Modeling Pregnancy Outcomes Through Sequentially Nested Regression Models

Xuan Bi, Long Feng, Cai Li, Heping Zhang

Research output: Contribution to journalArticlepeer-review


The polycystic ovary syndrome (PCOS) is a most common cause of infertility among women of reproductive age. Unfortunately, the etiology of PCOS is poorly understood. Large-scale clinical trials for pregnancy in polycystic ovary syndrome (PPCOS) were conducted to evaluate the effectiveness of treatments. Ovulation, pregnancy, and live birth are three sequentially nested binary outcomes, typically analyzed separately. However, the separate models may lose power in detecting the treatment effects and influential variables for live birth, due to decreased sample sizes and unbalanced event counts. It has been a long-held hypothesis among the clinicians that some of the important variables for early pregnancy outcomes may continue their influence on live birth. To consider this possibility, we develop an (Formula presented.) -norm based regularization method in favor of variables that have been identified from an earlier stage. Our approach explicitly bridges the connections across nested outcomes through computationally easy algorithms and enjoys theoretical guarantee of estimation and variable selection. By analyzing the PPCOS data, we successfully uncover the hidden influence of risk factors on live birth, which confirm clinical experience. Moreover, we provide novel infertility treatment recommendations (e.g., letrozole vs. clomiphene citrate) for women with PCOS to improve their chances of live birth. Supplementary materials for this article are available online.

Original languageEnglish (US)
Pages (from-to)602-616
Number of pages15
JournalJournal of the American Statistical Association
Issue number538
StatePublished - 2022

Bibliographical note

Funding Information:
This work is supported in part by grants U10HD055925 from the National Institutes of Health. The authors wish to thank the Reproductive Medicine Network for sharing the dataset.

Publisher Copyright:
© 2021 The Author(s). Published with license by Taylor & Francis Group, LLC.


  • Infertility study
  • Sequentially nested binary outcome
  • Variable selection
  • penalization

PubMed: MeSH publication types

  • Journal Article


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