Quality & Quantity

, Volume 52, Issue 3, pp 999–1013 | Cite as

Comparing hazard models for the growth failure of children in Iran

  • Mohammad Salehi Veisi
  • Sadegh Rezaei
  • Saralees Nadarajah


One of the statistical methods deployed in medical sciences to investigate time to event data is the survival analysis. This study, comparing efficiency of some parametric and semiparametric survival models, aims at investigating the effect of demographic and socio-economic factors on the growth failure of children below 2 years of age in Iran. The survival models including exponential, Weibull, log-logistic and log-normal models were compared to proportional hazards and extended Cox models by Akaike Information Criterion and variability of the estimated parameters. Based on the results, the log-normal model is recommended for analyzing the growth failure data of children in Iran. Furthermore, it is suggested that female children, children born to illiterate mothers and children born in larger households receive more attention in terms of growth failure.


Accelerated failure time models Cox proportional hazards model Model efficacy Survival analysis 



This work was a part of a Ph.D. dissertation in mathematical statistics supported by Amirkabir University. The authors are thankful to the Deputy of Health of Lorestan University of Medical Sciences for providing data for this research. The authors would like to thank the Editor and the two referees for careful reading and comments which improved the paper.

Compliance with ethical standards

Conflict of interest

The authors declare that there are no conflicts of interest.


  1. Abubakar, A., Uriyo, J., Msuya, S.E., Swai, M., Stray-Pedersen, B.: Prevalence and risk factors for poor nutritional status among children in the Kilimanjaro region of Tanzania. Int. J. Environ. Res. Public Health 9, 3506–3518 (2012)CrossRefGoogle Scholar
  2. Abuya, B.A., Ciera, J., Kimani-Murage, E.: Effect of mother’s education on child’s nutritional status in the slums of Nairobi. BMC Pediatr. 12, 80 (2012)CrossRefGoogle Scholar
  3. Adelian, R., Jamali, J., Zare, N., Ayatollahi, S.M.T., Pooladfar, G.R., Roustaei, N.: Comparison of Cox’s regression model and parametric models in evaluating the prognostic factors for survival after liver transplantation in Shiraz during 2000–2012. Int. J. Organ Transplant Med. 6, 119–125 (2015)Google Scholar
  4. Akaike, H.: A new look at the statistical model identification. IEEE Trans. Autom. Control 19, 716–723 (1974)CrossRefGoogle Scholar
  5. Alizadeh, A., Mohammadpour, R.A., Barzegar, M.R.: Comparing Cox model and parametric models in estimating the survival rate of patients with prostate cancer on radiation therapy. J. Mazand. Univ. Med. Sci. 23, 21–29 (2013). (In Persian)Google Scholar
  6. Altman, D.G., De Stavola, B.L., Love, S.B., Stepniewska, K.A.: Review of survival analyses published in cancer journals. Br. J. Cancer 72, 511–518 (1985)CrossRefGoogle Scholar
  7. Baghestani, A.R., Hajizadeh, E., Fatemi, S.R.: Parametric model to analyse the survival of gastric cancer in the presence of interval censoring. Tumori 96, 433–437 (2010)CrossRefGoogle Scholar
  8. Cole, S.Z., Lanham, J.S.: Failure to thrive: an update. Am. Fam. Phys. 83, 829–834 (2011)Google Scholar
  9. Cox, D.R.: Regression models and life-tables. J. R. Stat. Soc. Ser. B (Methodol.) 34, 187–220 (1972)Google Scholar
  10. Delpeuch, F., Traissac, P., Martin-Prével, Y., Massamba, J.P., Maire, B.: Economic crisis and malnutrition: socio-economic determinants of anthropometric status of preschool children and their mothers in an African urban area. Public Health Nutr. 3, 39–47 (2000)CrossRefGoogle Scholar
  11. Dewey, K.G., Peerson, J.M., Brown, K.H., Krebs, N.F., Michaelsen, K.F., Persson, L.A., et al.: Growth of breast-fed infants deviates from current reference data: a pooled analysis of US, Canadian, and European data sets. Pediatrics 96, 495–503 (1995)Google Scholar
  12. Efron, B.: The efficiency of Cox’s likelihood function for censored data. J. Am. Stat. Assoc. 72, 557–565 (1977)CrossRefGoogle Scholar
  13. Emamian, M.H., Fateh, M., Gorgani, N., Fotouhi, A.: Mother’s education is the most important factor in socio-economic inequality of child stunting in Iran. Public Health Nutr. 17, 2010–2015 (2014)CrossRefGoogle Scholar
  14. Garcia, S., Sarmiento, O.L., Forde, I., Velasco, T.: Socio-economic inequalities in malnutrition among children and adolescents in Colombia: the role of individual-, household- and community-level characteristics. Public Health Nutr. 16, 1703–1718 (2012)CrossRefGoogle Scholar
  15. George, B., Seals, S., Aban, I.: Survival analysis and regression models. J. Nucl. Cardiol. 21, 686–694 (2014)CrossRefGoogle Scholar
  16. Ghadimi, M.R., Rasouli, M., Mahmoodi, M., Mohammad, K.: Prognostic factors for the survival of patients with esophageal cancer in Northern Iran. J. Res. Med. Sci. 16, 1261–1272 (2011)Google Scholar
  17. Ghadimi, M.R., Mahmoodi, M., Mohammad, K., Rasouli, M., Zeraati, H., Fotouhi, A.: Factors affecting survival of patients with esophageal cancer: a study using inverse Gaussian frailty models. Singap. Med. J. 53, 336–343 (2012)Google Scholar
  18. Gong, Q., Fang, L.: Comparison of different parametric proportional hazards models for interval-censored data: a simulation study. Contemp. Clin. Trials 36, 276–283 (2013)CrossRefGoogle Scholar
  19. Gupta, R.C., Kannan, N., Raychaudhuri, A.: Analysis of lognormal survival data. Math. Biosci. 139, 103–115 (1997)CrossRefGoogle Scholar
  20. Habibzadeh, H., Jafarizadeh, H., Didarloo, A.: Determinants of failure to thrive (FTT) among infants aged 6–24 months: a case-control study. J. Prev. Med. Hyg. 56, E180–E186 (2015)Google Scholar
  21. Harrell, F., Lee, K.: Proceedings of the Eleventh Annual SASW User’s Group International, pp. 823–828 (1986)Google Scholar
  22. Haschke, F., Van’t Hof, M.: Euro-Growth references for breast-fed boys and girls: influence of breast-feeding and solids on growth until 36 months of age. Euro-Growth Study Groups. J. Pediatr. Gastroenterol. Nutr. 31, S60–S71 (2000)CrossRefGoogle Scholar
  23. Kalbfleisch, J., Prentice, R.L.: The Statistical Analysis of Failure Time Data, 2nd edn. Wiley, New York (2002)CrossRefGoogle Scholar
  24. Khanal, S.H.P., Sreenivas, V., Acharya, S.K.: Accelerated failure time models: an application in the survival of acute liver failure patients in India. Int. J. Sci. Res. 3, 161–166 (2014)Google Scholar
  25. Klein, J.P., Moeschberger, M.L.: Survival Analysis: Techniques for Censored and Truncated Data, 2nd edn. Springer, New York (2003)Google Scholar
  26. Kleinbaum, D.G., Klein, M.: Survival Analysis: A Self-Learning Text, 3rd edn. Springer, New York (2012)CrossRefGoogle Scholar
  27. Kramer, M.S., Kakuma, R.: Optimal duration of exclusive breastfeeding. Cochrane Database Syst. Rev. (2012). doi: 10.1002/14651858.CD003517.pub2 Google Scholar
  28. Lee, E.T., Oscar, O.T.: Survival analysis in public health research. Annu. Rev. Public Health 18, 105–134 (1997)CrossRefGoogle Scholar
  29. Munoz, A., Sunyer, J.: Comparison of semiparametric and parametric survival models for the analysis of bronchial responsiveness. Am. J. Respir. Crit. Care Med. 154, S234–S239 (1996)CrossRefGoogle Scholar
  30. Nardi, A., Schemper, M.: Comparing Cox and parametric models in clinical studies. Stat. Med. 22, 3597–3610 (2003)CrossRefGoogle Scholar
  31. Nützenadel, W.: Failure to thrive in childhood. Dtsch. Arztebl. Int. 108, 642–649 (2011)Google Scholar
  32. Oakes, D.: The asymptotic information in censored survival data. Biometrika 64, 441–448 (1977)CrossRefGoogle Scholar
  33. Orbe, J., Ferreira, E., Nunez-Anton, V.: Comparing proportional hazards and accelerated failure time models for survival analysis. Stat. Med. 21, 3493–3510 (2002)CrossRefGoogle Scholar
  34. Patel, K., Kay, R., Rowell, L.: Comparing proportional hazards and accelerated failure time models: an application in influenza. Pharm. Stat. 5, 213–224 (2006)CrossRefGoogle Scholar
  35. Pourhoseingholi, M.A., Hajizadeh, E., Moghimi Dehkordi, B., Safaee, A., Abadi, A., Zali, M.R.: Comparing Cox regression and parametric models for survival of patients with gastric carcinoma. Asian Pac. J. Cancer Prev. 8, 412–416 (2007)Google Scholar
  36. Ravangard, R., Arab, M., Rashidian, A., Akbarisari, A., Zare, A., Zeraati, H.: Comparison of the results of Cox proportional hazards model and parametric models in the study of length of stay in a tertiary teaching hospital in Tehran. Iran. Acta Med. Iran. 49, 650–658 (2011)Google Scholar
  37. Saki Malehi, A., Hajizadeh, E., Ahmadi, K., Kholdi, N.: Modeling the recurrent failure to thrive in less than two-year children: recurrent events survival analysis. J. Res. Health Sci. 14, 96–99 (2014)Google Scholar
  38. Shah, M.D.: Failure to thrive in children. J. Clin. Gastroenterol. 35, 371–374 (2002)CrossRefGoogle Scholar
  39. Sheykholeslam, R., Naghavi, M., Abd Elahi, Z., Zarati, M., Vaseghi, S., Sadeghi Ghotbabadi, F., Kolahdooz, F., Samadpour, K., Minaei, M.: Current status and the 10 years trend in the malnutrition indexes of children under 5 years in Iran. Iran. J. Epidemiol. 4, 21–28 (2008). (In Persian)Google Scholar
  40. Stamenkovic, Z., Djikanovic, B., Laaser, U., Bjegovic-Mikanovic, V.: The role of mother’s education in the nutritional status of children in Serbia. Public Health Nutr. 18, 1–9 (2016)Google Scholar
  41. Tette, E.M., Sifah, E.K., Nartey, E.T., Nuro-Ameyaw, P., Tete-Donkor, P., Biritwum, R.B.: Maternal profiles and social determinants of malnutrition and the MDGs: what have we learnt? BMC Public Health 16, 214 (2016)CrossRefGoogle Scholar
  42. Vahabi, N., Zayeri, F., Fazeli Moghadam, E., Safari, M., Ebrahimzadeh, F.: Assessing the factors affecting height and weight trends among children under two years of age in Khorramabad: an application of marginal modeling. Iran. J. Epidemiol. 11, 52–61 (2015). (In Persian)Google Scholar
  43. Vahedi, M., Mahmoodi, M., Mohammad, K., Ossareh, S., Zeraati, H.: What is the best parametric survival models for analyzing hemodialysis data? Glob. J. Health Sci. 8, 118–126 (2016)CrossRefGoogle Scholar
  44. Wang, S.J., Kalpathy-Cramer, J., Kim, J.S., Fuller, C.D., Thomas, C.R.: Parametric survival models for predicting the benefit of adjuvant chemo-radiotherapy in gallbladder cancer. In: AMIA 2010 Symposium Proceedings, pp. 847–851 (2010)Google Scholar
  45. Wright, C.M.: Identification and management of failure to thrive: a community perspective. Arch. Dis. Child. 82, 5–9 (2000)CrossRefGoogle Scholar
  46. Zare, A., Hosseini, M., Mahmoodi, M., Mohammad, K., Zeraati, H., Holakouie Naieni, K.: A comparison between accelerated failure-time and Cox proportional hazards models in analyzing the survival of gastric cancer patients. Iran. J. Public Health 44, 1095–1102 (2015)Google Scholar

Copyright information

© Springer Science+Business Media Dordrecht 2017

Authors and Affiliations

  • Mohammad Salehi Veisi
    • 1
  • Sadegh Rezaei
    • 1
  • Saralees Nadarajah
    • 2
  1. 1.Department of StatisticsAmirkabir University of TechnologyTehranIran
  2. 2.School of MathematicsUniversity of ManchesterManchesterUK

Personalised recommendations