Mats J Stensrud and Aaron L. Sarvet's contribution to the Discussion of 'Assumption‐lean inference for generalised linear model parameters' by Vansteelandt and Dukes.

Suppose that I Y i is determined by the structural equation HT <math altimg="urn:x-wiley:13697412:media:rssb12516:rssb12516-math-0001" display="block" xmlns="http://www.w3.org/1998/Math/MathML"><mrow><mi>Y</mi><mo>=</mo><mi> </mi><mo>+</mo><mi> </mi><msup><mrow><mo>(</mo><mo>-</mo><mn>1</mn><mo>)</mo></mrow><mi>L</mi></msup><mi>A</mi><mo>,</mo></mrow></math> ht For HT <math altimg="urn:x-wiley:13697412:media:rssb12516:rssb12516-math-0002" xmlns="http://www.w3.org/1998/Math/MathML"><mrow><mi> </mi><mo> </mo><mi mathvariant="double-struck">R</mi></mrow></math> ht and I i > 0, the average treatment effect (ATE) is HT <math altimg="urn:x-wiley:13697412:media:rssb12516:rssb12516-math-0003" display="block" xmlns="http://www.w3.org/1998/Math/MathML"><mrow><mi mathvariant="double-struck">E</mi><mfenced close=")" open="(" separators=""><msup><mi>Y</mi><mrow><mi>a</mi><mo>=</mo><mn>1</mn></mrow></msup></mfenced><mo>-</mo><mi mathvariant="double-struck">E</mi><mfenced close=")" open="(" separators=""><msup><mi>Y</mi><mrow><mi>a</mi><mo>=</mo><mn>0</mn></mrow></msup></mfenced><mo>=</mo><mi> </mi><mfenced close="}" open="{" separators=""><mrow><mi>P</mi><mfenced close=")" open="(" separators=""><mrow><mi>L</mi><mo>=</mo><mn>0</mn></mrow></mfenced><mo>-</mo><mi>P</mi><mfenced close=")" open="(" separators=""><mrow><mi>L</mi><mo>=</mo><mn>1</mn></mrow></mfenced></mrow></mfenced><mo>=</mo><mn>0</mn><mo>,</mo></mrow></math> ht regardless of I p i and I q i . Mats J Stensrud and Aaron L. Sarvet's contribution to the Discussion of 'Assumption-lean inference for generalised linear model parameters' by Vansteelandt and Dukes We congratulate Vansteelandt and Dukes (V & D) with their innovative and interesting article. [Extracted from the article]