Design and Inference for Cancer Biomarker Study with an Outcome and Auxiliary-Dependent Subsampling

In cancer research, it is important to evaluate the performance of a biomarker (e.g., molecular, genetic, or imaging) that correlates patients' prognosis or predicts patients' response to treatment in a large prospective study. Due to overall budget constraint and high cost associated with...

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Published inBiometrics Vol. 66; no. 2; pp. 502 - 511
Main Authors Wang, Xiaofei, Zhou, Haibo
Format Journal Article
LanguageEnglish
Published Malden, USA Blackwell Publishing Inc 01.06.2010
Wiley-Blackwell
Blackwell Publishing Ltd
Subjects
Online AccessGet full text
ISSN0006-341X
1541-0420
1541-0420
DOI10.1111/j.1541-0420.2009.01280.x

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Abstract In cancer research, it is important to evaluate the performance of a biomarker (e.g., molecular, genetic, or imaging) that correlates patients' prognosis or predicts patients' response to treatment in a large prospective study. Due to overall budget constraint and high cost associated with bioassays, investigators often have to select a subset from all registered patients for biomarker assessment. To detect a potentially moderate association between the biomarker and the outcome, investigators need to decide how to select the subset of a fixed size such that the study efficiency can be enhanced. We show that, instead of drawing a simple random sample from the study cohort, greater efficiency can be achieved by allowing the selection probability to depend on the outcome and an auxiliary variable; we refer to such a sampling scheme as outcome and auxiliary-dependent subsampling (OADS). This article is motivated by the need to analyze data from a lung cancer biomarker study that adopts the OADS design to assess epidermal growth factor receptor (EGFR) mutations as a predictive biomarker for whether a subject responds to a greater extent to EGFR inhibitor drugs. We propose an estimated maximum-likelihood method that accommodates the OADS design and utilizes all observed information, especially those contained in the likelihood score of EGFR mutations (an auxiliary variable of EGFR mutations) that is available to all patients. We derive the asymptotic properties of the proposed estimator and evaluate its finite sample properties via simulation. We illustrate the proposed method with a data example.
AbstractList In cancer research, it is important to evaluate the performance of a biomarker (e.g., molecular, genetic, or imaging) that correlates patients' prognosis or predicts patients' response to treatment in a large prospective study. Due to overall budget constraint and high cost associated with bioassays, investigators often have to select a subset from all registered patients for biomarker assessment. To detect a potentially moderate association between the biomarker and the outcome, investigators need to decide how to select the subset of a fixed size such that the study efficiency can be enhanced. We show that, instead of drawing a simple random sample from the study cohort, greater efficiency can be achieved by allowing the selection probability to depend on the outcome and an auxiliary variable; we refer to such a sampling scheme as outcome and auxiliary-dependent subsampling (OADS). This article is motivated by the need to analyze data from a lung cancer biomarker study that adopts the OADS design to assess epidermal growth factor receptor (EGFR) mutations as a predictive biomarker for whether a subject responds to a greater extent to EGFR inhibitor drugs. We propose an estimated maximum-likelihood method that accommodates the OADS design and utilizes all observed information, especially those contained in the likelihood score of EGFR mutations (an auxiliary variable of EGFR mutations) that is available to all patients. We derive the asymptotic properties of the proposed estimator and evaluate its finite sample properties via simulation. We illustrate the proposed method with a data example.
Summary In cancer research, it is important to evaluate the performance of a biomarker (e.g., molecular, genetic, or imaging) that correlates patients' prognosis or predicts patients' response to treatment in a large prospective study. Due to overall budget constraint and high cost associated with bioassays, investigators often have to select a subset from all registered patients for biomarker assessment. To detect a potentially moderate association between the biomarker and the outcome, investigators need to decide how to select the subset of a fixed size such that the study efficiency can be enhanced. We show that, instead of drawing a simple random sample from the study cohort, greater efficiency can be achieved by allowing the selection probability to depend on the outcome and an auxiliary variable; we refer to such a sampling scheme as outcome and auxiliary‐dependent subsampling (OADS). This article is motivated by the need to analyze data from a lung cancer biomarker study that adopts the OADS design to assess epidermal growth factor receptor (EGFR) mutations as a predictive biomarker for whether a subject responds to a greater extent to EGFR inhibitor drugs. We propose an estimated maximum‐likelihood method that accommodates the OADS design and utilizes all observed information, especially those contained in the likelihood score of EGFR mutations (an auxiliary variable of EGFR mutations) that is available to all patients. We derive the asymptotic properties of the proposed estimator and evaluate its finite sample properties via simulation. We illustrate the proposed method with a data example.
In cancer research, it is important to evaluate the performance of a biomarker (e.g. molecular, genetic, or imaging) that correlates patients’ prognosis or predicts patients’ response to a treatment in large prospective study. Due to overall budget constraint and high cost associated with bioassays, investigators often have to select a subset from all registered patients for biomarker assessment. To detect a potentially moderate association between the biomarker and the outcome, investigators need to decide how to select the subset of a fixed size such that the study efficiency can be enhanced. We show that, instead of drawing a simple random sample from the study cohort, greater efficiency can be achieved by allowing the selection probability to depend on the outcome and an auxiliary variable; we refer to such a sampling scheme as outcome and auxiliary-dependent subsampling (OADS). This paper is motivated by the need to analyze data from a lung cancer biomarker study that adopts the OADS design to assess EGFR mutations as a predictive biomarker for whether a subject responds to a greater extent to EGFR inhibitor drugs. We propose an estimated maximum likelihood method that accommodates the OADS design and utilizes all observed information, especially those contained in the likelihood score of EGFR mutations (an auxiliary variable of EGFR mutations) that is available to all patients. We derive the asymptotic properties of the proposed estimator and evaluate its finite sample properties via simulation. We illustrate the proposed method with a data example.
Summary In cancer research, it is important to evaluate the performance of a biomarker (e.g., molecular, genetic, or imaging) that correlates patients' prognosis or predicts patients' response to treatment in a large prospective study. Due to overall budget constraint and high cost associated with bioassays, investigators often have to select a subset from all registered patients for biomarker assessment. To detect a potentially moderate association between the biomarker and the outcome, investigators need to decide how to select the subset of a fixed size such that the study efficiency can be enhanced. We show that, instead of drawing a simple random sample from the study cohort, greater efficiency can be achieved by allowing the selection probability to depend on the outcome and an auxiliary variable; we refer to such a sampling scheme as  outcome and auxiliary‐dependent subsampling  (OADS). This article is motivated by the need to analyze data from a lung cancer biomarker study that adopts the OADS design to assess epidermal growth factor receptor (EGFR) mutations as a predictive biomarker for whether a subject responds to a greater extent to EGFR inhibitor drugs. We propose an estimated maximum‐likelihood method that accommodates the OADS design and utilizes all observed information, especially those contained in the likelihood score of EGFR mutations (an auxiliary variable of EGFR mutations) that is available to all patients. We derive the asymptotic properties of the proposed estimator and evaluate its finite sample properties via simulation. We illustrate the proposed method with a data example.
In cancer research, it is important to evaluate the performance of a biomarker (e.g., molecular, genetic, or imaging) that correlates patients' prognosis or predicts patients' response to treatment in a large prospective study. Due to overall budget constraint and high cost associated with bioassays, investigators often have to select a subset from all registered patients for biomarker assessment. To detect a potentially moderate association between the biomarker and the outcome, investigators need to decide how to select the subset of a fixed size such that the study efficiency can be enhanced. We show that, instead of drawing a simple random sample from the study cohort, greater efficiency can be achieved by allowing the selection probability to depend on the outcome and an auxiliary variable; we refer to such a sampling scheme as€,outcome and auxiliary-dependent subsampling€,(OADS). This article is motivated by the need to analyze data from a lung cancer biomarker study that adopts the OADS design to assess epidermal growth factor receptor (EGFR) mutations as a predictive biomarker for whether a subject responds to a greater extent to EGFR inhibitor drugs. We propose an estimated maximum-likelihood method that accommodates the OADS design and utilizes all observed information, especially those contained in the likelihood score of EGFR mutations (an auxiliary variable of EGFR mutations) that is available to all patients. We derive the asymptotic properties of the proposed estimator and evaluate its finite sample properties via simulation. We illustrate the proposed method with a data example.
In cancer research, it is important to evaluate the performance of a biomarker (e.g., molecular, genetic, or imaging) that correlates patients' prognosis or predicts patients' response to treatment in a large prospective study. Due to overall budget constraint and high cost associated with bioassays, investigators often have to select a subset from all registered patients for biomarker assessment. To detect a potentially moderate association between the biomarker and the outcome, investigators need to decide how to select the subset of a fixed size such that the study efficiency can be enhanced. We show that, instead of drawing a simple random sample from the study cohort, greater efficiency can be achieved by allowing the selection probability to depend on the outcome and an auxiliary variable; we refer to such a sampling scheme as outcome and auxiliary-dependent subsampling (OADS). This article is motivated by the need to analyze data from a lung cancer biomarker study that adopts the OADS design to assess epidermal growth factor receptor (EGFR) mutations as a predictive biomarker for whether a subject responds to a greater extent to EGFR inhibitor drugs. We propose an estimated maximum-likelihood method that accommodates the OADS design and utilizes all observed information, especially those contained in the likelihood score of EGFR mutations (an auxiliary variable of EGFR mutations) that is available to all patients. We derive the asymptotic properties of the proposed estimator and evaluate its finite sample properties via simulation. We illustrate the proposed method with a data example. [PUBLICATION ABSTRACT]
In cancer research, it is important to evaluate the performance of a biomarker (e.g., molecular, genetic, or imaging) that correlates patients' prognosis or predicts patients' response to treatment in a large prospective study. Due to overall budget constraint and high cost associated with bioassays, investigators often have to select a subset from all registered patients for biomarker assessment. To detect a potentially moderate association between the biomarker and the outcome, investigators need to decide how to select the subset of a fixed size such that the study efficiency can be enhanced. We show that, instead of drawing a simple random sample from the study cohort, greater efficiency can be achieved by allowing the selection probability to depend on the outcome and an auxiliary variable; we refer to such a sampling scheme as outcome and auxiliary-dependent subsampling (OADS). This article is motivated by the need to analyze data from a lung cancer biomarker study that adopts the OADS design to assess epidermal growth factor receptor (EGFR) mutations as a predictive biomarker for whether a subject responds to a greater extent to EGFR inhibitor drugs. We propose an estimated maximumlikelihood method that accommodates the OADS design and utilizes all observed information, especially those contained in the likelihood score of EGFR mutations (an auxiliary variable of EGFR mutations) that is available to all patients. We derive the asymptotic properties of the proposed estimator and evaluate its finite sample properties via simulation. We illustrate the proposed method with a data example.
In cancer research, it is important to evaluate the performance of a biomarker (e.g., molecular, genetic, or imaging) that correlates patients' prognosis or predicts patients' response to treatment in a large prospective study. Due to overall budget constraint and high cost associated with bioassays, investigators often have to select a subset from all registered patients for biomarker assessment. To detect a potentially moderate association between the biomarker and the outcome, investigators need to decide how to select the subset of a fixed size such that the study efficiency can be enhanced. We show that, instead of drawing a simple random sample from the study cohort, greater efficiency can be achieved by allowing the selection probability to depend on the outcome and an auxiliary variable; we refer to such a sampling scheme as outcome and auxiliary-dependent subsampling (OADS). This article is motivated by the need to analyze data from a lung cancer biomarker study that adopts the OADS design to assess epidermal growth factor receptor (EGFR) mutations as a predictive biomarker for whether a subject responds to a greater extent to EGFR inhibitor drugs. We propose an estimated maximum-likelihood method that accommodates the OADS design and utilizes all observed information, especially those contained in the likelihood score of EGFR mutations (an auxiliary variable of EGFR mutations) that is available to all patients. We derive the asymptotic properties of the proposed estimator and evaluate its finite sample properties via simulation. We illustrate the proposed method with a data example.In cancer research, it is important to evaluate the performance of a biomarker (e.g., molecular, genetic, or imaging) that correlates patients' prognosis or predicts patients' response to treatment in a large prospective study. Due to overall budget constraint and high cost associated with bioassays, investigators often have to select a subset from all registered patients for biomarker assessment. To detect a potentially moderate association between the biomarker and the outcome, investigators need to decide how to select the subset of a fixed size such that the study efficiency can be enhanced. We show that, instead of drawing a simple random sample from the study cohort, greater efficiency can be achieved by allowing the selection probability to depend on the outcome and an auxiliary variable; we refer to such a sampling scheme as outcome and auxiliary-dependent subsampling (OADS). This article is motivated by the need to analyze data from a lung cancer biomarker study that adopts the OADS design to assess epidermal growth factor receptor (EGFR) mutations as a predictive biomarker for whether a subject responds to a greater extent to EGFR inhibitor drugs. We propose an estimated maximum-likelihood method that accommodates the OADS design and utilizes all observed information, especially those contained in the likelihood score of EGFR mutations (an auxiliary variable of EGFR mutations) that is available to all patients. We derive the asymptotic properties of the proposed estimator and evaluate its finite sample properties via simulation. We illustrate the proposed method with a data example.
Author Wang, Xiaofei
Zhou, Haibo
AuthorAffiliation 1 Department of Biostatistics and Bioinformatics, Cancer Leukemia Group B Statistical Center, Duke University Medical Center, DUMC 2721, Durham, N.C. 27710, U.S.A
2 Department of Biostatistics, University of North Carolina at Chapel Hill Chapel Hill, N.C. 27599-7420, U.S.A
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PublicationTitle Biometrics
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References Wacholder, S. and Weinberg, C. R. (1994). Flexible maximum likelihood methods for assessing joint effects in case-control studies with complex sampling. Biometrics 50, 350-357.
Zhou, H., Chen, J., and Cai, J. (2002). Random effects logistic regression analysis with auxiliary covariates. Biometrics 58, 352-360.
Baker, S. G. and Kramer, B. S. (2005). Statistics for weighing benefits and harms in a proposed genetic substudy of a randomized cancer prevention trial. Journal of the Royal Statistical Society, Series C 54, 941-954.
Weaver, M. A. and Zhou, H. (2005). An estimated likelihood method for continuous outcome regression models with outcome-dependent sampling. Journal of the American Statistical Association 100, 459-469.
Breslow, N. E. and Cain, K. C. (1988). Logistic regression for two-stage case-control data. Biometrika 75, 11-20.
Zhao, L. P. and Lipsitz, S. (1992). Designs and analysis of two-stage studies. Statistics in Medicine 11, 769-782.
Fan, J. (1993). Local linear regression smoothers and their minimax efficiencies. Annals of Statistics 21, 196-216.
Wild, C. J. (1991). Fitting prospective regression models to case-control data. Biometrika 78, 705-717.
Prentice, R. L. and Pyke, R. (1979). Logistic disease incidence models and case control studies. Biometrika 66, 403-411.
Horvitz, D. G. and Thompson, D. J. (1952). A generalization of sampling without replacement from a finite universe. Journal of the American Statistical Association 47, 663-685.
Nadaraya, E. A. (1964). On estimating regression. Theory of Probability and Its Applications 10, 186-190.
Eubank, R. L. (1999). Nonparametric Regression and Spline Smoothing. New York : Marcel Dekker, Inc.
Breslow, N. E. and Day, N. E. (1980). Statistical Methods in Cancer Research I: The Analysis of Case-Control Studies. Lyon , France : International Agency for Research on Cancer .
Paez, J. G., Jänne, P. A., and Lee J. C., Tracy, S., Greulich, H., Gabriel, S., Herman, P., Kaye, F. J., Lindeman, N., Boggon, T. J., Naoki, K., Sasaki, H., Fujii, Y., Eck, M. J., Sellers, W. R., Johnson, B. E., and Meyerson, M. (2004). EGFR mutations in lung cancer: Correlation with clinical response to gefitinib therapy. Science 304, 1497-500.
Breslow, N. C. and Holubkov, R. (1997). Maximum likelihood estimation of logistic regression parameters under two-phase, outcome-dependent sampling. Journal of the Royal Statistical Society, Series B 59, 447-461.
Wand, M. P. and Jones, M. C. (1995). Kernel Smoothing. London : Chapman and Hall.
Zhou, H., Weaver, M. A., Qin, J., Longnecker, M. P., and Wang, M. C. (2002). A semiparametric empirical likelihood method for data from an outcome-dependent sampling design with a continuous outcome. Biometrics 58, 413-421.
Zhou, H., Chen, J., Rissanen, T., Korrick, S., Hu, H., Salonen, J. T., and Longnecker, M. P. (2007). An efficient sampling and inference procedure for studies with a continuous outcome. Epidemiology 18, 461-468.
Lynch, T. J., Bell, D. W., Sordella, R., Gurubhagavatula, S., Okimoto, R. A., Brannigan, B. W., Harris, P. L., Haserlat, S. M., Supko, J. G., Haluska, F. G., Louis, D. N., Christiani, D. C., Settleman, J., and Haber, D. A. (2004). Activating mutations in the epidermal growth factor receptor underlying responsiveness of non-small-cell lung cancer to gefitinib. New England Journal of Medicine 350, 2129-2139.
Song, R., Zhou, H., and Kosorok, M. R. (2009). A note on semiparametric efficient inference for two-stage outcome-dependent sampling with a continuous outcome. Biometrika 96, 221-228.
Wang, X. F. and Zhou, H. (2006). A semiparametric empirical likelihood method for biased sampling schemes in epidemiologic studies with auxiliary covariates. Biometrics 62, 1149-1160.
Pepe, M. S. and Fleming, R. R. (1991). A nonparametric method for dealing with mismeasured covariate data. Journal of the American Statistical Association 86, 108-113.
Zhou, H. and Wang, C. Y. (2000). Failure time regression analysis with measurement error in Covariates. Journal of the Royal Statistical Society, Series B 62, 657-665.
Eberhard, D. A., Giaccone, G., Johnson, B. E. on behalf of the Molecular Assays in Non-Small-Cell Lung Cancer Working Group. (2008). Biomarkers of response to epidermal growth factor receptor inhibitors in non-small-cell lung cancer: Standardization for use in the clinical trial setting. Journal of Clinical Oncology 26, 983-994.
Flanders, W. D. and Greenland, S. (1991). Analytic methods for two-stage case-control studies and other stratified designs. Statistics in Medicine 10, 739-747.
Cosslett, S. R. (1981). Maximum likelihood estimator for choice-based samples. Econometrica 49, 1289-1316.
Schill, W., Jöckel, K.-H., Drescher, K., and Timm, J. (1993). Logistic analysis in case-control studies under validation sampling. Biometrika 80, 339-352.
Watson, G. S. (1964). Smooth regression analysis. Sankhya, Series A 26, 359-372.
Breslow, N. E. and Chatterjee, N. (1999). Design and analysis of two-phase studies with binary outcome applied to Wilms tumor prognosis. Applied Statistics 48, 457-468.
White, J. E. (1982). A two stage design for the study of the relationship between a rare exposure and a rare disease. American Journal of Epidemiology 115, 119-128.
Carroll, R. J. and Wand, M. P. (1991). Semiparametric estimation in logistic measurement error models. Journal of the Royal Statistical Society, Series B 53, 573-585.
Zhou, H. and Pepe, M. S. (1995). Auxiliary covariate data in failure time regression. Biometrika 82, 139-149.
Prentice, R. L. (1986). A case-cohort design for epidemiologic cohort studies and disease prevention trials. Biometrika 73, 1-11.
Prentice, R. L. (1989). Surrogate endpoints in clinical trials: Definition and operational criteria. Statistics in Medicine 8, 431-440.
Maddaus, M. A., Wang, X. F., Vollmer, R. T., Abraham, N. Z., D'Cunha, J., Herzan, D. L., Patterson, A., Kohman, L. J., Green, M. R., and Kratzke, R. A. (2006). CALGB 9761: A prospective analysis of IHC and PCR based detection of occult metastatic disease in stage I NSCLC. Journal of Clinical Oncology, 2006 ASCO Annual Meeting Proceedings Part I. Vol 24, No. 18S (June 20 Supplement), 2006: 7030.
2007; 18
2002; 58
1986; 73
1991; 78
1991; 10
1991; 53
1993; 21
1999; 48
1989; 8
1981; 49
2006
1995
1964; 26
1988; 75
1992; 11
2004; 304
1999
1952; 47
2009; 96
1995; 82
2006; 62
2005; 100
1997; 59
2004; 350
1991; 86
1964; 10
2008; 26
2000; 62
2005; 54
1993; 80
1982; 115
1980
1979; 66
1994; 50
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Maddaus M. A. (e_1_2_9_15_1) 2006
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– reference: Prentice, R. L. (1989). Surrogate endpoints in clinical trials: Definition and operational criteria. Statistics in Medicine 8, 431-440.
– reference: Wacholder, S. and Weinberg, C. R. (1994). Flexible maximum likelihood methods for assessing joint effects in case-control studies with complex sampling. Biometrics 50, 350-357.
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– reference: Flanders, W. D. and Greenland, S. (1991). Analytic methods for two-stage case-control studies and other stratified designs. Statistics in Medicine 10, 739-747.
– reference: Cosslett, S. R. (1981). Maximum likelihood estimator for choice-based samples. Econometrica 49, 1289-1316.
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– reference: Wang, X. F. and Zhou, H. (2006). A semiparametric empirical likelihood method for biased sampling schemes in epidemiologic studies with auxiliary covariates. Biometrics 62, 1149-1160.
– reference: Zhou, H., Weaver, M. A., Qin, J., Longnecker, M. P., and Wang, M. C. (2002). A semiparametric empirical likelihood method for data from an outcome-dependent sampling design with a continuous outcome. Biometrics 58, 413-421.
– reference: Breslow, N. E. and Cain, K. C. (1988). Logistic regression for two-stage case-control data. Biometrika 75, 11-20.
– reference: Prentice, R. L. and Pyke, R. (1979). Logistic disease incidence models and case control studies. Biometrika 66, 403-411.
– reference: Zhao, L. P. and Lipsitz, S. (1992). Designs and analysis of two-stage studies. Statistics in Medicine 11, 769-782.
– reference: Breslow, N. E. and Chatterjee, N. (1999). Design and analysis of two-phase studies with binary outcome applied to Wilms tumor prognosis. Applied Statistics 48, 457-468.
– reference: Zhou, H. and Pepe, M. S. (1995). Auxiliary covariate data in failure time regression. Biometrika 82, 139-149.
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– reference: Zhou, H. and Wang, C. Y. (2000). Failure time regression analysis with measurement error in Covariates. Journal of the Royal Statistical Society, Series B 62, 657-665.
– reference: Weaver, M. A. and Zhou, H. (2005). An estimated likelihood method for continuous outcome regression models with outcome-dependent sampling. Journal of the American Statistical Association 100, 459-469.
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Snippet In cancer research, it is important to evaluate the performance of a biomarker (e.g., molecular, genetic, or imaging) that correlates patients' prognosis or...
Summary In cancer research, it is important to evaluate the performance of a biomarker (e.g., molecular, genetic, or imaging) that correlates patients'...
Summary In cancer research, it is important to evaluate the performance of a biomarker (e.g., molecular, genetic, or imaging) that correlates patients'...
In cancer research, it is important to evaluate the performance of a biomarker (e.g. molecular, genetic, or imaging) that correlates patients’ prognosis or...
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SubjectTerms Auxiliary variable
bioassays
Biological markers
Biomarker
Biomarkers
Biomarkers, Tumor
BIOMETRIC METHODOLOGY
Biometrics
biometry
Cancer
Clinical outcomes
Computer Simulation
Consistent estimators
Data models
Design efficiency
drugs
Efficiency
Epidermal Growth Factor - antagonists & inhibitors
Epidermal Growth Factor - genetics
epidermal growth factor receptors
Estimated likelihood method
Estimation methods
Estimators
Genetic mutation
Humans
image analysis
Inference
Kernel smoother
Lung neoplasms
Lung Neoplasms - drug therapy
Lung Neoplasms - genetics
Methods
Mutation
Neoplasms - diagnosis
Outcome and auxiliary-dependent subsampling
Patient Selection
patients
Precision Medicine - methods
Predictive Value of Tests
probability
Prognosis
prospective studies
Sampling techniques
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Title Design and Inference for Cancer Biomarker Study with an Outcome and Auxiliary-Dependent Subsampling
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