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Growth mixture cace modeling: A statistical approach for evaluating causal effects in longitudinal interventions with noncompliance

Chaorong Wu, University of Nebraska - Lincoln


The importance of accessing treatment fidelity or compliance in intervention studies has long been recognized. Few studies have been conducted that investigated how noncompliance influenced intervention effects in longitudinal intervention studies. This study used Monte Carlo simulation to evaluate a series of factors in a long-term randomized intervention data with noncompliance. Data from the Conjoint Behavioral Consultation (CBC) in Rural Communities was used to demonstrate the estimation of CACE with growth mixture modeling and inform the simulation study. Using a growth mixture modeling framework, simulation analyses examined factors that influenced statistical power/Type-I error rates and parameter recovery. The five factors included in the study were: attrition rate, compliance rate, intervention effect for noncompliers, sample size, and the violation of the exclusion restriction. The difference between Complier-Average Causal Effect (CACE) and intend-to-treat (ITT) in power and Type-I error rate was also evaluated using a latent growth mixture modeling and an ANCOVA approaches. Simulation results showed that attrition had a minor impact on the power and no impact on Type-I error rates for CACE and ITT. The results suggest that the violation of the exclusion restriction assumption for noncompliers may not have any impact on the power, Type-I error rate, or parameters recovery for CACE. The exclusion restriction assumption for noncompliers could be relaxed if a mixture model was used to estimate CACE. When the exclusion restriction assumption was not violated, CACE was more powerful than ITT when compliance rate was low. When compliance rate was high, the power difference between CACE and ITT was small. ITT had more power than CACE when the exclusion restriction assumption did not hold. Compliance rate had a positive effect on the power for CACE and ITT and benefited the parameter recovery of CACE. Compliance rate also benefited Type-I error rate of CACE but not ITT. Results demonstrated that Type-I error rate of CACE was higher than ITT, especially when sample size was small. The Type-I error for CACE tended to be inflated with small sample sizes. This might be due to an underestimation of the standard error for CACE when sample sizes were small. Finally, growth modeling was more powerful than ANCOVA for both CACE and ITT and had fewer Type-I errors in long-term randomized intervention studies. Finally, guideline in longitudinal RCTs with noncompliance and suggestions for future research were discussed.

Subject Area

Statistics|Quantitative psychology

Recommended Citation

Wu, Chaorong, "Growth mixture cace modeling: A statistical approach for evaluating causal effects in longitudinal interventions with noncompliance" (2016). ETD collection for University of Nebraska-Lincoln. AAI10130881.