A new generalization of Weibull distribution with application to a breast cancer data set

Statistics in Medicine

Volumn 28, Issue 16, 2009, Pages 2077-2094

  Wahed, Abdus S ^a   Luong, The Minh ^a   Jeong, Jong Hyeon ^a  

^a UNIVERSITY OF PITTSBURGH GRADUATE SCHOOL OF PUBLIC HEALTH   (United States)

Author keywords

Competing risks; Cumulative incidence; Hazard function; Maximum likelihood; Weibull distribution

Indexed keywords

CYCLOPHOSPHAMIDE; TAMOXIFEN; ANTINEOPLASTIC AGENT; CISPLATIN; CMF PROTOCOL; FLUOROURACIL; METHOTREXATE; SELECTIVE ESTROGEN RECEPTOR MODULATOR;

ARTICLE; BREAST CANCER; CANCER RISK; CANCER SURVIVAL; CONTROLLED STUDY; DATA ANALYSIS; HUMAN; INFERENTIAL STATISTICS; MATHEMATICAL ANALYSIS; MATHEMATICAL COMPUTING; PARAMETRIC TEST; STATISTICAL DISTRIBUTION; STATISTICAL MODEL; STATISTICAL SIGNIFICANCE; THERAPY EFFECT; WEIBULL DISTRIBUTION; BIOMETRY; BREAST TUMOR; DISEASE FREE SURVIVAL; FACTUAL DATABASE; FEMALE; METHODOLOGY; MORTALITY; PROPORTIONAL HAZARDS MODEL; RANDOMIZED CONTROLLED TRIAL; RISK FACTOR; STATISTICS; SURVIVAL; UNITED STATES;

ANTINEOPLASTIC COMBINED CHEMOTHERAPY PROTOCOLS; BIOMETRY; BREAST NEOPLASMS; CISPLATIN; DATABASES, FACTUAL; DISEASE-FREE SURVIVAL; ESTROGEN RECEPTOR MODULATORS; FEMALE; FLUOROURACIL; HUMANS; LIKELIHOOD FUNCTIONS; METHOTREXATE; MODELS, STATISTICAL; PROPORTIONAL HAZARDS MODELS; RANDOMIZED CONTROLLED TRIALS AS TOPIC; RISK FACTORS; SURVIVAL ANALYSIS; TAMOXIFEN; UNITED STATES;

EID: 69149096678     PISSN: 02776715     EISSN: 10970258     Source Type: Journal    
DOI: 10.1002/sim.3598     Document Type: Article

References (21)

1. Weibull WA. A statistical distribution of wide applicability. Journal of Applied Mechanics 1951; 18:293-297.
2. Miller RG. What price Kaplan-Meier? Biometrics 1983; 39:1077-1081.
3. Cox DR, Oakes D. Analysis of Survival Data. Chapman & Hall Ltd: New York, 1984.
4. Kalbfleisch JD, Prentice RL. The Statistical Analysis of Failure Time Data. Wiley: New York, 1980; 321.
5. Mudholkar GS, Srivastava DK. Exponentiated Weibull family for analyzing bathtub failure-rate data. IEEE Transactions on Reliability 1993; 42:299-302.
6. Mudholkar GS, Srivastava DK, Kollia GD. A generalization of the Weibull distribution with application to the analysis of survival data. Journal of the American Statistical Association 1996; 91:1575-1583.
7. Jeong JH. A new parametric family for modelling cumulative incidence function: application to breast cancer data. Journal of the Royal Statistical Society, Series A 2006; 169:289-303.
8. Hougaard P. Survival models for heterogeneous populations derived from stable distributions. Biometrika 1986; 73:387-396.
9. Taghian A, Jeong JH, Mamounas E, Anderson S, Bryant J, Deutsch M, Wolmark N. Patterns of locoregional failure in patients with operable breast cancer treated by mastectomy and adjuvant chemotherapy with or without tamoxifen and without radiotherapy: results from five National Surgical Adjuvant Breast and Bowel Project randomized clinical trials. Journal of Clinical Oncology 2004; 22:4237-4239.
10. Gooley T, Leisenring W, Crowley J, Storer B. Estimation of failure probabilities in the presence of competing risks: new representations of old estimators. Statistics in Medicine 1999; 18:695-706.
11. Smith RL. Maximum likelihood estimation in a class of nonregular cases. Biometrika 1985; 72:67-90.
12. Wahed AS. A general method of constructing extended families of distributions from an existing continuous class. Journal of Probability and Statistical Science 2006; 4:165-177.
13. Ferreira JT, Steel M. A constructive representation of univariate skewed distributions. Journal of the American Statistical Association, Theory and Methods 2006; 101:823-829.
14. Jones MC. Families of distributions arising from distributions of order statistics. Test 2004; 13:1-43.
15. Ferreira JT, Steel M. Model comparison of coordinate-free multivariate skewed distributions with an application to stochastic frontiers. Journal of Econometrics 2007; 137:641-673.
16. Mudholkar GS, Srivastava DK, Freimer M. The exponentiated Weibull family: a reanalysis of the bus-motor-failure data. Technometrics 1995; 37:436-445.
17. Rodriguez RN. A guide to the Burr type XII distributions. Biometrika 1977; 64:129-134.
18. Thisted RA. Elements of Statistical Computing. Chapman & Hall: New York, 1988.
19. Fisher B, Dignam J, Wolmark N, DeCillis A, Emir B, Wickerham DL, Bryant J, Dimitrov N, Abramson N, Atkins J, Shibata H, Deschenes L, Margolese R. Tamoxifen and chemotherapy for lymph node-negative, estrogen receptor-positive breast cancer. Journal of the National Cancer Institute 1997; 89.22:1673-1682.
20. Efron B. Logistic regression, survival analysis, and the Kaplan-Meier curve. Journal of the American Statistical Association 1988; 83:414-425.
21. Gray R. A class of k-sample tests for comparing the cumulative incidence of a competing risk. Annals of Statistics 1988; 16:1141-1154.