Analysis of Historical Data Suggests Long-lasting Protective Effects of Smallpox Vaccination
Martin Eichner
From the Department of Medical Biometry, University of Tübingen, Tübingen, Germany.
Received for publication April 17, 2003; accepted for publication August 6, 2003.
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ABSTRACT
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More than half of the US population has received the smallpox vaccine, but it is unknown what fraction is still protected against infection and disease. Residual protection and age-dependent case-fatality ratios have therefore been widely neglected in the current bioterrorism debate. The author analyzed 19021903 data from Liverpool, United Kingdom, and from reintroductions of the disease to Europe in 19501971 to estimate to what degree vaccinated cases were protected against developing severe or fatal disease and how quickly this protection waned over time. Protection against severe and fatal disease was lost at the rate of 1.41% per year, corresponding to a half-life of 49.2 years (95% confidence interval: 42.0, 57.3), and protection against fatal disease alone declined 0.363% per year. Thus, even 70 years after primary vaccination, 77.6% of cases were still protected (95% confidence interval: 66.6, 85.4). Protection against severe disease should therefore extend for many decades after a single vaccination, and protection against death from smallpox may even be lifelong for the majority of vaccinees. This protection should greatly reduce the number of severe and fatal cases of disease expected in a bioterrorist attack, but residual protection may also increase the risk that some previously vaccinated cases who develop mild disease may remain unrecognized longer, while moving around freely and disseminating the infection.
age factors; models, theoretical; mortality; smallpox; smallpox vaccine; vaccination; variola virus
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INTRODUCTION
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Recent bioterrorist attack scenarios have conjured up devastating smallpox epidemics with hundreds of thousands of deaths following the deliberate release of variola virus (13). More than half of the US population has received the smallpox vaccine, but residual protection often has been neglected in the current discussion because it is not known how long immunity lasts (4). Diminishing protection against infection conferred by a single vaccination has necessitated revaccinations, but even a single vaccination has been reported to alleviate the course of disease and reduce case fatality in those who acquire the infection decades after vaccination (5, 6). The Centers for Disease Control and Prevention (Atlanta, Georgia) claims that most estimates suggest that immunity as a result of vaccination lasts 35 years (7). Contrary to their statement, a recent study by the Israel Defense Forces Medical Corps observed that the smallpox "titer significantly decreased during the first three years after the re-vaccination but remained stable for at least 30 years thereafter," which led them to conclude that "there is probably no need for routine re-vaccinations beyond the primary and two revaccinations" (8, p. 446). The protective significance of antibody titers is uncertain, and immunologic memory may be of higher importance (9, 10): a US group studying the duration of T-cell memory in humans recently reported that "specific vaccinia virus T-cell immunity can persist for up to 50 years after immunization against smallpox in childhood in the presumed absence of exposure to vaccinia virus" (11, p. 2627; 12).
This study analyzed data from the United Kingdom collected in the beginning of the 20th century and from smallpox epidemics following reintroductions to Europe from 1950 to 1971. The goal was to estimate the degree of residual protection against developing severe or fatal disease.
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MATERIALS AND METHODS
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Mack (13) documented 680 cases of smallpox (with 109 deaths) that occurred after introductions to European countries from 1950 to 1971. He classified the cases according to age and time since successful vaccination. Omitting cases of unknown age or vaccination status and those who were vaccinated after exposure left 475 cases, described in table 1. In this paper, I first characterize the fate of unvaccinated cases by assuming age-specific case-fatality ratios. For vaccinees, I assume that a fraction dependent on time since vaccination is still protected against disease, so six parameters have to be estimated: three baseline case-fatality ratios and three probabilities of residual protection. The observed numbers of deaths can be regarded as the result of a binomial sampling process with probabilities that depend on age at infection and on time since vaccination (details of the estimation procedure are given in appendix 1).
Hanna (14) reported that there were 943 vaccinated and 220 unvaccinated smallpox cases during an epidemic in Liverpool, United Kingdom, in 19021903 and thereafter. Data on these cases were used to study the effects of smallpox vaccination. These 1,163 cases were admitted to hospitals and constitute a subset for which sufficient information was available from a total of 2,280 cases (with 161 deaths). The cases described in table 2 were either unvaccinated or vaccinated during infancy and were classified according to severity of disease. Here, I distinguish three groups: 1) mild cases (surviving cases with "discrete" and "modified discrete" disease), 2) severe cases (surviving cases with "profuse discrete," "semiconfluent," or "confluent" disease), and 3) fatal cases (I have moved the 18 "confluent cases" from Hannas class "confluent and death" to group 2 because their age distribution rather resembled these cases than that of the fatal cases).
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TABLE 2. Age, vaccination status, and severity of disease in 1,163 variola major cases* in an outbreak in Liverpool, United Kingdom, 19021903
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Before I can examine the residual protection of childhood vaccination, I have to characterize the age-dependent course of disease in unvaccinated cases. About the same fraction of unvaccinated cases developed mild disease, irrespective of their age. The case-fatality ratio depends on age a and can be described empirically by
. I assume that all successfully vaccinated persons are initially protected against severe and fatal disease and then gradually lose their protection. To use different levels of protection against severe and fatal disease, I estimate two decay rates of residual protection. The probability that a vaccinated case dies from smallpox is the product of the probability of having lost vaccine-induced protection and of the age-dependent fatality of unprotected cases. Because three different disease severity classes are used, the observed numbers of cases can be regarded as the result of a multinomial sampling process (details of the estimation of the age-dependent probabilities are given in appendix 2).
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RESULTS
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For the Liverpool epidemic (19021903), the estimated fraction of mild cases was 17.3 percent for unvaccinated cases, irrespective of their age (95 percent confidence interval: 12.6, 22.6) (figure 1). The probability that unvaccinated cases died was lowest at about 11 years of age, counterbalancing the probability of severe but nonfatal disease that peaked at that time (figures 2 and 3, solid lines). Protection against severe and fatal disease was lost at the rate of 1.41 percent per year (figure 4, solid line), which corresponds to a half-life of protection of 49.2 years (95 percent confidence interval: 42.0, 57.3); protection against fatal disease alone declined 0.363 percent per year (figure 4, dashed line). Thus, even 70 years after primary vaccination, 77.6 percent of cases were still protected (95 percent confidence interval: 66.6, 85.4). Combining the residual protection with the age-dependent probabilities of unvaccinated cases yields predictions for the corresponding probabilities of vaccinated cases, shown as dashed lines in figures 1, 2, and 3. The probability of mild disease is much higher for vaccinated cases than for unvaccinated cases (figure 1), and the probability of fatal disease is much lower (figure 3) even if vaccination occurred decades before infection. Because the probabilities for mild, severe, and fatal disease add up to 1, and because the probability of mild disease declines more strongly than the probability of fatal disease rises, cases vaccinated some 40 years ago had a higher probability of experiencing severe (but nonfatal) disease than unvaccinated cases did (figures 1, 2, and 3). The case-fatality ratio of unvaccinated cases in Europe (19501971) was nearly 40 percent for those less than 50 years of age and more than 90 percent for older cases (table 3). The case-fatality ratio was reduced by 96.7 percent during the first decade after vaccination, by 83.6 percent during the second decade, and still by 79.0 percent if cases had been vaccinated more than 20 years ago.

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FIGURE 1. Predicted probability that a vaccinated (dashed line) or unvaccinated (solid line) smallpox case will experience mild disease. Vaccinated cases are assumed to have received a single vaccination during infancy. Predictions are based on the parameter estimates given in table 4 for the 19021903 outbreak in Liverpool, United Kingdom (refer to the text and to appendix 2 for details).
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FIGURE 2. Predicted probability that a smallpox case will experience severe but nonfatal disease, by age and time since vaccination (dashed curves). Predictions are based on the parameter estimates given in table 4 for the 19021903 outbreak in Liverpool, United Kingdom (refer to the text and to appendix 2 for details).
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FIGURE 3. Predicted probability that a case will die from smallpox, by age and time since vaccination (dashed curves). Vaccinated cases are assumed to have received a single vaccination during infancy. Predictions are based on the parameter estimates in table 4 for the 19021903 outbreak in Liverpool, United Kingdom (refer to the text and to appendix 2 for details).
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FIGURE 4. Residual protection, by time since successful smallpox vaccination, based on the parameter estimates given in table 4 for the 19021903 outbreak in Liverpool, United Kingdom (solid line: protection against fatal disease, dashed line: protection against severe and fatal disease; refer to the text and to appendix 2 for details). Cases are assumed to have received a single vaccination during infancy.
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TABLE 3. Parameter estimates of the case-fatality ratios and of the residual protection offered by smallpox vaccination for 680 variola major cases in Europe, 19501971*
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DISCUSSION
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Vaccinated smallpox cases still enjoyed a considerable degree of protection against severe and fatal disease even decades after a single successful vaccination. Thirty years after vaccination, smallpox case fatality was still reduced by about 8090 percent according to my estimates (table 3 and figure 4, dashed line). All smallpox cases from Liverpool and most of the cases in Europe were hospitalized, which may have caused a bias toward observing severe or fatal cases. Such bias would lead to an overrepresentation of severe and fatal cases, especially among vaccinated cases, and thus to an underestimation of the protective effects of vaccination. As smallpox outbreaks occurred in 19th century Liverpool, some of the vaccinated cases described in table 2 may have experienced subclinical booster infections (15), which, on the other hand, may have exaggerated the effect of vaccination. The smallpox pandemic of 18701875 (16) may have been responsible for the sudden decline in unvaccinated and vaccinated cases over 30 years of age (figure 5) (a sensitivity analysis that excluded all cases over 30 years of age led to estimates of µ = 1.39 percent per year and
= 0.185 percent per year, which correspond to even longer protection times than the values shown in table 4). Revaccinations were very uncommon in England during the 19th century (5, 16, 17), but evidence was accumulating that "the experience of those who have done much vaccination in adolescents or adults shows that the protection afforded to adults by re-vaccination lasts much longer than the same operation in children. It is well known that this restored protection again diminishes, but much more slowly" (14, p. 24). Smallpox case fatality depended not only on age and vaccination status but also on the nutrition and general health of the afflicted population (5, 17), and historical estimates may overestimate the risk that cases will die of smallpox in a 21st-century industrialized country.

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FIGURE 5. Numbers of vaccinated and unvaccinated cases, by age, in a 19021903 outbreak of smallpox in Liverpool, United Kingdom.
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TABLE 4. Parameter estimates of the age-dependent course of smallpox disease and the residual protection offered by vaccination for 1,163 variola major cases in an outbreak in Liverpool, United Kingdom, 19021903*
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Age-dependent risks and residual protection have been widely neglected in the current discussion about vaccination strategies (1, 18). A variety of mathematical models have been proposed to predict what might happen if terrorists released smallpox virus (2, 3, 1921). Most of these studies completely neglect age dependency in relation to case fatality and assume that 22.530 percent of all cases will die from smallpox. Kaplan et al. (3) did not consider residual vaccine protection in their model. Halloran et al. (19) examined a scenario in which they, too, neglected residual protection and contrasted it with another scenario in which newly vaccinated cases had the same case-fatality ratio of 3 percent as cases who were vaccinated decades ago. Bozzette et al. (20) used a case-fatality ratio of 8.5 percent for all previously vaccinated cases, which agrees with my estimates (figure 3), but they did not consider age-dependent differences in the case-fatality ratio of unvaccinated cases.
It is difficult to extract information from the given data on protection against infection. Figure 5 depicts the total number of vaccinated and unvaccinated cases from the Liverpool epidemic (also refer to table 2). Whereas the number of unvaccinated cases per age class remained approximately constant up to age 30 years, the number of vaccinated cases strongly increased, indicating an accumulation of susceptible persons who had lost their protection against infection. Estimations based on this comparison show that protection against infection is lost about 2040 years after primary vaccination, but the results strongly depend on the assumptions that have to be made to set up the estimation model (results not shown). In other outbreaks, the age-dependent fraction of vaccinated cases monotonically increased up to age 40 years (22) or 50 years (23), showing the same gradual loss of protection. Examination of material from many outbreaks led Dixon (17) to conjecture that, in the absence of natural booster infections, 99.9 percent of exposed persons were protected against infection 1 year after vaccination, 99.5 percent after 3 years, 87.5 percent after 10 years, and 50 percent after 20 years. Further evidence of residual protection comes from outbreaks of variola minor, the less pathogenic type of smallpox, where the duration and degree of protection were even more pronounced (17, 24, 25).
Fenner et al. (5) stated that vaccination in infancy protected most of those under 10 years of age and at least half of those aged 1020 years from overt disease. Only a few vaccinated children less than 5 years of age developed smallpox in the Liverpool outbreak (table 2), indicating that protection against infection usually lasted longer than half a decade.
The statement by the Centers for Disease Control and Prevention that immunity from smallpox vaccination lasts 35 years (7) must therefore be interpreted as the period during which practically all successfully vaccinated persons are protected against infection and disease, although the majority of those vaccinated may be protected much longer. The residual protection against severe disease may extend for many decades, and residual protection against death from smallpox may even be lifelong for the majority of vaccinees (figure 4). Such residual protection should greatly reduce the number of severe and fatal cases expected in case of a bioterrorist attack, but it may also increase the risk that some previously vaccinated cases who develop mild disease may remain unrecognized for a longer period of time, while moving around freely and disseminating the infection.
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APPENDIX 1
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I assume that, in Europe (19501971), an unvaccinated case of age a died given probability f(a) and that a vaccinated person of age a who was vaccinated t years before infection had residual protection p(t), so that his or her probability of death from smallpox was f(a)(1 p(t)). Because the small numbers for age and vaccination classes shown in table 1 did not enable me to apply smooth curves to the age and time dependencies in the data, I estimate average case-fatality ratios fl, f2, and f3 for the three age classes and average protection levels pl, p2, and p3 for the three vaccination time classes. If a binomial sampling process is assumed, the probability of observing di deaths among ni unvaccinated cases in age class i is
and the probability of observing dij deaths among vij vaccinated cases in age class i and vaccination class j is
Therefore, the total likelihood of all observations is given by
The estimates of the parameters p1, p2, p3, fl, f2, and f3 are given in table 3 together with their 95 percent confidence intervals, which are based on the profile likelihood. Expected numbers of fatal cases were calculated as fini and as fi(l pj)vij for unvaccinated and vaccinated cases, respectively.
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APPENDIX 2
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To estimate residual protection against severe and fatal disease by using the data observed during the Liverpool smallpox epidemic in 19021903, I make the following six assumptions:
1. A constant fraction pM(a) = m of unvaccinated cases experiences mild disease irrespective of age a.
2. The probability that an unvaccinated case of age a dies from smallpox is given by
, where l is the maximum case fatality reached for newborn children (figure 3, solid line).
3. Because the probabilities for mild, severe, and fatal disease add up to 1, I implicitly obtain the probability of severe disease pS(a) from pM(a) + pS(a) + pF (a) = 1.
4. All successfully vaccinated persons are initially protected against severe and fatal disease. This protection is lost at rate µ, so that cases vaccinated as infants develop mild disease at age a with probability of qM(a) = m + (1 m)eµa.
5. Protection against fatal disease alone is lost at rate
, so that vaccinated cases die from smallpox with probability qF(a) = (1 e
a)pF(a) when infected at age a.
6. Again, the probability qS(a) that a vaccinated case develops severe disease when infected at age a is given implicitly by qM(a) + qS(a) + qF(a) = 1.
The probability of observing nM(a) mild, nS(a) severe, and nF(a) fatal unvaccinated cases of age a is given by the multinomial distribution as
(with n(a) = nM(a) + nS(a) + nF(a)), and the probability of observing vM(a) mild, vS(a) severe, and vF(a) fatal vaccinated cases of age a is
(with v(a) = vM(a) + vS(a) + vF(a)). Therefore, the total likelihood of all observations is given by
When calculating the likelihood, I use the midpoint of ages a of the age classes. The estimates of the parameters m, l, µ,
, ß1, and ß2 are given in table 4 together with their 95 percent confidence intervals, which are based on the profile likelihood. Expected values (shown in table 1) were calculated as pM(a)n(a), pS(a)n(a), and pF(a)n(a) for unvaccinated persons and as qM(a)v(a), qS(a)v(a), and qF(a)v(a) for vaccinated cases, respectively, by using the most likely parameter values (shown in table 4).
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NOTES
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Correspondence to Dr. Martin Eichner, Department of Medical Biometry, University of Tübingen, Westbahnhofstr. 55, 72070 Tübingen, Germany (e-mail: martin.eichner{at}uni-tuebingen.de). 
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