1. Cervical Cancer Case Study Eshetu Atenafu, Sandra Gardner, So-hee Kang, Anjela Tzontcheva University of Toronto Department of Public Health Sciences (Biostatistics) Acknowledgments: Professors P.Corey, J. Hsieh, W. Lou, J.Stafford

2. Outcome Variable Time to event calculated as recurrence date - surgery date; otherwise censored at death or last follow up date 4 cases where recurrence date > follow up date Decided there were no cases of left-censoring N=871, 68 recurrent events, 92% censored for a total of 3,573 person-years of follow up over the time period of 1984 to 2001

3. Covariate manipulation PELLYMPHAGE - 40SURGYR - 1993 0 1 - + CLS 0 1 clear other MARGINS 0 1  1cm >1cm MAXDEPTH HIST 1 (SCC) HIST 3 (AC) HISTOLOG 0 1  3cm >3cm SIZE GRADE 2GRADE 3 GRADE 0 1 non treated ADJ_RAD

4. Covariate Summary (1) Age - median 40 years 3% with disease left after surgery 13% received radiation therapy 46% capillary-lymphatic space invasion 6% positive pelvic lymph nodes Histology –SCC 62%, AC 28%

5. Covariate Summary (2) Tumor grade (cell differentiation) –better 21%, moderate 52%, worst 27% Maximum depth of tumor –22% greater than 1 cm Tumor size –5% greater than 3 cm Median year of surgery is 1993

6. Methods Univariate log-rank tests Non-parametric survival trees (CART-SD) Semi-parametric (Cox regression) Parametric models (Exponential, Weibull, Log-normal)

7. Log-rank tests

8. Using all available data per variable

9. Complete data (n=549)

10. MAXDEPTH Loss of power concerns We are losing 23 recurrent event cases due to missing Maxdepth and only 4 for other missing covariates We developed models including and excluding Maxdepth Attempted imputation of all missing values (TRANSCAN and IMPUTE, Design and Hmisc S-plus/R libraries, F.Harrell)

11. Survival Trees Builds a binary decision tree and groups patients with similar prognosis Uses maximized version of Log-rank test to split the data into groups with different survival Advantages: non-parametric, “ranks” covariates by importance, captures interactions Disadvantages: non-interpretability of large trees, excludes cases with missing values

12. Survival Tree including Maxdepth

13. Survival Tree excluding Maxdepth

14. Comparisons of Cox models

15. Using imputed data

16. Using all available data per variable

17. Model Comparison

18. Exponential Model Prognostic Groups

21. Log-normal Model Prognostic Groups

22. Comparison of Prognostic Groups

23. Conclusions (1) Important prognostic factors are: – tumor size >3cm – capillary-lymphatic space invasion – positive pelvic lymph nodes – Squamous cell carcoma type histology Missing values and imputation issues with respect to maximum depth of tumor are of concern

24. Conclusions (2) We have selected 3 prognostic groups using non-parametric and parametric methods Parametric models appear to overestimate the 5 year survival probability for the high risk group Non-parametric and parametric 5 years survival estimates for the prognostic groups are similar, but the parametric models group fewer patients for high and moderate risk compared to the survival tree We are concerned, however, that the predictive ability of these models is poor.

25. Another Cohort Ishikawa H. et al. (1999) Prognostic Factors of Adenocarcinoma of the Uterine Cervix, Gynecologic Oncology 73:42-46 Nakanishi T. et al. (2000) A Comparison of Prognoses of Pathologic Stage 1b Adenocarinoma and Squamous Cell Carcinoma of the Uterine Cervix, Gynecologic Oncology 79:289-293 Nakanishi T. et al. (2000) The significance of tumor size in clinical stage 1b cervical cancer: Can a cut-off figure be determined?, International Journal of Gynecologic Cancer 10:397-401

26. References LeBlanc, M. and Crowley J. (1993) Survival Trees by Goodness of Split. JASA 88: 457-467 Segal, M. R.(1988) Regression Trees for Censored Data. Biometrics 44: 35-47 Lausen B and Schumacher M. (1992) Maximally Selected Rank Statistics. Biometrics 48: 73-85 Haupt G. Survival Trees in S-plus (library survcart demo)