Complier Average Causal Effect Estimation Research Articles

Effects of Compliance to a Training Intervention for High School Students with ADHD

ABSTRACT 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.

Effects of Cross-Age Peer Mentoring Program within a Randomized Controlled Trial

This paper summarizes results from an impact study that employed a randomized controlled trial to estimate the efficacy of a cross-age peer mentor program designed to prevent school dropout during the transition from middle to high school. We present findings from the intent-to-treat (ITT) analyses, which included 1,351 ninth-grade students, alongside those of two different methods that estimate the complier average causal effect (CACE) of participating in the program. Although the confirmatory study, which investigated impact on attendance and credit accrual in ninth grade, was null, ITT analyses on exploratory outcomes indicate modest, yet potentially meaningful program impact on ninth-grade outcomes of discipline, school attachment, and expectations of degree attainment across varying dosage levels. CACE estimates also suggest that a threshold level of program participation broadens the program’s impact on additional exploratory academic achievement and social and emotional learning outcomes. Given the adverse effects of the transition to high school, this promising evidence indicates that the cross-age peer mentoring intervention could be an effective strategy for high schools to implement that leverages existing staff and students.

The Good Behaviour Game intervention to improve behavioural and other outcomes for children aged 7–8 years: a cluster RCT

BackgroundUniversal, school-based behaviour management interventions can produce meaningful improvements in children’s behaviour and other outcomes. However, the UK evidence base for these remains limited.ObjectiveThe objective of this trial was to investigate the impact, value for money and longer-term outcomes of the Good Behaviour Game. Study hypotheses centred on immediate impact (hypothesis 1); subgroup effects (at-risk boys, hypothesis 2); implementation effects (dosage, hypothesis 3); maintenance/sleeper effects (12- and 24-month post-intervention follow-ups, hypothesis 4); the temporal association between mental health and academic attainment (hypothesis 5); and the health economic impact of the Good Behaviour Game (hypothesis 6).DesignThis was a two-group, parallel, cluster-randomised controlled trial. Primary schools (n = 77) were randomly assigned to implement the Good Behaviour Game for 2 years or continue their usual practice, after which there was a 2-year follow-up period.SettingThe trial was set in primary schools across 23 local authorities in England.ParticipantsParticipants were children (n = 3084) aged 7–8 years attending participating schools.InterventionThe Good Behaviour Game is a universal behaviour management intervention. Its core components are classroom rules, team membership, monitoring behaviour and positive reinforcement. It is played alongside a normal classroom activity for a set time, during which children work in teams to win the game to access the agreed rewards. The Good Behaviour Game is a manualised intervention delivered by teachers who receive initial training and ongoing coaching.Main outcome measuresThe measures were conduct problems (primary outcome; teacher-rated Strengths and Difficulties Questionnaire scores); emotional symptoms (teacher-rated Strengths and Difficulties Questionnaire scores); psychological well-being, peer and social support, bullying (i.e. social acceptance) and school environment (self-report Kidscreen survey results); and school absence and exclusion from school (measured using National Pupil Database records). Measures of academic attainment (reading, standardised tests), disruptive behaviour, concentration problems and prosocial behaviour (Teacher Observation of Child Adaptation Checklist scores) were also collected during the 2-year follow-up period.ResultsThere was no evidence that the Good Behaviour Game improved any outcomes (hypothesis 1). The only significant subgroup moderator effect identified was contrary to expectations: at-risk boys in Good Behaviour Game schools reported higher rates of bullying (hypothesis 2). The moderating effect of the amount of time spent playing the Good Behaviour Game was unclear; in the context of both moderate (≥ 1030 minutes over 2 years) and high (≥ 1348 minutes over 2 years) intervention compliance, there were significant reductions in children’s psychological well-being, but also significant reductions in their school absence (hypothesis 3). The only medium-term intervention effect was for peer and social support at 24 months, but this was in a negative direction (hypothesis 4). After disaggregating within- and between-individual effects, we found no temporal within-individual associations between children’s mental health and their academic attainment (hypothesis 5). Last, our cost–consequences analysis indicated that the Good Behaviour Game does not provide value for money (hypothesis 6).LimitationsLimitations included the post-test-only design for several secondary outcomes; suboptimal implementation dosage (mitigated by complier-average causal effect estimation); and moderate child-level attrition (18.5% for the primary outcome analysis), particularly in the post-trial follow-up period (mitigated by the use of full information maximum likelihood procedures).Future workQuestions remain regarding programme differentiation (e.g. how distinct is the Good Behaviour Game from existing behaviour management practices, and does this makes a difference in terms of its impact?) and if the Good Behaviour Game is impactful when combined with a complementary preventative intervention (as has been the case in several earlier trials).ConclusionThe Good Behaviour Game cannot be recommended based on the findings reported here.Trial registrationThis trial is registered as ISRCTN64152096.FundingThis project was funded by the National Institute for Health and Care Research (NIHR) Public Health Research programme and will be published in full inPublic Health Research; Vol. 10, No. 7. See the NIHR Journals Library website for further project information.

Assessing complier average causal effects from longitudinal trials with multiple endpoints and treatment noncompliance: An application to a study of Arthritis Health Journal.

Treatment noncompliance often occurs in longitudinal randomized controlled trials (RCTs) on human subjects, and can greatly complicate treatment effect assessment. The complier average causal effect (CACE) informs the intervention efficacy for the subpopulation who would comply regardless of assigned treatment and has been considered as patient-oriented treatment effects of interest in the presence of noncompliance. Real-world RCTs evaluating multifaceted interventions often employ multiple study endpoints to measure treatment success. In such trials, limited sample sizes, low compliance rates, and small to moderate effect sizes on individual endpoints can significantly reduce the power to detect CACE when these correlated endpoints are analyzed separately. To overcome the challenge, we develop a multivariate longitudinal potential outcome model with stratification on latent compliance types to efficiently assess multivariate CACEs (MCACE) by combining information across multiple endpoints and visits. Evaluation using simulation data shows a significant increase in the estimation efficiency with the MCACE model, including up to 50% reduction in standard errors (SEs) of CACE estimates and 1-fold increase in the power to detect CACE. Finally, we apply the proposed MCACE model to an RCT on Arthritis Health Journal online tool. Results show that the MCACE analysis detects significant and beneficial intervention effects on two of the six endpoints while estimating CACEs for these endpoints separately fail to detect treatment effect on any endpoint.

Compliance with telephone-based lifestyle weight loss programs improves low back pain but not knee pain outcomes: complier average causal effects analyses of 2 randomised trials.

We conducted a complier average causal effect (CACE) analyses for 2 pragmatic randomised controlled trials. We aimed to assess the effectiveness of telephone-based lifestyle weight loss interventions compared with usual care among compliers. Participants from 2 trials with low back pain (n = 160) and knee osteoarthritis (n = 120) with a body mass index ≥27 kg/m2 were included. We defined adherence to the telephone-based lifestyle weight loss program as completing 60% (6 from 10) of telephone health coaching calls. The primary outcomes for CACE analyses were pain intensity (0-10 Numerical Rating Scale) and disability (Roland Morris Disability Questionnaire for low back pain and Western Ontario and McMaster Universities Osteoarthritis Index for knee osteoarthritis). Secondary outcomes were weight, physical activity, and diet. We used an instrumental variable approach to estimate CACE in compliers. From the intervention groups of the trials, 29% of those with low back pain (n = 23/80) and 34% of those with knee osteoarthritis (n = 20/60) complied. Complier average causal effect estimates showed potentially clinically meaningful effects, but with low certainty because of wide confidence intervals, for pain intensity (-1.4; 95% confidence interval, -3.1, 0.4) and small but also uncertain effects for disability (-2.1; 95% confidence interval, -8.6, 4.5) among compliers in the low back pain trial intervention compared with control but not in the knee osteoarthritis trial. Our findings showed that compliers of a telephone-based weight loss intervention in the low back pain trial generally had improved outcomes; however, there were inconsistent effects in compliers from the knee osteoarthritis trial. Complier average causal effect estimates were larger than intention-to-treat results but must be considered with caution.

Treatment effect modifiers in a randomized trial of the good behavior game during middle childhood.

Objective: Two key treatment effect modifiers-implementation variability and participant cumulative risk status-are examined as predictors of disruptive behavior outcomes in the context of a large cluster randomized controlled trial of a universal, school-based behavior management intervention. The core components of the Good Behavior Game (GBG) are classroom rules, team membership, monitoring behavior, and positive reinforcement. Children work in teams to win the game, which is played alongside a normal classroom activity, during which their teacher monitors infractions to classroom rules. Teams with four or fewer infractions at the end of the game win and are rewarded. Method: Seventy-seven English primary schools (N = 3,084 children, aged 6-7) were randomly assigned to deliver the GBG or continue their usual practice over 2 years. Results: Intent-to-treat analysis found no discernible impact of the intervention on children's disruptive behavior. Additionally, subgroup analyses revealed no differential gains among children at low, moderate or high levels of cumulative risk exposure (CRE). However, complier average causal effect estimation (CACE) using dosage as a compliance marker identified a large, statistically significant intervention effect (d = -1.35) among compliers (>1,030 min of cumulative intervention exposure). Furthermore, this compliance effect varied by participant CRE, such that children at high and low levels of exposure experienced significantly greater and lesser reductions in disruptive behavior, respectively. Conclusions: These findings highlight the importance of optimizing implementation and demonstrate the utility of CRE as a theoretically informed approach to subgroup moderator analysis. Implications are discussed and study strengths and limitations are noted. (PsycInfo Database Record (c) 2021 APA, all rights reserved).

Using Complier Average Causal Effect Estimation to Examine Student Outcomes of the PAX Good Behavior Game When Integrated with the PATHS Curriculum.

A growing body of research has documented a link between variation in implementation dosage and outcomes associated with preventive interventions. Complier Average Causal Effect (CACE; Jo in J Educ Behav Stat 27:385-409, 2002) analysis allows for estimating program impacts in light of variation in implementation. This study reports intent-to-treat (ITT) and CACE findings from a randomized controlled trial (RCT) testing the impacts of the universal PAX Good Behavior Game (PAX GBG)integrated with Promoting Alternative Thinking Strategies (i.e., PATHS to PAX) and PAX GBG only compared to a control. This study used ratings by 318K-5 teachers of 1526 at-risk children who, at baseline, were rated as displaying the top 33rd percentile of aggressive-disruptive behavior. Leveraging a prior study on these data (Berg et al. in Admin Policy Ment Health Ment Health Serv Res 44:558-571, https://doi.org/10.1007/s10488-016-0738-1 , 2017), CACE was defined as the effect of intervention assignment for compliers, using two compliance cut points (50th and 75th percentile), on posttest ratings of student academic engagement, social competence, peer relations, emotion regulation, hyperactivity, and aggressive-disruptive behavior. The ITT analyses indicated improvements for students in the integrated condition on ratings of social competence compared to the control condition. The CACE analyses also indicated significant effects of the integrated intervention on social competence, as well as academic engagement and emotion regulation for students in high compliance classrooms. These findings illustrate the importance of considering variation in implementation within the context of RCTs.

Implementation matters: Using complier average causal effect estimation to determine the impact of the Promoting Alternative Thinking Strategies (PATHS) curriculum on children’s quality of life.

This cluster randomized trial evaluated the impact of the Promoting Alternative Thinking Strategies (PATHS) curriculum on children’s psychological wellbeing, peer social support, and school connectedness. Forty-five schools in England were randomly assigned to implement PATHS or continue their usual provision for 2 years. The trial sample was 5,218 students, aged 7–9 at baseline (M = 8.12, SD = .87). Teachers in PATHS schools received initial training and ongoing implementation support and assistance from trained coaches. Multilevel intent-to-treat (ITT) analysis of outcome data indicated that PATHS led to a small, statistically significantly improvement in children’s psychological wellbeing but had no discernible impact on their peer social support or school connectedness. Multilevel complier average causal effect estimation using dosage as a compliance marker increased the intervention effect size for psychological wellbeing and revealed significant medium to large effects for peer social support and school connectedness. The implications of these findings are discussed, and study limitations are noted. (PsycINFO Database Record (c) 2020 APA, all rights reserved)

Family-centered alcohol use prevention for African American adolescents: A randomized clinical trial.

The efficacy of the Strong African American Families (SAAF) alcohol use prevention program was tested. SAAF is a 7-session family skills training program offered in community settings. To overcome limitations of a past trial that used intent-to-treat (ITT) analyses, a Complier Average Causal Effect (CACE) analysis was used to estimate intervention effects and to determine the precise dosage of the intervention needed to achieve alcohol deterrence. A sample of 472 African American youth and their caregivers were recruited randomly from public schools in 7 rural Georgia counties. Families were assigned randomly to receive SAAF or a no-treatment control. Youth provided data on their alcohol use during the past 3 months at 4 home visits, the final occurring 34 months after baseline and 28 months after the intervention. Efficacy was tested with Poisson latent growth curve models. SAAF deterred growth in alcohol use in models using both ITT and CACE estimation. CACE analyses revealed that, among participants who received a full dose of the intervention (7 sessions), a large treatment effect on slowed growth in alcohol use emerged (β = -.83, p < .001). Dose-response analyses in CACE models revealed a medium-sized effect (d [95% CI] = 1.51 [1.25, 1.75]) when participants attended at least 5 of the 7 sessions offered. Replication of SAAF in a second randomized prevention trial supports the robustness of program effects. It is critical, however, that participant engagement protocols be designed to encourage participation in as at least 5 of the 7 sessions. (PsycINFO Database Record (c) 2019 APA, all rights reserved).

Supplemental Material for Implementation Matters: Using Complier Average Causal Effect Estimation to Determine the Impact of the Promoting Alternative Thinking Strategies (PATHS) Curriculum on Children’s Quality of Life

Supplemental Material for Implementation Matters: Using Complier Average Causal Effect Estimation to Determine the Impact of the Promoting Alternative Thinking Strategies (PATHS) Curriculum on Children’s Quality of Life

Efficacy of the Fun For Wellness Online Intervention to Promote Well-Being Actions: A Secondary Data Analysis

Fun For Wellness (FFW) is a new online intervention designed to promote growth in well-being by providing capability-enhancing learning opportunities (e.g., play an interactive game) to participants. The purpose of this study was to provide an initial evaluation of the efficacy of the FFW intervention to increase well-being actions. The study design was a secondary data analysis of a large-scale prospective, double-blind, parallel-group randomized controlled trial. Data were collected at baseline and 30 and 60 days postbaseline. A total of 479 adult employees at a major university in the southeast of the United States of America were enrolled. Participants who were randomly assigned to the FFW group were provided with 30 days of 24-hour access to the intervention. A two-class linear regression model with complier average causal effect estimation was fitted to well-being actions scores at 30 and 60 days. Intent-to-treat analysis provided evidence that the effect of being assigned to the FFW intervention, without considering actual participation in the FFW intervention, had a null effect on each dimension of well-being actions at 30 and 60 days. Participants who complied with the FFW intervention, however, had significantly higher well-being actions scores, compared to potential compliers in the Usual Care group, in the interpersonal dimension at 60 days, and the physical dimension at 30 days. Results from this secondary data analysis provide some supportive evidence for both the efficacy of and possible revisions to the FFW intervention in regard to promoting well-being actions.

Efficacy of the Fun For Wellness Online Intervention to Promote Multidimensional Well-Being: a Randomized Controlled Trial.

Subjective well-being refers to people's level of satisfaction with life as a whole and with multiple dimensions within it. Interventions that promote subjective well-being are important because there is evidence that physical health, mental health, substance use, and health care costs may be related to subjective well-being. Fun For Wellness (FFW) is a new online universal intervention designed to promote growth in multiple dimensions of subjective well-being. The purpose of this study was to provide an initial evaluation of the efficacy of FFW to increase subjective well-being in multiple dimensions in a universal sample. The study design was a prospective, double-blind, parallel group randomized controlled trial. Data were collected at baseline and 30 and 60days-post baseline. A total of 479 adult employees at a major university in the southeast of the USA were enrolled. Recruitment, eligibility verification, and data collection were conducted online. Measures of interpersonal, community, occupational, physical, psychological, economic (i.e., I COPPE), and overall subjective well-being were constructed based on responses to the I COPPE Scale. A two-class linear regression model with complier average causal effect estimation was imposed for each dimension of subjective well-being. Participants who complied with the FFW intervention had significantly higher subjective well-being, as compared to potential compliers in the Usual Care group, in the following dimensions: interpersonal at 60days, community at 30 and 60days, psychological at 60days, and economic at 30 and 60days. Results from this study provide some initial evidence for both the efficacy of, and possible revisions to, the FFW intervention.

Well-being self-efficacy and complier average causal effect estimation: A substantive-methodological synergy

ObjectivesThe purpose of this manuscript was to provide a substantive (i.e., well-being self-efficacy) – methodological (i.e., complier average causal effect estimation) synergy of potential importance to future research in the psychology of sport and exercise with secondary data analyses from the Fun For Wellness intervention. Fun For Wellness is a new on-line intervention designed to promote growth in well-being. Well-being self-efficacy is a proposed mechanism by which the effect of Fun For Wellness on well-being may be transmitted. Complier average causal effect estimation is a methodology that estimates the effect of complying with an intervention. DesignThe study design was a prospective, double-blind, parallel group randomized controlled trial (RCT) detailed in Myers, Prilleltensky, et al. (2016). Data were collected at baseline, 30 days- and 60 days-post baseline. A total of 479 adult employees at a major university in the southeast of the United States of America were enrolled. MethodA two-class linear regression model with complier average causal effect estimation was fitted to well-being self-efficacy scores at 30- and 60-days. ResultsThe adjusted mean difference in well-being self-efficacy scores for participants who complied with the intervention, as compared to potential compliers in the Usual Care group, was equal to 0.21, p = 0.061, Cohen's d = 0.36 at 30-days and 0.28, p = 0.050, Cohen's d = 0.49 at 60-days. ConclusionComplier average causal effect estimation may be a useful approach for RCTs in sport and exercise psychology when at least some of the participants do not comply with the intervention.

Using Complier Average Causal Effect Estimation toDetermine the Impacts of the Good Behavior Game Preventive Intervention on Teacher Implementers.

Complier average causal effect (CACE) analysis is a causal inference approach that accounts for levels of teacher implementation compliance. In the current study, CACE was used to examine one-year impacts of PAX good behavior game (PAX GBG) and promoting alternative thinking strategies (PATHS) on teacher efficacy and burnout. Teachers in 27 elementary schools were randomized to PAX GBG, an integration of PAX GBG and PATHS, or a control condition. There were positive overall effects on teachers' efficacy beliefs, but high implementing teachers also reported increases in burnout across the school year. The CACE approach may offer new information not captured using a traditional intent-to-treat approach.

The efficacy of interpersonal psychotherapy for depression among economically disadvantaged mothers.

A randomized clinical trial was conducted to evaluate the efficacy of interpersonal psychotherapy (IPT) for ethnically and racially diverse, economically disadvantaged women with major depressive disorder. Non-treatment-seeking urban women (N = 128; M age = 25.40, SD = 4.98) with infants were recruited from the community. Participants were at or below the poverty level: 59.4% were Black and 21.1% were Hispanic. Women were screened for depressive symptoms using the Center for Epidemiologic Studies Depression Scale; the Diagnostic Interview Schedule was used to confirm major depressive disorder diagnosis. Participants were randomized to individual IPT or enhanced community standard. Depressive symptoms were assessed before, after, and 8 months posttreatment with the Beck Depression Inventory-II and the Revised Hamilton Rating Scale for Depression. The Social Support Behaviors Scale, the Social Adjustment Scale-Self-Report, and the Perceived Stress Scale were administered to examine mediators of outcome at follow-up. Treatment effects were evaluated with a growth mixture model for randomized trials using complier-average causal effect estimation. Depressive symptoms trajectories from baseline through postintervention to follow-up showed significant decreases among the IPT group compared to the enhanced community standard group. Changes on the Perceived Stress Scale and the Social Support Behaviors Scale mediated sustained treatment outcome.

Effectiveness of Music Education for the Improvement of Reading Skills and Academic Achievement in Young Poor Readers: A Pragmatic Cluster-Randomized, Controlled Clinical Trial

IntroductionDifficulties in word-level reading skills are prevalent in Brazilian schools and may deter children from gaining the knowledge obtained through reading and academic achievement. Music education has emerged as a potential method to improve reading skills because due to a common neurobiological substratum.ObjectiveTo evaluate the effectiveness of music education for the improvement of reading skills and academic achievement among children (eight to 10 years of age) with reading difficulties.Method235 children with reading difficulties in 10 schools participated in a five-month, randomized clinical trial in cluster (RCT) in an impoverished zone within the city of São Paulo to test the effects of music education intervention while assessing reading skills and academic achievement during the school year. Five schools were chosen randomly to incorporate music classes (n = 114), and five served as controls (n = 121). Two different methods of analysis were used to evaluate the effectiveness of the intervention: The standard method was intention-to-treat (ITT), and the other was the Complier Average Causal Effect (CACE) estimation method, which took compliance status into account.ResultsThe ITT analyses were not very promising; only one marginal effect existed for the rate of correct real words read per minute. Indeed, considering ITT, improvements were observed in the secondary outcomes (slope of Portuguese = 0.21 [p<0.001] and slope of math = 0.25 [p<0.001]). As for CACE estimation (i.e., complier children versus non-complier children), more promising effects were observed in terms of the rate of correct words read per minute [β = 13.98, p<0.001] and phonological awareness [β = 19.72, p<0.001] as well as secondary outcomes (academic achievement in Portuguese [β = 0.77, p<0.0001] and math [β = 0.49, p<0.001] throughout the school year).ConclusionThe results may be seen as promising, but they are not, in themselves, enough to make music lessons as public policy.

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.

Sensitivity analysis for unmeasured confounding in principal stratification settings with binary variables

Within causal inference, principal stratification (PS) is a popular approach for dealing with intermediate variables, that is, variables affected by treatment that also potentially affect the response. However, when there exists unmeasured confounding in the treatment arms--as can happen in observational studies--causal estimands resulting from PS analyses can be biased. We identify the various pathways of confounding present in PS contexts and their effects for PS inference. We present model-based approaches for assessing the sensitivity of complier average causal effect estimates to unmeasured confounding in the setting of binary treatments, binary intermediate variables, and binary outcomes. These same approaches can be used to assess sensitivity to unknown direct effects of treatments on outcomes because, as we show, direct effects are operationally equivalent to one of the pathways of unmeasured confounding. We illustrate the methodology using a randomized study with artificially introduced confounding and a sensitivity analysis for an observational study of the effects of physical activity and body mass index on cardiovascular disease.

School Choice as a Latent Variable: Estimating the “Complier Average Causal Effect” of Vouchers in Charlotte

Randomized field trials of school voucher policy interventions face major statistical hurdles in the measurement of a voucher effect on student achievement. Selection bias undermines the benefits of randomization when the treatment, a random offer of a voucher, is declined by participants who systematically differ from those who accept. This article argues that the complier average causal effect (CACE) is the parameter of interest in voucher evaluations. As an example, the CACE is estimated using data from a small, one‐year field trial of vouchers in Charlotte, NC. In this estimation, voucher impacts in Charlotte are positive, but appear to be moderated by the probability of compliance. For math achievement, maximum likelihood CACE estimates are smaller and insignificant compared to intention to treat and instrumental variable estimates of mean treatment effects.

Estimating treatment effects from randomized clinical trials with noncompliance and loss to follow-up: the role of instrumental variable methods

Perfectly implemented randomized clinical trials, particularly of complex interventions, are extremely rare. Almost always they are characterized by imperfect adherence to the randomly allocated treatment and variable amounts of missing outcome data. Here we start by describing a wide variety of examples and then introduce instrumental variable methods for the analysis of such trials. We concentrate mainly on situations in which compliance is all or nothing (either the patient receives the allocated treatment or they do not--in the latter case they may receive no treatment or a treatment other than the one allocated). The main purpose of the review is to illustrate the use of latent class (finite mixture) models, using maximum likelihood, for complier-average causal effect estimation under varying assumptions concerning the mechanism of the missing outcome data.