guide.Rmd

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title: "guide"
output: html_document
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# Loh 2014

The problem of searching for subgroups with differential treatment effect is known as subgroup identification.

Response: Y; Treatment: Z; Predictors: X

A subgroup S defined in terms X, let $R(S) = max_{i,j} |E(Y|Z = i, S) - E(Y|Z = j, S)|$ denote the effect size of S.
The goal is to find the maximal subgroup with the largest value of R(S).

# cons of regression model in subgroup identification

1, nonparametric; 2, naturally define subgroups; 3, handles large p small n

# prognostic variable provides inforrmation about the response distribution of an untreated subject
# predictive variable defines subgroups of subjects who are more likely to respond to a given treatment

# 2-step approach to split selection

- find the split variable by chi-squared tests 
- search for the best split on the selected variable