Parametric Potential-Outcome Survival Models for Causal Inference

This study examines alternative ways of specifying models in the complier average causal effect (CACE) estimation method, where the major interest is in estimating causal effects of treatments for compliers. A fundamental difficulty involved in the CACE estimation method is in dealing with missing compliance information among study participants. Given that, the assumption of the exclusion restriction plays a critical role in separating the distributions of compliers and non-compliers. If no pretreatment covariates are available, assuming the exclusion restriction is unavoidable to obtain unique ML estimates in CACE models, although the assumption can be often unrealistic. One disadvantage of assuming the exclusion restriction is that the CACE estimate can be biased if the assumption is violated. Another disadvantage is that the assumption limits the flexibility of CACE modeling in practice. However, if pretreatment covariates are available, more modeling options other than strictly forcing the exclusion restriction can be considered to establish identifiability of CACE models. This study explores modeling possibilities of CACE estimation within an ML-EM framework in the presence of covariate information.

Non-compliance, or non-receipt of randomized intervention, is a common problem in randomized controlled trials. An intention-to-treat (ITT) analysis, which compares individuals as randomized, under-estimates the efficacy of the intervention and leads to a loss of power. We explore the possibility of regaining some of this power in a setting with all-or-nothing compliance, without making any assumptions about the comparability of compliers and non-compliers. Efficacy may be specified as the complier average causal effect (CACE), which is the difference in mean outcome among compliers. Compliance is only partially observed, but under an exclusion restriction assumption, the CACE may be estimated using maximum likelihood. In order to quantify the possible gain in power, we derive an expression for the asymptotic relative efficiency (ARE) of the CACE relative to the ITT effect with a Normally distributed outcome. Under the assumption of a common CACE across covariate strata, the CACE estimate is at least as powerful as ITT analysis. The inclusion of covariates that predict compliance enables an additional gain in power, which is investigated algebraically. Using data from three clinical trials, we obtain values of the ARE ranging up to 1.05 due to covariates alone, and 1.13 due to CACE modelling alone, corresponding to gains in power of up to 5 per cent. This implies that a large gain in power obtained using as-treated or per-protocol analyses is likely to be due to the strong and often implausible assumptions such analyses require to be valid.

Chen and Heitjan (Sensitivity of estimands in clinical trials with imperfect compliance. Int J Biostat. 2023) used linear extrapolation to estimate the population average causal effect (PACE) from the complier average causal effect (CACE) in multiple randomized trials with all-or-none compliance. For extrapolating from CACE to PACE in this setting and in the paired availability design involving different availabilities of treatment among before-and-after studies, we recommend the sensitivity analysis in Baker and Lindeman (J Causal Inference, 2013) because it is not restricted to a linear model, as it involves various random effect and trend models.

The intention-to-treat (ITT) rate ratio estimator is conservatively biased for the treatment effect among compliers (who stick with their assigned arm) when individuals switch treatment in two-arm randomised trials. In this article we propose simple ways to estimate the complier average causal effect (CACE) with mid-trial switching. The estimators use aggregate data of events and times rather than individualised data. The motivating model considers survival times as exponentially distributed conditional on whether the individual would comply with randomisation. To estimate the CACE the ante-switch treatment effect and the post-switch treatment effect amongst the compliers are combined. Furthermore, we discuss ways of estimating the counterfactual intent-to-treat (ITT) effect, which is defined as the rate ratio if switching was not permitted. This approach might be a useful alternative to CACE estimation, and so a time and event adjustment of the non-compliers data is developed. Finally, simulated switching scenarios are used to illustrate the importance of correcting for informative switching.

When identification of causal effects relies on untestable assumptions regarding nonidentified parameters, sensitivity of causal effect estimates is often questioned. For proper interpretation of causal effect estimates in this situation, deriving bounds on causal parameters or exploring the sensitivity of estimates to scientifically plausible alternative assumptions can be critical. In this paper, we propose a practical way of bounding and sensitivity analysis, where multiple identifying assumptions are combined to construct tighter common bounds. In particular, we focus on the use of competing identifying assumptions that impose different restrictions on the same non-identified parameter. Since these assumptions are connected through the same parameter, direct translation across them is possible. Based on this cross-translatability, various information in the data, carried by alternative assumptions, can be effectively combined to construct tighter bounds on causal effects. Flexibility of the suggested approach is demonstrated focusing on the estimation of the complier average causal effect (CACE) in a randomized job search intervention trial that suffers from noncompliance and subsequent missing outcomes.

BackgroundThe Cessation in Pregnancy Incentives Trial (CPIT), which offered financial incentives for smoking cessation during pregnancy showed a clinically and statistically significant improvement in cessation. However, infant birth weight was not seen to be affected. This study re-examines birth weight using an intuitive and a complier average causal effects (CACE) method to uncover important information missed by intention-to-treat analysis.MethodsCPIT offered financial incentives up to £400 to pregnant smokers to quit. With incentives, 68 women (23.1%) were confirmed non-smokers at primary outcome, compared to 25 (8.7%) without incentives, a difference of 14.3% (Fisher test, p < 0.0001). For this analysis, randomised groups were split into three theoretical sub-groups: independent quitters - quit without incentives, hardened smokers - could not quit even with incentives and potential quitters - required the addition of financial incentives to quit. Viewed in this way, the overall birth weight gain with incentives is attributable only to potential quitters. We compared an intuitive approach to a CACE analysis.ResultsMean birth weight of potential quitters in the incentives intervention group (who therefore quit) was 3338 g compared with potential quitters in the control group (who did not quit) 3193 g. The difference attributable to incentives, was 3338 – 3193 = 145 g (95% CI −617, +803). The mean difference in birth weight between the intervention and control groups was 21 g, and the difference in the proportion who managed to quit was 14.3%. Since the intervention consisted of the offer of incentives to quit smoking, the intervention was received by all women in the intervention group. However, “compliance” was successfully quitting with incentives, and the CACE analysis yielded an identical result, causal birth weight increase 21 g ÷ 0.143 = 145 g.ConclusionsPolicy makers have great difficulty giving pregnant women money to stop smoking. This study indicates that a small clinically insignificant improvement in average birth weight is likely to hide an important clinically significant increase in infants born to pregnant smokers who want to stop but cannot achieve smoking cessation without the addition of financial voucher incentives.Trial RegistrationISRCTN Registry, ISRCTN87508788. Registered on 1 September 2011.

An increasing number of recent studies have suggested that doubly robust estimators with cross-fitting should be used when estimating causal effects with machine learning methods. However, not all existing programs that implement doubly robust estimators support machine learning methods and cross-fitting, or provide estimates on multiplicative scales. To address these needs, we developed AIPW, a software package implementing augmented inverse probability weighting (AIPW) estimation of average causal effects in R (R Foundation for Statistical Computing, Vienna, Austria). Key features of the AIPW package include cross-fitting and flexible covariate adjustment for observational studies and randomized controlled trials (RCTs). In this paper, we use a simulated RCT to illustrate implementation of the AIPW estimator. We also perform a simulation study to evaluate the performance of the AIPW package compared with other doubly robust implementations, including CausalGAM, npcausal, tmle, and tmle3. Our simulation showed that the AIPW package yields performance comparable to that of other programs. Furthermore, we also found that cross-fitting substantively decreases the bias and improves the confidence interval coverage for doubly robust estimators fitted with machine learning algorithms. Our findings suggest that the AIPW package can be a useful tool for estimating average causal effects with machine learning methods in RCTs and observational studies.

Assessing the causal effects of interventions on ordinal outcomes is an important objective of many educational and behavioral studies. Under the potential outcomes framework, we can define causal effects as comparisons between the potential outcomes under treatment and control. However, unfortunately, the average causal effect, often the parameter of interest, is difficult to interpret for ordinal outcomes. To address this challenge, we propose to use two causal parameters, which are defined as the probabilities that the treatment is beneficial and strictly beneficial for the experimental units. However, although well-defined for any outcomes and of particular interest for ordinal outcomes, the two aforementioned parameters depend on the association between the potential outcomes and are therefore not identifiable from the observed data without additional assumptions. Echoing recent advances in the econometrics and biostatistics literature, we present the sharp bounds of the aforementioned causal parameters for ordinal outcomes, under fixed marginal distributions of the potential outcomes. Because the causal estimands and their corresponding sharp bounds are based on the potential outcomes themselves, the proposed framework can be flexibly incorporated into any chosen models of the potential outcomes and is directly applicable to randomized experiments, unconfounded observational studies, and randomized experiments with noncompliance. We illustrate our methodology via numerical examples and three real-life applications related to educational and behavioral research.

Impact of a community-policing initiative promoting substance use disorder treatment over criminal charges on arrest recidivism

The Causal Effect of Fertility on Female Labor Supply: Evidence from Taiwanese Son Preference

In randomised controlled trials that have non-compliance with the treatment assigned, policy makers require unbiased estimates of the causal effect of the treatment received.Instrumental variable (IV) approaches provide complier average causal effects (CACE) estimates.Common IV methods such as two-stage least squares (2SLS) have not been extended to settings with multivariate outcomes.We propose a three-stage least squares (3SLS) regression approach, whereby estimates from the first stage regression of treatment received conditional on assignment, feed into a seemingly unrelated regression (SUR) system of equations that recognise the correlation between the outcomes.We also develop Bayesian IV approaches which jointly model the effects of random assignment on treatment received, and the bivariate outcome, which here is assume to be cost-effectiveness.We also apply 2SLS individually to each outcome, for comparison.We consider the performance of these methods in a simulation study, where costs are assumed to follow Normal or Gamma distributions, to have positive and negative correlation with health outcomes, the instrument is strong (30% non-compliance) or weak (70% noncompliance), and the sample size, moderate (n=1,000) or small (n=100).We find that the proposed IV methods generally perform well.For example, in scenarios with Normally distributed cost data and a strong instrument, each method reports unbiased estimates.However, in these settings the 2SLS approach reports levels of Confidence Interval (CI) coverage that are above (positive correlation) and below (negative correlation) nominal levels.By contrast both the 3SLS and Bayesian methods report CI coverage close to nominal levels.

Many scientific problems require that treatment comparisons be adjusted for posttreatment variables, but the estimands underlying standard methods are not causal effects. To address this deficiency, we propose a general framework for comparing treatments adjusting for posttreatment variables that yields principal effects based on principal stratification. Principal stratification with respect to a posttreatment variable is a cross-classification of subjects defined by the joint potential values of that posttreatment variable tinder each of the treatments being compared. Principal effects are causal effects within a principal stratum. The key property of principal strata is that they are not affected by treatment assignment and therefore can be used just as any pretreatment covariate. such as age category. As a result, the central property of our principal effects is that they are always causal effects and do not suffer from the complications of standard posttreatment-adjusted estimands. We discuss briefly that such principal causal effects are the link between three recent applications with adjustment for posttreatment variables: (i) treatment noncompliance, (ii) missing outcomes (dropout) following treatment noncompliance. and (iii) censoring by death. We then attack the problem of surrogate or biomarker endpoints, where we show, using principal causal effects, that all current definitions of surrogacy, even when perfectly true, do not generally have the desired interpretation as causal effects of treatment on outcome. We go on to forrmulate estimands based on principal stratification and principal causal effects and show their superiority.

BackgroundThe impact of both implementation strategies (IS) and evidence-based interventions (EBI) can vary across contexts, and a better understanding of how and why this occurs presents fundamental but challenging questions that implementation science as a field will need to grapple with. We use causal epidemiologic methods to explore the mechanisms of why sharp distinctions between implementation strategies (IS) and efficacy of an evidence-based intervention (EBI) may fail to recognize that the effect of an EBI can be deeply intertwined and dependent on the context of the IS leading to its uptake.MethodsWe explore the use of instrumental variable (IV) analyses as a critical tool for implementation science methods to isolate three relevant quantities within the same intervention context when exposure to an implementation strategy is random: (1) the effect of an IS on implementation outcomes (e.g., uptake), (2) effect of EBI uptake on patient outcomes, and (3) overall effectiveness of the IS (i.e., ~ implementation*efficacy). We discuss the mechanisms by which an implementation strategy can alter the context, and therefore effect, of an EBI using the underlying IV assumptions. We illustrate these concepts using examples of the implementation of new ART initiation guidelines in Zambia and community-based masking programs in Bangladesh.ResultsCausal questions relevant to implementation science are answered at each stage of an IV analysis. The first stage assesses the effect of the IS (e.g., new guidelines) on EBI uptake (e.g., same-day treatment initiation). The second stage leverages the IS as an IV to estimate the complier average causal effect (CACE) of the EBI on patient outcomes (e.g., effect of same-day treatment initiation on viral suppression). The underlying assumptions of CACE formalize that the causal effect of EBI may differ in the context of a different IS because (1) the mechanisms by which individuals uptake an intervention may differ and (2) the subgroup of individuals who take up an EBI may differ. IV methods thus provide a conceptual framework for how IS and EBIs are linked and that the IS itself needs to be considered a critical contextual determinant. Moreover, it also provides rigorous methodologic tools to isolate the effect of an IS, EBI, and combined effect of the IS and EBI.DiscussionLeveraging IV methods when exposure to an implementation strategy is random helps to conceptualize the context-dependent nature of implementation strategies, EBIs, and patient outcomes. IV methods formalize that the causal effect of an EBI may be specific to the context of the implementation strategy used to promote uptake. This integration of implementation science concepts and theory with rigorous causal epidemiologic methods yields novel insights and provides important tools for exploring the next generation of questions related to mechanisms and context in implementation science.

Dishion and Patterson's work on the unique role of fathers in the coercive family process showed that fathers' coercion explained twice the variance of mothers' in predicting children's antisocial behavior and how treatment and prevention of coercion and promotion of prosocial parenting can mitigate children's problem behaviors. Using these ideas, we employed a sample of 426 divorced or separated fathers randomly assigned to Fathering Through Change (FTC), an interactive online behavioral parent training program or to a waitlist control. Participating fathers had been separated or divorced within the past 24 months with children ages 4 to 12 years. We tested an intent to treat (ITT) mediation hypothesis positing that intervention-induced changes in child problem behaviors would be mediated by changes in fathers' coercive parenting. We also tested complier average causal effects (CACE) models to estimate intervention effects, accounting for compliers and noncompliers in the treatment group and would-be compliers in the controls. Mediation was supported. ITT analyses showed the FTC obtained a small direct effect on father-reported pre-post changes in child adjustment problems (d = .20), a medium effect on pre-post changes in fathers' coercive parenting (d = .61), and a moderate indirect effect to changes in child adjustment (d = .30). Larger effects were observed in CACE analyses.

Objective We evaluated the effects of treatment compliance with the Challenging Horizons Program (CHP) for high school aged adolescents with attention-deficit hyperactivity disorder (ADHD). Method Participants were 185 high school aged adolescents (65% non-Hispanic White; 79% male) with a diagnosis of ADHD who were randomly assigned to either CHP or community control. Outcomes included parent-rated academic functioning, parent- and self-rated social-emotional functioning, and GPA. The complier average causal effect (CACE) was estimated using propensity-weighted models for youth engaging in ≥ 30 CHP individual sessions (15–20 min) across the academic year. Results Most (78%) CHP participants engaged in≥30 CHP sessions. CACE analyses using latent growth curve modeling revealed significant treatment effects among treatment compliers across ratings of academic and social outcomes relative to similar control participants. For most outcomes, CACE estimates were larger than those found in intent-to-treat analyses, especially at 6-months follow-up. Conclusions Compliance with 30 or more individual CHP sessions appeared to be an attainable threshold associated with incremental gains across several academic and social outcomes. Effects of compliance were amplified at 6-months follow-up, supporting the hypothesized theory of change of training interventions. Future work should focus on facilitators of treatment engagement and feasibility of the CHP as delivered by high school personnel.