Predicting Time to Reflux of Children With Antenatal Hydronephrosis: A Competing Risks Approach

  • Maryam Nazemipour Department of Epidemiology and Biostatistics, School of Public Health, International Campus, Tehran University of Medical Sciences, Tehran, Iran.
  • Abdol-Mohammad Kajbafzadeh Mail Department of Pediatric Urology, Pediatric Urology Research Center, Children’s Medical Center, Tehran University of Medical Sciences, Tehran, Iran.
  • Kazem Mohammad Department of Epidemiology and Biostatistics, School of Public Health, Tehran University of Medical Sciences, Tehran, Iran.
  • Abbas Rahimi Foroushani Department of Epidemiology and Biostatistics, School of Public Health, Tehran University of Medical Sciences, Tehran, Iran.
  • Mahmood Mahmoudi Department of Epidemiology and Biostatistics, School of Public Health, Tehran University of Medical Sciences, Tehran, Iran
Competing risks, Trivariate weibull survival, Reflux, Hydronephrosis


The aim of this study was describing methodological aspects and applying a trivariate Weibull survival model using the competing risks concept to predict time to occurrence different types of reflux (unilateral (left, right) or bilateral) in children with antenatal hydronephrosis. Data from 333 children in Pediatric Urology Research Center of Children’s Hospital Medical Center, affiliated with Tehran University of Medical Sciences was used. The effect of some demographic and clinical factors on child’s reflux was studied. The assumption of independent between times of different types of reflux was evaluated. Of infants 80.5% were boy. The percentage of children experienced right, left and bilateral reflux or have been censored are 15.3%, 14.1%, 60.4% and 10.2% respectively. For the time of left reflux, variables, Week of diagnosis ANH, UC, UA, HUN, HN, APD_Right, Direction of ANH, CA19-9 baby, Urethra were significant. For the time of right reflux, variables, constipation, UC, UA, HUN, APD_Right, Direction and Severity of ANH, Bladder, and finally for the time of bilateral reflux, variables, Week of diagnosis ANH, Gender, UA, HUN, HN, APD_Left, Urethra, and Bladder were significant P<0.05. In the presence of competing risks, it is inappropriate to use the Kaplan-Meier method and standard Cox model which do not take competing risks into account. Trivariate Weibull survival model using competing risks not only is able to calculate the hazard rate of variables with different type of events but also it will be able to compare the hazard rate within the same type of event with different covariates.


Rushton H. Vesicoureteral reflux and scarring. In: Avner ED, Harmon WE, Niaudet P, eds. Pediatric Nephrology.5th ed. Lippincott Williams and Wilkins: Philadelphia,2004:1027-48.

Vesicoureteric reflux: all in the genes? Report of ameeting of physicians at the Hospital for Sick Children,Great Ormond Street, London. Lancet 1996;348:725-8.

Kramer S. Vesico-Ureteral reflux. In: Belman AK,Kramer SA, eds. Clinical Pediatric Urology. 4th ed.London: Martin Dunitz, 2002:749.

Williams G. Fletcher JT, Alexander SI, Craig JC.Vesicoureteral reflux. J Am Soc Nephrol 2008;19:847-62.

Hellstrom A, Hanson E, Hansson S, Hjalmas K, Jodal U.Association between urinary symptoms at 7 years old andprevious urinary tract infection. Arch Dis Child1991;66:232-4.

Mathews R, Carpenter M, Chesney R, Hoberman A,Keren R, Mattoo T, et al. Controversies in themanagement of vesicoureteral reflux: the rationale for theRIVUR study. J Pediatr Urol 2009;5:336-41.

Sharbaf FG, Fallahzadeh MH, Modarresi AR. EsmaeiliM. Primary vesicoureteral reflux in Iranian children. Indian Pediatr 2007;44:128-30.

Dick PT, Feldman W. Routine diagnostic imaging forchildhood urinary tract infections: a systematic overview. J Pediatr 1996;128:15-22.

Nakai H, Kakizaki H, Konda R, Hayashi Y, Hosokawa S,Kawaguchi S, et al. Clinical characteristics of primary vesico-ureteral reflux in infants: multicenter retrospectivestudy in Japan. J Urol 2003;169: 309-12.

Putter H, Fiocco M, Geskus RB. Tutorial in biostatistics:competing risks and multi-state models. Stat Med2007;26:2389-430.

.Southern DA, Faris PD, Brant R, Galbraith PD, NorrisCM, Knudtson ML, et al. Kaplan-Meier methods yielded misleading results in competing risk scenarios. J ClinEpidemiol 2006;59:1110-4.

Klein JP, Moeschberger ML, eds. Survival analysis:techniques for censored and truncated data. 2nd ed.Statistics for biology and health. New York Springer,2003:536.

Lawless JF. Statistical models and methods for lifetimedata. 2nd ed. Wiley series in probability and statistics.Hoboken, N.J: Wiley-Interscience, 2003:630.

Mann NR. Statistical Estimation of Parameters of the Weibull and Frechet Distributions In: Tiago J, Oliveira D,eds. Statistical Extremes and Applications. Netherlands:Springer 1984:81-89,

Collett D. Modelling survival data in medical research.2nd ed. Chapman & Hall/CRC texts in statistical scienceseries. Boca Raton, Fla.: Chapman & Hall/CRC,2003:391.

Saleem M, Mahmud Z, and Khan K. Survival Analysis ofCABG Patients by Parametric Estimations In ModifiableRisk Factors - Hypertension and Diabetes. Am J MathStat 2012;2:120-8.

Abernethy RB, editor. The New Weibull Handbook. 3rded. Distributed by Society of Automotive Engineers,1998.

Crow LH. Confidence Interval Procedures for the WeibullProcess with Applications to Reliability Growth.Technometrics 1982;24:67-72.

Gross AJ, Clark VA. Survival Distributions, ReliabilityApplications in the Biomedical Sciences. J. Wiley &Sons, New York-London-Sydney-Toronto 1976. XV, 331S., £ 11.50; $23.00. Biom J 1976;18:671.

Khan KH, Saleem M, Mahmud Z. Survival Proportions ofCABG Patients: A New Approch. 2011;3.

Kleinbaum DG, Klein M. Survival analysis: a selflearningtext. 2nd ed. Statistics for biology and health. New York, N.Y.: Springer, 2005:590.

Leemis LM. Reliability: probabilistic models and statistical methods. Englewood Cliffs: N.J: Prentice Hall,1995.

Gelman R, Gelber R, Henderson IC, Coleman CN, Harris JR. Improved methodology for analyzing local and distantrecurrence. J Clin Oncol 1990;8:548-55.

Kaplan EL, Meier P. Nonparametric Estimation from Incomplete Observations. J Am Stat Assoc 1958;53:457-81.

Gooley TA, Leisenring W, Crowley J, Storer BE.Estimation of failure probabilities in the presence ofcompeting risks: new representations of old estimators.Stat26. Pintilie M. Competing risks: a practical perspective.Statistics in practice. Chichester, England; Hoboken, NJ:John Wiley & Sons, 2006:224.

Lee KC, Wen M. A Multivariate Weibull DistributionModel. working paper. (Accessed March 2016, 12, at

Carroll KJ. On the use and utility of the Weibull model inthe analysis of survival data. Control Clin Trials2003;24:682-701.. Med 1999;18:695-706.

How to Cite
Nazemipour M, Kajbafzadeh A-M, Mohammad K, Rahimi Foroushani A, Mahmoudi M. Predicting Time to Reflux of Children With Antenatal Hydronephrosis: A Competing Risks Approach. Acta Med Iran. 55(7):437-446.
Original Article(s)