Counting Defiers: Examples from Health Care Amanda
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Counting Defiers: Examples from Health Care Amanda E. Kowalski Gail Wilensky Professor of Applied Economics and Public Policy University of Michigan May 2021 1 of 51 Doing More When Youre Running LATE: Applying Marginal Treatment Effect
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01
Counting Defiers: Examples from Health Care Amanda E. Kowalski
Gail Wilensky Professor of Applied Economics and Public Policy
University of Michigan
May 2021 1 of 51<br>
Gail Wilensky Professor of Applied Economics and Public Policy
University of Michigan
May 2021 1 of 51<br>
02
“Doing More When You’re Running LATE: Applying Marginal Treatment Effect Methods to Examine Treatment Effect Heterogeneity in Experiments.” NBER WP 22363.
“Reconciling Seemingly Contradictory Results from the Oregon Health Insurance Experiment and the Massachusetts Health Reform.” Accepted, Review of Economics and Statistics.
“Behavior within a Clinical Trial and Implications for Mammography Guidelines.” Revise & Resubmit, Review of Economic Studies.
“How to Examine External Validity Within an Experiment.” Revised & Resubmitted, Journal of Economics and Management Strategy.
“A Model of a Randomized Experiment with an Application to the PROWESS Clinical Trial.” NBER WP 25670.
“Counting Defiers.” NBER WP 25671.
“Counting Defiers: Examples from Health Care.” arXiv:1912.06739. 2 of 51<br>
“Reconciling Seemingly Contradictory Results from the Oregon Health Insurance Experiment and the Massachusetts Health Reform.” Accepted, Review of Economics and Statistics.
“Behavior within a Clinical Trial and Implications for Mammography Guidelines.” Revise & Resubmit, Review of Economic Studies.
“How to Examine External Validity Within an Experiment.” Revised & Resubmitted, Journal of Economics and Management Strategy.
“A Model of a Randomized Experiment with an Application to the PROWESS Clinical Trial.” NBER WP 25670.
“Counting Defiers.” NBER WP 25671.
“Counting Defiers: Examples from Health Care.” arXiv:1912.06739. 2 of 51<br>
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3 of 51<br>
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4 of 51<br>
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Conduct informative finite sample inference on # defiers and analogous quantities that capture heterogeneous intervention effects, provide novel test of LATE monotonicity
Perform inference on count in finite sample, not fraction in infinite population
Model randomization process using explicit likelihood function, unlike Fisher (1935), Dwass (1957), Canay et al. (2017), etc.
Do not treat # defiers as nuisance parameter, unlike Copas (1973), Chung et al. (2013), Chiba (2015), Rigdon and Hudgens (2015), Ding, Feller, and Miratrix (2016), Li and Ding (2016), Ding and Miratrix (2019), Wu and Ding (2020)
Conduct exact inference, even when testing multiple hypotheses simultaneously
Use likelihood ratio test statistic, which also facilitates informative inference on other quantities
Engage with impossibility results based on Boole-Fréchet-Hoeffding bounds
Use more data and a stronger assumption about the randomization process than applications in the treatment effects literature: Heckman et al. (1997), Manski (1997), Tian and Pearl (2000), Zhang and Rubin (2003), Fan and Park (2010), Mullahy (2018), Ding and Miratrix (2019)
Demonstrate importance of stronger assumption: conduct informative inference on # defiers even with limited data
Engage with impossibility results and tests of LATE monotonicity based on simplifying asymptotic assumptions
Use less data than applications, which require Z, D, and Y, as opposed to Z and D or Y: Balke and Pearl (1997), Imbens and Rubin (1997), Heckman and Vytlacil (2001), Heckman and Vytlacil (2005), Richardson and Robins (2010), Huber and Mellace (2013, 2015), Kitagawa (2015), Mourifié and Wan (2017), Machado et al. (2019)
Demonstrate asymptotic assumption obscures information by adding one to model: demonstrate that resulting likelihood is an average of the finite sample likelihood and does not vary with # defiers. Also demonstrate equivalence with likelihood used by Barnard (1947), Kline and Walters (2020) for informative inference on average intervention effect
Demonstrate usefulness in hypothetical drug trial
Point estimate implies that at least 40 out of 100 individuals would be saved, but I infer with 95% confidence that at least 3 individuals would be killed 5 of 51<br>
Perform inference on count in finite sample, not fraction in infinite population
Model randomization process using explicit likelihood function, unlike Fisher (1935), Dwass (1957), Canay et al. (2017), etc.
Do not treat # defiers as nuisance parameter, unlike Copas (1973), Chung et al. (2013), Chiba (2015), Rigdon and Hudgens (2015), Ding, Feller, and Miratrix (2016), Li and Ding (2016), Ding and Miratrix (2019), Wu and Ding (2020)
Conduct exact inference, even when testing multiple hypotheses simultaneously
Use likelihood ratio test statistic, which also facilitates informative inference on other quantities
Engage with impossibility results based on Boole-Fréchet-Hoeffding bounds
Use more data and a stronger assumption about the randomization process than applications in the treatment effects literature: Heckman et al. (1997), Manski (1997), Tian and Pearl (2000), Zhang and Rubin (2003), Fan and Park (2010), Mullahy (2018), Ding and Miratrix (2019)
Demonstrate importance of stronger assumption: conduct informative inference on # defiers even with limited data
Engage with impossibility results and tests of LATE monotonicity based on simplifying asymptotic assumptions
Use less data than applications, which require Z, D, and Y, as opposed to Z and D or Y: Balke and Pearl (1997), Imbens and Rubin (1997), Heckman and Vytlacil (2001), Heckman and Vytlacil (2005), Richardson and Robins (2010), Huber and Mellace (2013, 2015), Kitagawa (2015), Mourifié and Wan (2017), Machado et al. (2019)
Demonstrate asymptotic assumption obscures information by adding one to model: demonstrate that resulting likelihood is an average of the finite sample likelihood and does not vary with # defiers. Also demonstrate equivalence with likelihood used by Barnard (1947), Kline and Walters (2020) for informative inference on average intervention effect
Demonstrate usefulness in hypothetical drug trial
Point estimate implies that at least 40 out of 100 individuals would be saved, but I infer with 95% confidence that at least 3 individuals would be killed 5 of 51<br>
06
Conduct informative finite sample inference on # defiers and analogous quantities that capture heterogeneous intervention effects, provide novel test of LATE monotonicity
Perform inference on count in finite sample, not fraction in infinite population
Model randomization process using explicit likelihood function, unlike Fisher (1935), Dwass (1957), Canay et al. (2017), etc.
Do not treat # defiers as nuisance parameter, unlike Copas (1973), Chung et al. (2013), Chiba (2015), Rigdon and Hudgens (2015), Ding, Feller, and Miratrix (2016), Li and Ding (2016), Ding and Miratrix (2019), Wu and Ding (2020)
Conduct exact inference, even when testing multiple hypotheses simultaneously
Use likelihood ratio test statistic, which also facilitates informative inference on other quantities
Engage with impossibility results based on Boole-Fréchet-Hoeffding bounds
Use more data and a stronger assumption about the randomization process than applications in the treatment effects literature: Heckman et al. (1997), Manski (1997), Tian and Pearl (2000), Zhang and Rubin (2003), Fan and Park (2010), Mullahy (2018), Ding and Miratrix (2019)
Demonstrate importance of stronger assumption: conduct informative inference on # defiers even with limited data
Engage with impossibility results and tests of LATE monotonicity based on simplifying asymptotic assumptions
Use less data than applications, which require Z, D, and Y, as opposed to Z and D or Y: Balke and Pearl (1997), Imbens and Rubin (1997), Heckman and Vytlacil (2001), Heckman and Vytlacil (2005), Richardson and Robins (2010), Huber and Mellace (2013, 2015), Kitagawa (2015), Mourifié and Wan (2017), Machado et al. (2019)
Demonstrate asymptotic assumption obscures information by adding one to model: demonstrate that resulting likelihood is an average of the finite sample likelihood and does not vary with # defiers. Also demonstrate equivalence with likelihood used by Barnard (1947), Kline and Walters (2020) for informative inference on average intervention effect
Demonstrate usefulness in hypothetical drug trial
Point estimate implies that at least 40 out of 100 individuals would be saved, but I infer with 95% confidence that at least 3 individuals would be killed 6 of 51<br>
Perform inference on count in finite sample, not fraction in infinite population
Model randomization process using explicit likelihood function, unlike Fisher (1935), Dwass (1957), Canay et al. (2017), etc.
Do not treat # defiers as nuisance parameter, unlike Copas (1973), Chung et al. (2013), Chiba (2015), Rigdon and Hudgens (2015), Ding, Feller, and Miratrix (2016), Li and Ding (2016), Ding and Miratrix (2019), Wu and Ding (2020)
Conduct exact inference, even when testing multiple hypotheses simultaneously
Use likelihood ratio test statistic, which also facilitates informative inference on other quantities
Engage with impossibility results based on Boole-Fréchet-Hoeffding bounds
Use more data and a stronger assumption about the randomization process than applications in the treatment effects literature: Heckman et al. (1997), Manski (1997), Tian and Pearl (2000), Zhang and Rubin (2003), Fan and Park (2010), Mullahy (2018), Ding and Miratrix (2019)
Demonstrate importance of stronger assumption: conduct informative inference on # defiers even with limited data
Engage with impossibility results and tests of LATE monotonicity based on simplifying asymptotic assumptions
Use less data than applications, which require Z, D, and Y, as opposed to Z and D or Y: Balke and Pearl (1997), Imbens and Rubin (1997), Heckman and Vytlacil (2001), Heckman and Vytlacil (2005), Richardson and Robins (2010), Huber and Mellace (2013, 2015), Kitagawa (2015), Mourifié and Wan (2017), Machado et al. (2019)
Demonstrate asymptotic assumption obscures information by adding one to model: demonstrate that resulting likelihood is an average of the finite sample likelihood and does not vary with # defiers. Also demonstrate equivalence with likelihood used by Barnard (1947), Kline and Walters (2020) for informative inference on average intervention effect
Demonstrate usefulness in hypothetical drug trial
Point estimate implies that at least 40 out of 100 individuals would be saved, but I infer with 95% confidence that at least 3 individuals would be killed 6 of 51<br>
07
Conduct informative finite sample inference on # defiers and analogous quantities that capture heterogeneous intervention effects, provide novel test of LATE monotonicity
Perform inference on count in finite sample, not fraction in infinite population
Model randomization process using explicit likelihood function, unlike Fisher (1935), Dwass (1957), Canay et al. (2017), etc.
Do not treat # defiers as nuisance parameter, unlike Copas (1973), Chung et al. (2013), Chiba (2015), Rigdon and Hudgens (2015), Ding, Feller, and Miratrix (2016), Li and Ding (2016), Ding and Miratrix (2019), Wu and Ding (2020)
Conduct exact inference, even when testing multiple hypotheses simultaneously
Use likelihood ratio test statistic, which also facilitates informative inference on other quantities
Engage with impossibility results based on Boole-Fréchet-Hoeffding bounds
Use more data and a stronger assumption about the randomization process than applications in the treatment effects literature: Heckman et al. (1997), Manski (1997), Tian and Pearl (2000), Zhang and Rubin (2003), Fan and Park (2010), Mullahy (2018), Ding and Miratrix (2019)
Demonstrate importance of stronger assumption: conduct informative inference on # defiers even with limited data
Engage with impossibility results and tests of LATE monotonicity based on simplifying asymptotic assumptions
Use less data than applications, which require Z, D, and Y, as opposed to Z and D or Y: Balke and Pearl (1997), Imbens and Rubin (1997), Heckman and Vytlacil (2001), Heckman and Vytlacil (2005), Richardson and Robins (2010), Huber and Mellace (2013, 2015), Kitagawa (2015), Mourifié and Wan (2017), Machado et al. (2019)
Demonstrate asymptotic assumption obscures information by adding one to model: demonstrate that resulting likelihood is an average of the finite sample likelihood and does not vary with # defiers. Also demonstrate equivalence with likelihood used by Barnard (1947), Kline and Walters (2021) for inference on average intervention effect
Demonstrate usefulness in hypothetical drug trial
Point estimate implies that at least 40 out of 100 individuals would be saved, but I infer with 95% confidence that at least 3 individuals would be killed 7 of 51<br>
Perform inference on count in finite sample, not fraction in infinite population
Model randomization process using explicit likelihood function, unlike Fisher (1935), Dwass (1957), Canay et al. (2017), etc.
Do not treat # defiers as nuisance parameter, unlike Copas (1973), Chung et al. (2013), Chiba (2015), Rigdon and Hudgens (2015), Ding, Feller, and Miratrix (2016), Li and Ding (2016), Ding and Miratrix (2019), Wu and Ding (2020)
Conduct exact inference, even when testing multiple hypotheses simultaneously
Use likelihood ratio test statistic, which also facilitates informative inference on other quantities
Engage with impossibility results based on Boole-Fréchet-Hoeffding bounds
Use more data and a stronger assumption about the randomization process than applications in the treatment effects literature: Heckman et al. (1997), Manski (1997), Tian and Pearl (2000), Zhang and Rubin (2003), Fan and Park (2010), Mullahy (2018), Ding and Miratrix (2019)
Demonstrate importance of stronger assumption: conduct informative inference on # defiers even with limited data
Engage with impossibility results and tests of LATE monotonicity based on simplifying asymptotic assumptions
Use less data than applications, which require Z, D, and Y, as opposed to Z and D or Y: Balke and Pearl (1997), Imbens and Rubin (1997), Heckman and Vytlacil (2001), Heckman and Vytlacil (2005), Richardson and Robins (2010), Huber and Mellace (2013, 2015), Kitagawa (2015), Mourifié and Wan (2017), Machado et al. (2019)
Demonstrate asymptotic assumption obscures information by adding one to model: demonstrate that resulting likelihood is an average of the finite sample likelihood and does not vary with # defiers. Also demonstrate equivalence with likelihood used by Barnard (1947), Kline and Walters (2021) for inference on average intervention effect
Demonstrate usefulness in hypothetical drug trial
Point estimate implies that at least 40 out of 100 individuals would be saved, but I infer with 95% confidence that at least 3 individuals would be killed 7 of 51<br>
08
Conduct informative finite sample inference on # defiers and analogous quantities that capture heterogeneous intervention effects, provide novel test of LATE monotonicity
Perform inference on count in finite sample, not fraction in infinite population
Model randomization process using explicit likelihood function, unlike Fisher (1935), Dwass (1957), Canay et al. (2017), etc.
Do not treat # defiers as nuisance parameter, unlike Copas (1973), Chung et al. (2013), Chiba (2015), Rigdon and Hudgens (2015), Ding, Feller, and Miratrix (2016), Li and Ding (2016), Ding and Miratrix (2019), Wu and Ding (2020)
Conduct exact inference, even when testing multiple hypotheses simultaneously
Use likelihood ratio test statistic, which also facilitates informative inference on other quantities
Engage with impossibility results based on Boole-Fréchet-Hoeffding bounds
Use more data and a stronger assumption about the randomization process than applications in the treatment effects literature: Heckman et al. (1997), Manski (1997), Tian and Pearl (2000), Zhang and Rubin (2003), Fan and Park (2010), Mullahy (2018), Ding and Miratrix (2019)
Demonstrate importance of stronger assumption: conduct informative inference on # defiers even with limited data
Engage with impossibility results and tests of LATE monotonicity based on simplifying asymptotic assumptions
Use less data than applications, which require Z, D, and Y, as opposed to Z and D or Y: Balke and Pearl (1997), Imbens and Rubin (1997), Heckman and Vytlacil (2001), Heckman and Vytlacil (2005), Richardson and Robins (2010), Huber and Mellace (2013, 2015), Kitagawa (2015), Mourifié and Wan (2017), Machado et al. (2019)
Demonstrate asymptotic assumption obscures information by adding one to model: demonstrate that resulting likelihood is an average of the finite sample likelihood and does not vary with # defiers. Also demonstrate equivalence with likelihood used by Barnard (1947), Kline and Walters (2021) for inference on average intervention effect
Demonstrate usefulness in hypothetical drug trial
Point estimate implies that at least 40 out of 100 individuals would be saved, but I infer with 95% confidence that at least 3 individuals would be killed 8 of 51<br>
Perform inference on count in finite sample, not fraction in infinite population
Model randomization process using explicit likelihood function, unlike Fisher (1935), Dwass (1957), Canay et al. (2017), etc.
Do not treat # defiers as nuisance parameter, unlike Copas (1973), Chung et al. (2013), Chiba (2015), Rigdon and Hudgens (2015), Ding, Feller, and Miratrix (2016), Li and Ding (2016), Ding and Miratrix (2019), Wu and Ding (2020)
Conduct exact inference, even when testing multiple hypotheses simultaneously
Use likelihood ratio test statistic, which also facilitates informative inference on other quantities
Engage with impossibility results based on Boole-Fréchet-Hoeffding bounds
Use more data and a stronger assumption about the randomization process than applications in the treatment effects literature: Heckman et al. (1997), Manski (1997), Tian and Pearl (2000), Zhang and Rubin (2003), Fan and Park (2010), Mullahy (2018), Ding and Miratrix (2019)
Demonstrate importance of stronger assumption: conduct informative inference on # defiers even with limited data
Engage with impossibility results and tests of LATE monotonicity based on simplifying asymptotic assumptions
Use less data than applications, which require Z, D, and Y, as opposed to Z and D or Y: Balke and Pearl (1997), Imbens and Rubin (1997), Heckman and Vytlacil (2001), Heckman and Vytlacil (2005), Richardson and Robins (2010), Huber and Mellace (2013, 2015), Kitagawa (2015), Mourifié and Wan (2017), Machado et al. (2019)
Demonstrate asymptotic assumption obscures information by adding one to model: demonstrate that resulting likelihood is an average of the finite sample likelihood and does not vary with # defiers. Also demonstrate equivalence with likelihood used by Barnard (1947), Kline and Walters (2021) for inference on average intervention effect
Demonstrate usefulness in hypothetical drug trial
Point estimate implies that at least 40 out of 100 individuals would be saved, but I infer with 95% confidence that at least 3 individuals would be killed 8 of 51<br>
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Model
Hypothesis Testing
Examples from Health Care
Impossibility Results Outline 9 of 51<br>
Hypothesis Testing
Examples from Health Care
Impossibility Results Outline 9 of 51<br>
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A.1. (No interference) Each individual has one potential outcome in the control arm and one potential outcome in the intervention arm. 10 of 51<br>
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Model
Hypothesis Testing
Examples from Health Care
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Hypothesis Testing
Examples from Health Care
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Model
Hypothesis Testing
Examples from Health Care
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Hypothesis Testing
Examples from Health Care
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Example: Hypothetical Clinical Trial Results 47 of 51<br>
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Model
Hypothesis Testing
Examples from Health Care
Impossibility Results Outline 48 of 51<br>
Hypothesis Testing
Examples from Health Care
Impossibility Results Outline 48 of 51<br>
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Impossibility Results Based on Boole-Fréchet-Hoeffding Bounds I use more data: full data configuration vs shares treated in intervention & control
I make a stronger assumption: A.2(iid) vs independence of intervention and potential outcomes
I can still conduct informative inference on # defiers even with limited data
Therefore, the stronger assumption is important 49 of 51<br>
I make a stronger assumption: A.2(iid) vs independence of intervention and potential outcomes
I can still conduct informative inference on # defiers even with limited data
Therefore, the stronger assumption is important 49 of 51<br>
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Impossibility Results Based on Simplifying Asymptotic Assumptions 50 of 51<br>
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Conduct informative finite sample inference on # defiers and analogous quantities that capture heterogeneous intervention effects, provide novel test of LATE monotonicity
Model randomization process using explicit likelihood function, unlike Fisher (1935), Dwass (1957), Canay et al. (2017), etc.
Do not treat # defiers as nuisance parameter, unlike Copas (1973), Chung et al. (2013), Chiba (2015), Rigdon and Hudgens (2015), Ding, Feller, and Miratrix (2016), Li and Ding (2016), Ding and Miratrix (2019), Wu and Ding (2020)
Perform inference on count in finite sample, not fraction in infinite population
Conduct exact inference, even when testing multiple hypotheses simultaneously
Use likelihood ratio test statistic, which also facilitates informative inference on other quantities
Engage with impossibility results based on Boole-Fréchet-Hoeffding bounds
Use more data and a stronger assumption about the randomization process than applications in the treatment effects literature: Heckman et al. (1997), Manski (1997), Tian and Pearl (2000), Zhang and Rubin (2003), Fan and Park (2010), Mullahy (2018), Ding and Miratrix (2019)
Demonstrate importance of stronger assumption: conduct informative inference on # defiers even with limited data
Engage with impossibility results and tests of LATE monotonicity based on simplifying asymptotic assumptions
Use less data than applications, which require Z, D, and Y, as opposed to Z and D or Y: Balke and Pearl (1997), Imbens and Rubin (1997), Heckman and Vytlacil (2001), Heckman and Vytlacil (2005), Richardson and Robins (2010), Huber and Mellace (2013, 2015), Kitagawa (2015), Mourifié and Wan (2017), Machado et al. (2019)
Demonstrate asymptotic assumption obscures information by adding one to model: demonstrate that resulting likelihood is an average of the finite sample likelihood and does not vary with # defiers. Also demonstrate equivalence with likelihood used by Barnard (1947), Kline and Walters (2021) for informative inference on average intervention effect
Demonstrate usefulness in hypothetical drug trial
Point estimate implies that at least 40 out of 100 individuals would be saved, but I infer with 95% confidence that at least 3 individuals would be killed 51 of 51<br>
Model randomization process using explicit likelihood function, unlike Fisher (1935), Dwass (1957), Canay et al. (2017), etc.
Do not treat # defiers as nuisance parameter, unlike Copas (1973), Chung et al. (2013), Chiba (2015), Rigdon and Hudgens (2015), Ding, Feller, and Miratrix (2016), Li and Ding (2016), Ding and Miratrix (2019), Wu and Ding (2020)
Perform inference on count in finite sample, not fraction in infinite population
Conduct exact inference, even when testing multiple hypotheses simultaneously
Use likelihood ratio test statistic, which also facilitates informative inference on other quantities
Engage with impossibility results based on Boole-Fréchet-Hoeffding bounds
Use more data and a stronger assumption about the randomization process than applications in the treatment effects literature: Heckman et al. (1997), Manski (1997), Tian and Pearl (2000), Zhang and Rubin (2003), Fan and Park (2010), Mullahy (2018), Ding and Miratrix (2019)
Demonstrate importance of stronger assumption: conduct informative inference on # defiers even with limited data
Engage with impossibility results and tests of LATE monotonicity based on simplifying asymptotic assumptions
Use less data than applications, which require Z, D, and Y, as opposed to Z and D or Y: Balke and Pearl (1997), Imbens and Rubin (1997), Heckman and Vytlacil (2001), Heckman and Vytlacil (2005), Richardson and Robins (2010), Huber and Mellace (2013, 2015), Kitagawa (2015), Mourifié and Wan (2017), Machado et al. (2019)
Demonstrate asymptotic assumption obscures information by adding one to model: demonstrate that resulting likelihood is an average of the finite sample likelihood and does not vary with # defiers. Also demonstrate equivalence with likelihood used by Barnard (1947), Kline and Walters (2021) for informative inference on average intervention effect
Demonstrate usefulness in hypothetical drug trial
Point estimate implies that at least 40 out of 100 individuals would be saved, but I infer with 95% confidence that at least 3 individuals would be killed 51 of 51<br>
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Appendix 52 of 51<br>
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