Rejoinder: Optimal Individualized Decision Rules Using Instrumental Variable Methods.

One potential disadvantage of this sketched method is that it may be difficult to correctly specify Graph HT <math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><mi mathvariant="script">T</mi></math> ht so that Graph HT <math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><mrow><msub><mrow><mi>t</mi></mrow><mn>0</mn></msub><mo> </mo><mi mathvariant="script">T</mi></mrow></math> ht while the maximization problem remains easy to solve. All the above results can be easily adapted to the case where the estimand of interest is instead an AEE Graph HT <math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><mrow><msubsup><mrow><mi> </mi></mrow><mrow><msub><mrow><mi>e</mi></mrow><mn>0</mn></msub></mrow><mi>E</mi></msubsup><mo stretchy="false">(</mo><msub><mrow><mi>P</mi></mrow><mn>0</mn></msub><mo stretchy="false">)</mo><mo>-</mo><msubsup><mrow><mi> </mi></mrow><mrow><msub><mrow><mi>e</mi></mrow><mi>r</mi></msub></mrow><mi>E</mi></msubsup><mo stretchy="false">(</mo><msub><mrow><mi>P</mi></mrow><mn>0</mn></msub><mo stretchy="false">)</mo></mrow></math> ht for a reference rule I e SB r sb i . Let Graph HT <math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><mrow><msub><mrow><mrow><mover accent="true"><mi>t</mi><mo stretchy="true">˜</mo></mover></mrow></mrow><mn>0</mn></msub><mo> </mo><msub><mrow><mrow><mtext>argmax</mtext></mrow></mrow><mrow><mi>t</mi><mo> </mo><mi mathvariant="script">T</mi></mrow></msub><msubsup><mrow><mi> </mi></mrow><mi>t</mi><mi>T</mi></msubsup><mo stretchy="false">(</mo><msub><mrow><mi>P</mi></mrow><mn>0</mn></msub><mo stretchy="false">)</mo></mrow></math> ht be a true optimal ITR in Graph HT <math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><mi mathvariant="script">T</mi></math> ht . [Extracted from the article]