Annals of Applied Statistics

Fused comparative intervention scoring for heterogeneity of longitudinal intervention effects

Jared D. Huling, Menggang Yu, and Maureen Smith

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With the growing cost of health care in the United States, the need to improve efficiency and efficacy has become increasingly urgent. There has been a keen interest in developing interventions to effectively coordinate the typically fragmented care of patients with many comorbidities. Evaluation of such interventions is often challenging given their long-term nature and their differential effectiveness among different patients. Furthermore, care coordination interventions are often highly resource-intensive. Hence there is pressing need to identify which patients would benefit the most from a care coordination program. In this work we introduce a subgroup identification procedure for long-term interventions whose effects are expected to change smoothly over time. We allow differential effects of an intervention to vary over time and encourage these effects to be more similar for closer time points by utilizing a fused lasso penalty. Our approach allows for flexible modeling of temporally changing intervention effects while also borrowing strength in estimation over time. We utilize our approach to construct a personalized enrollment decision rule for a complex case management intervention in a large health system and demonstrate that the enrollment decision rule results in improvement in health outcomes and care costs. The proposed methodology could have broad usage for the analysis of different types of long-term interventions or treatments including other interventions commonly implemented in health systems.

Article information

Ann. Appl. Stat., Volume 13, Number 2 (2019), 824-847.

Received: December 2017
Revised: September 2018
First available in Project Euclid: 17 June 2019

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Zentralblatt MATH identifier

Fused lasso precision medicine comparative effectiveness research electronic health records interaction modeling


Huling, Jared D.; Yu, Menggang; Smith, Maureen. Fused comparative intervention scoring for heterogeneity of longitudinal intervention effects. Ann. Appl. Stat. 13 (2019), no. 2, 824--847. doi:10.1214/18-AOAS1216.

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  • Blumenthal, D., Anderson, G., Burke, S., et al. (2016). Tailoring complex-care management, coordination, and integration for high need, high cost patients. Technical report, Discussion paper, National Academy of Medicine, Washington, DC.
  • Bodenheimer, T. and Berry-Millett, R. (2009). Care management of patients with complex health care needs. In The Synthesis Project. Research synthesis report 19. Robert Wood Johnson Foundation, Princeton, NJ.
  • Boyd, S., Parikh, N., Chu, E., Peleato, B., Eckstein, J.. (2011). Distributed optimization and statistical learning via the alternating direction method of multipliers. Found. Trends Mach. Learn. 3 1–122.
  • Chen, S., Tian, L., Cai, T. and Yu, M. (2017). A general statistical framework for subgroup identification and comparative treatment scoring. Biometrics 73 1199–1209.
  • Cheung, W. Y., Neville, B. A., Cameron, D. B., Cook, E. F. and Earle, C. C. (2009). Comparisons of patient and physician expectations for cancer survivorship care. J. Clin. Oncol. 27 2489–2495.
  • Cohen, S. B. and Yu, W. (2012). Statistical brief # 354 2008–2009. Agency for Healthcare Research and Quality, Washington, DC.
  • Efron, B. (2014). Estimation and accuracy after model selection. J. Amer. Statist. Assoc. 109 991–1007.
  • Fan, J. and Zhang, W. (1999). Statistical estimation in varying coefficient models. Ann. Statist. 27 1491–1518.
  • Fan, J. and Zhang, W. (2008). Statistical methods with varying coefficient models. Stat. Interface 1 179–195.
  • Foster, J. C., Taylor, J. M. G. and Ruberg, S. J. (2011). Subgroup identification from randomized clinical trial data. Stat. Med. 30 2867–2880.
  • Harrell, F. E., Lee, K. L. and Mark, D. B. (1996). Multivariable prognostic models: Issues in developing models, evaluating assumptions and adequacy, and measuring and reducing errors. Stat. Med. 15 361–387.
  • Hastie, T. and Tibshirani, R. (1993). Varying-coefficient models. J. Roy. Statist. Soc. Ser. B 55 757–796.
  • Hickham, D., Weiss, J. W., Guise, J., Buckley, D., Motu’apuaka, M., Graham, E., Wasson, N. and Saha, S. (2013). Case management for adults with medical illness and complex care needs. Comparative Effectiveness Reviews No. 99, AHRQ Publication No. 13-EHC031-EF. Accessed on November 13, 2015. Available at
  • Huling, J. D., Yu, M. and Smith, M. (2019). Supplement to “Fused comparative intervention scoring for heterogeneity of longitudinal intervention effects.” DOI:10.1214/18-AOAS1216SUPPA, DOI:10.1214/18-AOAS1216SUPPB.
  • Imbens, G. W. and Rubin, D. B. (2015). Causal Inference—For Statistics, Social, and Biomedical Sciences: An Introduction. Cambridge Univ. Press, New York.
  • Pope, G. C., Ellis, R. P., Ash, A. S., Ayanian, J. Z., Bates, D. W., Burstin, H., Iezzoni, L. I., Marcantonio, E. and Wu, B. (2000). Diagnostic cost group hierarchical condition category models for Medicare risk adjustment. Health Economics Research, Inc., Waltham, MA.
  • Qian, M. and Murphy, S. A. (2011). Performance guarantees for individualized treatment rules. Ann. Statist. 39 1180–1210.
  • Robins, J. M. and Finkelstein, D. M. (2000). Correcting for noncompliance and dependent censoring in an AIDS clinical trial with inverse probability of censoring weighted (IPCW) log-rank tests. Biometrics 56 779–788.
  • Rosenbaum, P. R. and Rubin, D. B. (1983). The central role of the propensity score in observational studies for causal effects. Biometrika 70 41–55.
  • Rubin, D. B. (2005). Causal inference using potential outcomes: Design, modeling, decisions. J. Amer. Statist. Assoc. 100 322–331.
  • Schneeweiss, S., Rassen, J. A., Glynn, R. J., Avorn, J., Mogun, H. and Brookhart, M. A. (2009). High-dimensional propensity score adjustment in studies of treatment effects using health care claims data. Epidemiology 20 512.
  • Stange, K. C. (2009). The problem of fragmentation and the need for integrative solutions. Ann. Fam. Med. 7 100–103.
  • Stange, K. C. (2012). In this issue: Challenges of managing multimorbidity. Ann. Fam. Med. 10 2–3.
  • Tian, L., Alizadeh, A. A., Gentles, A. J. and Tibshirani, R. (2014). A simple method for estimating interactions between a treatment and a large number of covariates. J. Amer. Statist. Assoc. 109 1517–1532.
  • Tibshirani, R. (1996). Regression shrinkage and selection via the lasso. J. Roy. Statist. Soc. Ser. B 58 267–288.
  • Tibshirani, R. J. and Taylor, J. (2011). The solution path of the generalized lasso. Ann. Statist. 39 1335–1371.
  • Tibshirani, R., Saunders, M., Rosset, S., Zhu, J. and Knight, K. (2005). Sparsity and smoothness via the fused lasso. J. R. Stat. Soc. Ser. B. Stat. Methodol. 67 91–108.
  • U.S. Department of Health and Human Services (2012). Multiple Chronic Conditions Initiative. Private Sector Activities Focused on Improving the Health of Individuals with Multiple Chronic Conditions: Innovative Profiles. U.S. Dept. Health and Human Services, Washington, DC. Available at
  • Zhou, X., Kosorok, M. R. (2017). Augmented outcome-weighted learning for optimal treatment regimes. Preprint. Available at arXiv:1711.10654.
  • Zhao, Y., Zeng, D., Rush, A. J. and Kosorok, M. R. (2012). Estimating individualized treatment rules using outcome weighted learning. J. Amer. Statist. Assoc. 107 1106–1118.
  • Zhou, X., Mayer-Hamblett, N., Khan, U. and Kosorok, M. R. (2017). Residual weighted learning for estimating individualized treatment rules. J. Amer. Statist. Assoc. 112 169–187.

Supplemental materials

  • Supplement A: “Fused comparative intervention scoring for heterogeneity of longitudinal intervention effects”. We provide derivation of the validity of the matching version of our estimator and additional simulation results under nonlinear main effects.
  • Supplement B: personalizedLong_0.0.1. We provide an R implementation of the proposed methodology.