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The authors have declared that no competing interests exist.

Analyzed the data: MN KA. Wrote the paper: MN KA. Developed the mathematical model: MN KA. Developed the computational approach: MN KA.

Pneumococcal conjugate vaccination has proved highly effective in eliminating vaccine-type pneumococcal carriage and disease. However, the potential adverse effects of serotype replacement remain a major concern when implementing routine childhood pneumococcal conjugate vaccination programmes. Applying a concise predictive model, we present a ready-to-use quantitative tool to investigate the implications of serotype replacement on the net effectiveness of vaccination against invasive pneumococcal disease (IPD) and to guide in the selection of optimal vaccine serotype compositions. We utilise pre-vaccination data on pneumococcal carriage and IPD and assume partial or complete elimination of vaccine-type carriage, its replacement by non-vaccine-type carriage, and stable case-to-carrier ratios (probability of IPD per carriage episode). The model predicts that the post-vaccination IPD incidences in Finland for currently available vaccine serotype compositions can eventually decrease among the target age group of children <5 years of age by 75%. However, due to replacement through herd effects, the decrease among the older population is predicted to be much less (20–40%). We introduce a sequential algorithm for the search of optimal serotype compositions and assess the robustness of inferences to uncertainties in data and assumptions about carriage and IPD. The optimal serotype composition depends on the age group of interest and some serotypes may be highly beneficial vaccine types in one age category (e.g. 6B in children), while being disadvantageous in another. The net effectiveness will be improved only if the added serotype has a higher case-to-carrier ratio than the average case-to-carrier ratio of the current non-vaccine types and the degree of improvement in effectiveness depends on the carriage incidence of the serotype. The serotype compositions of currently available pneumococcal vaccines are not optimal and the effectiveness of vaccination in the population at large could be improved by including new serotypes in the vaccine (e.g. 22 and 9N).

The bacterial pathogen Streptococcus pneumoniae (pneumococcus) is a major contributor to child mortality worldwide. Hence, effective pneumococcal vaccination programmes are globally among the most cost-effective public health interventions. Three different conjugate vaccine compositions, targeting 7, 10 or 13 pneumococcal serotypes, have been used in infant vaccination programmes. The use of these vaccines has both decreased the disease burden and changed the patterns of pneumococcal carriage in locations where they have been in use. However, due to serotype replacement, where the lost vaccine serotype carriage is replaced by carriage of the non-vaccine serotypes, the net effect of vaccination on the disease burden has generally been milder than expected. Here, we apply a concise model for serotype replacement and present a ready-to-use tool for the prediction of patterns in post-vaccination pneumococcal incidence of carriage and invasive disease. We introduce a sequential algorithm for the identification of the most optimal additional serotypes to current vaccine formulations and demonstrate how differences in the invasiveness across serotypes imply that the disease incidence may either decrease or increase after vaccination. The methods we outline have direct relevance in decision making while reviewing the performance of the current pneumococcal vaccination programmes.

The bacterial pathogen

As population-wide changes in serotype-specific carriage and disease will not fully emerge until several years after the onset of a vaccination programme

In this paper, we elaborate the above ideas to develop a concise model for serotype replacement and present a ready-to-use tool for the prediction of patterns in post-vaccination pneumococcal incidence of carriage and disease, based solely on pre-vaccination data on carriage and disease. For a given vaccine composition, corresponding either to a current or a prospective vaccine, we show in detail how the net effectiveness of vaccination under serotype replacement depends on the invasiveness of the vaccine types relative to that of the non-vaccine types. We demonstrate how differences in the invasiveness across serotypes imply that the disease incidence may either decrease or increase after vaccination and introduce a sequential algorithm for the identification of the most optimal additional serotypes to current vaccine formulations.

The data on the prevalence of pneumococcal carriage in Finland originated from Syrjänen et al.

Both carriage and IPD samples were utilised on the serogroup level, except for PCV7 serotypes, for which carriage data on the serotype level were available. IPD samples with serotype 6A were re-analysed to distinguish between serotypes 6A and 6C

Our analysis of serotype replacement is based solely on age-specific serotype distributions in carriage and disease in the pre-vaccination era. Here, serotype distribution refers to the stationary (steady-state) distribution, assumed to be applicable in the pre-vaccination era or under a PCV programme with the current vaccine composition.

We first consider a single age stratum within which the proportion of vaccine-type (VT) carriage does not have notable trends with age. The pre-vaccination incidence of carriage and disease with serotype _{i}_{i}_{i}_{i}_{i}_{i}

For the set of non-vaccine serotypes (NVT), the quantities _{NVT}_{,} _{NVT}_{NVT}

Our model of serotype replacement is built on two assumptions regarding the new steady-state after vaccination:

(A1) the relative serotype proportions among the non-vaccine types are not affected by vaccination (proportionality assumption);

(A2) the case-to-carrier ratios remain at their pre-vaccination levels.

It follows from assumptions (1) and (2) that the case-to-carrier ratios remain at their pre-vaccination values also for the aggregate VT and NVT sets.

Let

The incidence of pneumococcal carriage (x-axis) and case-to-carrier ratios (y-axis) for vaccine serotypes (VT) and non-vaccine serotypes (NVT) before (panel A) and after vaccination (panel B). The incidences of disease (_{NVT}_{VT}

The reduction in the disease incidence is thus

As _{VT}_{VT}_{VT}_{NVT}_{NVT}_{NVT}

According to these, the disease incidence can either decrease or increase after vaccination. In particular, whether or not vaccination will be beneficial depends on the magnitude of the case-to-carrier ratio of the vaccine types compared to that of the non-vaccine types. According to _{VT}_{NVT}_{VT}_{NVT}

Age is a confounder in any analysis of replacement, because of its association with both the distribution of VT/NVT and the risk of disease (i.e. case-to-carrier ratios). Therefore, the analysis needs to be adjusted for age by appropriate stratification by age categories. If not adjusted, predictions of serotype replacement may be biased due to collapsed heterogeneous sub-strata.

Rewriting _{VT} = d_{i}_{NVT} = D_{i}_{VT}_{i}_{NVT}_{i}

The optimal serotype is the one that maximises expression (3). Clearly, the best single vaccine type is neither necessarily the one with the highest pre-vaccination incidence of IPD nor the one with the highest case-to-carrier ratio. In fact, the optimal single serotype may not correspond to the highest value of either of these two quantities. Importantly, the optimal type may be different for different age groups. Furthermore, if _{i}_{i}

Note that the optimal serotype composition is independent of the assumed level of VT elimination. If the elimination of VT carriage is expected to be incomplete (

A program code implementing the tools proposed above, including instructions on how to use the code, is provided in

As small changes in the VT/NVT carriage proportions may result in notable shifts in projected IPD incidences, uncertainties in carriage data should be accounted for using sensitivity analysis. When assessing the net effectiveness of vaccination with a given vaccine composition, the effect of a change in the VT/NVT carriage proportions is obtained directly from (2). To investigate the robustness of the optimal serotype composition, we calculated the order of inclusion of individual serotypes in the optimal vaccine composition for a large number of sets of carriage proportions, which were generated from an uncertainty distribution. For more details, see

We investigated the similarity of pre- and post-vaccination serotype proportions for the non-vaccine types, based on published data from three different locations

We applied the replacement model to the pre-vaccination IPD incidence and carriage prevalence data to predict the post-vaccination IPD incidence in Finland.

The effects of complete replacement in carriage for 2 vaccine formulations (PCV10 and PCV13) for under 5 year old children (panels A, C and E) and the rest of the population (panels B, D and F). The x-axes correspond to average annual incidences of pneumococcal carriage per 100,000 persons. The incidences are scaled from the prevalence data by dividing by the mean duration of carriage (1.5 months for under 5 olds and 1 month for the rest). The width of each rectangle corresponds to the average annual serotype-specific carriage incidence and the height (y-axes) to the case-to-carrier ratio. In the “no vaccination” panels (A and B) the area of each rectangle is the observed annual IPD incidence in Finland (average number of cases from 2000–2009) and in the other panels the area corresponds to the projected IPD incidence. The analysis pertains to serogroup level, except for the PCV7 serotypes. The observed (panels A and B) and projected (other panels) incidences of IPD are indicated in red under the serotype labels. The projected total IPD incidences are indicated under the PCV labels. In panels A and B, the PCV10 types are listed first and the 3 additional PCV13 types are indicated by a horizontal yellow stripe near the bottom of the bars in panels A–D. For clarity, some of the bars with high case-to-carrier ratios are truncated. These are indicated by horizontal white stripes near the top of the bars. Category “other” includes the following 19 serotypes or serogroups with small IPD incidences: 13, 17, 18BF, 19BCD, 2, 21, 24, 25, 27, 28, 29, 31, 34, 37, 39, 40, 41, 46, 9A.

According to these predictions, PCV10 and PCV13 are highly effective in reducing the IPD incidence among the under 5 year olds. For example, use of PCV10 is expected to eventually reduce the IPD incidence in this age group by 40% and the use of PCV13 by 75%, i.e. from 99 to 59 and 25 annual cases, respectively, in a population of approximately 300,000 children. No clear candidates emerge as additional vaccine types to supplement PCV13. However, for the older population, the predicted reductions are clearly smaller (20% for PCV10 and 36% for PCV13) and neither of the two serotype compositions is optimal as inclusion of some of the commonly carried serotypes appears not to be beneficial. In particular, serotypes 19F and 6B have low case-to-carrier ratios as compared to the non-vaccine types and are thus good candidates for the set of replacing non-vaccine types in this age group.

The proportion of serotype 6C among 6A/C isolates from IPD was 0% in children and 24% in the 5+ age group. Because 6C has relatively low case-to-carrier ratios in both age categories, it is an ideal non-vaccine type. If the proportion 6C carriers among 6A/C carriers would be smaller than the assumed 33%, the predicted IPD incidence for any of the vaccine compositions including 6A, but not 6C, would be higher. The incidence would be 5–10% higher if no 6C carriage is assumed (

Each curve (drawn in grey colour) corresponds to all possible combinations of the pre-vaccination proportions of VT carriage (x-axis) and VT disease (y-axis) that lead to the indicated level of reduction in IPD incidence (95, 75, 50, 25, 0 and −25%). The results are shown for complete replacement in carriage. The locations of 12 combinations regarding the VT carriage and VT disease proportions are superimposed. These combinations pertain to 4 different vaccine formulations (PCV7, PCV10, PCV13, Opt14p) and two age groups (<5 or 5+ year olds); for the older age group, two alternative carriage proportions are presented. In each case, the Finnish IPD data were used. The 14-valent vaccine composition Opt14p refers to a hypothetical vaccine discussed in

Contour plots of the effect of a single vaccine type as a function of serotype-specific IPD incidence (horizontal axis) and case-to-carrier ratio (CCR, vertical axis) under the complete replacement model. Panel (A) corresponds to children under 5 years of age and panel (B) to the rest of the population. The predicted decrease in annual IPD incidence from the IPD incidence under no vaccination (99 and 658 for <5 and 5+ year olds, among populations of size 300,000 and 5,000,000, respectively) is indicated by colour codes. Interpretation of the colour codes in terms of decrease in IPD incidence, separately for each panel, is shown below the panels. The horizontal white dashed line corresponds to no effect. The axes are in log scale. Serotypes outside of the range of the plot due to a high case-to-carrier ratio or a low IPD incidence are indicated by arrows.

Applying criterion (3) sequentially provides an optimal order of introducing serotypes to a vaccine. Panel B in

(

Irrespective of the age class, serotypes 14, 4, 9V and 7 are beneficial. Apart from these serotypes, however, the optimal serotypes depend on the age class of interest. Serotype 6B is beneficial only among children <5 years and serotype 3 only among the 5+ year olds. Among the <5 year olds, inclusion of the 7 most optimal serotypes results in a reduction of 60% in IPD. Similarly 13 most optimal types lead to a reduction of 80%. For the 5+ year old population the corresponding reductions are smaller (45% and 60%).

In addition, a composition of a 14-valent vaccine was identified so that the resulting reduction in IPD is no worse among under 5 five years olds than with the current PCV13 and at the same time substantial in the general population. This vaccine composition results in a 75% reduction among under 5 year olds and 40% among the rest of the population (

We derived a simple expression for the expected net effectiveness of childhood vaccination against invasive pneumococcal disease (IPD) under serotype replacement. This expression depends only on the pre-vaccination incidences of vaccine-type (VT) and non-vaccine-type (NVT) carriage and disease. Our analysis explicates that vaccination will result in a notable reduction in the IPD incidence only if the average case-to-carrier ratio of the vaccine types clearly exceeds that of the non-vaccine types. In Finland, this would be expected to occur among children with any of the currently available PCV formulations. However, the same might not hold to the same extent in the general population not targeted by the vaccination, and our analysis indicates there are vaccine compositions with higher expected net effectiveness. These compositions are projected to be no worse than the current ones among children while clearly outperforming them in older age categories.

We formulated the expected net effectiveness of vaccination in terms of serotype-specific incidences of carriage and disease. Equivalently, one could use either of the two quantities together with the case-to-carrier ratios (i.e. disease incidences divided by carriage incidences) as any two of the three quantities determine the third one. Importantly, while beneficial vaccine serotypes can be identified using carriage and disease data, they are not necessarily those with the highest carriage incidence, disease incidence or case-to-carrier ratios. The net effectiveness will be improved only if the average VT case-to-carrier ratio is larger than the average NVT case-to-carrier ratio.

Furthermore, the above rule is not transparent, unless some serotype had the largest incidence of either carriage or disease and at the same the largest case-to-carrier ratio. In addition, a trivial rule applies in two special situations. First, if all serotypes have identical case-to-carrier ratios, as may be a good first approximation in case of pneumococcal otitis media, there is essentially no change in disease incidence. Second, if there is no replacement in carriage, the expected change in disease only depends on the pre-vaccination disease incidence.

Stratification of carriage and disease data by age is essential in the analysis of replacement. For example, an individual serotype included in a vaccine may decrease IPD in one age category while increasing it in another (cf. serotype 6B among <5 and 5+ year olds in Finland;

In practice, evaluation of optimal PCV vaccination for the whole population should be based on a cost-effectiveness analysis that takes into account health benefits and costs in the vaccine target population as well as in the older cohorts. Of note, all of the serotype compositions we consider refer to an infant vaccination programme assuming an adequate level of coverage of vaccination to induce a substantial herd effect in the whole population.

The algebraic simplicity of our model is a direct consequence of the two key assumptions that neither the serotype proportions in carriage nor the invasiveness (case-to-carrier ratios) of the non-vaccine types are altered by vaccination. Examples of post-vaccination scenarios not covered by our model are a disproportionally large increase in carriage of a previously rare invasive type or an increase in invasiveness of a commonly carried type. Either of these scenarios would increase the IPD in excess of our model predictions. However, there is some empirical evidence in support of the key assumptions. In particular, our analysis confirmed the similarity in pre- and post-vaccination serotype proportions using four different datasets (

The pre- and post-vaccination incidences of carriage and disease involved in our method correspond to the respective stationary (steady-state) serotype distributions. These distributions can be characterised by the average annual serotype-specific incidences over a period where they do not manifest any systematic trends. The post-vaccination stationary distribution is typically achieved some years after the onset of a new infant vaccination programme

There are further assumptions that may pose limitations on the applicability of the proposed method. An identical degree of elimination and replacement in all age classes, i.e. the same values of

We assumed the long-term impact of vaccination on VT carriage is the same for all serotypes, i.e. complete or partial elimination. In addition, NVT carriage was assumed to be affected by vaccination only through replacement and vaccine-induced cross-protection was not included (for 6A, however, see

Poor availability or reliability of serotype-specific carriage data across all age classes may limit the applicability of the model. In particular, the predictions are typically sensitive to assumptions regarding the VT carriage proportion. However, carriage data on the adult population are often sparse. Overestimating the VT proportion among adults may lead to underestimation of the effectiveness of vaccination. We demonstrated this by using two alternative VT carriage proportions (53% and 62% for PCV10) in the non-target population (individuals 5+ years of age) in the context of existing PCVs (

Several authors have previously discussed the importance of the invasiveness and the carriage incidences of the vaccine types relative to the non-vaccine types in assessing the net effectiveness of a vaccine

Based on whole-genomic sequencing data, Croucher et al.

We have proposed tools for the quantification of the relative importance of individual pneumococcal serotypes in conjugate vaccine compositions under serotype replacement. Our examples used IPD data from Finland and carriage data from Finland and the UK. Contingent on the availability of data, our tools are easily applicable in other settings as well. However, in contrast to the relative succinctness of the underlying model, the data requirements for a successful application of the proposed tools are not straightforward to satisfy and underline the importance of the availability of age- and serotype-specific data on both pneumococcal carriage and disease.

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The rationale applied in

We thank Lotta Siira for re-analysing the earlier 6A (i.e. 6A/C) IPD samples and providing us the related data, which were utilised in the revised version of the manuscript, distinguishing between 6A and 6C.

Parts of this study were presented as a poster at the 29th Annual Meeting of the European Society for Paediatric Infectious Diseases (ESPID), the Hague, June 2011, and as a poster at the 8th International Symposium on Pneumococci & Pneumococcal Diseases (ISPPD), Iguaçu Falls, Brazil, March 2012.