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Illustration of average controlled potential infection outcomes under different values of the infection time wj and joint treatment x, under time-invariant baseline hazards α(t) = 0.2 and γ(t − wj) = 10 and coefficients eβ⁰ = eβ¹ = 0.3 and eσ = 0.5. Contrasts of potential outcomes in (a), (b) and (c) show the controlled contagion effect, the infectiousness effect, and the susceptibility effect evaluated at different times, shown together in (d).
Source publication
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 partne...
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Introduction
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Citations
... Evaluation of spillover among first-degree contacts in networks may be more relevant for HIV-related interventions than other types of spillover set (i.e., groups of individuals for which spillover is possible) definitions, such as those based on the distance in the network from the person receiving the intervention, because HIV transmission usually occurs through direct contact, sexual or parenteral [39]. Spillover with infectious disease outcomes can be further disentangled into contagion (i.e., when one participant's outcome affects another participant's outcome), peer effects (i.e., when one participant's outcome affects their contact's future outcomes), and infectiousness (i.e., when an intervention renders a participant less likely to transmit the disease to another participant) [49][50][51]. In this tutorial, we focus on the spillover of individual interventions delivered in networks and network-based interventions more broadly without consideration of the underlying disease mechanisms. ...
Human Immunodeficiency Virus (HIV) interventions among people who use drugs (PWUD) often have spillover, also known as interference or dissemination, which occurs when one participant’s exposure affects another participant’s outcome. PWUD are often members of networks defined by social, sexual, and drug-use partnerships and their receipt of interventions can affect other members in their network. For example, HIV interventions with possible spillover include educational training about HIV risk reduction, pre-exposure prophylaxis, or treatment as prevention. In turn, intervention effects frequently depend on the network structure, and intervention coverage levels and spillover can occur even if not measured in a study, possibly resulting in an underestimation of intervention effects. Recent methodological approaches were developed to assess spillover in the context of network-based studies. This tutorial provides an overview of different study designs for network-based studies and related methodological approaches for assessing spillover in each design. We also provide an overview of other important methodological issues in network studies, including causal influence in networks and missing data. Finally, we highlight applications of different designs and methods from studies of PWUD and conclude with an illustrative example from the Transmission Reduction Intervention Project (TRIP) in Athens, Greece.
... But even when treatment is randomized, exposure to infection can be systematically different among treated and untreated individuals during the study. Researchers have warned that this differential exposure can confound estimates of the "direct effect" of the intervention (Halloran and Struchiner 1995;Halloran et al. 2010;Kenah 2014;Morozova et al. 2018;Cai et al. 2021), but the relationship between the randomization design and the disease transmission process remains obscure (Struchiner and Halloran 2007;van Boven et al. 2013;O'Hagan et al. 2014). Do contrasts of infection outcomes between treated and untreated subjects, as proposed by Hudgens and Halloran (2008) as the "direct effect", recover the susceptibility effect of the intervention when the population is clustered, treatment is randomized, and outcomes are contagious? ...
... The results outlined here may apply in cases where the true susceptibility effect β is nonzero: when the average infection outcome Y i j (t, x i ) is a continuous function of β, there may exist an interval around β = 0 in which the direct effect is biased across the null hypothesis of no susceptibility effect under some designs. Indeed, prior work demonstrated analytically that in a simple 2-person cluster case under block randomization the direct effect can have a sign opposite that of a non-null susceptibility effect (Morozova et al. 2018;Cai et al. 2021). ...
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.
... Different methods suitable for inference on infectious diseases have been proposed [45][46][47][48]. The problem with many of these methods is that they are hard to use and may require detailed data about the contact pattern of the population. ...
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.
... These methods do not require complete knowledge of the causal structure between outcomes, but they also ignore individual characteristics and the dynamics of of infectious disease transmission. Cai et al. [22] study causal identification in the symmetric partnership setting, where infection can be transmitted in both directions. Their continuous-time strategy clarifies the causal structure of contagion and vaccine effects in groups of two, when both individuals have covariates, treatments, and can transmit infections to each other, but its usefulness is limited to the partnership scenario. ...
... Following the strategy developed for two-person partnerships by Cai et al. [22], we decompose the potential infection time T i (x, h (i) ) of a given individual i into a series of latent infection waiting times following the infections of individuals other than i. To illustrate, let (t 1 (i) , t 2 (i) , . . . ...
... A simplified version of Theorem 1, derived under a two-person partnership model, is given in Theorem 1 of Cai et al. [22], which we restate here. ...
Causal identification of treatment effects for infectious disease outcomes in interconnected populations is challenging because infection outcomes may be transmissible to others, and treatment given to one individual may affect others' outcomes. Contagion, or transmissibility of outcomes, complicates standard conceptions of treatment interference in which an intervention delivered to one individual can affect outcomes of others. Several statistical frameworks have been proposed to measure causal treatment effects in this setting, including structural transmission models, mediation-based partnership models, and randomized trial designs. However, existing estimands for infectious disease intervention effects are of limited conceptual usefulness: Some are parameters in a structural model whose causal interpretation is unclear, others are causal effects defined only in a restricted two-person setting, and still others are nonparametric estimands that arise naturally in the context of a randomized trial but may not measure any biologically meaningful effect. In this paper, we describe a unifying formalism for defining nonparametric structural causal estimands and an identification strategy for learning about infectious disease intervention effects in clusters of interacting individuals when infection times are observed. The estimands generalize existing quantities and provide a framework for causal identification in randomized and observational studies, including situations where only binary infection outcomes are observed. A semiparametric class of pairwise Cox-type transmission hazard models is used to facilitate statistical inference in finite samples. A comprehensive simulation study compares existing and proposed estimands under a variety of randomized and observational vaccine trial designs.
There are two prominent paradigms for the modelling of networks: in the first, referred to as the mechanistic approach, one specifies a set of domain-specific mechanistic rules that are used to grow or evolve the network over time; in the second, referred to as the probabilistic approach, one describes a model that specifies the likelihood of observing a given network. Mechanistic models (models developed based on the mechanistic approach) are appealing because they capture scientific processes that are believed to be responsible for network generation; however, they do not easily lend themselves to the use of inferential techniques when compared with probabilistic models. We introduce a general framework for converting a mechanistic network model (MNM) to a probabilistic network model (PNM). The proposed framework makes it possible to identify the essential network properties and their joint probability distribution for some MNMs; doing so makes it possible to address questions such as whether two different mechanistic models generate networks with identical distributions of properties, or whether a network property, such as clustering, is over- or under-represented in the networks generated by the model of interest compared with a reference model. The proposed framework is intended to bridge some of the gap that currently exists between the formulation and representation of mechanistic and PNMs. We also highlight limitations of PNMs that need to be addressed in order to close this gap.
Despite the growing interest in causal and statistical inference for settings with data dependence, few methods currently exist to account for missing data in dependent data settings; most classical missing data methods in statistics and causal inference treat data units as independent and identically distributed (i.i.d.). We develop a graphical modeling based framework for causal inference in the presence of entangled missingness, defined as missingness with data dependence. We distinguish three different types of entanglements that can occur, supported by real-world examples. We give sound and complete identification results for all three settings. We show that existing missing data models may be extended to cover entanglements arising from (1) target law dependence and (2) missingness process dependence, while those arising from (3) missingness interference require a novel approach. We demonstrate the use of our entangled missingness framework on synthetic data. Finally, we discuss how, subject to a certain reinterpretation of the variables in the model, our model for missingness interference extends missing data methods to novel missing data patterns in i.i.d. settings.
