Preference design analysis
The final aim will be to determine if participant preference
impacts intervention effectiveness when compared to
the control group. This aim will be accomplished through
comparing the estimated effectiveness across the two groups
(i.e., RCT and preference). If the preference towards programs
has significant impact on the program effectiveness,
we would expect the preference group participants to have
extra motivation to adhere to the program they choose and
achieve a relatively larger weight loss when compared to the
similar program participants in the RCT group. Parametric and
nonparametric testswill be employed to performthe statistical
comparison of the weight loss of the same program participants
across the two groups. Furthermore, we will employ
econometric selection models (e.g., Heckman two-stage selection
model, Double-Hurdle model, and two-part model)
to evaluate potential bias brought to the treatment effect
estimators when participants in the programare not randomly
assigned, but instead they make their own decision of which
program to participate. Through modeling the participation
stage decision-making, the second-stage program effect estimation
will be able to control for this preference impact and
result in consistent programimpact estimation. The preference
impact on the program effectiveness can be tested statistically.
For example, the Heckman two-stage model involves a first
step of Probit model that estimate the participation decision
and then generate an inverse Mills ratio (IMR) term that
captures the selection bias; then this IMRwill be entered in the
second step weight loss equation as an extra regressor to
control for the selection bias. The coefficient of the IMR in the
second-step can be tested to see whether it is significantly
different from zero. If it is significant, it confirms the existence
of the preference impact on the program effectiveness.