Ecological inference for infectious disease data, with application to vaccination strategies

Inference under superspreading: Determinants of SARS-CoV-2 transmission in Germany

Superspreading, under-reporting, reporting delay, and confounding complicate statistical inference on determinants of disease transmission. A model that accounts for these factors within a Bayesian framework is estimated using German Covid-19 surveillance data. Compartments based on date of symptom onset, location, and age group allow to identify age-specific changes in transmission, adjusting for weather, reported prevalence, and testing and tracing. Several factors were associated with a reduction in transmission: public awareness rising, information on local prevalence, testing and tracing, high temperature, stay-at-home orders, and restaurant closures. However, substantial uncertainty remains for other interventions including school closures and mandatory face coverings. The challenge of disentangling the effects of different determinants is discussed and examined through a simulation study. On a broader perspective, the study illustrates the potential of surveillance data with demographic information and date of symptom onset to improve inference in the presence of under-reporting and reporting delay.

A zero-inflated endemic-epidemic model with an application to measles time series in Germany

Count data with an excess of zeros are often encountered when modeling infectious disease occurrence. The degree of zero inflation can vary over time due to nonepidemic periods as well as by age group or region. A well-established approach to analyze multivariate incidence time series is the endemic-epidemic modeling framework, also known as the HHH approach. However, it assumes Poisson or negative binomial distributions and is thus not tailored to surveillance data with excess zeros. Here, we propose a multivariate zero-inflated endemic-epidemic model with random effects that extends HHH. Parameters of both the zero-inflation probability and the HHH part of this mixture model can be estimated jointly and efficiently via (penalized) maximum likelihood inference using analytical derivatives. We found proper convergence and good coverage of confidence intervals in simulation studies. An application to measles counts in the 16 German states, 2005-2018, showed that zero inflation is more pronounced in the Eastern states characterized by a higher vaccination coverage. Probabilistic forecasts of measles cases improved when accounting for zero inflation. We anticipate zero-inflated HHH models to be a useful extension also for other applications and provide an implementation in an R package.

Association between pertussis vaccination coverage and other sociodemographic factors and pertussis incidence using surveillance data

Routine vaccination with pertussis vaccines has been successful in driving down pertussis mortality and morbidity globally. Despite high vaccination coverage, countries such as Australia, USA, and UK have experienced increase in pertussis activity over the last few decades. This may be due to local pockets of low vaccination coverage that result in persistence of pertussis in the population and occasionally lead to large outbreaks. The objective of this study was to characterize the association between pertussis vaccination coverage and sociodemographic factors and pertussis incidence at the school district level in King County, Washington, USA. We used monthly pertussis incidence data for all ages reported to the Public Health Seattle and King County between January 1, 2010 and December 31, 2017 to obtain school district level pertussis incidence. We obtained immunization data from the Washington State Immunization Information System to estimate school-district level vaccination coverage as proportion of 19-35 month old children fully vaccinated with ≥4 doses of the Diphtheria-Tetanus-acellular-Pertussis (DTaP) vaccine in a school district. We used two methods to quantify the effects of vaccination coverage on pertussis incidence: an ecological vaccine model and an endemic-epidemic model. Even though the effect of vaccination is modeled differently in the two approaches, both models can be used to estimate the association between vaccination coverage and pertussis incidence. Using the ecological vaccine model, we estimated the vaccine effectiveness of 4 doses of Diphtheria-Tetanus-acellular-Pertussis vaccine to be 83% (95% credible interval: 63%, 95%). In the endemic-epidemic model, under-vaccination was statistically significantly associated with epidemic risk of pertussis (adjusted Relative Risk, aRR: 2.76; 95% confidence interval: 1.44, 16.6). Household size and median income were statistically significantly associated with endemic pertussis risk. The endemic-epidemic model suffers from ecological bias, whereas the ecological vaccine model provides less biased and more interpretable estimates of epidemiological parameters, such as DTaP vaccine effectiveness, for each school district.

Assessing uncertainty of voter transitions estimated from aggregated data. Application to the 2017 French presidential election

Inferring electoral individual behaviour from aggregated data is a very active research area, with ramifications in sociology and political science. A new approach based on linear programming is proposed to estimate voter transitions among parties (or candidates) between two elections. Compared to other linear and quadratic programming models previously published, our approach presents two important innovations. Firstly, it explicitly deals with new entries and exits in the election census without assuming unrealistic hypotheses, enabling a reasonable estimation of vote behaviour of young electors voting for the first time. Secondly, by exploiting the information contained in the model residuals, we develop a procedure to assess the uncertainty in the estimates. This significantly distinguishes our model from other published mathematical programming methods. The method is illustrated estimating the vote transfer matrix between the first and second rounds of the 2017 French presidential election and measuring its level of uncertainty. Likewise, compared to the most current alternatives based on ecological regression, our approach is considerably simpler and faster, and has provided reasonable results in all the actual elections to which it has been applied. Interested scholars can easily use our procedure with the aid of the R-function provided in the Supplemental Material.