Home > Archives > IJSRST151538 IJSRST-Library

An Approach to Survival Analysis when Frailty is Evident

Authors(3) :-Jude Nwoji Oguejiofor, AbubakarBoyi Dalatu, KabiruYanusa Gorin Dikko

The problem with survival estimation using traditional life-table method alone is not only grouping of survival times, but also its insensitivity to existence of frailty in population. In this work, an approach has been proposed for the analysis of time from infection to occurrence of an event vis-a-vis the contributions of frailty along with some covariates. The approach involves the use of nonparametric product limit otherwise known as the Kaplan-Meier (KM) to estimate individual survivals and the use of frailty estimation method to estimate the hazard. In a simulation, the life-table and product limit methods were compared using the standard error estimates and plots of the empirical survivor function. While empirical estimates did not show significant differences, the product limit plot is more informative than the life table plots. The result of hazard estimation shows that event is largely caused by the baseline hazard with significant contribution from frailty and little contribution from age. There is also significant association between individual's events possibly as a result of frailty. This procedure will find wider application in survival estimation in a population-based setting.
Jude Nwoji Oguejiofor, AbubakarBoyi Dalatu, KabiruYanusa Gorin Dikko
Survival Estimation, Empirical Survivor Function Plot, Frailty
  1. Ardino, V., De Angelis, R., Francis, S. and Grande, E. (2007).Methodology for Estimation of Cancer Incidence Survival and Prevalence in Italian Regions. Tumore 93: 337 – 344.
  2. Berkson, J. and Gage, R. P. (1952).Survival Curve for Cancer Patients Following Treatment. Journal of The American Statistical Association, 47: 501 – 515.
  3. Baili, P., Micheli, A., Angelis, R. D., Weir, H. K., Francis, S., Santaguilic, M., Hakulinen, T., Quaresma, M., Coleman, M. P., and the Concord working group (2008). Life Tables for Worldwide Comparison of Relative Survival for Cancer (Concord Study).Tumori, 94: 658 – 668.
  4. Collet D (2003). Modeling Survival Data in Medical Research. Chapman & Hall/CRC
  5. Cox DR (1972). “Regression Models and Lifetables” Journal of the Royal Statistical Society Series B (Methodological) 34(2) 187 – 220.
  6. Dickman, P. W. (2010). An Introduction and Some Recent Development in Statistical Methods for Population-Based Cancer Survival Analysis. Statistical Methods for Population-Based Cancer Survival Analysis. Milan.
  7. Dickman PW, Hakilinen I (2001). Population Based Cancer Survival Analysis. Chapman & Hall.
  8. Duchateau L, Janssen P (2008). The Frailty Model. Springer-Verlag
  9. Duchateau L, Janssen P, Lindsey P, Legrand C, Nguti R, Sylvester R (2002). “The Shared Frailty Model and the Power of Heterogeneity Tests in Multicenter Trials.” Computational Statistics and Data Analysis, 40(3), 603 – 620. doi:10.1016/S0167-9473(02)00057 – 9.
  10. Geham, E. H. (1969). Estimating Survival Functions From the Life Table. Journal of Chronic Diseases, 21: 629 – 694.
  11. Hanagal D (2011). Modelling Survival Data using frailty models. Chapman & Hall/CRC Press. Taylor and Francis Group, LCC.
  12. Hougaard P (1995). “Frailty Models for Survival Data.” Lifetime Data Analysis,1(3), 255 – 273. doi:10.1007/BF00985760.
  13. Hougaard P (2000). Analysis of Multivariate Survival Data. Springer-Verlag.
  14. Kaplan, E. L., Meier, P. (1958). Nonparametric Estimation From Incomplete Observations. J Am. Stat. Association.55: 457 – 81.
  15. Mantel N (1966). Evaluation of Survival Data and Two New Rank Order Statistics Arising in its Consideration. Cancer Chemotherapy Report, 50, 163 – 170.
  16. Peto, R., Pike, M. C., Armitage, P., Breslow, N. E., Cox, D. R., Howard, S. V., Mantel, N., McPherson, K., Peto, J. and Smith, P. G. (1976). Design and Analysis of Randomised Critical Trials Requiring Prolonged Observation of Each Patient. Introduction and Design. British Journal of Cancer. 34: 585 – 612.
  17. Ramadurai, M. and Ponnuraja, C. (2011).Nonparametric Estimation of the Survival Probability of Children Affected by TB Meningitis. Journal of Arts and Science and Commerce. 2231 – 4172.
  18. Ravichandran, K., AlHandam, N., Al Dyab, A. (2006). Asian Pacific Journal of Cancer Prevention. Vol. 6.
  19. Rotolo F, Munda M (2012). Parfm; Parametric Frailty Models. R package version 0.66, URL http://CRAN.R-project.org/package=parfm
  20. Therneau TM, Grambsch PM (2000). Modeling Survival Data:Extending the Cox Model. Springer-Verlag.
  21. Vaupel JW, Manton KG, Stallard E (1979). “The Impact of Heterogeneity in Individual Frailty on the Dynamics of Mortality.” Demography, 16(3), 439 – 454.
  22. Wang ST, Klein JP, Moeschberger ML (1995). “Semi-parametric Estimation of Covariate Effects Using the Positive Stable Frailty Model.” Applied stochastic models and data analysis, 11(2), 121 – 133.
  23. Wienke A (2010). Frailty Models in Survival Analysis. Chapman & Hall CRC Biostatistics  Series. Taylor and Francis. doi: 10.1201/9781420073911.
Publication Details
  Published in : Volume 1 | Issue 5 | November-December 2015
  Date of Publication : 2015-12-25
License:  This work is licensed under a Creative Commons Attribution 4.0 International License.
Page(s) : 163-169
Manuscript Number : IJSRST151538
Publisher : Technoscience Academy
PRINT ISSN : 2395-6011
ONLINE ISSN : 2395-602X
Cite This Article :
Jude Nwoji Oguejiofor, AbubakarBoyi Dalatu, KabiruYanusa Gorin Dikko, "An Approach to Survival Analysis when Frailty is Evident", International Journal of Scientific Research in Science and Technology(IJSRST), Print ISSN : 2395-6011, Online ISSN : 2395-602X, Volume 1, Issue 5, pp.163-169, November-December-2015.
Journal URL : http://ijsrst.com/IJSRST151538

Article Preview