The potential for bias in principal causal effect estimation when treatment received depends on a key covariate

Motivated by a potential-outcomes perspective, the idea of principal stratification has been widely recognized for its relevance in settings susceptible to posttreatment selection bias such as randomized clinical trials where treatment received can differ from treatment assigned. In one such setting, we address subtleties involved in inference for causal effects when using a key covariate to predict membership in latent principal strata. We show that when treatment received can differ from treatment assigned in both study arms, incorporating a stratum-predictive covariate can make estimates of the "complier average causal effect" (CACE) derive from observations in the two treatment arms with different covariate distributions. Adopting a Bayesian perspective and using Markov chain Monte Carlo for computation, we develop posterior checks that characterize the extent to which incorporating the pretreatment covariate endangers estimation of the CACE. We apply the method to analyze a clinical trial comparing two treatments for jaw fractures in which the study protocol allowed surgeons to overrule both possible randomized treatment assignments based on their clinical judgment and the data contained a key covariate (injury severity) predictive of treatment received.Comment: Published in at http://dx.doi.org/10.1214/11-AOAS477 the Annals of Applied Statistics (http://www.imstat.org/aoas/) by the Institute of Mathematical Statistics (http://www.imstat.org

ESTIMATING THE LONGITUDINAL COMPLIER AVERAGE CAUSAL EFFECT USING THE LATENT GROWTH MODEL: A SIMULATION STUDY

When noncompliance happens to longitudinal experiments, the randomness for drawing causal inferences is contaminated. In such cases, the longitudinal Complier Average Causal Effect (CACE) is often estimated. The Latent Growth Model (LGM) is very useful in estimating longitudinal trajectories and can be easily adapted for estimating longitudinal CACE. Two popular CACE approaches, the Standard IV approach and the Mixture Model Based (MMB) approach, are both readily applicable to the LGM framework. The Standard IV approach is simple in modelling and has a low computational burden, but it is also criticized for ignoring distributions of subgroups and leading to biased estimations. The MMB approach is capable of not only estimating the CACE but also answering research questions regarding distributions of subpopulations, but this method may yield unstable results under unfavorable conditions, especially when the estimation model is complicated. Previous studies laid out a theoretical background for applying LGMs to longitudinal CACE estimation using both approaches. However, 1) very little was known regarding the factors that might influence the longitudinal CACE estimation, 2) the three compliance classes scenario was not thoroughly investigated, and 3) it was still unclear about how and to what extent the Standard IV approach would perform better or worse than the MMB approach in the longitudinal CACE estimation. The present study used an intensive simulation design to investigate the performance of the Standard IV and the MMB approaches while manipulating six factors that were related to most experimental designs: sample size, compliance composition, effect size, reliability of measurements, mean distances, and noncomplier-complier Level 2 covariance ratio. Their performance was evaluated on four criteria, estimation success rate, estimation bias, power, and type I error rate. With the analysis result, suggestions regarding experiment designs were provided for researchers and practitioners

Estimating the Complier Average Causal Effect for Exponential Survival in the Presence of Mid-Trial Switching

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

Treatment compliance and effectiveness of a cognitive behavioural intervention for low back pain : a complier average causal effect approach to the BeST data set

Background: Group cognitive behavioural intervention (CBI) is effective in reducing low-back pain and disability in comparison to advice in primary care. The aim of this analysis was to investigate the impact of compliance on estimates of treatment effect and to identify factors associated with compliance. Methods: In this multicentre trial, 701 adults with troublesome sub-acute or chronic low-back pain were recruited from 56 general practices. Participants were randomised to advice (control n = 233) or advice plus CBI (n = 468). Compliance was specified a priori as attending a minimum of three group sessions and the individual assessment. We estimated the complier average causal effect (CACE) of treatment. Results: Comparison of the CACE estimate of the mean treatment difference to the intention-to-treat (ITT) estimate at 12 months showed a greater benefit of CBI amongst participants compliant with treatment on the Roland Morris Questionnaire (CACE: 1.6 points, 95% CI 0.51 to 2.74; ITT: 1.3 points, 95% CI 0.55 to 2.07), the Modified Von Korff disability score (CACE: 12.1 points, 95% CI 6.07 to 18.17; ITT: 8.6 points, 95% CI 4.58 to 12.64) and the Modified von Korff pain score (CACE: 10.4 points, 95% CI 4.64 to 16.10; ITT: 7.0 points, 95% CI 3.26 to 10.74). People who were non-compliant were younger and had higher pain scores at randomisation. Conclusions: Treatment compliance is important in the effectiveness of group CBI. Younger people and those with more pain are at greater risk of non-compliance

Estimation of causal effects using instrumental variables with nonignorable missing covariates: Application to effect of type of delivery NICU on premature infants

Understanding how effective high-level NICUs (neonatal intensive care units that have the capacity for sustained mechanical assisted ventilation and high volume) are compared to low-level NICUs is important and valuable for both individual mothers and for public policy decisions. The goal of this paper is to estimate the effect on mortality of premature babies being delivered in a high-level NICU vs. a low-level NICU through an observational study where there are unmeasured confounders as well as nonignorable missing covariates. We consider the use of excess travel time as an instrumental variable (IV) to control for unmeasured confounders. In order for an IV to be valid, we must condition on confounders of the IV---outcome relationship, for example, month prenatal care started must be conditioned on for excess travel time to be a valid IV. However, sometimes month prenatal care started is missing, and the missingness may be nonignorable because it is related to the not fully measured mother's/infant's risk of complications. We develop a method to estimate the causal effect of a treatment using an IV when there are nonignorable missing covariates as in our data, where we allow the missingness to depend on the fully observed outcome as well as the partially observed compliance class, which is a proxy for the unmeasured risk of complications. A simulation study shows that under our nonignorable missingness assumption, the commonly used estimation methods, complete-case analysis and multiple imputation by chained equations assuming missingness at random, provide biased estimates, while our method provides approximately unbiased estimates. We apply our method to the NICU study and find evidence that high-level NICUs significantly reduce deaths for babies of small gestational age, whereas for almost mature babies like 37 weeks, the level of NICUs makes little difference. A sensitivity analysis is conducted to assess the sensitivity of our conclusions to key assumptions about the missing covariates. The method we develop in this paper may be useful for many observational studies facing similar issues of unmeasured confounders and nonignorable missing data as ours.Comment: Published in at http://dx.doi.org/10.1214/13-AOAS699 the Annals of Applied Statistics (http://www.imstat.org/aoas/) by the Institute of Mathematical Statistics (http://www.imstat.org

An Application of the Complier Average Causal Effect Analysis to Examine the Effects of a Family Intervention in Reducing Illicit Drug Use among High‐Risk Hispanic Adolescents

Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/107494/1/famp12068.pd