replication_code.pdf from 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

simulation_functions.R from 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

rr_bias_supplement.pdf from 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

Hidden Population Size Estimation From Respondent-Driven Sampling: A Network Approach

<p>Estimating the size of stigmatized, hidden, or hard-to-reach populations is a major problem in epidemiology, demography, and public health research. Capture–recapture and multiplier methods are standard tools for inference of hidden population sizes, but they require random sampling of target population members, which is rarely possible. Respondent-driven sampling (RDS) is a survey method for hidden populations that relies on social link tracing. The RDS recruitment process is designed to spread through the social network connecting members of the target population. In this article, we show how to use network data revealed by RDS to estimate hidden population size. The key insight is that the recruitment chain, timing of recruitments, and network degrees of recruited subjects provide information about the number of individuals belonging to the target population who are not yet in the sample. We use a computationally efficient Bayesian method to integrate over the missing edges in the subgraph of recruited individuals. We validate the method using simulated data and apply the technique to estimate the number of people who inject drugs in St. Petersburg, Russia. Supplementary materials for this article are available online.</p

rase_0.2-1.tar

Range ancestral state estimation (rase) R package used for the analyses. The most up to date version can be found on https://bitbucket.org/ignacioq/rase

Online Appendix about Monte Carlo Error

Mathematical derivations for the Monte Carlo sampling routine used and analyses of Monte Carlo error for approximating the likelihood of a domain

Using data from respondent-driven sampling studies to estimate the number of people who inject drugs: Application to the Kohtla-Järve region of Estonia

<div><p>Estimating the size of key risk populations is essential for determining the resources needed to implement effective public health intervention programs. Several standard methods for population size estimation exist, but the statistical and practical assumptions required for their use may not be met when applied to HIV risk groups. We apply three approaches to estimate the number of people who inject drugs (PWID) in the Kohtla-Järve region of Estonia using data from a respondent-driven sampling (RDS) study: the standard “multiplier” estimate gives 654 people (95% CI 509–804), the “successive sampling” method gives estimates between 600 and 2500 people, and a network-based estimate that uses the RDS recruitment chain gives between 700 and 2800 people. We critically assess the strengths and weaknesses of these statistical approaches for estimating the size of hidden or hard-to-reach HIV risk groups.</p></div

Comparison of results from the multiplier, network-based, and SS methods for population size estimation.

<p>The dashed horizontal line is the minimum number of population size (600); this is a lower bound for the PWID population size. For the multiplier method, results from the raw and weighted proportion of traits are presented. For the network-based method, results from <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0185711#pone.0185711.t002" target="_blank">Table 2</a> are shown, where the prior mean of the link probability and <i>α</i> vary. Black points and lines correspond to point estimates and posterior quantiles while grey lines represent the semi-parametric bounds. For the SS method, results from <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0185711#pone.0185711.t001" target="_blank">Table 1</a> are shown where prior selection and degree specification vary.</p

Estimates from the SS method of the number of people who inject drugs in the Kohtla-Järve region, Estonia.

<p>We obtain posterior estimates under two degree conditions (imputed and raw degree) and two priors for population size (beta and uniform). Imputed degree substitutes the raw degree with the fitted degree by Conway-Maxwell-Poisson distribution. The beta prior models the proportion of sampled subjects among target population. We set the maximum possible number of population size as 1500 and 2500 in uniform prior. Posterior mean, 5% and 95% quantiles are reported.</p

Descriptive summary of RDS data of PWID in Estonia in 2012.

<p>The top left panel shows the recruitment tree of 600 recruited subjects originating from six seeds. The top right panel shows the number of recruited subjects daily; gaps correspond to weekends. The bottom left panel illustrates the cumulative number of recruitment at each day of the study. The bottom right panel shows a histogram of subjects’ reported degrees.</p