Skip to main content

Advertisement

SpringerLink
Log in

Survival Modeling of Suicide Risk with Rare and Uncertain Diagnoses

  • Published:
Statistics in Biosciences Aims and scope Submit manuscript

Abstract

Motivated by the pressing need for suicide prevention through improving behavioral healthcare, we use medical claims data to study the risk of subsequent suicide attempts (SA) for patients who were hospitalized due to suicide attempts and later discharged. Understanding the risk behaviors of such patients at elevated suicide risk is an important step towards the goal of “Zero Suicide”. An immediate and unconventional challenge is that the identification of SA from medical claims contains substantial uncertainty: almost 20% of “suspected” SA are identified from diagnosis codes indicating external causes of injury and poisoning with undermined intent. It is thus of great interest to learn which of these undetermined events are more likely actual SA and how to properly utilize them in survival analysis with severe censoring. To tackle these interrelated problems, we develop an integrative Cox cure model with regularization to perform survival regression with uncertain events and a latent cure fraction. We apply the proposed approach to study the risk of subsequent SA after suicide-related hospitalization for the adolescent and young adult population, using medical claims data from Connecticut. The identified risk factors are highly interpretable; more intriguingly, our method distinguishes the risk factors that are most helpful in assessing either susceptibility or timing of subsequent attempts. The predicted statuses of the uncertain attempts are further investigated, leading to several new insights on suicide event identification.

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

Access this article

Log in via an institution

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

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4

Similar content being viewed by others

References

  1. Amico M, Keilegom IV (2018) Cure models in survival analysis. Annu Rev Stat Appl 5:311–342

    Article  MathSciNet  Google Scholar 

  2. Barak-Corren Y, Castro VM, Javitt S, Hoffnagle AG, Dai Y, Perlis RH, Nock MK, Smoller JW, Reis BY (2017) Predicting suicidal behavior from longitudinal electronic health records. Am J Psychiatry 174:154–162

    Article  Google Scholar 

  3. Bell SK, Delbanco T, Elmore JG, Fitzgerald PS, Fossa A, Harcourt K, Leveille SG, Payne TH, Stametz RA, Walker J, DesRoches CM (2020) Frequency and types of patient-reported errors in electronic health record ambulatory care notes. JAMA Netw Open 3:e205867

    Article  Google Scholar 

  4. Belsher BE, Smolenski DJ, Pruitt LD, Bush NE, Beech EH, Workman DE, Morgan RL, Evatt DP, Tucker J, Skopp NA (2019) Prediction models for suicide attempts and deaths: a systematic review and simulation. JAMA Psychiatry 76:642–651

    Article  Google Scholar 

  5. Berkson J, Gage RP (1952) Survival curve for cancer patients following treatment. J Am Stat Assoc 47:501–515

    Article  Google Scholar 

  6. Berman AL, Schwartz RH (1990) Suicide attempts among adolescent drug users. Am J Dis Child 144:310–314

    Google Scholar 

  7. Bhise V, Rajan SS, Sittig DF, Morgan RO, Chaudhary P, Singh H (2018) Defining and measuring diagnostic uncertainty in medicine: a systematic review. J Gen Intern Med 33:103–115

    Article  Google Scholar 

  8. Bostwick MJ, Pabbati C, Geske JR, McKean AJ (2015) Suicide attempt as a risk factor for completed suicide: even more lethal than we knew. Am J Psychiatry 173:1094–1100

    Article  Google Scholar 

  9. Breslow N (1974) Covariance analysis of censored survival data. Biometrics 30:89–99

    Article  Google Scholar 

  10. Böhning D, Lindsay BG (1988) Monotonicity of quadratic-approximation algorithms. Ann Inst Stat Math 40:641–663

    Article  MathSciNet  MATH  Google Scholar 

  11. Brodsky BS, Spruch-Feiner A, Stanley B (2018) The zero suicide model: applying evidence-based suicide prevention practices to clinical care. Front Psychiatry 9:33

    Article  Google Scholar 

  12. Chang S, Aseltine R, Riddhi D, Chen K, Rogers S, Wang F (2020) Machine learning for suicide risk prediction in children and adolescents with electronic health records. Transl Psychiatry 10:413

    Article  Google Scholar 

  13. Chen K, Aseltine RH (2017) Using hospitalization and mortality data to identify areas at risk for adolescent suicide. J Adolesc Health 61:192–197

    Article  Google Scholar 

  14. Chen J, Aseltine R, Wang F, Chen K (2022) Tree-guided rare feature selection and logic aggregation with electronic health records data. arXiv:2206.09107

  15. Cox DR (1972) Regression models and life-tables. J R Stat Soc Ser B (Methodol) 34:187–220

    MathSciNet  MATH  Google Scholar 

  16. Cox DR (1975) Partial likelihood. Biometrika 62:269–276

    Article  MathSciNet  MATH  Google Scholar 

  17. Dahlberg SE, Wang M (2007) A proportional hazards cure model for the analysis of time to event with frequently unidentifiable causes. Biometrics 63:1237–1244

    Article  MathSciNet  MATH  Google Scholar 

  18. Dempster AP, Laird NM, Rubin DB (1977) Maximum likelihood from incomplete data via the EM algorithm. J R Stat Soc Ser B (Methodol) 39:1–38

    MathSciNet  MATH  Google Scholar 

  19. Doshi R, Chen K, Wang F, Schwartz H, Herzog A, Aseltine R (2020) Identifying risk factors for mortality among patients previously hospitalized for a suicide attempt. Sci Rep 10:1–9

    Article  Google Scholar 

  20. Falcone T, Mishra L, Carlton E, Lee C, Butler RS, Janigro D, Simon B, Franco K (2010) Suicidal behavior in adolescents with first-episode psychosis. Clin Schizophr Relat Psychoses 4:34–40

    Article  Google Scholar 

  21. Fan X, Liu M, Fang K, Huang Y, Ma S (2017) Promoting structural effects of covariates in the cure rate model with penalization. Stat Methods Med Res 26:2078–2092

    Article  MathSciNet  Google Scholar 

  22. Farewell VT (1982) The use of mixture models for the analysis of survival data with long-term survivors. Biometrics 38:1041–1046

    Article  Google Scholar 

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

    Article  Google Scholar 

  24. Fu WJ (1998) Penalized regressions: the bridge versus the Lasso. J Comput Graph Stat 7:397–416

    MathSciNet  Google Scholar 

  25. Hanin L, Huang L-S (2014) Identifiability of cure models revisited. J Multivar Anal 130:261–274

    Article  MathSciNet  MATH  Google Scholar 

  26. Harris EC, Barraclough B (1997) Suicide as an outcome for mental disorders. A meta-analysis. Brit J Psychiatry 170:205–228

    Article  Google Scholar 

  27. Hedegaard H, Curtin SC, Warner M (2018) Suicide mortality in the United States, 1999–2017. Tech. Rep. 330. National Center for Health Statistics, Hyattsville

  28. Hunter DR, Lange K (2004) A tutorial on MM algorithms. Am Stat 58:30–37

    Article  MathSciNet  Google Scholar 

  29. Kalbfleisch JD, Prentice RL (2002) The statistical analysis of failure time data, vol 360. Wiley, New York

    Book  MATH  Google Scholar 

  30. Kaplan EL, Meier P (1958) Nonparametric estimation from incomplete observations. J Am Stat Assoc 53:457–481

    Article  MathSciNet  MATH  Google Scholar 

  31. Kessler RC, Bossarte RM, Luedtke A, Zaslavsky AM, Zubizarreta JR (2020) Suicide prediction models: a critical review of recent research with recommendations for the way forward. Mol Psychiatry 25:168–179

    Article  Google Scholar 

  32. Kuk AYC, Chen C-H (1992) A mixture model combining logistic regression with proportional hazards regression. Biometrika 79:531–541

    Article  MATH  Google Scholar 

  33. Lange K, Hunter DR, Yang I (2000) Optimization transfer using surrogate objective functions. J Comput Graph Stat 9:1–20

    MathSciNet  Google Scholar 

  34. Li C-S, Taylor JMG, Sy JP (2001) Identifiability of cure models. Stat Probab Lett 54:389–395

    Article  MathSciNet  MATH  Google Scholar 

  35. Lieb K, Zanarini MC, Schmahl C, Linehan MM, Bohus M (2004) Borderline personality disorder. Lancet 364:453–461

    Article  Google Scholar 

  36. Linker J, Gillespie NA, Maes H, Eaves L, Silberg JL (2012) Suicidal ideation, depression, and conduct disorder in a sample of adolescent and young adult twins. Suicide Life-Threat Behav 42:426–436

    Article  Google Scholar 

  37. Ludi E, Ballard ED, Greenbaum R, Pao M, Bridge J, Reynolds W, Horowitz L (2012) Suicide risk in youth with intellectual disabilities: the challenges of screening. J Dev Behav Pediatr 33:431–440

    Article  Google Scholar 

  38. Luo C, Chen K, Doshi R, Rickles N, Chen Y, Schwartz H, Aseltine RH (2022) The association of prescription opioid use with suicide attempts: an analysis of statewide medical claims data. PLoS ONE 17:e0269809

    Article  Google Scholar 

  39. Maller RA, Zhou S (1994) Testing for sufficient follow-up and outliers in survival data. J Am Stat Assoc 89:1499–1506

    Article  MathSciNet  MATH  Google Scholar 

  40. Maller RA, Zhou S (1995) Testing for the presence of immune or cured individuals in censored survival data. Biometrics 51:1197–1205

    Article  MathSciNet  MATH  Google Scholar 

  41. Masud A, Tu W, Yu Z (2018) Variable selection for mixture and promotion time cure rate models. Stat Methods Med Res 27:2185–2199

    Article  MathSciNet  Google Scholar 

  42. McGirr A, Paris J, Lesage A, Renaud J, Turecki G (2007) Risk factors for suicide completion in borderline personality disorder: a case-control study of cluster B comorbidity and impulsive aggression. J Clin Psychiatry 68:721–729

    Article  Google Scholar 

  43. Meier AS, Richardson BA, Hughes JP (2003) Discrete proportional hazards models for mismeasured outcomes. Biometrics 59:947–954

    Article  MathSciNet  MATH  Google Scholar 

  44. Parra-Uribe I, Blasco-Fontecilla H, Garcia-Parés G, Martínez-Naval L, Valero-Coppin O, Cebrià-Meca A, Oquendo MA, Palao-Vidal D (2017) Risk of re-attempts and suicide death after a suicide attempt: a survival analysis. BMC Psychiatry 17:1–11

    Article  Google Scholar 

  45. Patrick AR, Miller M, Barber CW, Wang PS, Canning CF, Schneeweiss S (2010) Identification of hospitalizations for intentional self-harm when E-codes are incompletely recorded. Pharmacoepidemiol Drug Saf 19:1263–1275

    Article  Google Scholar 

  46. Peng Y (2003) Estimating baseline distribution in proportional hazards cure models. Comput Stat Data Anal 42:187–201

    Article  MathSciNet  MATH  Google Scholar 

  47. Peng Y, Dear KBG (2000) A nonparametric mixture model for cure rate estimation. Biometrics 56:237–243

    Article  MATH  Google Scholar 

  48. Richardson BA, Hughes JP (2000) Product limit estimation for infectious disease data when the diagnostic test for the outcome is measured with uncertainty. Biostatistics 1:341–354

    Article  MATH  Google Scholar 

  49. Scolas S, El Ghouch A, Legrand C, Oulhaj A (2016) Variable selection in a flexible parametric mixture cure model with interval-censored data. Stat Med 35:1210–1225

    Article  MathSciNet  Google Scholar 

  50. Shepard DS, Gurewich D, Lwin AK, Reed GA Jr, Silverman MM (2016) Suicide and suicidal attempts in the United States: costs and policy implications. Suicide Life-Threat Behav 46:352–362

    Article  Google Scholar 

  51. Shi X, Ma S, Huang Y (2019) Promoting sign consistency in the cure model estimation and selection. Stat Methods Med Res 29(1):15–28

    Article  MathSciNet  Google Scholar 

  52. Simon N, Friedman J, Hastie T, Tibshirani R (2011) Regularization paths for Cox’s proportional hazards model via coordinate descent. J Stat Softw 39:1–13

    Article  Google Scholar 

  53. Spiegel B, Schoenfeld P, Naliboff B (2007) Systematic review: the prevalence of suicidal behaviour in patients with chronic abdominal pain and irritable bowel syndrome. Aliment Pharmacol Ther 26:183–193

    Article  Google Scholar 

  54. Strom BL (2001) Data validity issues in using claims data. Pharmacoepidemiol Drug Saf 10:389–392

    Article  Google Scholar 

  55. Suominen K, Isometsä E, Suokas J, Haukka J, Achte K, Lönnqvist J (2004) Completed suicide after a suicide attempt: a 37-year follow-up study. Am J Psychiatry 161:562–563

    Article  Google Scholar 

  56. Sy JP, Taylor JMG (2000) Estimation in a Cox proportional hazards cure model. Biometrics 56:227–236

    Article  MathSciNet  MATH  Google Scholar 

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

    MathSciNet  MATH  Google Scholar 

  58. Uno H, Cai T, Tian L, Wei L-J (2007) Evaluating prediction rules for t-year survivors with censored regression models. J Am Stat Assoc 102:527–537

    Article  MathSciNet  MATH  Google Scholar 

  59. Volinsky CT, Raftery AE (2000) Bayesian information criterion for censored survival models. Biometrics 56:256–262

    Article  MATH  Google Scholar 

  60. Walsh CG, Ribeiro JD, Franklin JC (2018) Predicting suicide attempts in adolescents with longitudinal clinical data and machine learning. J Child Psychol Psychiatry 59:1261–1270

    Article  Google Scholar 

  61. Wang W, Li Y, Yan J (2018) touch: tools of utilization and cost in healthcare. R package version 0.1-4

  62. Wang W, Aseltine RH, Chen K, Yan J (2020) Integrative survival analysis with uncertain event times in application to a suicide risk study. Ann Appl Stat 14:51–73

    Article  MathSciNet  MATH  Google Scholar 

  63. Wei L-J (1992) The accelerated failure time model: a useful alternative to the Cox regression model in survival analysis. Stat Med 11:1871–1879

    Article  Google Scholar 

  64. Wileyto EP, Li Y, Chen J, Heitjan DF (2013) Assessing the fit of parametric cure models. Biostatistics 14:340–350

    Article  Google Scholar 

  65. Yan X, Bien J (2021) Rare feature selection in high dimensions. J Am Stat Assoc 116:887–900

    Article  MathSciNet  MATH  Google Scholar 

  66. Yang Y, Zou H (2013) A cocktail algorithm for solving the elastic net penalized Cox’s regression in high dimensions. Stat Interface 6:167–173

    Article  MathSciNet  MATH  Google Scholar 

  67. Zhang JJ, Wang M (2009) An accelerated failure time mixture cure model with masked event. J Math Methods Biosci 51:932–945

    MathSciNet  MATH  Google Scholar 

  68. Zhao S, Witten D, Shojaie A (2021) In defense of the indefensible: a very naive approach to high-dimensional inference. Stat Sci 36:562–577

    Article  MathSciNet  MATH  Google Scholar 

  69. Zou H, Hastie T (2005) Regularization and variable selection via the elastic net. J R Stat Soc Ser B (Stat Methodol) 67:301–320

    Article  MathSciNet  MATH  Google Scholar 

  70. Zou H, Zhang HH (2009) On the adaptive elastic-net with a diverging number of parameters. Ann Stat 37:1733–1751

    Article  MathSciNet  MATH  Google Scholar 

Download references

Acknowledgements

Chen’s work was partially supported U.S. National Science Foundation (DMS-1613295, IIS-1718798) and U.S. National Institutes of Health (R01-MH124740).

Author information

Authors and Affiliations

  1. Department of Statistics, University of Connecticut, Storrs, USA

    Wenjie Wang, Jun Yan & Kun Chen

  2. Division of Public Health Sciences, Washington University School of Medicine in St. Louis, St. Louis, USA

    Chongliang Luo

  3. Center for Population Health, University of Connecticut Health Center, Farmington, USA

    Robert H. Aseltine, Jun Yan & Kun Chen

  4. Weill Cornell Medical College, Cornell University, New York, USA

    Fei Wang

  5. Division of Behavioral Sciences and Community Health, University of Connecticut Health Center, Farmington, USA

    Robert H. Aseltine

Authors
  1. Wenjie Wang
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Chongliang Luo
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Robert H. Aseltine
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Fei Wang
    View author publications

    You can also search for this author in PubMed Google Scholar

  5. Jun Yan
    View author publications

    You can also search for this author in PubMed Google Scholar

  6. Kun Chen
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Kun Chen.

Supplementary Information

Below is the link to the electronic supplementary material.

Electronic supplementary material 1 (PDF 271 kb)

Rights and permissions

Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Wang, W., Luo, C., Aseltine, R.H. et al. Survival Modeling of Suicide Risk with Rare and Uncertain Diagnoses. Stat Biosci (2023). https://doi.org/10.1007/s12561-023-09374-w

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • DOI: https://doi.org/10.1007/s12561-023-09374-w

Keywords

Search

Navigation