Linking data and models: the importance of statistical analyses to inform models for the transmission dynamics of infections

A compelling demonstration of why traditional statistical regression models cannot be used to identify risk factors from case data on infectious diseases: a simulation study

BACKGROUND

Regression models are often used to explain the relative risk of infectious diseases among groups. For example, overrepresentation of immigrants among COVID-19 cases has been found in multiple countries. Several studies apply regression models to investigate whether different risk factors can explain this overrepresentation among immigrants without considering dependence between the cases.

METHODS

We study the appropriateness of traditional statistical regression methods for identifying risk factors for infectious diseases, by a simulation study. We model infectious disease spread by a simple, population-structured version of an SIR (susceptible-infected-recovered)-model, which is one of the most famous and well-established models for infectious disease spread. The population is thus divided into different sub-groups. We vary the contact structure between the sub-groups of the population. We analyse the relation between individual-level risk of infection and group-level relative risk. We analyse whether Poisson regression estimators can capture the true, underlying parameters of transmission. We assess both the quantitative and qualitative accuracy of the estimated regression coefficients.

RESULTS

We illustrate that there is no clear relationship between differences in individual characteristics and group-level overrepresentation -small differences on the individual level can result in arbitrarily high overrepresentation. We demonstrate that individual risk of infection cannot be properly defined without simultaneous specification of the infection level of the population. We argue that the estimated regression coefficients are not interpretable and show that it is not possible to adjust for other variables by standard regression methods. Finally, we illustrate that regression models can result in the significance of variables unrelated to infection risk in the constructed simulation example (e.g. ethnicity), particularly when a large proportion of contacts is within the same group.

CONCLUSIONS

Traditional regression models which are valid for modelling risk between groups for non-communicable diseases are not valid for infectious diseases. By applying such methods to identify risk factors of infectious diseases, one risks ending up with wrong conclusions. Output from such analyses should therefore be treated with great caution.

Immunological heterogeneity informs estimation of the durability of vaccine protection

Deciphering the properties of vaccines against an emerging pathogen is essential for optimizing immunization strategies. Early after vaccine roll-out, however, uncertainties about vaccine immunity raise the question of how much time is needed to estimate these properties, particularly the durability of vaccine protection. Here we designed a simulation study, based on a generic transmission model of vaccination, to simulate the impact of a breadth of vaccines with different mean (range: 10 months-2 years) and variability (coefficient of variation range: 50-100%) of the duration of protection. Focusing on the dynamics of SARS-CoV-2 in the year after start of mass immunization in Germany as a case study, we then assessed how confidently the duration of protection could be estimated under a range of epidemiological scenarios. We found that lower mean and higher heterogeneity facilitated estimation of the duration of vaccine protection. Across the vaccines tested, rapid waning and high heterogeneity permitted complete identification of the duration of protection; by contrast, slow waning and low heterogeneity allowed only estimation of the fraction of vaccinees with rapid loss of immunity. These findings suggest that limited epidemiological data can inform the duration of vaccine immunity. More generally, they highlight the need to carefully consider immunological heterogeneity when designing transmission models to evaluate vaccines.

Surveillance data confirm multiyear predictions of rotavirus dynamics in New York City

Prediction skill is a key test of models for epidemic dynamics. However, future validation of models against out-of-sample data is rare, partly because of a lack of timely surveillance data. We address this gap by analyzing the response of rotavirus dynamics to infant vaccination. Syndromic surveillance of emergency department visits for diarrhea in New York City reveals a marked decline in diarrheal incidence among infants and young children, in line with data on rotavirus-coded hospitalizations and laboratory-confirmed cases, and a shift from annual to biennial epidemics increasingly affecting older children and adults. A published mechanistic model qualitatively predicted these patterns more than 2 years in advance. Future efforts to increase vaccination coverage may disrupt these patterns and lead to further declines in the incidence of rotavirus-attributable gastroenteritis.

Risk ratios for contagious outcomes

Epidemiologists commonly use the risk ratio to summarize the relationship between a binary covariate and outcome, even when outcomes may be dependent. Investigations of transmissible diseases in clusters-households, villages or small groups-often report risk ratios. Epidemiologists have warned that risk ratios may be misleading when outcomes are contagious, but the nature of this error is poorly understood. In this study, we assess the meaning of the risk ratio when outcomes are contagious. We provide a mathematical definition of infectious disease transmission within clusters, based on the canonical stochastic susceptible-infective model. From this characterization, we define the individual-level ratio of instantaneous infection risks as the inferential target, and evaluate the properties of the risk ratio as an approximation of this quantity. We exhibit analytically and by simulation the circumstances under which the risk ratio implies an effect whose direction is opposite that of the true effect of the covariate. In particular, the risk ratio can be greater than one even when the covariate reduces both individual-level susceptibility to infection, and transmissibility once infected. We explain these findings in the epidemiologic language of confounding and Simpson's paradox, underscoring the pitfalls of failing to account for transmission when outcomes are contagious.

Estimating the per-exposure effect of infectious disease interventions

The average effect of an infectious disease intervention (eg, a vaccine) varies across populations with different degrees of exposure to the pathogen. As a result, many investigators favor a per-exposure effect measure that is considered independent of the population level of exposure and that can be used in simulations to estimate the total disease burden averted by an intervention across different populations. However, while per-exposure effects are frequently estimated, the quantity of interest is often poorly defined, and assumptions in its calculation are typically left implicit. In this article, we build upon work by Halloran and Struchiner (Epidemiology. 1995;6:142-151) to develop a formal definition of the per-exposure effect and discuss conditions necessary for its unbiased estimation. With greater care paid to the parameterization of transmission models, their results can be better understood and can thereby be of greater value to decision-makers.

Estimating a Markovian epidemic model using household serial interval data from the early phase of an epidemic

The clinical serial interval of an infectious disease is the time between date of symptom onset in an index case and the date of symptom onset in one of its secondary cases. It is a quantity which is commonly collected during a pandemic and is of fundamental importance to public health policy and mathematical modelling. In this paper we present a novel method for calculating the serial interval distribution for a Markovian model of household transmission dynamics. This allows the use of Bayesian MCMC methods, with explicit evaluation of the likelihood, to fit to serial interval data and infer parameters of the underlying model. We use simulated and real data to verify the accuracy of our methodology and illustrate the importance of accounting for household size. The output of our approach can be used to produce posterior distributions of population level epidemic characteristics.