Use of Penalized Count Regression to Determine Factors Affecting the Length of Stay of Trauma Patients in the Intensive Care Unit


Penalized variable selection

How to Cite

Shayan, Z. ., Paydar, S., Maghsoudi, F., Taheri Akerdi, A., & Shayan, L. (2021). Use of Penalized Count Regression to Determine Factors Affecting the Length of Stay of Trauma Patients in the Intensive Care Unit . Iranian Red Crescent Medical Journal, 23(11).


Background: Trauma is considered an important issue in most countries. Identification of the factors affecting the length of stay (LOS) in the intensive care unit (ICU) plays a crucial role in controlling the costs and complications of prolonged hospitalization.

Objectives: This study aimed to identify the factors affecting the LOS of trauma patients in the ICU using stepwise and new penalized variable selection methods in count data regression.

Methods: The patients’ information was evaluated in Emtiaz Hospital and Shahid Rajaee trauma center in Shiraz from March 2016 to September 2017. Count regression model was used to determine the factors affecting the LOS of patients in the ICU using penalized variable selection including, Enet, Snet, and Mnet.

Results: The mean age of the patients (n=382) was obtained at 36.7±16.7 years, and the majority (88.4%) of the patients were male. The mean LOS in the ICU was determined at 6.2±6.6 days. Mnet with a negative binomial distribution outperformed the other penalized variable selection methods. A Glasgow Coma Scale (GCS) of less than 9 (IRR=1.7), blunt brain trauma (IRR=1.8), chest trauma (IRR=2.2), and oxygen saturation of less than 90 (IRR=1.2) increased the LOS of trauma patients in the ICU.

Conclusions: Penalized variable selection methods effectively ignore or control the existing correlations between predictors. Amongst the penalized models, Mnet provided more acceptable results with smaller Akaike information criterion and fewer predictors. According to this penalty, the most important factors affecting the length of stay were chest trauma, blunt brain trauma, GCS, and oxygen saturation rate. Most clinical studies on trauma have also shown the importance of these factors.


  1. Texas Department of Health. Trauma Registry Overview USA.2002.
  2. Krug EG, Sharma GK, Lozano R. The global burden of injuries. Am J Public Health. 2000;90(4):523-26. doi: 10.2105/ajph.90.4.523.
  3. Siletz A, Jin K, Cohen M, Lewis C, Tillou A, Cryer HM, et al. Emergency department length of stay in critical nonoperative trauma. J Surg Res. 2017;214:102-8. doi:10.1016/j.jss.2017.02.079.
  4. Moore L, Stelfox HT,  Turgeon AF, Nathens A, Bourgeois G, Lapointe J, et. al. Hospital Length of Stay After Admission for Traumatic Injury in Canada: A Multicenter Cohort Study. Ann Surg. 2014;260(1): 179–87. doi: 10.1097/SLA.0000000000000624.
  5. Chaudhary MA, Schoenfeld AJ, Tracey P. Koehlmoos TP, Cooper Z, Haider AH, et al. Prolonged ICU stay and its association with 1-year trauma mortality: An analysis of 19,000 American patients. Am J Surg. 2019;218(1):21-26. doi: 10.1016/j.amjsurg.2019.01.025. Epub
  6. Böhmer AB, Just KS, Lefering R, Paffrath T, Bouillon B, Joppich R, et al. Factors influencing lengths of stay in the intensive care unit for surviving trauma patients: a retrospective analysis of 30,157 cases. Crit Care. 2014;18(4):R143. doi: 10.1186/cc13976.
  7. Moore L, Stelfox HT, Turgeon AF, Nathens AB, Lavoie A, Émond M, et al. Derivation and validation of a quality indicator of acute care length of stay to evaluate trauma care. Ann Surg. 2014;260(6):1121-27. doi: 10.1097/SLA.0000000000000648.
  8. Dvorak MF, Noonan VK, Fallah N, Fisher CG, Finkelstein J, Kwon BK, et al. The influence of time from injury to surgery on motor recovery and length of hospital stay in acute traumatic spinal cord injury: an observational Canadian cohort study. J neurotraum. 2015;32(9):645-54. doi: 10.1089/neu.2014.3632.
  9. Wang Z, Ma SH, Zappitelli M, Parikh C, Wang C-Y, Devarajan P, et al. Penalized count data regression with application to hospital stay after pediatric cardiac surgery. Stat Methods Med Res. 2016;25(6):2685-703. doi: 10.1177/0962280214530608.
  10. Wang Z, Ma SH, Wang C-Y, Zappitellid M, Devarajane P, Parikh Ch, et al. EM for Regularized Zero Inflated Regression Models with Applications to Postoperative Morbidity after Cardiac Surgery in Children. Stat Med. 2014; 33(29): 5192–5208. Doi: 10.1002/sim.6314.
  11. 11.Miller A. Subset selection in regression. Chapman and Hall/CRC. 2002.
  12. 12.Tibshirani R. Regression shrinkage and selection via the lasso. J R Statist Soc B. 1996; 58:267-288. doi: 10.1111/j.2517-6161.1996.tb02080.x.
  13. 13.Zou H. The adaptive lasso and its oracle properties. J Am Statist Ass. 2006; 101:1418-1429. doi: 10.1198/016214506000000735.
  14. 14.Fan J. , Li R. Variable selection via nonconcave penalized likelihood and its oracle properties. J Am Statist Ass. 2001; 96:1348-1360. doi: 10.1198/016214501753382273.
  15. 15.Zou H. ,Hastie T. Regularization and variable selection via the elastic net. J R Statist Soc B. 2005; 67:301-320. doi:10.1111/j.1467-9868.2005.00503.x.
  16. 16.Zhang CH. Nearly unbiased variable selection under minimax concave penalty. Ann Stat. 2010; 38:894–942. DOI: 10.1214/09-AOS729.
  17. Friedman J, Hastie T, Tibshirani R. Regularization paths for generalized linear models via coordinate descent. J Stat Software. 2010; 33:1–22.[PubMed: 20808728]
  18. Fan J, Lv J. Nonconcave penalized likelihood with NP-dimensionality. IEEE Transact Inform Theory. 2011; 57:5467–5484. doi: 10.1109/TIT.2011.2158486.
  19. Wang Z. mpath: Regularized Linear Models. R package version 0.2–4. 2014.
  20. Cowen TD, Meythaler JM, Michael J, Ivie III CS, Lebow J, Novack TA, et al. Influence of Early Variables in Traumatic Brain Injury on Functional Independence Measure Scores and Rehabilitation Length of Stay and Charges. Arch Phys Med Rehabil. 1995;76:797-803.
  21. High Jr WM, Hall KM, Rosenthal M, Mann N, Zafonte R, Cifu DX, et al. Factors affecting hospital length of stay and charges following traumatic brain injury. J Head Trauma Rehabil. 1996;11(5):85-96.
  22. Kamravan HR, Haghnegahdar A, Paydar S, Khalife M, Sedighi M, Ghaffarpasand F, et al. Epidemiological and clinical features of cervical column and cord injuries; a 2-year experience from a large trauma center in Southern Iran. Bull Emerg Trauma. 2014;2(1):32-37.[PubMed: PMID: 27162861].
  23. Glance LG, Stone PW, Mukamel DB, Dick AW. Increases in mortality, length of stay, and cost associated with hospital-acquired infections in trauma patients. Arch Surg. 2011;146(7):1-19. doi:10.1001/archsurg.2011.41.
  24. Salehpoor F , Meshkini A, Shokouhi G, Aghazade J, Lotfinia I, Shakeri M, et. al. Prognostic serum Factors in Traumatic Brain Injury: A Systematic Review. Iran J Neurosurg. 2015, 1(1): 10-22.
  25. Shaz B, Winkler A, James A, Hillyer C, MacLeod J. Pathophysiology of early trauma-induced coagulopathy: emerging evidence for hemodilution and coagulation factor depletion. J Trauma. 2011;70(6):1401-7. doi: 10.1097/TA.0b013e31821266e0.