Skip to main content

Advertisement

Log in

Estimation of a treatment effect based on a modified covariates method with \(L_0\) norm

  • Original Article
  • Published:
Artificial Life and Robotics Aims and scope Submit manuscript

Abstract

In randomized clinical trials, we assumed the situation that the new treatment is not adequate compared to the control treatment as a result. However, it is unknown if the new treatment is ineffective for all patients or if it is effective for only a subgroup of patients with specific characteristics. If such a subgroup exists and can be detected, the patients can receive effective therapy. To detect subgroups, we need to estimate treatment effects. To achieve this, various treatment effect estimation methods have been proposed based on the sparse regression method. However, these methods are affected by noise. Therefore, we propose new treatment effect estimation approaches based on the modified covariate method, one using lasso regression and the other ridge regression, using the \(L_0\) norm. The proposed approach was evaluated through numerical simulation and real data examples. As a result, the results of the proposed method were almost the same as those of existing methods in numerical simulations, but were effective in real data example.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Subscribe and save

Springer+ Basic
$34.99 /Month
  • Get 10 units per month
  • Download Article/Chapter or eBook
  • 1 Unit = 1 Article or 1 Chapter
  • Cancel anytime
Subscribe now

Buy Now

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Fig. 1
Fig. 2
Fig. 3

Similar content being viewed by others

Explore related subjects

Discover the latest articles, news and stories from top researchers in related subjects.

References

  1. Gail M, Simon R (1985) Testing for qualitative interactions between treatment effects and patient subsets. Biometrics 41(2):361–72

    Article  Google Scholar 

  2. Ryston O, Sauebrei W (2008) Interactions between treatment and continuous covariants: a step toward individualizing therapy. J Clin Oncol 26(9):1397–99

    Article  Google Scholar 

  3. Lipkovich I, Dmitrienko A, D’Agistino RB (2017) Tutorial in biostatistics: Data-driven subgroup identification and analysis in clinical trials. Stat Med 36(1):136–196

    Article  MathSciNet  Google Scholar 

  4. Sies A, Demyttenaere K, Mechelen IV (2019) Studying treatment-effect heterogeneity in precision medicine through induced subgroups. J Biopharm Stat 29(3):491–507

    Article  Google Scholar 

  5. Bonetti M, Gelber R (2004) Patterns of treatment effects in subsets of patients in clinical trials. Biostatistics 5(3):465–481

    Article  Google Scholar 

  6. Bonetti M, Zahrieh D, Cole BF, Gelber RD (2009) A small sample study of the STEPP approach to assessing treatment-covariate interactions in survival data. Stat Med 28(8):1255–68

    Article  MathSciNet  Google Scholar 

  7. Sauerbrei W, Royston P, Zapien K (2007) Detecting an interaction between treatment and a continuous covariate: a comparison of two approaches. Comput Stat Data Anal 51(8):40541–63

    Article  MathSciNet  Google Scholar 

  8. Su X, Tsai CL, Wang H, Nickerson DM, Li B (2009) Subgroup analysis via recursive partitioning. J Mach Learn Res 10:141–58

  9. Zhao Y, Zeng D, Rush AJ, Kosorok MR (2012) Estimating individualized treatment rules using outcome weighted learning. J Am Stat Assoc 107(499):1106–1118

  10. Imai K, Ratkovic M (2013) Estimating treatment effect heterogeneity in randomized program evaluation. Ann Appl Stat 7(1):443–470

    Article  MathSciNet  Google Scholar 

  11. Athey S, Imbens G (2016) Recursive partitioning for heterogeneous causal effects. Proc Natl Acad Sci USA 113(27):7353–7360

    Article  MathSciNet  Google Scholar 

  12. Wager S, Athey S (2018) Estimation and inference of heterogeneous treatment effects using random forests. J Am Stat Assoc 113(523):1228–1242

    Article  MathSciNet  Google Scholar 

  13. Tibshirani R (1996) Regression shrinkage and selection via the lasso. J R Stat Soc Ser B (Methodol) 58(1):267–288

    Article  MathSciNet  Google Scholar 

  14. Tian L, Alizadeh AA, Gentles AJ, Tibshirani R (2014) A simple method for estimating interactions between a treatment and large number of covariates. J Am Stat Assoc 109(508):1517–1532

    Article  MathSciNet  Google Scholar 

  15. Xie Y, Brand JE, Jann B (2012) Estimating heterogeneous treatment effects with observational data. Sociol Methodol 42(1):314–347

    Article  Google Scholar 

  16. Rosenbaum PR, Rubin DB (1983) The central role of the propensity score in observational studies for causal effects. Biometrika 70(1):41–55

    Article  MathSciNet  Google Scholar 

  17. Athey S, Tibshirani J, Wager S (2017) Solving heterogeneous estimating equations with gradient forest. https://arxiv.org/abs/1610.01271

  18. Powers S, Qian J, Jung K, Schuler A, Shah NH, Hastie T, Tibshirani R (2017) Some methods for heterogeneous treatment effect estimation in high dimensions. Stat Med 37(11):1767–1787

    Article  MathSciNet  Google Scholar 

  19. Tibshirani R, Friedman J (2020) A Pliable Lasso. J Comput Graph Stat 29(1):215–225

    Article  MathSciNet  Google Scholar 

  20. Chen S, Tian L, Cai T, Yu M (2017) A general statistical framework for subgroup identification and comparative treatment scoring. Biometrics 73(4):1199–1209

    Article  MathSciNet  Google Scholar 

  21. Mazumder R, Radchenko P, Dedieu A (2022) Subset selection with shrinkage: sparse linear modeling when the SNR is low. Oper Res Online

  22. Hazimeh H, Mazumder R (2020) Fast best subset selection: coordinate descent and local combinatorial optimization algorithms. Oper Res 68(5):1517–1537

    Article  MathSciNet  Google Scholar 

  23. R Core Team (2022) R: a language and environment for statistical computing. https://www.R-project.org/

  24. Friedman J, Hastie T, Tibshirani R (2010) Regularization paths for generalized linear models via coordinate descent. J Stat Softw 33(1):1–22

    Article  Google Scholar 

  25. Hazimeh H, Mazumder R, Nonet T (2021) L0Learn: fast algorithms for best subset selection. R package version 2.0.3. https://CRAN.R-project.org/package= L0Learn

  26. Juraska M, Gilbert PB, Lu X, Zhang M, Davidian M, Tsiatis AA (2022) speff2trial: semiparametric efficient estimation for a two-sample treatment effect. https://CRAN.R-project.org/package=speff2trial

  27. Hammer SM et al (1996) A trial comparing nucleoside monotherapy with combination therapy in HIV-infected adults with CD4 cell counts from 200 to 500 per cubic millimeter. N Engl J Med 335:1081–1090

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Kensuke Tanioka.

Additional information

Publisher's Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

This work was presented in part at the joint symposium of the 28th International Symposium on Artificial Life and Robotics, the 8th International Symposium on BioComplexity, and the 6th International Symposium on Swarm Behavior and Bio-Inspired Robotics (Beppu, Oita and Online, January 25–27, 2023).

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Tanioka, K., Okuda, K., Hiwa, S. et al. Estimation of a treatment effect based on a modified covariates method with \(L_0\) norm. Artif Life Robotics 29, 250–258 (2024). https://doi.org/10.1007/s10015-023-00929-0

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10015-023-00929-0

Keywords

Navigation