Treatment recommendation and parameter estimation under single-index contrast function

Model-free screening for variables with treatment interaction

“…Note that β t may not be identifiable and our focus here is to identify boldx A rather than to estimate β t. Model (1) actually accommodates a variety of parametric and semiparametric, models whose primary objective is to estimate the optimal treatment selection rule, such as the linear regression model, 14,35 the single-index model, 7,44 and the semiparametric single-index model. 5 Note that the difference of the conditional distribution functions of the outcomes under two different treatment categories, that is, F false( y falsefalse| x , T = t 1 false) − F false( y falsefalse| x , T = t 2 false) = F 0 false( y falsefalse| β t 1 ⊤ boldx A I false( T = t 1 false) , boldx I false) − F 0 false( y falsefalse| β t 2 ⊤ boldx A I false( T = t 2 false) , boldx I false), implicitly yields the set of predictive variables as defined in …”

“…Consider the following three models adopted by Xiong et al 7 and Siriwardhana et al, 44 where x is multivariate normal random vector with zero mean vector and covariance matrix normalΣ = false( σ i j ) .1em p × p given by σ i j = 0.8 falsefalse| i − j falsefalse| if both i , j ∈ A or I, otherwise σ i j = 0.1, T is discrete uniform random variable on falsefalse{ 1 , … , K falsefalse}, and ϵ is a normal variable with distribution N false( 0 , 2 false) which is independent to both x and T. Clearly, model 1 is linear and models 2 and 3 are non-linear.…”

“…Note that β t may not be identifiable and our focus here is to identify x A rather than to estimate β t . Model (1) actually accommodates a variety of parametric and semiparametric, models whose primary objective is to estimate the optimal treatment selection rule, such as the linear regression model, 14,35 the single-index model, 7,44 and the semiparametric single-index model. 5 Note that the difference of the conditional distribution functions of the outcomes under two different treatment categories, that is,…”

“…The regression-based methods include Q-learning 3–5 and A-learning. 6–8 Q-learning models the conditional mean of the outcome given the covariates and treatment, while A-learning models the contrast of outcome between two treatments. Regression-based methods rely on the correct specification of some or all of the modelled components of the conditional distribution of the clinical outcome.…”

Causal Effect Estimation for Multivariate Continuous Treatments

“…For decades, causal inference has been widely used in many fields, such as biology, psychology and economics, etc. Most of the current research is based on univariate treatment (binary treatment, multivalued treatment, continuous treatment) (Imai and Ratkovic (2014); Zhu et al (2015); Fong et al (2018); Zubizarreta (2015); Chan et al (2016); Xiong et al (2017); Yiu and Su (2018); Dong et al (2021); Hsu et al (2020)). Some research are focused on multivariate categorical treatments, such as factorial designs and conjoint analysis to estimate the main or interaction effect of any combination level of treatments (Hainmueller et al (2014); Dasgupta et al (2015)).…”