As with other instrumental variable (IV) analyses, Mendelian randomization (MR) studies rest on strong assumptions. These assumptions are not routinely systematically evaluated in MR applications, although such evaluation could add to the credibility of MR analyses. In this article, the authors present several methods that are useful for evaluating the validity of an MR study. They apply these methods to a recent MR study that used fat mass and obesity-associated (FTO) genotype as an IV to estimate the effect of obesity on mental disorder. These approaches to evaluating assumptions for valid IV analyses are not fail-safe, in that there are situations where the approaches might either fail to identify a biased IV or inappropriately suggest that a valid IV is biased. Therefore, the authors describe the assumptions upon which the IV assessments rely. The methods they describe are relevant to any IV analysis, regardless of whether it is based on a genetic IV or other possible sources of exogenous variation. Methods that assess the IV assumptions are generally not conclusive, but routinely applying such methods is nonetheless likely to improve the scientific contributions of MR studies.

We describe a novel approach to nonparametric point and interval estimation of a treatment effect in the presence of many continuous confounders. We show the problem can be reduced to that of point and interval estimation of the expected conditional covariance between treatment and response given the confounders. Our estimators are higher order U-statistics. The approach applies equally to the regular case where the expected conditional covariance is root-n estimable and to the irregular case where slower non-parametric rates prevail.

In the analysis of bivariate correlated failure time data, it is important to measure the strength of association among the correlated failure times. One commonly used measure is the cross ratio. Motivated by Cox’s partial likelihood idea, we propose a novel parametric cross ratio estimator that is a flexible continuous function of both components of the bivariate survival times. We show that the proposed estimator is consistent and asymptotically normal. Its finite sample performance is examined using simulation studies, and it is applied to the Australian twin data.

We consider the doubly robust estimation of the parameters in a semiparametric conditional odds ratio model. Our estimators are consistent and asymptotically normal in a union model that assumes either of two variation independent baseline functions is correctly modelled but not necessarily both. Furthermore, when either outcome has finite support, our estimators are semiparametric efficient in the union model at the intersection submodel where both nuisance functions models are correct. For general outcomes, we obtain doubly robust estimators that are nearly efficient at the intersection submodel. Our methods are easy to implement as they do not require the use of the alternating conditional expectations algorithm of Chen (2007).

The intention-to-treat (ITT) analysis provides a valid test of the null hypothesis and naturally results in both absolute and relative measures of risk. However, this analytic approach may miss the occurrence of serious adverse effects that would have been detected under full adherence to the assigned treatment. Inverse probability weighting of marginal structural models has been used to adjust for nonadherence, but most studies have provided only relative measures of risk. In this study, we used inverse probability weighting to estimate both absolute and relative measures of risk of invasive breast cancer under full adherence to the assigned treatment in the Women’s Health Initiative estrogen-plus-progestin trial. In contrast to an ITT hazard ratio (HR) of 1.25 (95% confidence interval [CI] = 1.01 to 1.54), the HR for 8-year continuous estrogen-plus-progestin use versus no use was 1.68 (1.24 to 2.28). The estimated risk difference (cases/100 women) at year 8 was 0.83 (−0.03 to 1.69) in the ITT analysis, compared with 1.44 (0.52 to 2.37) in the adherence-adjusted analysis. Results were robust across various dose-response models. We also compared the dynamic treatment regime “take hormone therapy until certain adverse events become apparent, then stop taking hormone therapy” with no use (HR= 1.64; 95% CI = 1.24 to 2.18). The methods described here are also applicable to observational studies with time-varying treatments.

Containing an emerging influenza H5N1 pandemic in its earliest stages may be feasible, but containing multiple introductions of a pandemic-capable strain would be more difficult. Mills and colleagues argue that multiple introductions are likely, especially if risk of a pandemic is high.

A primary focus of an increasing number of scientific studies is to determine whether two exposures interact in the effect that they produce on an outcome of interest. Interaction is commonly assessed by fitting regression models in which the linear predictor includes the product between those exposures. When the main interest lies in the interaction, this approach is not entirely satisfactory because it is prone to (possibly severe) bias when the main exposure effects or the association between outcome and extraneous factors are misspecified. In this article, we therefore consider conditional mean models with identity or log link which postulate the statistical interaction in terms of a finite-dimensional parameter, but which are otherwise unspecified. We show that estimation of the interaction parameter is often not feasible in this model because it would require nonparametric estimation of auxiliary conditional expectations given high-dimensional variables. We thus consider ‘multiply robust estimation’ under a union model that assumes at least one of several working submodels holds. Our approach is novel in that it makes use of information on the joint distribution of the exposures conditional on the extraneous factors in making inferences about the interaction parameter of interest. In the special case of a randomized trial or a family-based genetic study in which the joint exposure distribution is known by design or by Mendelian inheritance, the resulting multiply robust procedure leads to asymptotically distribution-free tests of the null hypothesis of no interaction on an additive scale. We illustrate the methods via simulation and the analysis of a randomized follow-up study.

Molly Franke, Megan Murray, and colleagues report that early cART reduces mortality among HIV-infected adults with tuberculosis and improves retention in care, regardless of CD4 count.

Background

Randomized clinical trials examining the optimal time to initiate combination antiretroviral therapy (cART) in HIV-infected adults with sputum smear-positive tuberculosis (TB) disease have demonstrated improved survival among those who initiate cART earlier during TB treatment. Since these trials incorporated rigorous diagnostic criteria, it is unclear whether these results are generalizable to the vast majority of HIV-infected patients with TB, for whom standard diagnostic tools are unavailable. We aimed to examine whether early cART initiation improved survival among HIV-infected adults who were diagnosed with TB in a clinical setting.

Methods and Findings

We retrospectively reviewed charts for 308 HIV-infected adults in Rwanda with a CD4 count≤350 cells/µl and a TB diagnosis. We estimated the effect of cART on survival using marginal structural models and simulated 2-y survival curves for the cohort under different cART strategies:start cART 15, 30, 60, or 180 d after TB treatment or never start cART. We conducted secondary analyses with composite endpoints of (1) death, default, or lost to follow-up and (2) death, hospitalization, or serious opportunistic infection. Early cART initiation led to a survival benefit that was most marked for individuals with low CD4 counts. For individuals with CD4 counts of 50 or 100 cells/µl, cART initiation at day 15 yielded 2-y survival probabilities of 0.82 (95% confidence interval: [0.76, 0.89]) and 0.86 (95% confidence interval: [0.80, 0.92]), respectively. These were significantly higher than the probabilities computed under later start times. Results were similar for the endpoint of death, hospitalization, or serious opportunistic infection. cART initiation at day 15 versus later times was protective against death, default, or loss to follow-up, regardless of CD4 count. As with any observational study, the validity of these findings assumes that biases from residual confounding by unmeasured factors and from model misspecification are small.

Conclusions

Early cART reduced mortality among individuals with low CD4 counts and improved retention in care, regardless of CD4 count.

Please see later in the article for the Editors' Summary

Editors' Summary

Background

HIV infection has exacerbated the global tuberculosis (TB) epidemic, especially in sub-Saharan Africa, in which in some countries, 70% of people with TB are currently also HIV positive—a condition commonly described as HIV/TB co-infection. The management of patients with HIV/TB co-infection is a major public health concern.

There is relatively little good evidence on the best time to initiate combination antiretroviral therapy (cART) in adults with HIV/TB co-infection. Clinicians sometimes defer cART in individuals initiating TB treatment because of concerns about complications (such as immune reconstitution inflammatory syndrome) and the risk of reduced adherence if patients have to remember to take two sets of pills. However, starting cART later in those patients who are infected with both HIV and TB can result in potentially avoidable deaths during therapy.

Why Was This Study Done?

Several randomized control trials (RCTs) have been carried out, and the results of three of these studies suggest that, among individuals with severe immune suppression, early initiation of cART (two to four weeks after the start of TB treatment) leads to better survival than later ART initiation (two to three months after the start of TB treatment). These results were reported in abstract form, but the full papers have not yet been published. One problem with RCTs is that they are carried out under controlled conditions that might not represent well the conditions in varied settings around the world. Therefore, observational studies that examine how effective a treatment is in routine clinical conditions can provide information that complements that obtained during clinical trials. In this study, the researchers aimed to confirm the results from RCTs among a cohort of adult patients with HIV/TB co-infection in Rwanda, diagnosed under routine program conditions and using routinely collected clinical data. The researchers also wanted to investigate whether early cART initiation reduced the risk of other adverse outcomes, including treatment default and loss to follow-up.

What Did the Researchers Do and Find?

The researchers retrospectively reviewed the charts and other program records of 308 patients with HIV, who had CD4 counts≤350 cells/µl, were aged 15 years or more, had never previously taken cART, and received their first TB treatment at one of five cART sites (two urban, three rural) in Rwanda between January 2004 and February 2007. Using this method, the researchers collected baseline demographic and clinical variables and relevant clinical follow-up data. They then used this data to estimate the effect of cART on survival by using sophisticated statistical models that calculated the effects of initiating cART at 15, 30, 60, or 180 d after the start of TB treatment or not at all.

The researchers then conducted a further analysis to assess combined outcomes of (1) death, default, lost to follow-up, and (2) death, hospitalization due to any cause, or occurrence of severe opportunistic infections, such as Kaposi's sarcoma. The researchers used the resulting multivariable model to estimate survival probabilities for each individual, based on his/her baseline characteristics.

The researchers found that when they set their model to first CD4 cell counts of 50 and 100 cells/µl, and starting cART at day 15, mean survival probabilities at two years were 0.82 and 0.86, respectively, statistically significantly higher than the survival probabilities calculated for each of the other treatment strategies, where cART was started later. They observed a similar pattern for the combined outcome of death, hospitalization, or serious opportunistic infection In addition, two-year outcomes for death or lost to follow-up were also improved with early cART, regardless of CD4 count at treatment initiation.

What Do These Findings Mean?

These findings show that in a real world program setting, starting cART 15 d after the start of TB treatment is more beneficial (measured by differences in survival probabilities) among patients with HIV/TB co-infection who have CD4 cell counts≤100 cells/µl than starting later. Early cART initiation may also increase retention in care for all individuals with CD4 cell counts≤350 cells/µl.

As the outcomes of this modeling study are based on data from a retrospective observational study, the biases associated with use of these data must be carefully addressed. However, the results support the recommendation of cART initiation after 15 d of TB treatment for patients with CD4 cell counts≤100 cells/µl and can be used as an advocacy base for TB treatment to be used as an opportunity to refer and retain HIV-infected individuals in care, regardless of CD4 cell count.

Additional Information

Please access these Web sites via the online version of this summary at http://dx.doi.org/10.1371/journal.pmed.1001029.

Information is available on HIV/TB co-infection from the World Health Organization, the US Centers for Disease Control and Prevention, and the International AIDS Society

Dynamic treatment regimes are the type of regime most commonly used in clinical practice. For example, physicians may initiate combined antiretroviral therapy the first time an individual’s recorded CD4 cell count drops below either 500 cells/mm3 or 350 cells/mm3. This paper describes an approach for using observational data to emulate randomized clinical trials that compare dynamic regimes of the form “initiate treatment within a certain time period of some time-varying covariate first crossing a particular threshold.” We applied this method to data from the French Hospital database on HIV (FHDH-ANRS CO4), an observational study of HIV-infected patients, in order to compare dynamic regimes of the form “initiate treatment within m months after the recorded CD4 cell count first drops below x cells/mm3” where x takes values from 200 to 500 in increments of 10 and m takes values 0 or 3. We describe the method in the context of this example and discuss some complications that arise in emulating a randomized experiment using observational data.

In this companion article to “Dynamic Regime Marginal Structural Mean Models for Estimation of Optimal Dynamic Treatment Regimes, Part I: Main Content” [Orellana, Rotnitzky and Robins (2010), IJB, Vol. 6, Iss. 2, Art. 7] we present (i) proofs of the claims in that paper, (ii) a proposal for the computation of a confidence set for the optimal index when this lies in a finite set, and (iii) an example to aid the interpretation of the positivity assumption.

Sufficient cause interactions concern cases in which there is a particular causal mechanism for some outcome that requires the presence of 2 or more specific causes to operate. Empirical conditions have been derived to test for sufficient cause interactions. However, when regression outcome models are used to control for confounding variables in tests for sufficient cause interactions, the outcome models impose restrictions on the relation between the confounding variables and certain unidentified background causes within the sufficient cause framework; often, these assumptions are implausible. By using marginal structural models, rather than outcome regression models, to test for sufficient cause interactions, modeling assumptions are instead made on the relation between the causes of interest and the confounding variables; these assumptions will often be more plausible. The use of marginal structural models also allows for testing for sufficient cause interactions in the presence of time-dependent confounding. Such time-dependent confounding may arise in cases in which one factor of interest affects both the second factor of interest and the outcome. It is furthermore shown that marginal structural models can be used not only to test for sufficient cause interactions but also to give lower bounds on the prevalence of such sufficient cause interactions.

Estimating the population risk of disease under hypothetical interventions—such as the population risk of coronary heart disease (CHD) were everyone to quit smoking and start exercising or to start exercising if diagnosed with diabetes—may not be possible using standard analytic techniques. The parametric g-formula, which appropriately adjusts for time-varying confounders affected by prior exposures, is especially well suited to estimating effects when the intervention involves multiple factors (joint interventions) or when the intervention involves decisions that depend on the value of evolving time-dependent factors (dynamic interventions). We describe the parametric g-formula, and use it to estimate the effect of various hypothetical lifestyle interventions on the risk of CHD using data from the Nurses’ Health Study. Over the period 1982–2002, the 20-year risk of CHD in this cohort was 3.50%. Under a joint intervention of no smoking, increased exercise, improved diet, moderate alcohol consumption and reduced body mass index, the estimated risk was 1.89% (95% confidence interval: 1.46–2.41). We discuss whether the assumptions required for the validity of the parametric g-formula hold in the Nurses’ Health Study data. This work represents the first large-scale application of the parametric g-formula in an epidemiologic cohort study.

Severe acute respiratory syndrome (SARS) is a recently described illness of humans that has spread widely over the past 6 months. With the use of detailed epidemiologic data from Singapore and epidemic curves from other settings, we estimated the reproductive number for SARS in the absence of interventions and in the presence of control efforts. We estimate that a single infectious case of SARS will infect about three secondary cases in a population that has not yet instituted control measures. Public-health efforts to reduce transmission are expected to have a substantial impact on reducing the size of the epidemic.

Summary

In randomized studies with missing outcomes, non-identifiable assumptions are required to hold for valid data analysis. As a result, statisticians have been advocating the use of sensitivity analysis to evaluate the effect of varying asssumptions on study conclusions. While this approach may be useful in assessing the sensitivity of treatment comparisons to missing data assumptions, it may be dissatisfying to some researchers/decision makers because a single summary is not provided. In this paper, we present a fully Bayesian methodology that allows the investigator to draw a ‘single’ conclusion by formally incorporating prior beliefs about non-identifiable, yet interpretable, selection bias parameters. Our Bayesian model provides robustness to prior specification of the distributional form of the continuous outcomes.

In 1986 the International Journal of Epidemiology published "Identifiability, Exchangeability and Epidemiological Confounding". We review the article from the perspective of a quarter century after it was first drafted and relate it to subsequent developments on confounding, ignorability, and collapsibility.

In ideal randomised experiments, association is causation: association measures can be interpreted as effect measures because randomisation ensures that the exposed and the unexposed are exchangeable. On the other hand, in observational studies, association is not generally causation: association measures cannot be interpreted as effect measures because the exposed and the unexposed are not generally exchangeable. However, observational research is often the only alternative for causal inference. This article reviews a condition that permits the estimation of causal effects from observational data, and two methods—standardisation and inverse probability weighting—to estimate population causal effects under that condition. For simplicity, the main description is restricted to dichotomous variables and assumes that no random error attributable to sampling variability exists. The appendix provides a generalisation of inverse probability weighting.

The generation interval is the time between the infection time of an infected person and the infection time of his or her infector. Probability density functions for generation intervals have been an important input for epidemic models and epidemic data analysis. In this paper, we specify a general stochastic SIR epidemic model and prove that the mean generation interval decreases when susceptible persons are at risk of infectious contact from multiple sources. The intuition behind this is that when a susceptible person has multiple potential infectors, there is a “race” to infect him or her in which only the first infectious contact leads to infection. In an epidemic, the mean generation interval contracts as the prevalence of infection increases. We call this global competition among potential infectors. When there is rapid transmission within clusters of contacts, generation interval contraction can be caused by a high local prevalence of infection even when the global prevalence is low. We call this local competition among potential infectors. Using simulations, we illustrate both types of competition. Finally, we show that hazards of infectious contact can be used instead of generation intervals to estimate the time course of the effective reproductive number in an epidemic. This approach leads naturally to partial likelihoods for epidemic data that are very similar to those that arise in survival analysis, opening a promising avenue of methodological research in infectious disease epidemiology.

In this paper, we outline the theory of epidemic percolation networks and their use in the analysis of stochastic SIR epidemic models on undirected contact networks. We then show how the same theory can be used to analyze stochastic SIR models with random and proportionate mixing. The epidemic percolation networks for these models are purely directed because undirected edges disappear in the limit of a large population. In a series of simulations, we show that epidemic percolation networks accurately predict the mean outbreak size and probability and final size of an epidemic for a variety of epidemic models in homogeneous and heterogeneous populations. Finally, we show that epidemic percolation networks can be used to re-derive classical results from several different areas of infectious disease epidemiology. In an appendix, we show that an epidemic percolation network can be defined for any time-homogeneous stochastic SIR model in a closed population and prove that the distribution of outbreak sizes given the infection of any given node in the SIR model is identical to the distribution of its out-component sizes in the corresponding probability space of epidemic percolation networks. We conclude that the theory of percolation on semi-directed networks provides a very general framework for the analysis of stochastic SIR models in closed populations.

In an important paper, M.E.J. Newman claimed that a general network-based stochastic Susceptible-Infectious-Removed (SIR) epidemic model is isomorphic to a bond percolation model, where the bonds are the edges of the contact network and the bond occupation probability is equal to the marginal probability of transmission from an infected node to a susceptible neighbor. In this paper, we show that this isomorphism is incorrect and define a semi-directed random network we call the epidemic percolation network that is exactly isomorphic to the SIR epidemic model in any finite population. In the limit of a large population, (i) the distribution of (self-limited) outbreak sizes is identical to the size distribution of (small) out-components, (ii) the epidemic threshold corresponds to the phase transition where a giant strongly-connected component appears, (iii) the probability of a large epidemic is equal to the probability that an initial infection occurs in the giant in-component, and (iv) the relative final size of an epidemic is equal to the proportion of the network contained in the giant out-component. For the SIR model considered by Newman, we show that the epidemic percolation network predicts the same mean outbreak size below the epidemic threshold, the same epidemic threshold, and the same final size of an epidemic as the bond percolation model. However, the bond percolation model fails to predict the correct outbreak size distribution and probability of an epidemic when there is a nondegenerate infectious period distribution. We confirm our findings by comparing predictions from percolation networks and bond percolation models to the results of simulations. In an appendix, we show that an isomorphism to an epidemic percolation network can be defined for any time-homogeneous stochastic SIR model.