Prostate cancer survival estimates: An application with piecewise hazard function derivation

Atanu Bhattacharjee; Atul Budukh; Rajesh Dikshit

doi:10.4103/sajc.sajc_245_18

South Asian Journal of Cancer, Table of Contents

CC BY-NC-ND 4.0 · South Asian J Cancer 2019; 08(03): 150-159
DOI: 10.4103/sajc.sajc_245_18

ORIGINAL ARTICLE: Genitourinary Cancers

Prostate cancer survival estimates: An application with piecewise hazard function derivation

Atanu Bhattacharjee

Centre for Cancer Epidemiology, The Advanced Centre for Treatment, Research and Education in Cancer, Tata Memorial Centre, Navi Mumbai, Maharastra, India

,

Atul Budukh

Centre for Cancer Epidemiology, The Advanced Centre for Treatment, Research and Education in Cancer, Tata Memorial Centre, Navi Mumbai, Maharastra, India

,

Rajesh Dikshit

Centre for Cancer Epidemiology, The Advanced Centre for Treatment, Research and Education in Cancer, Tata Memorial Centre, Navi Mumbai, Maharastra, India

› Author Affiliations

Abstract

PDF Download

Abstract

Background: The hazard function is defined as time-dependent. However, it is an overlooked area of research about the estimation of hazard function within the frame of time. The possible explanation could be carried by estimating function through the changes of time points. It is expected that it will provide us the overall idea of survival trend. This work is dedicated to propose a method to work with piecewise hazard rate. It is a data-driven method and provides us the estimates of hazard function with different time points. Methods: The proposed method is explored with prostate cancer patients, registered in the Surveillance, Epidemiology, and End Results Program and having aged at diagnosis with range 40–80 years and above. A total of 610,814 patients are included in this study. The piecewise hazard rate is formulated to serve the objective. The measurement of piecewise hazard rate is compared with Wald-type test statistics, and corresponding R function is provided. The duration of follow-ups is split into different intervals to obtain the piecewise hazard rate estimates. Results: The maximum duration of follow-up observed in this study is 40 years. The piecewise hazard rate changes at different intervals of follow-ups are observed almost same except few later intervals in the follow-up. The likelihood of hazard in earlier aged patients observed lower in comparison to older patients. The hazard rates in different grades of prostate cancer also observed separately. Conclusion: The application of piecewise hazard helps to generate statistical inference in a deeper manner. This analysis will provide us the better understanding of a requirement of effective treatment toward prolonged survival benefit for different aged patients.

Key words

Piecewise hazard function - prostate cancer - SEER

PDF (1749 kb)

References

References
1 Parikh RR, Kim S, Stein MN, Haffty BG, Kim IY, Goyal S, et al. Trends in active surveillance for very low-risk prostate cancer: Do guidelines influence modern practice? Cancer Med 2017;6:2410-8.
2 Badar F, Mahmood S. Epidemiology of cancers in Lahore, Pakistan, among children, adolescents and adults, 2010-2012: A cross-sectional study part 2. BMJ Open 2017;7:e016559.
3 Watts EL, Appleby PN, Albanes D, Black A, Chan JM, Chen C, et al. Circulating sex hormones in relation to anthropometric, sociodemographic and behavioural factors in an international dataset of 12,300 men. PLoS One 2017;12:e0187741.
4 Gijbels I, Gürler U. Estimation of a change point in a hazard function based on censored data. Lifetime Data Anal 2003;9:395-411.
5 Goodman MS, Li Y, Tiwari RC. Detecting multiple change points in piecewise constant hazard functions. J Appl Stat 2011;38:2523-32.
6 Kim HJ, Fay MP, Feuer EJ, Midthune DN. Permutation tests for joinpoint regression with applications to cancer rates. Stat Med 2000;19:335-51.
7 Yao YC. Maximum likelihood estimation in hazard rate models with a change-point. Commun Stat Theory Methods 1986;15:2455-66.
8 Henderson R. A problem with the likelihood ratio test for a change-point hazard rate model. Biometrika 1990;77:835-43.
9 Matthews DE, Farewell VT. On a singularity in the likelihood for a change-point hazard rate model. Biometrika 1985;72:703-4.
10 Nguyen HT, Rogers GS, Walker EA. Estimation in change-point hazard rate models. Biometrika 1984;71:299-304.
11 Rebora P, Galimberti S, Valsecchi MG. Using multiple timescale models for the evaluation of a time-dependent treatment. Stat Med 2015;34:3648-60.
12 Pepe MS, Mori M. Kaplan-Meier, marginal or conditional probability curves in summarizing competing risks failure time data? Stat Med 1993;12:737-51.
13 Walke R. Example for a Piecewise Constant Hazard Data Simulation in R. Max Planck Institute for Demographic Research; 2010. Available from: http://www.demogr.mpg.de/papers/technicalreports/tr-2010-003.pdf. [Last accessed details on 2018 Jul 07].
14 Yang S, Prentice RL. Assessing potentially time-dependent treatment effect from clinical trials and observational studies for survival data, with applications to the women's health initiative combined hormone therapy trial. Stat Med 2015;34:1801-17.
15 Kuate Defo B. Determinants of infant and early childhood mortality in Cameroon: The role of socioeconomic factors, housing characteristics, and immunization status. Soc Biol 1994;41:181-211.
16 Perl J, Na Y, Tennankore KK, Chan CT. Temporal trends and factors associated with home hemodialysis technique survival in Canada. Clin J Am Soc Nephrol 2017. pii: CJN.13271216.
17 Mantel N, Byar DP. Evaluation of response-time data involving transient states: An illustration using heart-transplant data. J Am Stat Assoc 1974;69:81-6.
18 Anderson JR, Cain KC, Gelber RD. Analysis of survival by tumor response. J Clin Oncol 1983;1:710-9.
19 Rebora P, Salim A, Reilly M. Bshazard: A flexible tool for nonparametric smoothing of the hazard function. R J 2014;6:114-22.
20 Lu-Yao GL, Albertsen PC, Moore DF, Shih W, Lin Y, DiPaola RS, et al. Outcomes of localized prostate cancer following conservative management. JAMA 2009;302:1202-9.
21 Epstein MM, Edgren G, Rider JR, Mucci LA, Adami HO. Temporal trends in cause of death among Swedish and US men with prostate cancer. J Natl Cancer Inst 2012;104:1335-42.

Supplementary Material

Appendix