IDEAS home Printed from https://ideas.repec.org/a/spr/stabio/v12y2020i3d10.1007_s12561-019-09262-2.html
   My bibliography  Save this article

Deductive Semiparametric Estimation in Double-Sampling Designs with Application to PEPFAR

Author

Listed:
  • Tianchen Qian

    (Harvard University)

  • Constantine Frangakis

    (Johns Hopkins University)

  • Constantin Yiannoutsos

    (Indiana University)

Abstract

Non-ignorable dropout is common in studies with long follow-up time, and it can bias study results unless handled carefully in the study design and the statistical analysis. A double-sampling design allocates additional resources to pursue a subsample of the dropouts and find out their outcomes, which can address potential biases due to non-ignorable dropout. It is desirable to construct semiparametric estimators for the double-sampling design because of their robustness properties. However, obtaining such semiparametric estimators remains a challenge due to the requirement of the analytic form of the efficient influence function (EIF), the derivation of which can be ad hoc and difficult for the double-sampling design. Recent work has shown how the derivation of EIF can be made deductive and computerizable using the functional derivative representation of the EIF in nonparametric models. This approach, however, requires deriving the mixture of a continuous distribution and a point mass, which can itself be challenging for complicated problems such as the double-sampling design. We propose semiparametric estimators for the survival probability in double-sampling designs by generalizing the deductive and computerizable estimation approach. In particular, we propose to build the semiparametric estimators based on a discretized support structure, which approximates the possibly continuous observed data distribution and circumvents the derivation of the mixture distribution. Our approach is deductive in the sense that it is expected to produce semiparametric locally efficient estimators within finite steps without knowledge of the EIF. We apply the proposed estimators to estimating the mortality rate in a double-sampling design component of the President’s Emergency Plan for AIDS Relief (PEPFAR) program. We evaluate the impact of double-sampling selection criteria on the mortality rate estimates. Simulation studies are conducted to evaluate the robustness of the proposed estimators.

Suggested Citation

  • Tianchen Qian & Constantine Frangakis & Constantin Yiannoutsos, 2020. "Deductive Semiparametric Estimation in Double-Sampling Designs with Application to PEPFAR," Statistics in Biosciences, Springer;International Chinese Statistical Association, vol. 12(3), pages 417-445, December.
  • Handle: RePEc:spr:stabio:v:12:y:2020:i:3:d:10.1007_s12561-019-09262-2
    DOI: 10.1007/s12561-019-09262-2
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s12561-019-09262-2
    File Function: Abstract
    Download Restriction: Access to the full text of the articles in this series is restricted.

    File URL: https://libkey.io/10.1007/s12561-019-09262-2?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Min Zhang & Anastasios A. Tsiatis & Marie Davidian, 2008. "Improving Efficiency of Inferences in Randomized Clinical Trials Using Auxiliary Covariates," Biometrics, The International Biometric Society, vol. 64(3), pages 707-715, September.
    2. Vaart,A. W. van der, 2000. "Asymptotic Statistics," Cambridge Books, Cambridge University Press, number 9780521784504, January.
    3. repec:bla:biomet:v:71:y:2015:i:4:p:867-874 is not listed on IDEAS
    4. Ming-Wen An & Constantine E. Frangakis & Beverly S. Musick & Constantin T. Yiannoutsos, 2009. "The Need for Double-Sampling Designs in Survival Studies: An Application to Monitor PEPFAR," Biometrics, The International Biometric Society, vol. 65(1), pages 301-306, March.
    5. repec:bla:biomet:v:71:y:2015:i:4:p:881-883 is not listed on IDEAS
    6. Newey, Whitney K, 1990. "Semiparametric Efficiency Bounds," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 5(2), pages 99-135, April-Jun.
    7. James Robins & Andrea Rotnitzky & Marco Bonetti, 2001. "Discussion of the Frangakis and Rubin Article," Biometrics, The International Biometric Society, vol. 57(2), pages 343-347, June.
    8. Chamberlain, Gary, 1987. "Asymptotic efficiency in estimation with conditional moment restrictions," Journal of Econometrics, Elsevier, vol. 34(3), pages 305-334, March.
    9. Constantine E. Frangakis & Donald B. Rubin, 2001. "Addressing an Idiosyncrasy in Estimating Survival Curves Using Double Sampling in the Presence of Self-Selected Right Censoring," Biometrics, The International Biometric Society, vol. 57(2), pages 333-342, June.
    10. Constantine E. Frangakis & Donald B. Rubin, 2001. "Rejoinder to Discussions on Addressing an Idiosyncrasy in Estimating Survival Curves Using Double Sampling in the Presence of Self-Selected Right Censoring," Biometrics, The International Biometric Society, vol. 57(2), pages 351-353, June.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Agnes N Kiragga & Barbara Castelnuovo & Rachel Musomba & Jonathan Levin & Andrew Kambugu & Yukari C Manabe & Constantin T Yiannoutsos & Noah Kiwanuka, 2013. "Comparison of Methods for Correction of Mortality Estimates for Loss to Follow-Up after ART Initiation: A Case of the Infectious Diseases Institute, Uganda," PLOS ONE, Public Library of Science, vol. 8(12), pages 1-7, December.
    2. Timothy B. Armstrong & Michal Kolesár, 2021. "Sensitivity analysis using approximate moment condition models," Quantitative Economics, Econometric Society, vol. 12(1), pages 77-108, January.
    3. Lancaster, Tony & Imbens, Guido, 1996. "Case-control studies with contaminated controls," Journal of Econometrics, Elsevier, vol. 71(1-2), pages 145-160.
    4. Park, Byeong U. & Sickles, Robin C. & Simar, Leopold, 2003. "Semiparametric-efficient estimation of AR(1) panel data models," Journal of Econometrics, Elsevier, vol. 117(2), pages 279-309, December.
    5. Robertson, Donald & Sarafidis, Vasilis, 2015. "IV estimation of panels with factor residuals," Journal of Econometrics, Elsevier, vol. 185(2), pages 526-541.
    6. Graham, Bryan S. & Hahn, Jinyong & Poirier, Alexandre & Powell, James L., 2018. "A quantile correlated random coefficients panel data model," Journal of Econometrics, Elsevier, vol. 206(2), pages 305-335.
    7. Dennis Kristensen, 2009. "Semiparametric Modelling and Estimation: A Selective Overview," CREATES Research Papers 2009-44, Department of Economics and Business Economics, Aarhus University.
    8. Stuart G. Baker, 2001. "Discussion of Double Sampling for Survival Analysis," Biometrics, The International Biometric Society, vol. 57(2), pages 348-350, June.
    9. Ai, Chunrong & Chen, Xiaohong, 2012. "The semiparametric efficiency bound for models of sequential moment restrictions containing unknown functions," Journal of Econometrics, Elsevier, vol. 170(2), pages 442-457.
    10. Severini, Thomas A. & Tripathi, Gautam, 2001. "A simplified approach to computing efficiency bounds in semiparametric models," Journal of Econometrics, Elsevier, vol. 102(1), pages 23-66, May.
    11. St'ephane Bonhomme & Martin Weidner, 2018. "Minimizing Sensitivity to Model Misspecification," Papers 1807.02161, arXiv.org, revised Oct 2021.
    12. Yannis Jemiai & Andrea Rotnitzky & Bryan E. Shepherd & Peter B. Gilbert, 2007. "Semiparametric estimation of treatment effects given base‐line covariates on an outcome measured after a post‐randomization event occurs," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 69(5), pages 879-901, November.
    13. Park, B. U. & Sickles, R. C. & Simar, L., 1998. "Stochastic panel frontiers: A semiparametric approach," Journal of Econometrics, Elsevier, vol. 84(2), pages 273-301, June.
    14. Vernon T. Farewell & Jerald F. Lawless & Dafna D. Gladman & Murray B. Urowitz, 2003. "Tracing studies and analysis of the effect of loss to follow‐up on mortality estimation from patient registry data," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 52(4), pages 445-456, October.
    15. Victor Chernozhukov & Denis Chetverikov & Mert Demirer & Esther Duflo & Christian Hansen & Whitney Newey & James Robins, 2018. "Double/debiased machine learning for treatment and structural parameters," Econometrics Journal, Royal Economic Society, vol. 21(1), pages 1-68, February.
    16. Stephens Alisa & Tchetgen Tchetgen Eric & De Gruttola Victor, 2014. "Locally Efficient Estimation of Marginal Treatment Effects When Outcomes Are Correlated: Is the Prize Worth the Chase?," The International Journal of Biostatistics, De Gruyter, vol. 10(1), pages 59-75, May.
    17. Graham, Bryan S. & Pinto, Cristine Campos de Xavier, 2022. "Semiparametrically efficient estimation of the average linear regression function," Journal of Econometrics, Elsevier, vol. 226(1), pages 115-138.
    18. Victor Chernozhukov & Denis Chetverikov & Mert Demirer & Esther Duflo & Christian Hansen & Whitney Newey & James Robins, 2016. "Double/Debiased Machine Learning for Treatment and Causal Parameters," Papers 1608.00060, arXiv.org, revised Nov 2024.
    19. Imbens, Guido W. & Lancaster, Tony, 1996. "Efficient estimation and stratified sampling," Journal of Econometrics, Elsevier, vol. 74(2), pages 289-318, October.
    20. Yassine Sbai Sassi, 2023. "The Ordinary Least Eigenvalues Estimator," Papers 2304.12554, arXiv.org.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:spr:stabio:v:12:y:2020:i:3:d:10.1007_s12561-019-09262-2. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.com .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.