Data
Acute Flaccid Paralysis (AFP) database
The global polio surveillance network detects AFP cases of any cause [10]. Surveillance officers collect stool samples from each case, which are tested in order to determine whether paralysis was caused by PV. Surveillance officers also collect basic demographic information on each AFP case, including age, sex, date of onset, and number of polio vaccinations received. Importantly, this information is collected before the cause of paralysis is known. The vast majority of AFP cases are classified as NP-AFP and serve as the basis of our analysis. In this analysis, we used the Nigerian AFP database and the LQAS database maintained by the Nigerian country office of the World Health Organization (WHO).
Lot quality assurance sampling (LQAS)
Following a vaccination campaign in which vaccine recipients had their fingers marked by vaccinators, independent surveyors visited six randomly chosen villages within a district and checked for the presence of finger-marking on 10 children [4]. Only a subset of districts participating in a vaccination campaign were visited by LQAS surveyors. In the course of a year, most districts were visited by surveyors at least one time. We included LQAS surveys from 2009 through 2015 in our analysis.
Supplementary immunization activities (SIA) database
The dose-histories of NP-AFP cases are referenced against the SIA database maintained by the Nigerian WHO. This records basic information for each polio vaccination campaign, including the date and location of the campaign, which vaccines were used, and which age groups were targeted. Case date of onset, age, and district were used herein to determine campaigns that could have contributed to reported doses.
Vaccine efficacy
There are five different formulations of OPV: trivalent OPV (tOPV), bivalent OPV (bOPV), and monovalent OPV (mOPV) for each serotype of PV (1, 2, or 3). tOPV contains antigen for types 1, 2, and 3 PV, while bOPV contains antigen for only types 1 and 3 PV. Each vaccine has a different associated efficacy against each serotype, which may vary with socio-economic context [7, 8, 11]. In our analysis, we used vaccine efficacy estimated by comparing dose-histories of polio and NP-AFP cases in northern Nigeria [8].
Institutional ethics approval was not sought for AFP surveillance and LQAS monitoring data as they are retrospective and anonymized.
Overview of statistical analysis
Figure 1 provides a visual overview of the statistical procedure. The first step in the process was estimating campaign effectiveness through NP-AFP data by comparing the reported doses – observed with error – with campaigns experienced (Fig. 1a). This effectiveness and an assumption of random, independent participation induces a distribution of doses for the population of interest as well as subgroups of interest. Generally, the more SIAs experienced, the more doses received (Fig. 1b); in particular, a SIA changes the dose distribution in the population over the short period in which it was executed. This change in the dose distribution is accompanied by a change in the immune fraction by serotype, related to the efficacy of the vaccine used and the campaign effectiveness (Fig. 1c).
Bayesian hierarchical modeling of campaign effectiveness
We considered model campaign effectiveness at the district level, called local government areas (LGA) in Nigeria. LGAs are an administrative level lower than province or states in Nigeria and are particularly meaningful units of analysis as many polio eradication operations (including vaccination and monitoring) are organized by LGAs.
We specified a Bayesian hierarchical model of campaign effectiveness to account for temporal patterns and between-LGA differences, with the aim of producing smoothed estimates by LGA and year. Let p
ijta
be the campaign effectiveness for state i, LGA j, year t, and age stratum a. We modeled yearly LGA-level campaign effectiveness by age p
ijta
with
$$ \log \mathrm{it}\left({p}_{ijta}\right)={\beta}_{ia}+{b}_{ij}+{u}_{it}+{v}_{ijt}, $$
where β
ia
is an age effect, b
ij
~ N(0, σ
i
2) is a random effect for LGA, and [u
i1, …, u
iT
]T ~ N
T
(0, Σ(σ
iu
2)) and [v
ij1, …, v
ijT
]T ~ N
T
(0, Σ(σ
iv
2)) are first order normal random walk priors for state and LGA temporal variation, respectively [12]. The index i appears in the subscript for parameters as we executed separate models for each state i. Priors for age effects and hyperpriors for variance parameters governing the random effects are diffuse; details of Bayesian specification may be found in Additional file 1.
We used a negative binomial distribution to model reported doses per child, where the expected value (mean) is the sum of campaign effectiveness across campaigns experienced by the child. The negative binomial distribution allows the variance to be flexibly fit in the estimation procedure, which may accommodate imprecise recall and heterogeneous vaccination coverage (further discussion of model details can be found in Additional file 1).
We assessed three models of different complexity. The full model was as specified above; other models considered were nested within this full model, removing age and then the district random walks. The Deviance Information Criterion was used to pick the model that best balanced fit and complexity [13].
Campaign-derived immunity
Polio has three serotypes, and high population immunity to each type is key to achieving elimination. Vaccines have different efficacies for different types [8]. Variable campaign effectiveness, the SIA database, and vaccine efficacies can be used to model the time course of expected immunity for an individual and the population of interest.
Let ϕ
k
be the efficacy – the probability of seroconversion – of the vaccine used in the kth campaign experienced by a child of age a by time t, and p
k
be the associated campaign effectiveness. With independent participation in campaigns and independent seroconversion, the probability of vaccine-based seroconversion for the child given all the campaigns experienced is
$$ I\left(t,a\right)=1-{\displaystyle \prod_k\left(1-{p}_k{\phi}_k\right)}. $$
Population immunity can then be calculated by integrating over an age distribution F: I(t) = ∫I(t, a)dF(a). Computational methods may be found in Additional file 1.
Implementation
All analyses were performed in R [14]. We used MC-STAN [15, 16] to obtain samples from the posterior distribution of campaign effectiveness p
ijta
for each campaign in each LGA, following the model described above. Using these posterior samples, we estimated effectiveness through the posterior mean and summarized uncertainty with 95 % credible intervals. We approximated the posterior distribution of functions of LGA-level campaign effectiveness, such as state-wide campaign effectiveness and immunity, by applying these functions to the posterior samples. As with campaign effectiveness, we summarized these distributions through their posterior means and 95 % credible intervals.
