Understanding differences in predictions of HPV vaccine effectiveness: A comparative model-based analysis
Introduction
In the past few years, there has been a steep increase in the number of modeling studies in the field of HPV due to the recent availability of prophylactic vaccines and new screening technologies [1], [2], [3], [4], [5], [6], [7], [8], [9], [10], [11], [12], [13], [14], [15], [16], [17], [18], [19], [20], [21], [22]. These studies differ substantially in the type of model used and the model structure chosen to represent the natural history of HPV. These differences are partly due to the complex natural history of HPV (it encompasses numerous stages of disease that depend on HPV type, screening and treatment) and the scarcity of detailed data on sexual behavior, and age and type-specific HPV transmission and progression rates in the scientific literature. The availability of many different models for comparison is very valuable. When results are similar, it provides evidence of the validity and robustness of conclusions. However, when model results diverge, it is important to identify which model structures and assumptions explain these differences in order to avoid confusion about how to interpret and use results to make critical decisions. Published literature reviews systematically comparing models have helped to explain some of the differences in methodology and results [23], [24], [25], [26]. However, due to the complexity of HPV models, and limitations in the amount of information available in published papers, these reviews have been unable to reconcile the effect of methods on results or explain differences in conclusions.
Below we describe key structural assumptions commonly made when modeling the effectiveness of HPV vaccines:
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Susceptible-infectious-susceptible (SIS) vs. susceptible-infectious-recovered (SIR) models: Currently, considerable uncertainty remains regarding the level of natural immunity following a natural HPV infection [27], [28], [29], [30]. In particular, it is unknown what proportion of infected individuals develop type-specific natural immunity and how long this protection lasts. Reflecting this lack of scientific understanding, there is great variability in how previous studies have modeled HPV natural immunity, from strict SIS (no immunity) [10], [17], [19], [20], [31], [32], [33] to strict SIR (100% are immune following infection) [1], [3], [4], [7], [8], [15], [22], [34], [35] structures. The choice between SIS and SIR models may be important when assessing vaccine impact since these assumptions can produce very different dynamics [36].
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Static vs. dynamic models: It is well known that vaccination against infectious diseases not only reduces the incidence of disease in those immunized but also indirectly protects non-vaccinated susceptibles against infection (produces herd immunity) [37]. However, many economic studies still ignore this externality and its consequences [38]. Models used to assess the impact of vaccination can be grossly divided into two main categories: (1) dynamic and (2) static (e.g., decision analysis, cohort models). The major difference between these types of models is that dynamic models capture herd-immunity effects, whereas static models do not. Nevertheless, when these limitations are fully acknowledged, static models can still be useful to provide initial conservative estimates of impact when herd immunity is unlikely to produce negative effects (i.e. increasing the mean age at infection when adverse outcomes are more frequent). The first modeling studies of HPV vaccination programs were based on such models [2], [3], [4], [9], [10], [15], [17], [19], [20], [22] and provided timely and useful information on the effectiveness and cost-effectiveness of vaccinating young girls. However, in general, dynamic models are deemed preferable to address a wider range of questions [1], [5], [7], [8], [13], [18], [21]. Comparing static and dynamic model results (given identical natural histories) is important to assess the extent of the herd immunity effects in the context of HPV vaccination.
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Instantaneous partnership vs. duration of partnership models: Most dynamic models of HPV infection have assumed that partnerships are instantaneous (no duration) and the transmission probability is per partnership. In contrast, pair formation models account for the duration of partnerships by explicitly modeling the dynamic process of partnership formation and separation [39]. In such models, transmission within a partnership depends on the duration of the partnership, frequency of sexual intercourse and the per sex act probability of transmission. Pair formation and duration of partnerships have been shown to influence the spread of other sexually transmitted diseases [40], [41], [42]. It is therefore important to examine how the two formalisms impact on the predictions of HPV vaccine effectiveness.
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Grouping of HPV types: Around 40 HPV genotypes are known to infect the human anogenital tract [43]. For simplicity, most published models have grouped HPV genotypes into different categories (e.g., HPV-16/18 and HPV-6/11) [7], [10], [44]. However, the grouping of HPV types requires modelers to make many assumptions which influence parameter estimates (e.g., whether or not infection with one type in the group confers complete cross immunity to the others, and how group-specific natural history of infection and disease, vaccine efficacy and cross-protection should be modeled). At present, the extent to which grouping HPV types influences model predictions of HPV vaccine effectiveness remains unclear.
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Waning of vaccine protection: Previous HPV modeling studies have shown the importance of the duration of vaccine protection on effectiveness and cost-effectiveness predictions [7], [13], [22], [45]. However, none of these studies have looked at the impact of different waning functions of vaccine induced immunity on vaccine effectiveness. Most HPV models assume that vaccinees loose their protection at a constant rate, which produces an exponential decline in the proportion of protected individuals. In the context of HPV, the main caveat with this assumption is that the initial decline in the proportion of individuals adequately protected is too steep to correspond with current clinical trial data, which show that vaccine efficacy remains stable for at least 8.5 years [46]. Thus, it is important to revise the constant waning rate assumption and explore the impact of other waning functions on HPV vaccine effectiveness predictions.
The objective of this study is to examine the impact of the following structural model assumptions on the population-level effectiveness of HPV vaccination: (1) natural immunity (SIR vs. SIS models), (2) herd immunity (static vs. dynamic models), (3) duration of partnership (vs. instantaneous partnership), (4) grouping HPV types (vs. individual types), and (5) functions of waning vaccine protection (different distributions of vaccine duration and decreasing vaccine efficacy).
Section snippets
Stochastic individual-based model
A stochastic individual-based dynamic model of sequential partnership formation and dissolution was developed to represent HPV transmission, infection and vaccination in the heterosexual population of Canada (see Table 1 for a list of all model parameters). In the model, each individual (Θi) is explicitly represented with the following set of sexual behavior and biological characteristics: (1) gender (g = 1 for females and 2 for males); (2) age (a); (3) level of sexual activity (from low sexual
Model fit and validation
Table 2 shows fit success percentages for the Base model and the alternative model structures. For the Base model, of the 50,000 different combinations of parameters sampled from the prior distributions, 44 parameter sets produced results within the pre specified targets. The Base model predictions based on the 44 posterior parameter sets produced good fit to the age-specific sexual behavior and epidemiologic data listed in Table 2. In addition, Base model predictions for outcomes not used in
Discussion
The aim of this article was to quantify and illustrate the impact of structural choices on model predictions of population-level HPV vaccine effectiveness. This is important because the various HPV vaccine modeling studies, designed to help public health decision making, have led to conflicting results. Under our baseline vaccine assumptions, results clearly show that HPV vaccine effectiveness predictions are lower when assuming high probability of natural immunity (e.g., SIR), excluding herd
Acknowledgements
We thank Professor M. Stanley and Dr. F. Coutlée for comments on how HPV natural history should be modeled, and Dr. E. Franco for providing us with type-specific prevalence stratified by age and sexual activity from CCAST, BCCR and the McGill/Concordia cohorts. We would also like to thank Dr. M. Drolet, V. Joumier and JF. Laprise for comments on the manuscript. Finally, we thank the Imperial College High Performance Computing Service (HPC) for providing us with the computing power necessary to
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