies for Pandemic and Seasonal Influenza Vaccination of Schoolchildren in the United States Am. J. Epidemiol., September 15, 2009; 170(6): 679 - 686. [Abstract] [Full Text] [PDF]
|
|
|
|
 |
|
 B. J Cowling, S. Ng, and I. M Longini Jr Antiviral drugs: distinguish treatment from prophylaxis BMJ, September 8, 2009; 339(sep08_1): b3620 - b3620. [Full Text]
|
|
|
|
|
|
J. Wood, J. McCaw, N. Becker, T. Nolan, and C. R. MacIntyre Optimal Dosing and Dynamic Distribution of Vaccines in an Influenza Pandemic Am. J. Epidemiol., June 15, 2009; 169(12): 1517 - 1524. [Abstract] [Full Text] [PDF]
|
|
|
|
 |
|
 Y. Yang, M. E. Halloran, and I. M. Longini Jr A Bayesian model for evaluating influenza antiviral efficacy in household studies with asymptomatic infections Biostat., April 1, 2009; 10(2): 390 - 403. [Abstract] [Full Text] [PDF]
|
|
|
|
|
|
N. E. Basta, M. E. Halloran, L. Matrajt, and I. M. Longini Jr. Estimating Influenza Vaccine Efficacy From Challenge and Community-based Study Data Am. J. Epidemiol., December 15, 2008; 168(12): 1343 - 1352. [Abstract] [Full Text] [PDF]
|
|
|
|
 |
|
 W. P. Glezen Prevention and Treatment of Seasonal Influenza N. Engl. J. Med., December 11, 2008; 359(24): 2579 - 2585. [Full Text] [PDF]
|
|
|
|
 |
|
 A Nicoll Children, avian influenza H5N1 and preparing for the next pandemic Arch. Dis. Child., May 1, 2008; 93(5): 433 - 438. [Abstract] [Full Text] [PDF]
|
|
|
|
 |
|
 M. E. Halloran, N. M. Ferguson, S. Eubank, I. M. Longini Jr., D. A. T. Cummings, B. Lewis, S. Xu, C. Fraser, A. Vullikanti, T. C. Germann, et al. Modeling targeted layered containment of an influenza pandemic in the United States PNAS, March 25, 2008; 105(12): 4639 - 4644. [Abstract] [Full Text] [PDF]
|
|
| ||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||