American Journal of Epidemiology Vol. 154, No. 1 : 85-92
Copyright © 2000 by The Johns Hopkins University School of Hygiene and Public Health
ORIGINAL CONTRIBUTIONS |
Interpreting Results from Trials of Pneumococcal Conjugate Vaccines: A Statistical Test for Detecting Vaccine-induced Increases in Carriage of Nonvaccine Serotypes
1 Department of Biology, Graduate School of Arts and Sciences, Emory University, Atlanta, GA.
2 Centers for Disease Control and Prevention, Atlanta, GA.
3 Department of Epidemiology, Harvard School of Public Health, Boston, MA.
 |
ABSTRACT |
|---|
 TOP ABSTRACT INTRODUCTIONSTATISTICAL APPROACH TO...TESTING THE FIT OF...APPLICATION TO DATA FROM...SENSITIVITY ANALYSIS: PRIOR...SENSITIVITY ANALYSIS:...DISCUSSIONREFERENCES |
|---|
Conjugate vaccines against Streptococcus pneumoniae (pneumococcus) protect against nasopharyngeal carriage of serotypes included in the vaccine. However, in several clinical trials, vaccinees have shown increased carriage of nonvaccine serotypes of pneumococcus. These increases may be due to serotype replacement, if vaccine-induced protection against carriage of vaccine serotypes increases susceptibility to carriage of nonvaccine serotypes. Alternatively, observed increases may be an artifact of "unmasking," in which nonvaccine serotypes are more readily detected among vaccinees than among controls because vaccine serotypes are not present. In this paper, a statistical test for distinguishing serotype replacement from unmasking is described. The test attempts to reject a null model of unmasking alone; serotype replacement is inferred if the observed increase in detectable nonvaccine serotype carriage among vaccinees is significantly greater than that expected under the null model. Significance is assessed using the Bayesian "posterior predictive p value" as modified by Robins et al. (J Am Stat Assoc 2000;95:1143–56). Analysis of data from a South African trial suggests that replacement may have occurred in the study, but results do not reach the conventional level of significance in rejecting the null hypothesis of unmasking (p = 0.074). The author performs sensitivity analyses for the prior and for unmeasured confounding by differences in susceptibility to pneumococcus carriage. The implications of the findings and the assumptions and limitations of this technique are then discussed.
bacterial vaccines; carrier state; models, statistical; Streptococcus pneumoniae; vaccination; vaccines, conjugate
Abbreviations: NVT, nonvaccine type; VT, vaccine type
|
INTRODUCTION |
|---|
|
TOPABSTRACTINTRODUCTIONSTATISTICAL APPROACH TO...TESTING THE FIT OF...APPLICATION TO DATA FROM...SENSITIVITY ANALYSIS: PRIOR...SENSITIVITY ANALYSIS:...DISCUSSIONREFERENCES |
|---|
Streptococcus pneumoniae (pneumococcus) is a leading cause of death worldwide and a leading cause of morbidity in the United States (1
). The human nasopharynx is the main reservoir of pneumococci. Human hosts usually remain asymptomatic despite colonization by the organism (2). Disease occurs when the bacteria breach the mucosal barriers of the host and invade sites such as the middle ear, lungs, blood, or cerebrospinal fluid.
Pneumococci are classified into approximately 90 serotypes defined by the capsular polysaccharide. Recently developed conjugate vaccines elicit anticapsular antibodies to serotypes included in the vaccine (vaccine types (VTs)). Clinical trials have shown that these conjugate vaccines are protective against nasopharyngeal carriage of (3–7) and invasive disease from (8) VT pneumococci. This experience parallels previous experience with conjugate vaccines against Haemophilus influenzae, type b (9, 10), which are now in widespread use.
Current conjugate vaccines include polysaccharides from seven or nine clinically important serotypes. Because these vaccines reduce carriage (and therefore probably transmission) of VT pneumococci, there has been concern that vaccination may increase the prevalence of nonvaccine type (NVT) pneumococci. Such "serotype replacement" would result if pneumococci of different types competed to colonize a host; hosts protected by the vaccine against VTs would then be more likely to carry NVTs (11–14). Such competition might occur by a variety of mechanisms. Bacteria of different serotypes may compete directly for attachment sites or nutrients; they may secrete allelopathic substances; or they may compete indirectly by stimulating cross-reactive or nonspecific immune responses (12).
Serotype replacement could have adverse public health effects if the NVT organisms went on to cause disease. The serotypes included in conjugate vaccines are those presently responsible for most serious pneumococcal disease in the United States (15, 16), but serotype coverage is less extensive in other countries (15, 16). In populations for which the vaccine covers a large proportion of disease-causing serotypes, the pattern of disease could shift if vaccination permits increases in the prevalence of potentially virulent NVTs or selects for organisms that have switched types of capsular polysaccharides by transformation (and that may have either higher or lower virulence (17) than their pro-genitors). On the other hand, serotype replacement may increase the effectiveness of vaccination if the replacing serotypes have low virulence and competitively inhibit VT pneumococci. The potential consequences of vaccination and serotype replacement have been discussed in more detail elsewhere (12, 18).
Several studies have provided evidence that serotype replacement may occur. Three clinical trials of conjugate pneumococcal vaccines (3, 4, 6) have detected rates of NVT carriage in vaccine recipients that were statistically significantly higher than the corresponding rates in controls. In a trial that showed the efficacy of a pneumococcal vaccine against VT otitis media, there was evidence of increased otitis media from NVTs in vaccinated individuals (27).
Interpretation of measured increases in NVT carriage by vaccinees is complicated by the fact that among subjects from whom a sample containing pneumococci of more than one serotype is obtained, sampling techniques frequently do not detect all of the serotypes carried. Detection is typically done by plating a sample from a nasopharyngeal swab on an agar plate and serotyping one or a few bacterial colonies that grow on the plate. Thus, in a study in which a single pneumococcal colony from each sampled individual is typed, the assay is likely to detect the serotype that is most prevalent in that individual and to miss other serotypes. Dual colonization can be common, reaching rates as high as 30–40 percent of all individuals sampled in some populations (6, 19, 20). Because assay sensitivity for detecting multiple serotypes is less than 100 percent, the nonvaccine strains will not always be detected in individuals carrying both vaccine and nonvaccine strains. These assays will therefore more easily detect NVTs among vaccinees, who are protected against carriage of vaccine strains, than among controls. Therefore, even if vaccinees and controls have the same true rates of NVT carriage, the measured prevalence of NVTs will be higher in vaccinees than in controls.
Because serotype replacement is of public health importance, while unmasking is an assay artifact, it is important to distinguish between them in clinical trials. In this paper, I describe a method for making this distinction and apply the method to a published data set.
|
STATISTICAL APPROACH TO DISTINGUISHING REPLACEMENT FROM UNMASKING |
|---|
|
TOPABSTRACTINTRODUCTIONSTATISTICAL APPROACH TO...TESTING THE FIT OF...APPLICATION TO DATA FROM...SENSITIVITY ANALYSIS: PRIOR...SENSITIVITY ANALYSIS:...DISCUSSIONREFERENCES |
|---|
Clinical trials of pneumococcal conjugate vaccines have typically tested for serotype replacement by comparing the proportion of vaccinees in whom NVT carriage is detected with the corresponding proportion of controls, using
2 or Fisher's exact tests. These tests evaluate the fit to the observed data of a null model in which the true proportions are the same in vaccinees and controls, producing a p value which represents the probability that a discrepancy of that size or larger would occur by chance alone if the null model were true. If this probability is sufficiently small, replacement is inferred. In this paper, I describe a test that generalizes this approach by broadening the null model to include the effects of unmasking. As before, the fit of the null model is evaluated by calculating the probability of observing a test quantity greater than or equal to the observed value. In this case, if the null model fits the data poorly, then the observed discrepancy is unlikely to have occurred by chance and unmasking alone, and serotype replacement is inferred.
The central assumption of the null model, of course, is that the proportion of persons actually carrying NVTs is the same in vaccinees as in controls. The alternative to the null model—serotype replacement—is built on the idea of competitive interactions between VTs and NVTs. Therefore, in the null model, we assume that such interactions are absent—that carriage of one type has no effect on carriage of the other. Furthermore, we must make some assumptions about the shortcomings of the assay in detecting simultaneous carriage of VTs and NVTs. Here, we formalize "unmasking" by assuming that if both NVT and VT colonies are present in a sample from an individual, the assay always detects at least one type but may sometimes fail to detect VTs and may sometimes fail to detect NVTs. The probabilities that it will fail to detect each type in a dual carrier are fixed and are the same in vaccinees and controls.
More formally, the null model is defined as follows. Unprimed variables refer to controls and primed variables refer to vaccinees.
Notation
Let N (N') denote the number of controls (vaccinees) in a clinical trial. Each of these individuals will be classified into one of four states in the study: 1) no pneumococci detected; 2) VTs only detected; 3) NVTs only detected; or 4) both VTs and NVTs detected. Let Z, A, B, and D (Z', A', B', and D') stand for the number of controls (vaccinees) in each of these states. Then N = Z + A + B + D and N' = Z' + A' + B' + D'. The probability that a control individual will be colonized with VT pneumococci (at sufficient density to appear as colonies when his/her nasopharyngeal swab is plated) is v, and the corresponding probability for a vaccinee is v'. For NVTs, the probabilities are w for controls and w' for vaccinees. In what follows, I do not repeat this precise condition of obtaining colonies but only refer to "true carriage."
Assumptions of the null model
Independence assumption: no biologic interaction between VT carriage and NVT carriage. As described above, the null model assumes that an individual's probability of actually carrying VTs is independent of whether s/he carries NVTs. This assumption has two consequences. First, the probability of actually carrying both VTs and NVTs is the product of the individual probabilities of carrying each type (vw for controls and v'w' for vaccinees). Similar independence conditions hold for carrying neither type, for carrying VTs only, or for carrying NVTs only. Second, the null model specifies that vaccination has no effect on an individual's probability of carrying NVT pneumococci, so w = w'.
Imperfect assay sensitivity in dual carriers. In individuals carrying both VTs and NVTs, the sampling method will detect VTs only with probability 
10; it will detect NVTs only with probability 01; and it will detect both with probability 1 - 10 - 01. These probabilities are assumed to be the same in vaccinees and controls.
Independence of individuals. The carriage status of each individual is independent of that of other individuals.
These assumptions fully define the null model and its likelihood function. Table 1 gives the probabilities for detected carriage in each group, which reflect the probability of actual carriage as well as the probabilities of detecting each strain, or both strains, in dual carriers. For example, individuals in group A will be a mixture of those actually carrying only VTs, in a proportion v(1 - w), and those who actually carry both VTs and NVTs but in whom only VT carriage is detected, in a proportion vw10. Individuals in group D are those who actually carry both types and in whom both types are actually detected (probability vw(1 - 10 - 01)).
|
Here and in what follows we have replaced w' with w, since they are equal under the null model. This corresponds to the likelihood (L):
 | (1) |
 |
 |
|
TESTING THE FIT OF THE NULL MODEL |
|---|
|
TOPABSTRACTINTRODUCTIONSTATISTICAL APPROACH TO...TESTING THE FIT OF...APPLICATION TO DATA FROM...SENSITIVITY ANALYSIS: PRIOR...SENSITIVITY ANALYSIS:...DISCUSSIONREFERENCES |
|---|
Once the model is specified, we need to assess its goodness of fit to the data actually observed. To do so, we apply the technique of posterior predictive model assessment (21
, 22). This technique uses Bayesian methods to obtain the joint posterior distribution for the parameters of the (null) model, conditional on the observed data. It then assesses the fit of the model to the data by calculating the probability that the null model, with parameters drawn from this posterior distribution, would have generated data at least as "extreme" as the data observed; the resulting probability is the posterior predictive p value. As in frequentist tests, the "extremeness" of the data is measured by a scalar test quantity; in this case, the test quantity is chosen by the investigator and can reflect characteristics of the data of particular scientific interest.
Recent research has indicated that a standard posterior predictive test will be asymptotically conservative whenever the mean of the test statistic depends on the data (23, 24), as it will for the test statistic to be used. To correct this discrepancy, my colleagues and I have obtained the posterior predictive p value both in the usual way (described above) and by using a centered test statistic following the procedure suggested by Robins et al. (24), which is computationally more intensive but yields a more valid test.
We have chosen a noninformative prior distribution to reflect our lack of advance information about the parameters of the null model. This distribution is uniform over [0,1] for each of the three parameters that are probabilities: v, v', and w. The only exception is that we have assumed that the vaccine has nonnegative efficacy, so that true carriage of VTs is not higher among vaccinees than among controls. We have also assumed, as described above, that the assay detects at least one of the two types in any individual carrying both VTs and NVTs. These assumptions produce the following prior distribution:
 | (2) |
(The nonnegative efficacy assumption can be relaxed by giving v' a prior that is uniform between 0 and 1. This has no substantial effect on the outcome in our example.)
By Bayes' rule, the joint posterior distribution of the parameters (v, w, v', 01, 10), which we abbreviate 
, is proportional to the product of the prior distribution and the likelihood of the data given the parameters (table 2). We abbreviate the data as y. Thus,
 | (3) |
 |
 |
|
To determine whether the observed data are unexpected under the null model, it is necessary to define some test quantity that summarizes the extremeness of the data in a single value. The choice of a test quantity is governed by the particular aspect of the model whose fit one is interested in testing. Since we are interested in the increase in NVT carriage among vaccinees as compared with controls, a natural summary of the aspects of the data that are of interest is the observed log odds ratio (OR) for detectable NVT carriage in vaccinees compared with controls. In our application, this statistic is given by
 | (4) |
If the value of this statistic, based on the actual data, is greater than that typically observed (e.g., observed 95 percent of the time) under the null model, we can conclude that the unmasking-alone hypothesis is inadequate to explain the observed increase in NVT carriage.
|
APPLICATION TO DATA FROM A SOUTH AFRICAN CLINICAL TRIAL |
|---|
|
TOPABSTRACTINTRODUCTIONSTATISTICAL APPROACH TO...TESTING THE FIT OF...APPLICATION TO DATA FROM...SENSITIVITY ANALYSIS: PRIOR...SENSITIVITY ANALYSIS:...DISCUSSIONREFERENCES |
|---|
Table 2 shows carriage data for vaccinees and controls from a clinical trial carried out in Soweto, South Africa (4
). The published account of this trial did not give the number of individuals carrying both VTs and NVTs, but this information was kindly supplied by one of the paper's authors (R. Huebner, South African Institute for Medical Research (Johannesburg, South Africa), personal communication, 1998).
The freeware program WinBUGS (25, 26) was used to calculate a posterior distribution for the five model parameters, given the dual-multinomial model corresponding to the likelihood in equation 1, the observed data from table 2, and the prior given by equation 2. Samples from this posterior distribution were used to simulate replicate data sets, and the test statistic 
was calculated for each data set, using equation 4. The Gibbs sampler was given 10,000 cycles to converge, producing results that were discarded, and the replicate data 
were generated during an additional 10,000 cycles of the Gibbs sampler. The standard posterior predictive p value pPP-std is defined as 
and is approximated as the proportion of the 10,000 replicates in which the replicated statistic exceeded that based on the data.
As stated above, we used both the standard posterior predictive method (21, 22) and a method based on the centered test statistic suggested by Robins et al. (24). The latter increased the computational complexity and necessitated some data manipulation outside of WinBUGS. The WinBUGS software and other coding used for these manipulations are available from the author.
The corrected posterior predictive p value based on the centered test statistic was calculated as follows (see the paper by Robins et al. (24) for the rationale). The posterior mean test statistic Tpm was calculated as the mean of the test statistics obtained when 10,000 pseudo-observations ypm are generated assuming as parameter values the mean values of the posterior distribution P(|y). The centered test statistic for the observed data, 
, was calculated as the difference between the observed test statistic T(yobs) = ln[(87 x 181)/(58 x 155)] = 0.56 and the posterior mean test statistic: 
. Next, we obtained 500 replicate centered test statistics 
for comparison with the observed centered test statistic and estimated the corrected p value, 
), as the proportion of the 's that were greater than .
The 's were obtained as follows, paralleling exactly the process for calculating . First, we obtained 500 replicate data sets by sampling from the posterior predictive distribution of y. For each , a test statistic 
was calculated according to equation 4. In addition, for each , a new posterior distribution 
was calculated, and the posterior means of this distribution were used to create 10,000 new simulated data sets 
. Then, was calculated as
 |
Table 3 summarizes the posterior distribution of the model parameters. Using the standard posterior predictive analysis, the observed test statistic was Tobs = 0.56, corresponding to a posterior predictive p value of pPP-std = 0.085. The centered test statistic gave a value of 
, corresponding to a corrected p value of pPP-corr = 0.074. Thus, the data suggest an effect larger than that explainable by unmasking alone, but the corrected p value for this increase falls short of the 0.05 level.
|
|
SENSITIVITY ANALYSIS: PRIOR DISTRIBUTION |
|---|
|
TOPABSTRACTINTRODUCTIONSTATISTICAL APPROACH TO...TESTING THE FIT OF...APPLICATION TO DATA FROM...SENSITIVITY ANALYSIS: PRIOR...SENSITIVITY ANALYSIS:...DISCUSSIONREFERENCES |
|---|
A standard criticism of Bayesian approaches to statistical inference is that their conclusions may be strongly dependent on the prior distribution chosen. Whatever the philosophical merits of this criticism, the practical answer to it is that, under certain conditions, the prior distribution of the parameters becomes irrelevant as the sample size grows, because the likelihood comes to dominate the posterior distribution (21
). This reply is valid for the parameters v, w, and v', as can be seen from table 3, which summarizes the posterior distributions of the various parameters in the model for the South African data. For all three parameters, the posterior distribution is fairly tightly concentrated around the median, with 95 percent of the values falling within ±0.1 of the median value. The answer is not valid, however, for the misclassification parameters 01 and 10, whose posterior distribution ranges widely over the possible values between 0 and 1.
Therefore, specification of the prior distribution over 01 and 10 may have an important effect on the outcome of the model. Unmasking occurs because NVT carriage is not detected in dual carriers. The probability of missing NVT carriage in a dual carrier is given by 10. Thus, the effect of unmasking is expected to be greatest for large values of 10 and reduced for small values of 10. We therefore reran the test using two highly peaked prior distributions.
First, we repeated the test under the prior defined by 10 + 01 
Beta(99,1) and 01/[01 1 10] Beta(49.5,49.5), which expresses a strong prior belief that dual carriers will be misclassified as single carriers and that they are equally likely to be misclassified as VT-only carriers or NVT-only carriers. Posterior distributions of the model parameters under this prior are given in the upper portion of table 4; the resulting uncorrected p value is pPP-uncorr = 0.033, and the corrected p value is pPP-corr = 0.028. Thus, if one assumes that misclassification of dual carriers is common and that misclassification rates for VTs and NVTs are highly likely to be equal, the null model is rejected. Intuitively, this can be understood from the fact that the greatest potential for unmasking will occur when NVT carriage is frequently overlooked in dual carriers (large 10); the original null model (with the noninformative priors) therefore tends toward large values of 10, which in turn generates large test statistics. Put another way, the unmasking-alone null model is most plausible if we assume a high value of 10. Thus, a strong prior emphasizing intermediate values of this parameter will make the null model less plausible.
|
We also ran the test under a prior designed to maximize the effect of unmasking by using a prior emphasizing very high values of
10: 10 + 01 Beta(99,1) and 10/[01 1 10] Beta(98,1). Under this prior, we obtained the posterior parameter values shown in the lower portion of table 4 and uncorrected and corrected p values, respectively, of pPP-uncorr = 0.17 and pPP-corr = 0.15; as expected, the null model is most plausible under the assumption that NVT carriage is nearly always masked when it occurs in dual carriers. |
SENSITIVITY ANALYSIS: CONFOUNDING CORRELATIONS IN VT AND NVT CARRIAGE |
|---|
|
TOPABSTRACTINTRODUCTIONSTATISTICAL APPROACH TO...TESTING THE FIT OF...APPLICATION TO DATA FROM...SENSITIVITY ANALYSIS: PRIOR...SENSITIVITY ANALYSIS:...DISCUSSIONREFERENCES |
|---|
The test is designed to detect an increased probability of NVT carriage in vaccinees by rejecting a null model that assumes that VT carriage and NVT carriage are independent (the second assumption described under "Assumptions" above). The idea is that if VT carriage has no biologic effect on NVT carriage, an individual's risk of NVT carriage should not be affected by whether s/he carries VTs. If this biologic assumption of the null model were true, there might still be confounding factors, such as age, sex, and place of residence, that might affect both the probability of carrying VT pneumococci and the probability of carrying NVT pneumococci. If this were the case, there could be more dual carriers than predicted by the null model. This excess of dual carriers could make it possible to reject the null model spuriously.
To assess the magnitude of this problem, we performed a sensitivity analysis based on the South African data (4). We generated 40 simulated data sets under the null model, using as parameter values the posterior means estimated from the South African data set. We then subjected each of these sets of simulated data to the corrected posterior predictive p value analysis. We found that in three of 40 cases, the null model was rejected at the 5 percent level, which is consistent with the expected value of two rejections in 40 runs generated under the null model. The simulation was then repeated under the assumption that the population (unbeknownst to the investigator) consisted of a high-risk group, with the values of v, w, and v' being x percent higher than the original values, and a low-risk group, with values of v, w, and v' that were x percent lower than the original values. Each group comprised half of the population, and we considered values of x = 0, 20, 50, and 80, corresponding to relative risks of 1, 1.5, 3, and 9 for both VT and NVT carriage in the high-risk group versus the low-risk group. The null hypothesis was rejected at the 5 percent level in three of 40 (7.5 percent) cases for no discrepancy in carriage rates, two of 40 (5 percent) cases for the 20 percent discrepancy, five of 40 (12.5 percent) cases for the 50 percent discrepancy, and 16 of 40 (40 percent) cases for the 80 percent discrepancy. Thus, the presence of extremely heterogeneous groups in the population with highly correlated probabilities of carrying VTs and NVTs could result in a spurious detection of replacement; however, at moderate or lower levels of heterogeneity, such correlations would be unlikely to distort the analysis substantially.
|
DISCUSSION |
|---|
|
TOPABSTRACTINTRODUCTIONSTATISTICAL APPROACH TO...TESTING THE FIT OF...APPLICATION TO DATA FROM...SENSITIVITY ANALYSIS: PRIOR...SENSITIVITY ANALYSIS:...DISCUSSIONREFERENCES |
|---|
In this paper, I have described a method, using Bayesian analysis, of distinguishing statistically between two hypotheses to explain the observation that recipients of pneumococcal conjugate vaccine show elevated levels of detectable nasopharyngeal carriage of pneumococcal sero-types not included in the vaccine. When this test was applied to data from a South African trial (4
), the unmasking-alone model attained a corrected p value of 0.074, which was short of the preset significance level of 0.05. Thus, the data suggest, albeit not compellingly, that the observed increase in NVT carriage among these vaccinees is too large to be explained by unmasking and chance alone. One advantage of the posterior predictive p value approach is that the test quantity for quantifying the evidence against the null hypothesis can be chosen according to the scientific question of interest. Here, the question is whether the observed increase in NVT carriage among vaccinees is greater than that which could be explained by unmasking alone. As a result, we quantify this increase as the logarithm of the sample odds ratio for observed NVT carriage.
The relation between the Bayesian posterior predictive test suggested here and two more commonly used frequentist concepts is worthy of comment. First, if one assumed perfect sensitivity of detection of dual carriers (fixing 01 = 10 = 0 and thereby assuming that unmasking does not occur), the test proposed here would reduce to the Bayesian analog of a 2 or Fisher's exact test, testing whether w = w'. Thus, the test suggested here simply extends a more conventional test to include the effects of unmasking.
An alternative approach to the problem would be the use of a likelihood ratio test to compare the null model in which w = w' with an unconstrained null model in which w may differ from w'. The problem with this approach is that for many data sets, including the one considered here, the maximum likelihood parameter estimate will be on or near the boundary of the parameter space, since the 0 or 1 counts for D and D' indicate that 
. When the parameter or its estimate is near the boundary, the asymptotic properties of the likelihood ratio test may not strictly hold for moderate-sized samples, so such a test would probably perform poorly in many plausible data sets from pneumococcal conjugate vaccine trials.
We have not proposed a method of estimating the replacement effect, only a test for replacement vs. unmasking. The reason is that if both unmasking and replacement are at work, as is very likely, their relative contributions to the observed increase in NVT carriage among vaccinees are not identifiable. We can test whether unmasking alone is sufficient to explain the observed increase, but we cannot say how much of the increase it actually explains relative to true replacement.
Sensitivity analysis indicated that the test is somewhat sensitive to the choice of prior for the misclassification parameters 01 and 10. Specifically, if the prior places a high probability on dual carriers' being misclassified as carrying only VTs, then the unmasking effect is maximized and the null model is less likely to be rejected; under a prior which places a high probability on equal rates of misclassification of dual carriers (appearing to be VT-only or NVT-only), the null model becomes less plausible and is in fact rejected by the South African data.
Our analysis is designed to rule out unmasking that occurs because VT pneumococci are absent in a larger fraction of vaccinated individuals than controls. However, an important limitation of this approach is that it cannot rule out a second, subtler form of unmasking. It is possible that in some patients, the vaccine could reduce carriage of VTs numerically, without eliminating it entirely. In this case, if there were no biologic interactions between VT and NVT pneumococci, misclassification of dual carriers as VT-only carriers would be more common among controls than among vaccinees. For reasons of identifiability, this phenomenon cannot be included in the null model, so rejection of the null model cannot reject the possibility that this has occurred. Note that the same phenomenon could lead to a second form of serotype replacement (R. Dagan, Soroka University Medical Center (Beer-Sheva, Israel), personal communication, 1998). If there were biologic inhibitions between VTs and NVTs, such partial inhibition of VT pneumococci among vaccinees would cause a proportional increase in the population of NVTs among vaccinated hosts carrying both types. This form of replacement would be detected by our test, because it would increase the detection of NVT pneumococci among vaccinees, resulting in an elevation in the sample odds ratio. We recently obtained data from an animal model showing that carriage of one pneumococcal type can inhibit acquisition of a second type (11).
It has been noted elsewhere (12) that individually randomized trials like the one analyzed in this paper will tend to underestimate the effect of serotype replacement in comparison with that which would occur when a whole community is vaccinated. However, apart from one community-randomized clinical trial of a pneumococcal conjugate vaccine that was recently completed (27), such trials provide the only data available on serotype replacement prior to licensure and widespread use of such a vaccine.
Serotype replacement could be an important public health issue in the use of pneumococcal conjugate vaccines. Therefore, every effort should be made in clinical trials to improve the detection of multiple serotypes in the same sample in order to maximize the information on serotype replacement that can be extracted. The conclusion reached here—that serotype replacement may well have occurred in the South African trial but is not statistically demonstrable (as opposed to unmasking)—can be tested in future trials with more refined techniques for detecting multiple carriage (27). Evidence recently reported from a clinical trial of pneumococcal conjugate vaccine suggests that vaccinated children have higher rates of otitis media from nonvaccine serotypes than do unvaccinated children (28).
|
ACKNOWLEDGMENTS |
|---|
This work was supported by grant GM19182 from the National Institutes of Health.
The authors thank Drs. J. Robins and M. E. Halloran for their assistance with Bayesian methods and Drs. M. Kolczak, I. Longini, M. Pagano, K. Klugman, K. O'Brien, S. Gupta, R. Dagan, A. Gelman, and B. Greenwood for valuable discussions.
|
NOTES |
|---|
Correspondence to Dr. Marc Lipsitch, Department of Epidemiology, Harvard School of Public Health, 677 Huntington Avenue, Boston, MA 02115 (e-mail: mlipsitc{at}hsph.harvard.edu).
|
REFERENCES |
|---|
|
TOPABSTRACTINTRODUCTIONSTATISTICAL APPROACH TO...TESTING THE FIT OF...APPLICATION TO DATA FROM...SENSITIVITY ANALYSIS: PRIOR...SENSITIVITY ANALYSIS:...DISCUSSIONREFERENCES |
|---|
- Prevention of pneumococcal disease: recommendations of the Advisory Committee on Immunization Practices (ACIP). MMWR Morb Mortal Wkly Rep 1997;46(RR-8):1–24.
-
Austrian R. Some aspects of the pneumococcal carrier state. J Antimicrob Chemother 1986;18(suppl A):35–45.
[Abstract/Free Full Text] - Dagan R, Givon N, Yagupsky P, et al. Effect of a 9-valent pneumococcal vaccine conjugated to CRM197 (PncCRM9) on nasopharyngeal (NP) carriage of vaccine type and non-vaccine type S. pneumoniae (Pnc) strains among day-care-center (DCC) attendees. Abstracts of the 38th International Conference on Antimicrobial Agents and Chemotherapy, San Diego, California, September 24–27, 1998. Washington, DC: American Society for Microbiology, 1998:G52.
- Mbelle N, Huebner RE, Wasas AD, et al. Immunogenicity and impact on nasopharyngeal carriage of a nonvalent pneumococcal conjugate vaccine. J Infect Dis 1999;180:1171–6.[ISI][Medline]
- Dagan R, Melamed R, Muallem M, et al. Reduction of nasopharyngeal carriage of pneumococci during the second year of life by a heptavalent conjugate pneumococcal vaccine. J Infect Dis 1996;174:1271–8.[ISI][Medline]
- Obaro SK, Adegbola RA, Banya WA, et al. Carriage of pneumococci after pneumococcal vaccination. (Letter). Lancet 1996;348:271–2.[ISI][Medline]
- Kristinsson KG, Sigurdardottir ST, Gudnason T, et al. Effect of vaccination with octavalent protein conjugated vaccines on pneumococcal carriage in infants. Abstracts of the 37th International Conference on Antimicrobial Agents and Chemotherapy, Toronto, Ontario, Canada, September 28–October 1, 1997. Washington, DC: American Society for Microbiology, 1997:G-5.
- Black S, Shinefield H, Ray P, et al. Efficacy of heptavalent conjugate pneumococcal vaccine (Wyeth Lederle) in 37,000 infants and children: results of the Northern California Kaiser Permanente Efficacy Trial. Abstracts of the 38th International Conference on Antimicrobial Agents and Chemotherapy, San Diego, California, September 24–27, 1998. Washington, DC: American Society for Microbiology, 1998:LB-9.
- Barbour ML. Conjugate vaccines and the carriage of Haemophilus influenzae type b. Emerg Infect Dis 1996;2:176–82.[ISI][Medline]
- Takala AK, Eskola J, Leinonen M, et al. Reduction of oropharyngeal carriage of Haemophilus influenzae type b (Hib) in children immunized with an Hib conjugate vaccine. J Infect Dis 1991;164:982–6.[ISI][Medline]
- Lipsitch M, Dykes JK, Johnson SE, et al. Competition among Streptococcus pneumoniae for intranasal colonization in a mouse model. Vaccine 2000;18:2895–901.[ISI][Medline]
-
Lipsitch M. Vaccination against colonizing bacteria with multiple serotypes. Proc Natl Acad Sci U S A 1997;94:6571–6.
[Abstract/Free Full Text] - Johanson WG Jr, Blackstock R, Pierce AK, et al. The role of bacterial antagonism in pneumococcal colonization of the human pharynx. J Lab Clin Med 1970;75:946–52.[ISI][Medline]
-
Sanders CC, Sanders WE Jr, Harrowe DJ. Bacterial interference: effects of oral antibiotics on the normal throat flora and its ability to interfere with group A streptococci. Infect Immun 1976;13:808–12.
[Abstract/Free Full Text] - Hausdorff WP, Bryant J, Paradiso PR, et al. Which pneumococcal serogroups cause the most invasive disease: implications for conjugate vaccine formulation and use, part I. Clin Infect Dis 2000;30:100–21.[ISI][Medline]
- Hausdorff WP, Bryant J, Kloek C, et al. The contribution of specific pneumococcal serogroups to different disease manifestations: implications for conjugate vaccine formulation and use, part II. Clin Infect Dis 2000;30:122–40.[ISI][Medline]
-
Kelly T, Dillard JP, Yother J. Effect of genetic switching of capsular type on virulence of Streptococcus pneumoniae. Infect Immun 1994;62:1813–19.
[Abstract/Free Full Text] - Lipsitch M. Bacterial vaccines and serotype replacement: lessons from Haemophilus influenzae and prospects for Streptococcus pneumoniae. Emerg Infect Dis 1999;5:336–45.[ISI][Medline]
- Hodges RG, MacLeod CM, Bernhard WG. Epidemic pneumococcal pneumonia. III. Carrier studies. Am J Hyg 1946;44:207–30.
- Gratten M, Montgomery J, Gerega G, et al. Multiple colonization of the upper respiratory tract of Papua New Guinea children with Haemophilus influenzae and Streptococcus pneumoniae. Southeast Asian J Trop Med Public Health 1989;20:501–9.[Medline]
- Gelman A, Carlin JB, Stern HS, et al. Bayesian data analysis. New York, NY: Chapman and Hall, 1995.
- Gelman A, Meng X-L, Stern H. Posterior predictive assessment of model fitness via realized discrepancies. Stat Sinica 1996;6:733–807.
- Robins JM. Comment. In: Bernardo JM, Berger JO, Dawid AP, et al, eds. Bayesian statistics 6. New York, NY: Oxford University Press, 1998:67–70.
- Robins JM, van der Vaart A, Ventura V. Asymptotic distribution of p-values in composite null models. J Am Stat Assoc 2000;95:1143–56.
- Spiegelhalter DJ, Thomas A, Best NG, et al. BUGS: Bayesian inference using Gibbs sampling. Version 0.50. Cambridge, United Kingdom: MRC Biostatistics Unit, 1995.
- Gilks WR, Spiegelhalter DJ. A language and program for complex Bayesian modeling. Statistician 1994;43:169–78.[ISI]
- O'Brien KL, Bronsdon MA, Carlone GM, et al. Effect of a 7-valent pneumococcal conjugate vaccine on nasopharyngeal (NP) carriage among Navajo and White Mountain Apache (N/WMA) infants. (Abstract 1463). Presented at the annual meeting of the Society for Pediatric Research, Baltimore, Maryland, April 28–May 1, 2001.
-
Eskola J, Kilpi T, Palmu A, et al. Efficacy of a pneumococcal conjugate vaccine against acute otitis media. N Engl J Med 2001;344:403–9.
[Abstract/Free Full Text]
CiteULike 
Connotea 
Del.icio.us What's this?
This article has been cited by other articles:
|
|
 |
|
  L. E. Nigrovic, N. Kuppermann, and R. Malley Development and Validation of a Multivariable Predictive Model to Distinguish Bacterial From Aseptic Meningitis in Children in the Post-Haemophilus influenzae Era Pediatrics, October 1, 2002; 110(4): 712 - 719. [Abstract] [Full Text] [PDF]
|
|
| ||||||||||||||||||||||||||||||||||||||||||||||||||||||||||