Risk ratios for contagious outcomes

Coughs, colds and "freshers' flu" survey in the University of Cambridge, 2007-2008

Universities provide many opportunities for the spread of infectious respiratory illnesses. Students are brought together into close proximity from all across the world and interact with one another in their accommodation, through lectures and small group teaching and in social settings. The COVID-19 global pandemic has highlighted the need for sufficient data to help determine which of these factors are important for infectious disease transmission in universities and hence control university morbidity as well as community spillover. We describe the data from a previously unpublished self-reported university survey of coughs, colds and influenza-like symptoms collected in Cambridge, UK, during winter 2007-2008. The online survey collected information on symptoms and socio-demographic, academic and lifestyle factors. There were 1076 responses, 97% from University of Cambridge students (5.7% of the total university student population), 3% from staff and <1% from other participants, reporting onset of symptoms between September 2007 and March 2008. Undergraduates are seen to report symptoms earlier in the term than postgraduates; differences in reported date of symptoms are also seen between subjects and accommodation types, although these descriptive results could be confounded by survey biases. Despite the historical and exploratory nature of the study, this is one of few recent detailed datasets of influenza-like infection in a university context and is especially valuable to share now to improve understanding of potential transmission dynamics in universities during the current COVID-19 pandemic.

Randomization for the susceptibility effect of an infectious disease intervention

Randomized trials of infectious disease interventions, such as vaccines, often focus on groups of connected or potentially interacting individuals. When the pathogen of interest is transmissible between study subjects, interference may occur: individual infection outcomes may depend on treatments received by others. Epidemiologists have defined the primary parameter of interest-called the "susceptibility effect"-as a contrast in infection risk under treatment versus no treatment, while holding exposure to infectiousness constant. A related quantity-the "direct effect"-is defined as an unconditional contrast between the infection risk under treatment versus no treatment. The purpose of this paper is to show that under a widely recommended randomization design, the direct effect may fail to recover the sign of the true susceptibility effect of the intervention in a randomized trial when outcomes are contagious. The analytical approach uses structural features of infectious disease transmission to define the susceptibility effect. A new probabilistic coupling argument reveals stochastic dominance relations between potential infection outcomes under different treatment allocations. The results suggest that estimating the direct effect under randomization may provide misleading conclusions about the effect of an intervention-such as a vaccine-when outcomes are contagious. Investigators who estimate the direct effect may wrongly conclude an intervention that protects treated individuals from infection is harmful, or that a harmful treatment is beneficial.

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.

The impact of temperature on the transmissibility potential and virulence of COVID-19 in Tokyo, Japan

Assessing the impact of temperature on COVID-19 epidemiology is critical for implementing non-pharmaceutical interventions. However, few studies have accounted for the nature of contagious diseases, i.e., their dependent happenings. We aimed to quantify the impact of temperature on the transmissibility and virulence of COVID-19 in Tokyo, Japan, employing two epidemiological measurements of transmissibility and severity: the effective reproduction number (\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$R_{t}$$\end{document}Rt) and case fatality risk (CFR). We estimated the \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$R_{t}$$\end{document}Rt and time-delay adjusted CFR and to subsequently assess the nonlinear and delayed effect of temperature on \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$R_{t}$$\end{document}Rt and time-delay adjusted CFR. For \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$R_{t}$$\end{document}Rt at low temperatures, the cumulative relative risk (RR) at the first temperature percentile (3.3 °C) was 1.3 (95% confidence interval (CI): 1.1–1.7). As for the virulence to humans, moderate cold temperatures were associated with higher CFR, and CFR also increased as the temperature rose. The cumulative RR at the 10th and 99th percentiles of temperature (5.8 °C and 30.8 °C) for CFR were 3.5 (95% CI: 1.3–10.0) and 6.4 (95% CI: 4.1–10.1). Our results suggest the importance to take precautions to avoid infection in both cold and warm seasons to avoid severe cases of COVID-19. The results and our proposed approach will also help in assessing the possible seasonal course of COVID-19 in the future.

Assortativity and Bias in Epidemiologic Studies of Contagious Outcomes: A Simulated Example in the Context of Vaccination

Assortativity is the tendency of individuals connected in a network to share traits and behaviors. Through simulations, we demonstrated the potential for bias resulting from assortativity by vaccination, where vaccinated individuals are more likely to be connected with other vaccinated individuals. We simulated outbreaks of a hypothetical infectious disease and vaccine in a randomly generated network and a contact network of university students living on campus. We varied protection of the vaccine to the individual, transmission potential of vaccinated-but-infected individuals, and assortativity by vaccination. We compared a traditional approach, which ignores the structural features of a network, with simple approaches which summarized information from the network. The traditional approach resulted in biased estimates of the unit-treatment effect when there was assortativity by vaccination. Several different approaches that included summary measures from the network reduced bias and improved confidence interval coverage. Through simulations, we showed the pitfalls of ignoring assortativity by vaccination. While our example is described in terms of vaccines, our results apply more widely to exposures for contagious outcomes. Assortativity should be considered when evaluating exposures for contagious outcomes.

Identifiability and Estimation Under the Test-negative Design With Population Controls With the Goal of Identifying Risk and Preventive Factors for SARS-CoV-2 Infection

Owing to the rapidly evolving coronavirus disease 2019 (COVID-19) pandemic caused by the severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) virus, quick public health investigations of the relationships between behaviors and infection risk are essential. Recently the test-negative design (TND) was proposed to recruit and survey participants who are symptomatic and being tested for SARS-CoV-2 infection with the goal of evaluating associations between the survey responses (including behaviors and environment) and testing positive on the test. It was also proposed to recruit additional controls who are part of the general population as a baseline comparison group to evaluate risk factors specific to SARS-CoV-2 infection. In this study, we consider an alternative design where we recruit among all individuals, symptomatic and asymptomatic, being tested for the virus in addition to population controls. We define a regression parameter related to a prospective risk factor analysis and investigate its identifiability under the two study designs. We review the difference between the prospective risk factor parameter and the parameter targeted in the typical TND where only symptomatic and tested people are recruited. Using missing data directed acyclic graphs, we provide conditions and required data collection under which identifiability of the prospective risk factor parameter is possible and compare the benefits and limitations of the alternative study designs and target parameters. We propose a novel inverse probability weighting estimator and demonstrate the performance of this estimator through simulation study.

Transmission Modeling with Regression Adjustment for Analyzing Household-based Studies of Infectious Disease: Application to Tuberculosis

BACKGROUND

Household contacts of people infected with a transmissible disease may be at risk due to this proximate exposure, or from other unobserved sources. Understanding variation in infection risk is essential for targeting interventions.

METHODS

We develop an analytical approach to estimate household and exogenous forces of infection, while accounting for individual-level characteristics that affect susceptibility to disease and transmissibility. We apply this approach to a cohort study conducted in Lima, Peru, of 18,544 subjects in 4,500 households with at least one active tuberculosis (TB) case and compare the results to those obtained by Poisson and logistic regression.

RESULTS

HIV-coinfected (susceptibility hazard ratio [SHR] = 3.80, 1.56-9.29), child (SHR = 1.72, 1.32-2.23), and teenage (SHR = 2.00, 1.49-2.68) household contacts of TB cases experience a higher hazard of TB than do adult contacts. Isoniazid preventive therapy (SHR = 0.30, 0.21-0.42) and Bacillus Calmette-Guérin (BCG) vaccination (SHR = 0.66, 0.51-0.86) reduce the risk of disease among household contacts. TB cases without microbiological confirmation exert a smaller hazard of TB among their close contacts compared with smear- or culture-positive cases (excess hazard ratio = 0.88, 0.82-0.93 for HIV- cases and 0.82, 0.57-0.94 for HIV+ cases). The extra household force of infection results in 0.01 (95% confidence interval [CI] = 0.004, 0.028) TB cases per susceptible household contact per year and the rate of transmission between a microbiologically confirmed TB case and susceptible household contact at 0.08 (95% CI = 0.045, 0.129) TB cases per pair per year.

CONCLUSIONS

Accounting for exposure to infected household contacts permits estimation of risk factors for disease susceptibility and transmissibility and comparison of within-household and exogenous forces of infection.

Estimating and interpreting secondary attack risk: Binomial considered biased

The household secondary attack risk (SAR), often called the secondary attack rate or secondary infection risk, is the probability of infectious contact from an infectious household member A to a given household member B, where we define infectious contact to be a contact sufficient to infect B if he or she is susceptible. Estimation of the SAR is an important part of understanding and controlling the transmission of infectious diseases. In practice, it is most often estimated using binomial models such as logistic regression, which implicitly attribute all secondary infections in a household to the primary case. In the simplest case, the number of secondary infections in a household with m susceptibles and a single primary case is modeled as a binomial(m, p) random variable where p is the SAR. Although it has long been understood that transmission within households is not binomial, it is thought that multiple generations of transmission can be neglected safely when p is small. We use probability generating functions and simulations to show that this is a mistake. The proportion of susceptible household members infected can be substantially larger than the SAR even when p is small. As a result, binomial estimates of the SAR are biased upward and their confidence intervals have poor coverage probabilities even if adjusted for clustering. Accurate point and interval estimates of the SAR can be obtained using longitudinal chain binomial models or pairwise survival analysis, which account for multiple generations of transmission within households, the ongoing risk of infection from outside the household, and incomplete follow-up. We illustrate the practical implications of these results in an analysis of household surveillance data collected by the Los Angeles County Department of Public Health during the 2009 influenza A (H1N1) pandemic.

The household secondary attack risk (SAR), often called the secondary attack rate or secondary infection risk, is the probability of infectious contact from an infectious household member A to a given household member B, where we define infectious contact to be a contact sufficient to infect B if he or she is susceptible. The most common statistical models used to estimate the SAR are binomial models such as logistic regression, which implicitly assume that all secondary infections in a household are infected by the primary case. Here, we use analytical calculations and simulations to show that estimation of the SAR must account for multiple generations of transmission within households. As an example, we show that binomial models and statistical models that account for multiple generations of within-household transmission reach different conclusions about the household SAR for 2009 influenza A (H1N1) in Los Angeles County, with the latter models fitting the data better. In an epidemic, accurate estimation of the SAR allows rigorous evaluation of the effectiveness of public health interventions such as social distancing, prophylaxis or treatment, and vaccination.

Identification of causal intervention effects under contagion

Defining and identifying causal intervention effects for transmissible infectious disease outcomes is challenging because a treatment - such as a vaccine - given to one individual may affect the infection outcomes of others. Epidemiologists have proposed causal estimands to quantify effects of interventions under contagion using a two-person partnership model. These simple conceptual models have helped researchers develop causal estimands relevant to clinical evaluation of vaccine effects. However, many of these partnership models are formulated under structural assumptions that preclude realistic infectious disease transmission dynamics, limiting their conceptual usefulness in defining and identifying causal treatment effects in empirical intervention trials. In this paper, we propose causal intervention effects in two-person partnerships under arbitrary infectious disease transmission dynamics, and give nonparametric identification results showing how effects can be estimated in empirical trials using time-to-infection or binary outcome data. The key insight is that contagion is a causal phenomenon that induces conditional independencies on infection outcomes that can be exploited for the identification of clinically meaningful causal estimands. These new estimands are compared to existing quantities, and results are illustrated using a realistic simulation of an HIV vaccine trial.

The relative fitness of drug-resistant Mycobacterium tuberculosis: a modelling study of household transmission in Peru

The relative fitness of drug-resistant versus susceptible bacteria in an environment dictates resistance prevalence. Estimates for the relative fitness of resistant Mycobacterium tuberculosis (Mtb) strains are highly heterogeneous and mostly derived from in vitro experiments. Measuring fitness in the field allows us to determine how the environment influences the spread of resistance. We designed a household structured, stochastic mathematical model to estimate the fitness costs associated with multidrug resistance (MDR) carriage in Mtb in Lima, Peru during 2010–2013. By fitting the model to data from a large prospective cohort study of TB disease in household contacts, we estimated the fitness, relative to susceptible strains with a fitness of 1, of MDR-Mtb to be 0.32 (95% credible interval: 0.15–0.62) or 0.38 (0.24–0.61), if only transmission or progression to disease, respectively, was affected. The relative fitness of MDR-Mtb increased to 0.56 (0.42–0.72) when the fitness cost influenced both transmission and progression to disease equally. We found the average relative fitness of MDR-Mtb circulating within households in Lima, Peru during 2010–2013 to be significantly lower than concurrent susceptible Mtb. If these fitness levels do not change, then existing TB control programmes are likely to keep MDR-TB prevalence at current levels in Lima, Peru.

Heterogeneous susceptibility to rotavirus infection and gastroenteritis in two birth cohort studies: Parameter estimation and epidemiological implications

Cohort studies, randomized trials, and post-licensure studies have reported reduced natural and vaccine-derived protection against rotavirus gastroenteritis (RVGE) in low- and middle-income countries. While susceptibility of children to rotavirus is known to vary within and between settings, implications for estimation of immune protection are not well understood. We sought to re-estimate naturally-acquired protection against rotavirus infection and RVGE, and to understand how differences in susceptibility among children impacted estimates. We re-analyzed data from studies conducted in Mexico City, Mexico and Vellore, India. Cumulatively, 573 rotavirus-unvaccinated children experienced 1418 rotavirus infections and 371 episodes of RVGE over 17,636 child-months. We developed a model that characterized susceptibility to rotavirus infection and RVGE among children, accounting for aspects of the natural history of rotavirus and differences in transmission rates between settings. We tested whether model-generated susceptibility measurements were associated with demographic and anthropometric factors, and with the severity of RVGE symptoms. We identified greater variation in susceptibility to rotavirus infection and RVGE in Vellore than in Mexico City. In both cohorts, susceptibility to rotavirus infection and RVGE were associated with male sex, lower birth weight, lower maternal education, and having fewer siblings; within Vellore, susceptibility was also associated with lower socioeconomic status. Children who were more susceptible to rotavirus also experienced higher rates of rotavirus-negative diarrhea, and higher risk of moderate-to-severe symptoms when experiencing RVGE. Simulations suggested that discrepant estimates of naturally-acquired immunity against RVGE can be attributed, in part, to between-setting differences in susceptibility of children, but result primarily from the interaction of transmission rates with age-dependent risk for infections to cause RVGE. We found that more children in Vellore than in Mexico City belong to a high-risk group for rotavirus infection and RVGE, and demonstrate that unmeasured individual- and age-dependent susceptibility may influence estimates of naturally-acquired immune protection against RVGE.

Differences in susceptibility can help explain why some individuals, and not others, acquire infection and exhibit symptoms when exposed to infectious disease agents. However, it is difficult to distinguish between differences in susceptibility versus exposure in epidemiological studies. We developed a modeling approach to distinguish transmission intensity and susceptibility in data from cohort studies of rotavirus infection among children in Mexico City, Mexico, and Vellore, India, and evaluated how these factors may have contributed to differences in estimates of naturally-acquired immune protection between the studies. Given the same exposure, more children were at high risk of acquiring rotavirus infection, and of experiencing gastroenteritis when infected, in Vellore than in Mexico City. The probability of belonging to this high-risk stratum was associated with well-known individual factors such as lower socioeconomic status, lower birth weight, and incidence of diarrhea due to other causes. We also found the risk for rotavirus infections to cause symptoms declined with age, independent of acquired immunity. These findings can, in part, account for estimates of lower protective efficacy of acquired immunity against rotavirus gastroenteritis in high-incidence settings, mirroring estimates of reduced effectiveness of live oral rotavirus vaccines in low- and middle-income countries.

A new approach to hierarchical data analysis: Targeted maximum likelihood estimation for the causal effect of a cluster-level exposure

We often seek to estimate the impact of an exposure naturally occurring or randomly assigned at the cluster-level. For example, the literature on neighborhood determinants of health continues to grow. Likewise, community randomized trials are applied to learn about real-world implementation, sustainability, and population effects of interventions with proven individual-level efficacy. In these settings, individual-level outcomes are correlated due to shared cluster-level factors, including the exposure, as well as social or biological interactions between individuals. To flexibly and efficiently estimate the effect of a cluster-level exposure, we present two targeted maximum likelihood estimators (TMLEs). The first TMLE is developed under a non-parametric causal model, which allows for arbitrary interactions between individuals within a cluster. These interactions include direct transmission of the outcome (i.e. contagion) and influence of one individual's covariates on another's outcome (i.e. covariate interference). The second TMLE is developed under a causal sub-model assuming the cluster-level and individual-specific covariates are sufficient to control for confounding. Simulations compare the alternative estimators and illustrate the potential gains from pairing individual-level risk factors and outcomes during estimation, while avoiding unwarranted assumptions. Our results suggest that estimation under the sub-model can result in bias and misleading inference in an observational setting. Incorporating working assumptions during estimation is more robust than assuming they hold in the underlying causal model. We illustrate our approach with an application to HIV prevention and treatment.