Use of instrumental variables in the presence of heterogeneity and self-selection: an application to treatments of breast cancer patients

Instrumental variable (IV) methods are widely used in the health economics literature to adjust for hidden selection biases in observational studies when estimating treatment effects. Less attention has been paid in the applied literature to the proper use of IVs if treatment effects are heterogeneo...

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Published inHealth economics Vol. 16; no. 11; pp. 1133 - 1157
Main Authors Basu, Anirban, Heckman, James J., Navarro-Lozano, Salvador, Urzua, Sergio
Format Journal Article
LanguageEnglish
Published Chichester, UK John Wiley & Sons, Ltd 01.11.2007
Wiley Periodicals Inc
SeriesHealth Economics
Subjects
Online AccessGet full text
ISSN1057-9230
1099-1050
DOI10.1002/hec.1291

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Abstract Instrumental variable (IV) methods are widely used in the health economics literature to adjust for hidden selection biases in observational studies when estimating treatment effects. Less attention has been paid in the applied literature to the proper use of IVs if treatment effects are heterogeneous across subjects and individuals select treatments based on expected idiosyncratic gains or losses from treatments. In this paper we compare conventional IV analysis with alternative approaches that use IVs to estimate treatment effects in models with response heterogeneity and self‐selection. Instead of interpreting IV estimates as the effect of treatment at an unknown margin of patients, we identify the marginal patients and we apply the method of local IVs to estimate the average treatment effect and the effect on the treated on 5‐year direct costs of breast‐conserving surgery and radiation therapy compared with mastectomy in breast cancer patients. We use a sample from the Outcomes and Preferences in Older Women, Nationwide Survey which is designed to be representative of all female Medicare beneficiaries (aged 67 or older) with newly diagnosed breast cancer between 1992 and 1994. Our results reveal some of the advantages and limitations of conventional and alternative IV methods in estimating mean treatment effect parameters. Copyright © 2007 John Wiley & Sons, Ltd.
AbstractList Instrumental variable (IV) methods are widely used in the health economics literature to adjust for hidden selection biases in observational studies when estimating treatment effects. Less attention has been paid in the applied literature to the proper use of IVs if treatment effects are heterogeneous across subjects and individuals select treatments based on expected idiosyncratic gains or losses from treatments. In this paper we compare conventional IV analysis with alternative approaches that use IVs to estimate treatment effects in models with response heterogeneity and self-selection. Instead of interpreting IV estimates as the effect of treatment at an unknown margin of patients, we identify the marginal patients and we apply the method of local IVs to estimate the average treatment effect and the effect on the treated on 5-year direct costs of breast-conserving surgery and radiation therapy compared with mastectomy in breast cancer patients. We use a sample from the Outcomes and Preferences in Older Women, Nationwide Survey which is designed to be representative of all female Medicare beneficiaries (aged 67 or older) with newly diagnosed breast cancer between 1992 and 1994. Our results reveal some of the advantages and limitations of conventional and alternative IV methods in estimating mean treatment effect parameters.Instrumental variable (IV) methods are widely used in the health economics literature to adjust for hidden selection biases in observational studies when estimating treatment effects. Less attention has been paid in the applied literature to the proper use of IVs if treatment effects are heterogeneous across subjects and individuals select treatments based on expected idiosyncratic gains or losses from treatments. In this paper we compare conventional IV analysis with alternative approaches that use IVs to estimate treatment effects in models with response heterogeneity and self-selection. Instead of interpreting IV estimates as the effect of treatment at an unknown margin of patients, we identify the marginal patients and we apply the method of local IVs to estimate the average treatment effect and the effect on the treated on 5-year direct costs of breast-conserving surgery and radiation therapy compared with mastectomy in breast cancer patients. We use a sample from the Outcomes and Preferences in Older Women, Nationwide Survey which is designed to be representative of all female Medicare beneficiaries (aged 67 or older) with newly diagnosed breast cancer between 1992 and 1994. Our results reveal some of the advantages and limitations of conventional and alternative IV methods in estimating mean treatment effect parameters.
Instrumental variable (IV) methods are widely used in the health economics literature to adjust for hidden selection biases in observational studies when estimating treatment effects. Less attention has been paid in the applied literature to the proper use of IVs if treatment effects are heterogeneous across subjects and individuals select treatments based on expected idiosyncratic gains or losses from treatments. In this paper we compare conventional IV analysis with alternative approaches that use IVs to estimate treatment effects in models with response heterogeneity and self-selection. Instead of interpreting IV estimates as the effect of treatment at an unknown margin of patients, we identify the marginal patients and we apply the method of local IVs to estimate the average treatment effect and the effect on the treated on 5-year direct costs of breast-conserving surgery and radiation therapy compared with mastectomy in breast cancer patients. We use a sample from the Outcomes and Preferences in Older Women, Nationwide Survey which is designed to be representative of all female Medicare beneficiaries (aged 67 or older) with newly diagnosed breast cancer between 1992 and 1994. Our results reveal some of the advantages and limitations of conventional and alternative IV methods in estimating mean treatment effect parameters.
Instrumental variable (IV) methods are widely used in the health economics literature to adjust for hidden selection biases in observational studies when estimating treatment effects. Less attention has been paid in the applied literature to the proper use of IVs if treatment effects are heterogeneous across subjects and individuals select treatments based on expected idiosyncratic gains or losses from treatments. In this paper we compare conventional IV analysis with alternative approaches that use IVs to estimate treatment effects in models with response heterogeneity and self‐selection. Instead of interpreting IV estimates as the effect of treatment at an unknown margin of patients, we identify the marginal patients and we apply the method of local IVs to estimate the average treatment effect and the effect on the treated on 5‐year direct costs of breast‐conserving surgery and radiation therapy compared with mastectomy in breast cancer patients. We use a sample from the Outcomes and Preferences in Older Women, Nationwide Survey which is designed to be representative of all female Medicare beneficiaries (aged 67 or older) with newly diagnosed breast cancer between 1992 and 1994. Our results reveal some of the advantages and limitations of conventional and alternative IV methods in estimating mean treatment effect parameters. Copyright © 2007 John Wiley & Sons, Ltd.
Instrumental variable (IV) methods are widely used in the health economics literature to adjust for hidden selection biases in observational studies when estimating treatment effects. Less attention has been paid in the applied literature to the proper use of IVs if treatment effects are heterogeneous across subjects and individuals select treatments based on expected idiosyncratic gains or losses from treatments. In this paper we compare conventional IV analysis with alternative approaches that use IVs to estimate treatment effects in models with response heterogeneity and self-selection. Instead of interpreting IV estimates as the effect of treatment at an unknown margin of patients, we identify the marginal patients and we apply the method of local IVs to estimate the average treatment effect and the effect on the treated on 5-year direct costs of breast-conserving surgery and radiation therapy compared with mastectomy in breast cancer patients. We use a sample from the Outcomes and Preferences in Older Women, Nationwide Survey which is designed to be representative of all female Medicare beneficiaries (aged 67 or older) with newly diagnosed breast cancer between 1992 and 1994. Our results reveal some of the advantages and limitations of conventional and alternative IV methods in estimating mean treatment effect parameters. [PUBLICATION ABSTRACT]
Instrumental variable (IV) methods are widely used in the health economics literature to adjust for hidden selection biases in observational studies when estimating treatment effects. Less attention has been paid in the applied literature to the proper use of IVs if treatment effects are heterogeneous across subjects and individuals select treatments based on expected idiosyncratic gains or losses from treatments. In this paper we compare conventional IV analysis with alternative approaches that use IVs to estimate treatment effects in models with response heterogeneity and self-selection. Instead of interpreting IV estimates as the effect of treatment at an unknown margin of patients, we identify the marginal patients and we apply the method of local IVs to estimate the average treatment effect and the effect on the treated on 5-year direct costs of breast-conserving surgery and radiation therapy compared with mastectomy in breast cancer patients. We use a sample from the Outcomes and Preferences in Older Women, Nationwide Survey which is designed to be representative of all female Medicare beneficiaries (aged 67 or older) with newly diagnosed breast cancer between 1992 and 1994. Our results reveal some of the advantages and limitations of conventional and alternative IV methods in estimating mean treatment effect parameters. [Copyright 2007 John Wiley and Sons, Ltd.]
Author Basu, Anirban
Urzua, Sergio
Heckman, James J.
Navarro-Lozano, Salvador
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  surname: Urzua
  fullname: Urzua, Sergio
  organization: Department of Economics, Northwestern University, Chicago, IL, USA
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PublicationDate November 2007
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  text: November 2007
PublicationDecade 2000
PublicationPlace Chichester, UK
PublicationPlace_xml – name: Chichester, UK
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PublicationSeriesTitle Health Economics
PublicationTitle Health economics
PublicationTitleAlternate Health Econ
PublicationYear 2007
Publisher John Wiley & Sons, Ltd
Wiley Periodicals Inc
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References Brooks JM, Chrischilles E, Scott S, Chen-Hardee S. 2003. Was lumpectomy underutilized for early stage breast cancer? - instrumental variables evidence for stage II patients from Iowa. Health Services Research 38(6, Part I): 1385-1402.
Heckman JJ. 2001. Microdata, heterogeneity, and the evaluation of public policy: Nobel Lecture. Journal of Political Economy 109(4): 673-748.
Manning WG, Basu A, Mullahy J. 2006. Generalized modeling approaches on risk adjustment to skewed outcomes. Journal of Health, Economics 24(3): 465-488.
Quandt RE. 1988. The Econometrics of Disequilibrium. Oxford: Blackwell.
Claxton K. 1999. The Irrelevance of Inference: a decision-making approach to the stochastic evaluation of health care technologies. Journal of Health Economics 18: 341-364.
Heckman JJ, Urzua S, Vytlacil E. 2006b. Understanding instrumental variables in models with essential heterogeneity. Review of Economics and Statistics 88(3): 389-432.
Harris KM, Remler DK. 1998. Who is the marginal patient? Understanding instrumental variable estimates of treatment effects. Health Services Research 33(5): 1337-1360.
Heckman JJ, Vytlacil E. 2005. Structural equations, treatment effects and econometric policy evaluation. Econometrica 73(3): 669-738.
Heckman JJ. 1978. Dummy endogenous variables in a simultaneous equations system. Econometrica 46(4): 931-959.
Heckman JJ, Vytlacil E. 2001b. Policy relevant treatment effects. American Economic Review 91(2): 107-111.
Imbens GW. 2004. Non-parametric estimation of average treatment effects under exogeneity. A review. Review of Economics and Statistics 19(3): 358-364.
Vytlacil E. 2002. Independence, monotonicity, and latent index models: an equivalence result. Econometrica 70(1): 331-341.
LaLonde R. 1986. Evaluating the econometric evaluations of training programs with experimental data. American Economic Review 76(4): 604-620.
Rubin D. 1978. Bayesian inference for causal effects: the role of randomization. Annals of Statistics 6: 34-58.
Veronesi U, Cascinelli N, Mariani L, Greco M, Saccozzi R, Luini A, Aguilar M, Marubini E. 2002. Twenty-year follow-up of a randomized study comparing breast-conserving surgery with radical mastectomy for early breast cancer. New England Journal of Medicine 347(16): 1127-1132.
Cox DR. 1958. The Planning of Experiments. Wiley: New York.
Fisher RA. 1935. Design of Experiments. Oliver and Boyd: Edinburgh.
Heckman JJ, Vytlacil E. 1999. Local instrumental variables and latent variable models for identifying and bounding treatment effects. Proceedings of the National Academy of Sciences of the United States of America 96: 4730-4734.
Polsky D, Mandelblatt JS, Weeks J, Venditti L, Hwang YT, Glick HA, Hadley J, Schulman KA. 2003. Economic evaluation of breast cancer treatment: considering the value of patient choice. Journal of Clinical Oncology 21: 1139-1146.
Earle CE, Tsai JS, Gelber RD, Weinstein MC, Neumann PJ, Weeks JC. 2001. Effectiveness of chemotherapy for advanced lung cancer in the elderly: Instrument variable and propensity analysis. Journal of Clinical Oncology 19(4): 1064-1070.
Heckman JJ, Stixrud J, Urzua S. 2006a. The effect of cognitive and noncognitive skills on labor market outcomes and social behavior. Journal of Labor Economics 24(3): 411-481.
Angrist J, Imbens G, Rubin G. 1996. Identification of causal effects using instrumental variables. Journal of the American Statistical Association 91: 444-455.
Heckman JJ, Sedlacek G. 1985. Heterogeneity, aggregation and market wage functions: An empirical model of self selection in the labor market. Journal of Political Economy 93(6): 1077-1125.
Hadley J, Polsky D, Mandelblatt JS, Mitchell JM, Weeks JC, Wang Q, Hwang YT, OPTIONS Research Team. 2003. An exploratory instrumental variable analysis of the outcomes of localized breast cancer treatments in a Medicare population. Health Economics 12: 171-186.
Card D. 2001. Estimating the return to schooling. Progress on some persistent econometric problems. Economterica 69(5): 1127-1160.
Heckman JJ, Honore B. 1990. The empirical content of the Roy model. Econometrica 58(5): 1121-1149.
Nold JR, Beamer L, Helmer SD, McBoyle MF. 2000. Factors influencing a women's choice to undergo breast-conserving surgery versus modified radical mastectomy. The American Journal of Surgery 180(6): 413-418.
Björklund A, Moffitt R. 1987. The estimation of wage gains and welfare gains in self-selection. Review of Economics and Statistics 69(1): 42-49.
Heckman JJ. 1996. Comments on Angrist, Imbens, and Rubin: identification of causal effects using instrumental variables. Journal of American Statistical Association 91: 434.
Heckman JJ, Navarro S. 2004. Using matching, instrumental variables, and control functions to estimate economic choice models. Review of Economics and Statistics 86(1): 30-57.
Heckman JJ, Vytlacil E. 2000. The relationship between treatment parameters within a latent variable framework. Economic Letters 66(1): 33-39.
Heckman JJ. 1997. Instrumental Variables: a study of implicit behavioral assumptions used in making program evaluations. Journal of Human Resources 32(3): 441-462.
Auld MC. 2005. Causal effect of early initiation on adolescent smoking patterns. Canadian Journal of Economics 38(3): 709-734.
Basu A, Manning WG, Mullahy J. 2004. Comparing alternative models: log vs proportional hazard? Health Economics 13(8): 749-765.
Hadley J, Mitchell JM, Mandelblatt J. 1992. Medicare fees and small area variations in the treatment of localized breast cancer. New England Journal of Medicine 52: 334-360.
Imbens G, Angrist J. 1994. Identification and estimation of local average treatment effects. Econometrica 62(2): 467-475.
Newhouse J, McClellan MB. 1998. Econometrics in outcomes research: the use of instrumental variables. Annual Review of Public Health 19: 17-34.
Neyman J. 1935. Statistical problems in agricultural experimentation (with discussions). Journal of the Royal Statistical Society, Series B (Supplement) 2: 107-180.
Quandt RE. 1972. A new approach to estimating switching regressions. Journal of the American Statistical Association 67: 306-310.
Roy AD. 1951. Some thoughts on the distribution of earnings. Oxford Economic Papers 3: 135-146.
Carneiro P, Hansen K, Heckman JJ. 2003. Estimating distribution of treatment effects with an application to returns to schooling and measurement of the effects of uncertainty on college choice. International Economic Review 44(2): 361-422.
McClellan MB, Newhouse JB, McNeil BJ. 1994. Does more intensive treatment of acute myocardial infarction in the elderly reduce mortality? Journal of the American Medical Association 272(11): 859-866.
1990; 58
1986; 76
2001; 109
1935
1994; 62
1951; 3
1978; 6
1992; 52
2003; 12
1998; 19
2006; 24
1999; 18
2001; 19
2005; 73
1986
2007; 6
2002; 347
1999; 96
1985; 93
2005; 38
2006a; 24
2003; 44
1989
1988
2004; 86
2006b; 88
2000; 66
1994; 272
1998
2003; 38
2006
2001a
1996; 91
1972; 67
2001; 69
1958
1987; 69
1997; 32
2004; 19
2004; 13
2002; 70
1978; 46
1998; 33
2003; 21
1994; 4
2001b; 91
1923
1935; 2
2000; 180
Heckman JJ (e_1_2_1_22_1) 1986
Heckman JJ (e_1_2_1_32_1) 2007
LaLonde R (e_1_2_1_35_1) 1986; 76
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McClellan MB (e_1_2_1_38_1) 1994; 272
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Heckman JJ (e_1_2_1_29_1) 2001
Hadley J (e_1_2_1_13_1) 1992; 52
Vanness DJ (e_1_2_1_50_1) 2006
Polsky D (e_1_2_1_43_1) 2006
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Manning WG (e_1_2_1_36_1) 2006
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Heckman JJ (e_1_2_1_24_1) 1998
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Imbens GW (e_1_2_1_34_1) 2004; 19
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Fisher RA (e_1_2_1_12_1) 1935
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Quandt RE (e_1_2_1_47_1) 1988
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References_xml – reference: Heckman JJ, Stixrud J, Urzua S. 2006a. The effect of cognitive and noncognitive skills on labor market outcomes and social behavior. Journal of Labor Economics 24(3): 411-481.
– reference: Neyman J. 1935. Statistical problems in agricultural experimentation (with discussions). Journal of the Royal Statistical Society, Series B (Supplement) 2: 107-180.
– reference: Manning WG, Basu A, Mullahy J. 2006. Generalized modeling approaches on risk adjustment to skewed outcomes. Journal of Health, Economics 24(3): 465-488.
– reference: Heckman JJ, Vytlacil E. 2005. Structural equations, treatment effects and econometric policy evaluation. Econometrica 73(3): 669-738.
– reference: Claxton K. 1999. The Irrelevance of Inference: a decision-making approach to the stochastic evaluation of health care technologies. Journal of Health Economics 18: 341-364.
– reference: Fisher RA. 1935. Design of Experiments. Oliver and Boyd: Edinburgh.
– reference: Cox DR. 1958. The Planning of Experiments. Wiley: New York.
– reference: Björklund A, Moffitt R. 1987. The estimation of wage gains and welfare gains in self-selection. Review of Economics and Statistics 69(1): 42-49.
– reference: Heckman JJ, Sedlacek G. 1985. Heterogeneity, aggregation and market wage functions: An empirical model of self selection in the labor market. Journal of Political Economy 93(6): 1077-1125.
– reference: Heckman JJ, Honore B. 1990. The empirical content of the Roy model. Econometrica 58(5): 1121-1149.
– reference: Nold JR, Beamer L, Helmer SD, McBoyle MF. 2000. Factors influencing a women's choice to undergo breast-conserving surgery versus modified radical mastectomy. The American Journal of Surgery 180(6): 413-418.
– reference: Rubin D. 1978. Bayesian inference for causal effects: the role of randomization. Annals of Statistics 6: 34-58.
– reference: Auld MC. 2005. Causal effect of early initiation on adolescent smoking patterns. Canadian Journal of Economics 38(3): 709-734.
– reference: McClellan MB, Newhouse JB, McNeil BJ. 1994. Does more intensive treatment of acute myocardial infarction in the elderly reduce mortality? Journal of the American Medical Association 272(11): 859-866.
– reference: Newhouse J, McClellan MB. 1998. Econometrics in outcomes research: the use of instrumental variables. Annual Review of Public Health 19: 17-34.
– reference: Quandt RE. 1988. The Econometrics of Disequilibrium. Oxford: Blackwell.
– reference: Heckman JJ. 2001. Microdata, heterogeneity, and the evaluation of public policy: Nobel Lecture. Journal of Political Economy 109(4): 673-748.
– reference: Brooks JM, Chrischilles E, Scott S, Chen-Hardee S. 2003. Was lumpectomy underutilized for early stage breast cancer? - instrumental variables evidence for stage II patients from Iowa. Health Services Research 38(6, Part I): 1385-1402.
– reference: Heckman JJ, Urzua S, Vytlacil E. 2006b. Understanding instrumental variables in models with essential heterogeneity. Review of Economics and Statistics 88(3): 389-432.
– reference: Polsky D, Mandelblatt JS, Weeks J, Venditti L, Hwang YT, Glick HA, Hadley J, Schulman KA. 2003. Economic evaluation of breast cancer treatment: considering the value of patient choice. Journal of Clinical Oncology 21: 1139-1146.
– reference: Hadley J, Polsky D, Mandelblatt JS, Mitchell JM, Weeks JC, Wang Q, Hwang YT, OPTIONS Research Team. 2003. An exploratory instrumental variable analysis of the outcomes of localized breast cancer treatments in a Medicare population. Health Economics 12: 171-186.
– reference: Hadley J, Mitchell JM, Mandelblatt J. 1992. Medicare fees and small area variations in the treatment of localized breast cancer. New England Journal of Medicine 52: 334-360.
– reference: LaLonde R. 1986. Evaluating the econometric evaluations of training programs with experimental data. American Economic Review 76(4): 604-620.
– reference: Quandt RE. 1972. A new approach to estimating switching regressions. Journal of the American Statistical Association 67: 306-310.
– reference: Heckman JJ. 1978. Dummy endogenous variables in a simultaneous equations system. Econometrica 46(4): 931-959.
– reference: Roy AD. 1951. Some thoughts on the distribution of earnings. Oxford Economic Papers 3: 135-146.
– reference: Heckman JJ, Vytlacil E. 2000. The relationship between treatment parameters within a latent variable framework. Economic Letters 66(1): 33-39.
– reference: Imbens G, Angrist J. 1994. Identification and estimation of local average treatment effects. Econometrica 62(2): 467-475.
– reference: Heckman JJ. 1997. Instrumental Variables: a study of implicit behavioral assumptions used in making program evaluations. Journal of Human Resources 32(3): 441-462.
– reference: Heckman JJ, Navarro S. 2004. Using matching, instrumental variables, and control functions to estimate economic choice models. Review of Economics and Statistics 86(1): 30-57.
– reference: Basu A, Manning WG, Mullahy J. 2004. Comparing alternative models: log vs proportional hazard? Health Economics 13(8): 749-765.
– reference: Heckman JJ. 1996. Comments on Angrist, Imbens, and Rubin: identification of causal effects using instrumental variables. Journal of American Statistical Association 91: 434.
– reference: Heckman JJ, Vytlacil E. 1999. Local instrumental variables and latent variable models for identifying and bounding treatment effects. Proceedings of the National Academy of Sciences of the United States of America 96: 4730-4734.
– reference: Veronesi U, Cascinelli N, Mariani L, Greco M, Saccozzi R, Luini A, Aguilar M, Marubini E. 2002. Twenty-year follow-up of a randomized study comparing breast-conserving surgery with radical mastectomy for early breast cancer. New England Journal of Medicine 347(16): 1127-1132.
– reference: Angrist J, Imbens G, Rubin G. 1996. Identification of causal effects using instrumental variables. Journal of the American Statistical Association 91: 444-455.
– reference: Harris KM, Remler DK. 1998. Who is the marginal patient? Understanding instrumental variable estimates of treatment effects. Health Services Research 33(5): 1337-1360.
– reference: Vytlacil E. 2002. Independence, monotonicity, and latent index models: an equivalence result. Econometrica 70(1): 331-341.
– reference: Imbens GW. 2004. Non-parametric estimation of average treatment effects under exogeneity. A review. Review of Economics and Statistics 19(3): 358-364.
– reference: Card D. 2001. Estimating the return to schooling. Progress on some persistent econometric problems. Economterica 69(5): 1127-1160.
– reference: Earle CE, Tsai JS, Gelber RD, Weinstein MC, Neumann PJ, Weeks JC. 2001. Effectiveness of chemotherapy for advanced lung cancer in the elderly: Instrument variable and propensity analysis. Journal of Clinical Oncology 19(4): 1064-1070.
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– reference: Heckman JJ, Vytlacil E. 2001b. Policy relevant treatment effects. American Economic Review 91(2): 107-111.
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Snippet Instrumental variable (IV) methods are widely used in the health economics literature to adjust for hidden selection biases in observational studies when...
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SubjectTerms Aged
Alternative approaches
Beneficiaries
Breast cancer
Breast Neoplasms - economics
Breast Neoplasms - therapy
Cancer therapies
Comparative analysis
essential heterogeneity
Female
Health Care Costs - statistics & numerical data
Health economics
Heterogeneity
Humans
instrumental variables
local instrumental variable method
Mastectomy
Mastectomy - economics
Mastectomy, Segmental - economics
Medical treatment
Medicare
Models, Statistical
Newly diagnosed
Observational studies
Older women
Outcome Assessment (Health Care) - methods
Outcome Assessment (Health Care) - statistics & numerical data
Parameter estimation
Radiation
Radiotherapy - economics
Selection Bias
self-selection
Selfselection
Studies
Surgery
Treatment
United States
Title Use of instrumental variables in the presence of heterogeneity and self-selection: an application to treatments of breast cancer patients
URI https://api.istex.fr/ark:/67375/WNG-3JS1TCD8-6/fulltext.pdf
https://onlinelibrary.wiley.com/doi/abs/10.1002%2Fhec.1291
https://www.ncbi.nlm.nih.gov/pubmed/17910109
http://econpapers.repec.org/article/wlyhlthec/v_3a16_3ay_3a2007_3ai_3a11_3ap_3a1133-1157.htm
https://www.proquest.com/docview/232064738
https://www.proquest.com/docview/57228914
https://www.proquest.com/docview/68422353
Volume 16
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