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We often estimate a parameter of interest ψ $$ \psi $$ when the identifying conditions involve a finite-dimensional nuisance parameter θ ∈ ℝ d $$ \theta \in {\mathbb{R}}^d $$ . Examples from causal inference are inverse probability weighting, marginal structural models and structural nested models, which all lead to unbiased estimating equations. This article presents a consistent sandwich estimator for the variance of estimators ψ ^ $$ \hat{\psi} $$ that solve unbiased estimating equations including θ $$ \theta $$ which is also estimated by solving unbiased estimating equations. This article presents four additional results for settings where θ ^ $$ \hat{\theta} $$ solves (partial) score equations and ψ $$ \psi $$ does not depend on θ $$ \theta $$ . This includes many causal inference settings where θ $$ \theta $$ describes the treatment probabilities, missing data settings where θ $$ \theta $$ describes the missingness probabilities, and measurement error settings where θ $$ \theta $$ describes the error distribution. These four additional results are: (1) Counter-intuitively, the asymptotic variance of ψ ^ $$ \hat{\psi} $$ is typically smaller when θ $$ \theta $$ is estimated. (2) If estimating θ $$ \theta $$ is ignored, the sandwich estimator for the variance of ψ ^ $$ \hat{\psi} $$ is conservative. (3) A consistent sandwich estimator for the variance of ψ ^ $$ \hat{\psi} $$ . (4) If ψ ^ $$ \hat{\psi} $$ with the true θ $$ \theta $$ plugged in is efficient, the asymptotic variance of ψ ^ $$ \hat{\psi} $$ does not depend on whether θ $$ \theta $$ is estimated. To illustrate we use observational data to calculate confidence intervals for (1) the effect of cazavi versus colistin on bacterial infections and (2) how the effect of antiretroviral treatment depends on its initiation time in HIV-infected patients., (© 2024 John Wiley & Sons Ltd.)

Censoring at death is the only feasible option if death is not recorded and individuals who died simply no longer contribute visits, such as in the setting of Barberio et al (Am J Epidemiol. 2024) before they acquired access to mortality information. Censoring at death is known to lead to biased estimates of the probability of the event of interest before time $t$. Barberio et al show through simulations that this bias increases with increasing mortality. However, when analyzing claims data it is often important to not exclude individuals with shorter life expectancies: an important strength of observational studies is that they allow estimating treatment effects in more varied populations than typically included in randomized clinical trials. We derive an analytic expression for the bias, and provide two upper bounds for the bias. The bounds inform the usefulness of obtaining mortality information. If the probability of death before the event is known to be small, wider confidence intervals can be created using the first bound on the bias; we provide an algorithm. If the bias is large, obtaining mortality information is important. Barberio et al show that obtaining mortality information can be essential in practice., (© The Author(s) 2024. Published by Oxford University Press on behalf of the Johns Hopkins Bloomberg School of Public Health. All rights reserved. For permissions, please e-mail: journals.permissions@oup.com.)

Background: Intervention packages may result in a greater public health impact than single interventions. Understanding the separate impact of each component on the overall package effectiveness can improve intervention delivery., Methods: We adapted an approach to evaluate the effects of a time-varying intervention package in a network-randomized study. In some network-randomized studies, only a subset of participants in exposed networks receive the intervention themselves. The spillover effect contrasts average potential outcomes if a person was not exposed to themselves under intervention in the network versus no intervention in a control network. We estimated the effects of components of the intervention package in HIV Prevention Trials Network 037, a Phase III network-randomized HIV prevention trial among people who inject drugs and their risk networks using marginal structural models to adjust for time-varying confounding. The index participant in an intervention network received a peer education intervention initially at baseline, then boosters at 6 and 12 months. All participants were followed to ascertain HIV risk behaviors., Results: There were 560 participants with at least one follow-up visit, 48% of whom were randomized to the intervention, and 1,598 participant visits were observed. The spillover effect of the boosters in the presence of initial peer education training was a 39% rate reduction (rate ratio = 0.61; 95% confidence interval = 0.43, 0.87)., Conclusions: These methods will be useful for evaluating intervention packages in studies with network features., Competing Interests: The authors report no conflicts of interest., (Copyright © 2024 Wolters Kluwer Health, Inc. All rights reserved.)

Causal indirect and direct effects provide an interpretable method for decomposing the total effect of an exposure on an outcome into the indirect effect through a mediator and the direct effect through all other pathways. A natural choice for a mediator in a randomized clinical trial is the treatment's targeted biomarker. However, when the mediator is a biomarker, values can be subject to an assay lower limit. The mediator is affected by the treatment and is a putative cause of the outcome, so the assay lower limit presents a compounded problem in mediation analysis. We propose two approaches to estimate indirect and direct effects with a mediator subject to an assay limit: (1) extrapolation and (2) numerical optimization and integration of the observed likelihood. Since these estimation methods solely rely on the so-called Mediation Formula, they apply to most approaches to causal mediation analysis: natural, separable, and organic indirect, and direct effects. A simulation study compares the two estimation approaches to imputing with half the assay limit. Using HIV interruption study data from the AIDS Clinical Trials Group described in Li et al 2016, AIDS; Lok and Bosch 2021, Epidemiology, we illustrate our methods by estimating the organic/pure indirect effect of a hypothetical HIV curative treatment on viral suppression mediated by two HIV persistence measures: cell-associated HIV-RNA and single-copy plasma HIV-RNA., (© 2024 John Wiley & Sons Ltd.)

We sought to disentangle effects of the components of a peer-education intervention on self-reported injection risk behaviors among people who inject drugs (n = 560) in Philadelphia, US. We examined 226 egocentric groups/networks randomized to receive (or not) the intervention. Peer-education training consisted of two components delivered to the intervention network index individual only: (1) an initial training and (2) "booster" training sessions during 6- and 12-month follow up visits. In this secondary data analysis, using inverse-probability-weighted log-binomial mixed effects models, we estimated the effects of the components of the network-level peer-education intervention upon subsequent risk behaviors. This included contrasting outcome rates if a participant is a network member [non-index] under the network exposure versus under the network control condition (i.e., spillover effects). We found that compared to control networks, among intervention networks, the overall rates of injection risk behaviors were lower in both those recently exposed (i.e., at the prior visit) to a booster (rate ratio [95% confidence interval]: 0.61 [0.46-0.82]) and those not recently exposed to it (0.81 [0.67-0.98]). Only the boosters had statistically significant spillover effects (e.g., 0.59 [0.41-0.86] for recent exposure). Thus, both intervention components reduced injection risk behaviors with evidence of spillover effects for the boosters. Spillover should be assessed for an intervention that has an observable behavioral measure. Efforts to fully understand the impact of peer education should include routine evaluation of spillover effects. To maximize impact, boosters can be provided along with strategies to recruit especially committed peer educators and to increase attendance at trainings. Clinical Trials Registration Clinicaltrials.gov NCT00038688 June 5, 2002., (© 2023. The Author(s), under exclusive licence to Springer Science+Business Media, LLC, part of Springer Nature.)

Many clinical studies evaluate the benefit of a treatment based on both survival and other continuous/ordinal clinical outcomes, such as quality of life scores. In these studies, when subjects die before the follow-up assessment, the clinical outcomes become undefined and are truncated by death. Treating outcomes as "missing" or "censored" due to death can be misleading for treatment effect evaluation. We show that if we use the median in the survivors or in the always-survivors as estimands to summarize clinical outcomes, we may conclude that a trade-off exists between the probability of survival and good clinical outcomes, even in settings where both the probability of survival and the probability of any good clinical outcome are better for one treatment. Therefore, we advocate not always treating death as a mechanism through which clinical outcomes are missing, but rather as part of the outcome measure. To account for the survival status, we describe the survival-incorporated median as an alternative summary measure for outcomes in the presence of death. The survival-incorporated median is the threshold such that 50% of the population is alive with an outcome above that threshold. Through conceptual examples and an application to a prostate cancer treatment study, we show that the survival-incorporated median provides a simple and useful summary measure to inform clinical practice., (© 2023 John Wiley & Sons Ltd.)

Background: Cumulative research show association of neutrophils and neutrophil extracellular traps (NETs) with poor outcomes in severe COVID-19. However, to date, there is no curative intent therapy able to block neutrophil/NETs-mediated progression of multi-organ dysfunction. Because of emerging neutrophil heterogeneity, the study of subsets of circulating NET-forming neutrophils [NET + Ns] as mediators of multi-organ failure progression among patients with COVID-19 is critical to identification of therapeutic targets., Methods: We conducted a prospective observational study of circulating levels of CD11b + [NET + N] immunotyped for dual endothelin-1/signal peptide receptor (DEspR ±) expression by quantitative immunofluorescence-cytology and causal mediation analysis. In 36 consented adults hospitalized with mod-severe COVID-19, May to September 2020, we measured acute multi-organ failure via SOFA-scores and respiratory failure via SaO2/FiO2 (SF)-ratio at time points t1 (average 5.5 days from ICU/hospital admission) and t2 (the day before ICU-discharge or death), and ICU-free days at day28 (ICUFD). Circulating absolute neutrophil counts (ANC) and [NET + N] subset-specific counts were measured at t1. Spearman correlation and causal mediation analyses were conducted., Results: Spearman correlation analyses showed correlations of t1-SOFA with t2-SOFA ( rho r S  = 0.80) and ICUFD ( r S  = -0.76); circulating DEspR + [NET + Ns] with t1-SOFA ( r S  = 0.71), t2-SOFA ( r S  = 0.62), and ICUFD ( r S  = -0.63), and ANC with t1-SOFA ( r S  = 0.71), and t2-SOFA ( r S  = 0.61).Causal mediation analysis identified DEspR + [NET + Ns] as mediator of 44.1% [95% CI:16.5,110.6] of the causal path between t1-SOFA (exposure) and t2-SOFA (outcome), with 46.9% [15.8,124.6] eliminated when DEspR + [NET + Ns] were theoretically reduced to zero. Concordantly, DEspR + [NET + Ns] mediated 47.1% [22.0,72.3%] of the t1-SOFA to ICUFD causal path, with 51.1% [22.8,80.4%] eliminated if DEspR + [NET + Ns] were reduced to zero. In patients with t1-SOFA > 1, the indirect effect of a hypothetical treatment eliminating DEspR + [NET + Ns] projected a reduction of t2-SOFA by 0.98 [0.29,2.06] points and ICUFD by 3.0 [0.85,7.09] days. In contrast, there was no significant mediation of SF-ratio through DEspR + [NET + Ns], and no significant mediation of SOFA-score through ANC., Conclusions: Despite equivalent correlations, DEspR + [NET + Ns], but not ANC, mediated progression of multi-organ failure in acute COVID-19, and its hypothetical reduction is projected to improve ICUFD. These translational findings warrant further studies of DEspR + [NET + Ns] as potential patient-stratifier and actionable therapeutic target for multi-organ failure in COVID-19., Supplementary Information: The online version contains supplementary material available at 10.1186/s41231-023-00143-x., Competing Interests: Competing interestsBoston University holds awarded patents on DEspR as novel therapeutic approach for cancer, stroke, COVID-19, NETosis and activated neutrophils. VLMH and NRO are co-inventors in patents filed by Boston University., (© The Author(s) 2023.)

Background: While increased CD8 counts and low CD4/CD8 ratio during treated HIV correlate with immunosenescence, their additional predictive values to identify individuals with HIV at higher risk of clinical events remain controversial., Methods: We selected treatment-naive individuals initiating ART from ACTG studies 384, 388, A5095, A5142, A5202, and A5257 who had achieved viral suppression at year 2. We examined the effect of CD8+ T cell counts and CD4/CD8 at year 2 on the probability of AIDS and serious non-AIDS events in years 3-7. We used inverse probability weighting methods to address informative censoring, combined with multivariable logistic regression models., Findings: We analyzed 5133 participants with a median age of 38 years; 959 (19%) were female, pre-ART median CD4 counts were 249 (Q1-Q3 91-372) cell/µL. Compared to participants with CD8 counts between 500/µL and 1499/µL, those with >1500/µL had a higher risk of clinical events during years 3-7 (aOR 1.75; 95%CI 1.33-2.32). CD4/CD8 ratio was not predictive of greater risk of events through year 7. Additional analyses revealed consistent CD8 count effect sizes for the risk of AIDS events and noninfectious non-AIDS events, but opposite effects for the risk of severe infections, which were more frequent among individuals with CD8 counts <500/µL (aOR 1.70; 95%CI 1.09-2.65)., Interpretation: The results of this analysis with pooled data from clinical trials support the value of the CD8 count as a predictor of clinical progression. People with very high CD8 counts during suppressive ART might benefit from closer monitoring and may be a target population for novel interventions., Funding: This research was supported by NIH/NIAID awards UM1 AI068634, UM1 AI068636, and UM1 AI106701 and Carlos III Health Institute and FEDER funds (BA21/00017 and BA21/00022)., Competing Interests: Declaration of interests Dr. Serrano-Villar reports grants from MSD, grants and personal fees from Gilead, non-financial support from ViiV, outside the submitted work; Dr. Hunt reports grants and personal fees from Gilead, non-financial support from Merck, personal fees from Viiv, personal fees from Biotron, outside the submitted work; Dr. Moreno reports grants, personal fees and non-financial support from Gilead Sciences, personal fees from Janssen Pharmaceuticals, grants, personal fees and non-financial support from Viiv Healthcare, grants, personal fees and non-financial support from MSD, outside the submitted work; Dr. Bosch reports grants from NIH/NIAID, during the conduct of the study; grants from NIH/NIAID, outside the submitted work., (Copyright © 2022 The Author(s). Published by Elsevier B.V. All rights reserved.)

Objectives: The causal impact method (CIM) was recently introduced for evaluation of binary interventions using observational time-series data. The CIM is appealing for practical use as it can adjust for temporal trends and account for the potential of unobserved confounding. However, the method was initially developed for applications involving large datasets and hence its potential in small epidemiological studies is still unclear. Further, the effects that measurement error can have on the performance of the CIM have not been studied yet. The objective of this work is to investigate both of these open problems., Methods: Motivated by an existing dataset of HCV surveillance in the UK, we perform simulation experiments to investigate the effect of several characteristics of the data on the performance of the CIM. Further, we quantify the effects of measurement error on the performance of the CIM and extend the method to deal with this problem., Results: We identify multiple characteristics of the data that affect the ability of the CIM to detect an intervention effect including the length of time-series, the variability of the outcome and the degree of correlation between the outcome of the treated unit and the outcomes of controls. We show that measurement error can introduce biases in the estimated intervention effects and heavily reduce the power of the CIM. Using an extended CIM, some of these adverse effects can be mitigated., Conclusions: The CIM can provide satisfactory power in public health interventions. The method may provide misleading results in the presence of measurement error., (© 2021 Walter de Gruyter GmbH, Berlin/Boston.)

Mediation analysis, which started in the mid-1980s, is used extensively by applied researchers. Indirect and direct effects are the part of a treatment effect that is mediated by a covariate and the part that is not. Subsequent work on natural indirect and direct effects provides a formal causal interpretation, based on cross-worlds counterfactuals: outcomes under treatment with the mediator set to its value without treatment. Organic indirect and direct effects avoid cross-worlds counterfactuals, using so-called organic interventions on the mediator while keeping the initial treatment fixed at treatment. Organic indirect and direct effects apply also to settings where the mediator cannot be set. In linear models where the outcome model does not have treatment-mediator interaction, both organic and natural indirect and direct effects lead to the same estimators as in the original formulation of mediation analysis. Here, we generalize organic interventions on the mediator to include interventions combined with the initial treatment fixed at no treatment. We show that the product method holds in linear models for organic indirect and direct effects relative to no treatment even if there is treatment-mediator interaction. Moreover, we find a product method for binary mediators. Furthermore, we argue that the organic indirect effect relative to no treatment is very relevant for drug development. We illustrate the benefits of our approach by estimating the organic indirect effect of curative HIV treatments mediated by two HIV persistence measures, using data on interruption of antiretroviral therapy without curative HIV treatments combined with an estimated or hypothesized effect of the curative HIV treatments on these mediators. See video abstract at http://links.lww.com/EDE/B796., (Copyright © 2021 Wolters Kluwer Health, Inc. All rights reserved.)

In Learn-As-you-GO (LAGO) adaptive studies, the intervention is a complex multicomponent package, and is adapted in stages during the study based on past outcome data. This design formalizes standard practice in public health intervention studies. An effective intervention package is sought, while minimizing intervention package cost. In LAGO study data, the interventions in later stages depend upon the outcomes in the previous stages, violating standard statistical theory. We develop an estimator for the intervention effects, and prove consistency and asymptotic normality using a novel coupling argument, ensuring the validity of the test for the hypothesis of no overall intervention effect. We develop a confidence set for the optimal intervention package and confidence bands for the success probabilities under alternative package compositions. We illustrate our methods in the BetterBirth Study, which aimed to improve maternal and neonatal outcomes among 157,689 births in Uttar Pradesh, India through a multicomponent intervention package.

Patient management is not based on a single decision. Rather, it is dynamic: based on a sequence of decisions, with therapeutic adjustments made over time. Adjustments are personalized: tailored to individual patients as new information becomes available. However, strategies allowing for such adjustments are infrequently studied. Traditional antibiotic trials are often nonpragmatic, comparing drugs for definitive therapy when drug susceptibilities are known. COMparing Personalized Antibiotic StrategieS (COMPASS) is a trial design that compares strategies consistent with clinical practice. Strategies are decision rules that guide empiric and definitive therapy decisions. Sequential, multiple-assignment, randomized (SMART) COMPASS allows evaluation when there are multiple, definitive therapy options. SMART COMPASS is pragmatic, mirroring clinical, antibiotic-treatment decision-making and addressing the most relevant issue for treating patients: identification of the patient-management strategy that optimizes the ultimate patient outcomes. SMART COMPASS is valuable in the setting of antibiotic resistance, when therapeutic adjustments may be necessary due to resistance., (© The Author(s) 2018. Published by Oxford University Press for the Infectious Diseases Society of America. All rights reserved. For permissions, e-mail: journals.permissions@oup.com.)

Coarse Structural Nested Mean Models (SNMMs, Robins (2000)) and G-estimation can be used to estimate the causal effect of a time-varying treatment from longitudinal observational studies. However, they rely on an untestable assumption of no unmeasured confounding. In the presence of unmeasured confounders, the unobserved potential outcomes are not missing at random, and standard G-estimation leads to biased effect estimates. To remedy this, we investigate the sensitivity of G-estimators of coarse SNMMs to unmeasured confounding, assuming a nonidentifiable bias function which quantifies the impact of unmeasured confounding on the average potential outcome. We present adjusted G-estimators of coarse SNMM parameters and prove their consistency, under the bias modeling for unmeasured confounding. We apply this to a sensitivity analysis for the effect of the ART initiation time on the mean CD4 count at year 2 after infection in HIV-positive patients, based on the prospective Acute and Early Disease Research Program.

Competing risks occur in a time-to-event analysis in which a patient can experience one of several types of events. Traditional methods for handling competing risks data presuppose one censoring process, which is assumed to be independent. In a controlled clinical trial, censoring can occur for several reasons: some independent, others dependent. We propose an estimator of the cumulative incidence function in the presence of both independent and dependent censoring mechanisms. We rely on semi-parametric theory to derive an augmented inverse probability of censoring weighted (AIPCW) estimator. We demonstrate the efficiency gained when using the AIPCW estimator compared to a non-augmented estimator via simulations. We then apply our method to evaluate the safety and efficacy of three anti-HIV regimens in a randomized trial conducted by the AIDS Clinical Trial Group, ACTG A5095.

Background: The efficacy of ceftazidime-avibactam-a cephalosporin-β-lactamase inhibitor combination with in vitro activity against Klebsiella pneumoniae carbapenemase-producing carbapenem-resistant Enterobacteriaceae (CRE)-compared with colistin remains unknown., Methods: Patients initially treated with either ceftazidime-avibactam or colistin for CRE infections were selected from the Consortium on Resistance Against Carbapenems in Klebsiella and other Enterobacteriaceae (CRACKLE), a prospective, multicenter, observational study. Efficacy, safety, and benefit-risk analyses were performed using intent-to-treat analyses with partial credit and the desirability of outcome ranking approaches. The ordinal efficacy outcome was based on disposition at day 30 after starting treatment (home vs not home but not observed to die in the hospital vs hospital death). All analyses were adjusted for confounding using inverse probability of treatment weighting (IPTW)., Results: Thirty-eight patients were treated first with ceftazidime-avibactam and 99 with colistin. Most patients received additional anti-CRE agents as part of their treatment. Bloodstream (n = 63; 46%) and respiratory (n = 30; 22%) infections were most common. In patients treated with ceftazidime-avibactam versus colistin, IPTW-adjusted all-cause hospital mortality 30 days after starting treatment was 9% versus 32%, respectively (difference, 23%; 95% bootstrap confidence interval, 9%-35%; P = .001). In an analysis of disposition at 30 days, patients treated with ceftazidime-avibactam, compared with those treated within colistin, had an IPTW-adjusted probability of a better outcome of 64% (95% confidence interval, 57%-71%). Partial credit analyses indicated uniform superiority of ceftazidime-avibactam to colistin., Conclusions: Ceftazidime-avibactam may be a reasonable alternative to colistin in the treatment of K. pneumoniae carbapenemase-producing CRE infections. These findings require confirmation in a randomized controlled trial., (© The Author 2017. Published by Oxford University Press for the Infectious Diseases Society of America. All rights reserved. For permissions, e-mail: journals.permissions@oup.com.)

Background: Although statins, angiotensin-converting enzyme inhibitors (ACEI) or angiotensin receptor blockers (ARB) are generally well tolerated, the impact of these therapies individually or in combination on the change in neurocognitive function in persons with human immunodeficiency virus infection is unknown., Methods: The study included participants in the AIDS Clinical Trials Group Longitudinal Linked Randomized Trials cohort participants not receiving a statin or ACEI/ARB within 30 days of first neurologic assessment (baseline), with assessments by NPZ-3 (z score of averaged Trailmaking A and B tests and digit symbol test [DST]) from ≥2 measurements. Marginal structural models estimated the causal effect of statin or ACEI/ARB initiation on neurocognitive function; initial constant slope was assumed during the first year of treatment and a second constant slope thereafter., Results: Of 3949 eligible participants, 16% started therapy with a statin, 11% with an ACEI/ARB, and 5% with both. Statin therapy had no significant effect on the composite NPZ-3 (primary outcome), Trailmaking B test, or DST. A small, nonsignificant positive effect on the Trailmaking A test was seen during year 1 (estimate, 0.088; 95% confidence interval, -.010 to .187; P = .08) and a small but significant negative effect (-0.033; -.058 to -.009; P = .007) in each subsequent year. ACEI/ARB therapy had a significant negative effect on the DST (-0.117; 95% confidence interval, -.217 to .016; P = .02) during year 1 but minimal effect in subsequent years or on other neurocognitive domains., Conclusions: In summary, although modest declines in neurocognitive performance were seen in single domains with statin or ACEI/ARB therapy, we did not find consistent evidence that statins or ACEI/ARB have an effect on global neurocognitive function. Future studies should focus on long-term neurocognitive effects., (© The Author 2017. Published by Oxford University Press for the Infectious Diseases Society of America. All rights reserved. For permissions, e-mail: journals.permissions@oup.com.)

In observational studies, treatment may be adapted to covariates at several times without a fixed protocol, in continuous time. Treatment influences covariates, which influence treatment, which influences covariates, and so on. Then even time-dependent Cox-models cannot be used to estimate the net treatment effect. Structural nested models have been applied in this setting. Structural nested models are based on counterfactuals: the outcome a person would have had had treatment been withheld after a certain time. Previous work on continuous-time structural nested models assumes that counterfactuals depend deterministically on observed data, while conjecturing that this assumption can be relaxed. This article proves that one can mimic counterfactuals by constructing random variables, solutions to a differential equation, that have the same distribution as the counterfactuals, even given past observed data. These "mimicking" variables can be used to estimate the parameters of structural nested models without assuming the treatment effect to be deterministic.

Natural direct and indirect effects decompose the effect of a treatment into the part that is mediated by a covariate (the mediator) and the part that is not. Their definitions rely on the concept of outcomes under treatment with the mediator 'set' to its value without treatment. Typically, the mechanism through which the mediator is set to this value is left unspecified, and in many applications, it may be challenging to fix the mediator to particular values for each unit or patient. Moreover, how one sets the mediator may affect the distribution of the outcome. This article introduces 'organic' direct and indirect effects, which can be defined and estimated without relying on setting the mediator to specific values. Organic direct and indirect effects can be applied, for example, to estimate how much of the effect of some treatments for HIV/AIDS on mother-to-child transmission of HIV infection is mediated by the effect of the treatment on the HIV viral load in the blood of the mother. Copyright © 2016 John Wiley & Sons, Ltd., (Copyright © 2016 John Wiley & Sons, Ltd.)

Coarse structural nested mean models are tools to estimate treatment effects from longitudinal observational data with time-dependent confounding. There is, however, no guidance on how to specify the treatment effect model, and model misspecification can lead to bias. We derive a goodness-of-fit test based on modified overidentification restrictions tests for evaluating a treatment effect model, and show that our test statistic is doubly-robust in the sense that, with a correct treatment effect model, the test has the correct type-I error if either the treatment initiation model or a nuisance regression outcome model is correctly specified. In a simulation study we show that the test has correct type-I error and can detect model misspecification. We use the test to study how the timing of antiretroviral treatment initiation after HIV infection predicts the effect of one year of treatment in HIV-positive patients with acute and early infection.

We propose a prediction model for the cumulative incidence functions of competing risks, based on a logit link. Because of a concern about censoring potentially depending on time-varying covariates in our motivating human immunodeficiency virus (HIV) application, we describe an approach for estimating the parameters in the prediction models using inverse probability of censoring weighting under a missingness at random assumption. We then illustrate the application of this methodology to identify predictors of the competing outcomes of virologic failure, an efficacy outcome, and treatment limiting adverse event, a safety outcome, among human immunodeficiency virus-infected patients first starting antiretroviral treatment. Copyright © 2016 John Wiley & Sons, Ltd., (Copyright © 2016 John Wiley & Sons, Ltd.)

This paper investigates the appropriateness of the integration of flexible propensity score modeling (nonparametric or machine learning approaches) in semiparametric models for the estimation of a causal quantity, such as the mean outcome under treatment. We begin with an overview of some of the issues involved in knowledge-based and statistical variable selection in causal inference and the potential pitfalls of automated selection based on the fit of the propensity score. Using a simple example, we directly show the consequences of adjusting for pure causes of the exposure when using inverse probability of treatment weighting (IPTW). Such variables are likely to be selected when using a naive approach to model selection for the propensity score. We describe how the method of Collaborative Targeted minimum loss-based estimation (C-TMLE; van der Laan and Gruber, 2010 [27]) capitalizes on the collaborative double robustness property of semiparametric efficient estimators to select covariates for the propensity score based on the error in the conditional outcome model. Finally, we compare several approaches to automated variable selection in low- and high-dimensional settings through a simulation study. From this simulation study, we conclude that using IPTW with flexible prediction for the propensity score can result in inferior estimation, while Targeted minimum loss-based estimation and C-TMLE may benefit from flexible prediction and remain robust to the presence of variables that are highly correlated with treatment. However, in our study, standard influence function-based methods for the variance underestimated the standard errors, resulting in poor coverage under certain data-generating scenarios.

In longitudinal data arising from observational or experimental studies, dependent subject drop-out is a common occurrence. If the goal is estimation of the parameters of a marginal complete-data model for the outcome, biased inference will result from fitting the model of interest with only uncensored subjects. For example, investigators are interested in estimating a prognostic model for clinical events in HIV-positive patients, under the counterfactual scenario in which everyone remained on ART (when in reality, only a subset had). Inverse probability of censoring weighting (IPCW) is a popular method that relies on correct estimation of the probability of censoring to produce consistent estimation, but is an inefficient estimator in its standard form. We introduce sequentially augmented regression (SAR), an adaptation of the Bang and Robins (2005. Doubly robust estimation in missing data and causal inference models. Biometrics 61, 962-972.) method to estimate a complete-data prediction model, adjusting for longitudinal missing at random censoring. In addition, we propose a closely related non-parametric approach using targeted maximum likelihood estimation (TMLE; van der Laan and Rubin, 2006. Targeted maximum likelihood learning. The International Journal of Biostatistics 2 (1), Article 11). We compare IPCW, SAR, and TMLE (implemented parametrically and with Super Learner) through simulation and the above-mentioned case study., (© The Author 2015. Published by Oxford University Press. All rights reserved. For permissions, please e-mail: journals.permissions@oup.com.)

Objective: Estimates of CD4 response to antiretroviral therapy (ART) obtained by averaging data from patients in care, overestimate population CD4 response and treatment program effectiveness because they do not consider data from patients who are deceased or not in care. We use mathematical methods to assess and adjust for this bias based on patient characteristics., Design: We examined data from 25,261 HIV-positive patients from the East Africa IeDEA Consortium., Methods: We used inverse probability of censoring weighting (IPCW) to represent patients not in care by patients in care with similar characteristics. We address two questions: What would the median CD4 be "had everyone starting ART remained on observation?" and "were everyone starting ART maintained on treatment?", Results: Routine CD4 count estimates were higher than adjusted estimates even under the best-case scenario of maintaining all patients on treatment. Two years after starting ART, differences between estimates diverged from 30 cells/µL, assuming similar mortality and treatment access among dropouts as patients in care, to over 100 cells/µL assuming 20% lower survival and 50% lower treatment access among dropouts. When considering only patients in care, the proportion of patients with CD4 above 350 cells/µL was 50% adjusted to below 30% when accounting for patients not in care. One-year mortality diverged 6-14% from the naïve estimates depending on assumptions about access to care among lost patients., Conclusions: Ignoring mortality and loss to care results in over-estimation of ART response for patients starting treatment and exaggerates the efficacy of treatment programs administering it.

Objective: To assess whether CD8 T-cell activation predicts risk of AIDS and non-AIDS morbidity during suppressive antiretroviral treatment (ART)., Design: Post-hoc analyses of ART-naive participants in prospective ART studies. Participants with HIV-RNA levels 200 copies/ml or less and CD8 T-cell activation data (%CD38HLA-DR) at year-1 of ART were selected to determine years 2-5 incidence of AIDS and non-AIDS events., Methods: We censored data at time of ART interruption or virologic failure. Inverse probability of censoring-weighted logistic regression was used to correct for informative censoring., Results: We included 1025 participants; 82% were men, median age 38 years, pre-ART CD4 cell count 255 cells/μl, and year-1-activated CD8 T cells 24%. Of these, 752 had 5 years of follow-up; 379 remained on ART and had no confirmed plasma HIV-RNA more than 200 copies/ml. The overall probability of an AIDS or non-AIDS event in years 2-5 was estimated at 13% [95% confidence interval (CI) 10-15%] had everyone remained on suppressive ART. Higher year-1-activated CD8 T-cell percentage increased the probability of subsequent events [odds ratio 1.22 per 10% higher (95% CI 1.04-1.44)]; this effect was not significant after adjusting for age. Among those age 50 years at least (n=108 at year 1), the probability of an event in years 2-5 was 37% and the effect of CD8 T-cell activation was more apparent (odds ratio=1.42, P=0.02 unadjusted and adjusted for age)., Conclusion: CD8 T-cell activation is prognostic of clinical events during suppressive ART, although this association is confounded by age. The consequences of HIV-associated immune activation may be more important in patients 50 years and older.

Objective: Efavirenz (EFV) along with two nucleoside reverse transcriptase inhibitors (NRTIs) is a recommended initial antiretroviral regimen. Understanding characteristics related to EFV success is clinically useful., Design: Data from 2220 antiretroviral-naive participants randomized to EFV and two to three NRTIs in four ACTG trials as well as a long-term cohort were analysed., Methods: Logistic regression, using inverse probability of censoring weighting to address selective-follow-up bias, was used to identify factors associated with EFV success (no treatment interruptions of >30 days, HIV RNA < 200 copies/ml) 1 year post initiation and at years 2-5 if successful at year 1., Results: Pretreatment characteristics were median age 38 years, 82% male, 40% white, 10% history of IDU (HxIDU), median CD4+ T-lymphocyte 227 cells/μl and 33% HIV RNA more than 100 ,000 copies/ml. In a multivariable model, factors associated with year 1 EFV success were race [white odds ratio (OR) 1.5; P < 0.001; Hispanic OR 1.5; P = 0.003 vs. black], no pretreatment sign/symptom grade 3 or higher (OR 1.7; P = 0.008) and no HxIDU (OR 1.7; P = 0.001). Predictors of EFV success at years 2-5 were no HxIDU (years 2-5; ORs 1.9-2.2); self-reported complete (4 days prior to study visit) adherence during year 1 (years 2-4; ORs 1.6-1.9); fewer missed visits during year 1 (years 2, 4, 5; ORs 0.92-0.98/1% increase); HIV RNA less than 50 copies/ml at year 1 (years 2, 3; ORs 1.9-2.2); and older age (>50 vs. ≤30 years) (years 2-4: ORs 2.3-3.7)., Conclusion: Characteristics predictive of EFV success in the short-term and longer term differed except for HxIDU. Behaviours occurring during year 1 were associated with EFV success over 5 years.

We estimate how the effect of antiretroviral treatment depends on the time from HIV-infection to initiation of treatment, using observational data. A major challenge in making inferences from such observational data arises from biases associated with the nonrandom assignment of treatment, for example bias induced by dependence of time of initiation on disease status. To address this concern, we develop a new class of Structural Nested Mean Models (SNMMs) to estimate the impact of time of initiation of treatment after infection on an outcome measured a fixed duration after initiation, compared to the effect of not initiating treatment. This leads to a SNMM that models the effect of multiple dosages of treatment on a time-dependent outcome, in contrast to most existing SNNMs, which focus on the effect of one dosage of treatment on an outcome measured at the end of the study. Our identifying assumption is that there are no unmeasured confounders. We illustrate our methods using the observational Acute Infection and Early Disease Research Program (AIEDRP) Core01 database on HIV. The current standard of care in HIV-infected patients is Highly Active Anti-Retroviral Treatment (HAART); however, the optimal time to start HAART has not yet been identified. The new class of SNNMs allows estimation of the dependence of the effect of 1 year of HAART on the time between estimated date of infection and treatment initiation, and on patient characteristics. Results of fitting this model imply that early use of HAART substantially improves immune reconstitution in the early and acute phase of HIV-infection., (© 2012, The International Biometric Society.)

Background: Observational and retrospective clinical trial cohorts have reported conflicting results for the association of abacavir use with risk of myocardial infarction (MI), possibly related to issues that may bias estimation of treatment effects, such as time-varying confounders, informative dropout, and cohort loss due to competing events., Methods: We analyzed data from 5056 individuals initiating randomized antiretroviral treatment (ART) in AIDS Clinical Trials Group studies; 1704 started abacavir therapy. An intent-to-treat analysis adjusted for pretreatment covariates and weighting for informative censoring was used to estimate the hazard ratio (HR) of MIs after initiation of a regimen with or without abacavir., Results: Through 6 years after ART initiation, 36 MI events were observed in 17,404 person-years of follow-up. No evidence of an increased hazard of MI in subjects using abacavir versus no abacavir was seen (over a 1-year period: P=.50; HR, 0.7 [95% confidence interval {CI}, 0.2-2.4]); over a 6-year period: P=.24; HR, 0.6 [95% CI, 0.3-1.4]); these results were robust over as-treated and sensitivity analyses. Although the risk of MI decreased over time, there was no evidence to suggest a time-dependent abacavir effect. Classic cardiovascular disease (CVD) risk factors were the strongest predictors of MI., Conclusion: We find no evidence to suggest that initial ART containing abacavir increases MI risk over short-term and long-term periods in this population with relatively low MI risk. Traditional CVD risk factors should be the main focus in assessing CVD risk in individuals with human immunodeficiency virus infection., (© The Author 2011. Published by Oxford University Press on behalf of the Infectious Diseases Society of America. All rights reserved.)

Objective: To inform guidelines concerning when to initiate combination antiretroviral therapy (ART), we investigated whether CD4(+) T-cell counts (CD4 cell counts) continue to increase over long periods of time on ART. Losses-to-follow-up and some patients discontinuing ART at higher CD4 cell counts hamper such evaluation, but novel statistical methods can help address these issues. We estimated the long-term CD4 cell count trajectory accounting for losses-to-follow-up and treatment discontinuations., Design: The study population included 898 US patients first initiating ART in a randomized trial (AIDS Clinical Trials Group 384); 575 were subsequently prospectively followed in an observational study (AIDS Clinical Trials Group Longitudinal Linked Randomized Trials)., Methods: Inverse probability of censoring weighting statistical methods were used to estimate the CD4 cell count trajectory accounting for losses-to-follow-up and ART discontinuations, overall and for pretreatment CD4 cell count categories (500 cells/microl)., Results: Median CD4 cell count increased from 270 cells/microl pre-ART to an estimated 556 cells/microl at 3 and 532 cells/microl at 7 years after starting ART in analyses ignoring treatment discontinuations, and to 570 and 640 cells/microl, respectively, had all patients continued ART. However, even had ART been continued, an estimated 25, 9, 3, and 2% of patients with pretreatment CD4 cell counts of 200 or less, 201-350, 351-500, and more than 500 cells/microl would have had CD4 cell counts of 350 cells/microl or less after 7 years., Conclusion: If patients remain on ART, CD4 cell counts increase in most patients for at least 7 years. However, the substantial percentage of patients starting therapy at low CD4 cell counts who still had low CD4 cell counts after 7 years provides support for ART initiation at higher CD4 cell counts.

Purpose: The Dutch Bone Metastasis Study on the effect on painful bone metastases of 8 Gy single fraction (SF) vs. 24 Gy in multiple fractions (MF) showed 24% retreatment after SF vs. 6% after MF (p < 0.001). The purpose of the present study was to evaluate factors influencing retreatment and its effect on response., Methods and Materials: The database on all randomized patients was reanalyzed with separately calculated responses to initial treatment and retreatment., Results: Response to initial treatment was 71% after SF vs. 73% after MF (p = 0.84). Retreatment raised response to 75% for SF; MF remained unaltered (p = 0.54). The response status after initial treatment did not predict occurrence of retreatment: 35% SF vs. 8% MF nonresponders and 22% SF vs. 10% MF patients with progressive pain were retreated. Logistic regression analyses showed the randomization arm and the pain score before retreatment to significantly predict retreatment (p < 0.001). Retreatment for nonresponders was successful in 66% SF vs. 33% MF patients (p = 0.13). Retreatment for progression was successful in 70% SF vs. 57% MF patients (p = 0.24)., Conclusions: With or without the effect of retreatment, SF and MF radiotherapy provided equal palliation for painful bone metastases. Irrespective of response to initial treatment, physicians were more willing to retreat after a single fraction. Overall, retreatment was effective in 63% of retreated patients.

A number of risk factors based upon mostly retrospective surgical data, have been formulated in order to identify impending pathological fractures of the femur from low-risk metastases. We have followed up patients taking part in a randomised trial of radiotherapy, prospectively, in order to determine if these factors were effective in predicting fractures. In 102 patients with 110 femoral lesions, 14 fractures occurred during follow-up. The risk factors studied were increasing pain, the size of the lesion, radiographic appearance, localisation, transverse/axial/circumferential involvement of the cortex and the scoring system of Mirels. Only axial cortical involvement >30 mm (p = 0.01), and circumferential cortical involvement >50% (p = 0.03) were predictive of fracture. Mirels' scoring system was insufficiently specific to predict a fracture (p = 0.36). Our results indicate that most conventional risk factors overestimate the actual occurrence of pathological fractures of the femur. The risk factor of axial cortical involvement provides a simple, objective tool in order to decide which treatment is appropriate.

Background: Postoperative exercise therapy aims at recovering, as soon as possible, independence in the basic physical activities; but the type, intensity, and therefore the costs of the programs, vary widely. The aim of this study was to compare the effectiveness of a low frequency (once daily, not in the weekend) program with a high frequency (twice daily, including the weekend) one and to assess whether the latter would yield sufficient benefit for the patient to justify higher costs in material and personnel (physiotherapists) after uncomplicated coronary artery bypass graft (CABG) surgery., Methods: Two-hundred and forty-six patients were randomly allocated to either a low or high frequency exercise program. Endpoints were the functional level as measured by the achievement of five activity milestones, the patient's independence (functional independence measures [FIM]) as assessed by a structured interview, the amount of daily physical activity (activity monitor), and patient satisfaction (questionnaire). Except for patient satisfaction, all measurements were done in the first week after surgery., Results: Patients with the high frequency exercise program achieved functional milestones faster than patients with the low frequency exercise program (p = 0.007). The frequency of the exercise program had no influence on functional independence as measured with the FIM or quantity of physical activity. The satisfaction degree was greater in the high frequency group (p = 0.032), although the low frequency group was not dissatisfied., Conclusions: A high frequency exercise program leads to earlier performance of functional milestones and yields more satisfaction after uncomplicated CABG surgery and this should lead to an earlier discharge. On the other hand, if the shortage of physiotherapists remains unchanged or even increases, the low frequency program also yields excellent functional results, albeit at the cost of a somewhat longer hospital stay: but it would allow a sensible redistribution of the physiotherapists activity towards complicated and, therefore, more demanding patients.

Background and Purpose: In the randomised Dutch Bone Metastasis Study on the palliative effect of a single fraction (SF) of 8 Gy versus six fractions of 4 Gy on painful bone metastases, 14 fractures occurred in 102 patients with femoral metastases. Purpose of the present study was to identify lesional risk factors for fracturing and to evaluate the influence of the treatment schedule., Material and Methods: Pretreatment radiographs of femoral metastases were collected. Three observers separately measured the lesions and scored radiographic characteristics., Results: Ten fractures occurred after median 7 weeks in 44 SF patients (23%) and four after median 20 weeks in 58 multiple fraction patients (7%) (UV, P=0.02). In 110 femoral metastases, an axial cortical involvement >30 mm significantly predicted fracturing (MV, P=0.02). Twelve out of 14 fractured lesions and 40 out of 96 non-fractured metastases had an axial cortical involvement >30 mm (negative predictive value, 97%). When correcting for the axial cortical involvement, the treatment schedule was not predictive anymore (MV, P=0.07)., Conclusions: Fracturing of the femur mostly depended on the amount of axial cortical involvement of the metastasis. We recommend to treat femoral metastases with an axial cortical involvement < or =30 mm with an SF of 8 Gy for relief of pain. If the axial cortical involvement is >30 mm, prophylactic surgery should be performed to minimize the risk of pathological fracturing or, if the patient's condition is limited, irradiation to a higher total dose.