Scenario 2: carry-over only
DECAY
In the second scenario, we investigate wash-in and a wash-out influences to our treatment variables. With these, the true simulated treatment effect slightly increases over time up to the full treatment effect for each treatment compared to no effect (i.e., zero). As a result, the sample mean model, linear model, G-estimation (independence), and the Bayesian Network with time adjustment all underestimate the simulated treatment effect difference of 2. As the treatment effect increases over time up to the full effect size, the models could not estimate the simulated treatment effect size. Compared to the unadjusted Bayesian Network, we expected the Bayesian Network with time adjustment to improve the estimated treatment effect difference, which was not reflected in the results as the model did not improve the estimate and also underestimated the treatment effect difference. G-estimation (AR1) assumes an AR1 dependence structure within the data, violated through the exponential decay. Hence, it strongly underestimates the treatment effect in simulation with carry over. The only model that yields unbiased estimates of the treatment effect difference for all sample sizes was the COAPM with parameters for wash-in and wash-out, which is close to the data simulation process.Within the data set with missing values, the COAPM tends to overestimate the treatment effect. The other models performed similarly poorly (with respect to bias) when there were missing values compared to no missing values, but with slightly increased standard errors.