Cervical CancerCase 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

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

Covariate manipulation

PELLYMPH AGE - 40 SURGYR - 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 2 GRADE 3

GRADE

0 1

non treated

ADJ_RAD

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%

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

Methods

• Univariate log-rank tests

• Non-parametric survival trees (CART-SD)

• Semi-parametric (Cox regression)

• Parametric models (Exponential, Weibull, Log-normal)

Log-rank testsVariable % Missing

Log-rank Wilcoxon Log-rank Wilcoxon

ADJ_RAD 0.0004 0.0002 0.6 0.02 0.01AGE 0.69 0.71 0.0 0.37 0.46CLS <0.0001 <0.0001 11.9 <0.0001 0.0003GRAD 0.03 0.01 15.6 0.1 0.05HISTOLOG 0.11 0.04 0.1 0.65 0.42MARGINS 0.05 0.03 0.1 0.31 0.24MAXDEPTH <0.0001 <0.0001 14.6 <0.0001 <0.0001PELLYMPH <0.0001 <0.0001 0.0 0.0002 0.0002SIZE <0.0001 <0.0001 2.9 0.0002 <0.0001SURGYR 0.67 0.79 0.0 0.47 0.53

All Data (n=871) Complete Data (n=549)

Using all available data per variable

Complete data (n=549)

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)

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

Survival Tree including Maxdepth

|maxdepth<17.95

cls:1

pellymph:1

size:1

549

491

273 218

197 21

58

49 9

low

moderate high

high high

0 1 2 3 4 5

Years

0.0

0.2

0.4

0.6

0.8

1.0 low

moderate

high

Survival Tree excluding Maxdepth

|size:1

pellymph:1

cls:1

645

610

569

322 247

41

35

low moderate

high

high

0 1 2 3 4 5

Years

0.0

0.2

0.4

0.6

0.8

1.0 low

moderate

high

Comparisons of Cox modelsStandard

Parameter Estimate Error p Exp(Estimate) Lower Upper

Including MaxdepthMAXDEPTH 1.14 0.33 0.0005 3.13 1.64 5.98CLS (1 or 2) 1.06 0.37 0.0047 2.89 1.40 5.96SIZE>3cm 1.02 0.49 0.0385 2.77 1.06 7.25

Excluding MaxdepthCLS (1 or 2) 1.28 0.31 <.0001 3.60 1.96 6.59SIZE>3cm 1.78 0.32 <.0001 5.91 3.17 11.03HISTOLOGY (SCC) -0.93 0.30 0.0021 0.39 0.22 0.71PELLYMPH(+) -0.28 0.65 0.6700 0.76 0.21 2.69SCC*PELLYMPH 1.57 0.73 0.0320 4.78 1.14 20.04

After imputationMAXDEPTH 1.20 0.27 <.0001 3.31 1.95 5.62CLS (1 or 2) 0.95 0.30 0.0014 2.59 1.44 4.66SIZE>3 cm 1.31 0.32 <.0001 3.71 1.98 6.94HISTOLOGY(SCC) -0.50 0.26 0.0500 0.61 0.36 1.01

95% CI

Using imputed data

Using all available data per variable

Model ComparisonStandard

Parameter Estimate Error p Exp(-Estimate) Lower Upper

ExponentialIntercept 4.31 0.26 <.0001 0.01 0.01 0.02CLS (1 or 2) -1.30 0.31 <.0001 3.69 2.01 6.77SIZE>3 cm -1.92 0.31 <.0001 6.83 3.69 12.65HISTOLOGY (SCC) 0.99 0.30 0.0010 0.37 0.20 0.67PELLYMPH(+) 0.36 0.65 0.5836 0.70 0.20 2.50SCC*PELLYMPH -1.74 0.73 0.0171 5.71 1.36 23.86

Cox Proportional Hazards Exp(Estimate)CLS (1 or 2) 1.28 0.31 <.0001 3.60 1.96 6.59SIZE>3 cm 1.78 0.32 <.0001 5.91 3.17 11.03HISTOLOGY(SCC) -0.93 0.30 0.0021 0.39 0.22 0.71PELLYMPH(+) -0.28 0.65 0.6700 0.76 0.21 2.69SCC*PELLYMPH 1.57 0.73 0.0320 4.78 1.14 20.04

Log NormalIntercept 5.12 0.50 <.0001 4.15 6.09CLS (1 or 2) -1.49 0.38 <.0001 -2.24 -0.75SIZE>3 cm -2.56 0.51 <.0001 -3.56 -1.57HISTOLOGY (SCC) 0.92 0.35 0.0084 0.24 1.61PELLYMPH(+) -1.22 0.48 0.0118 -2.17 -0.27Scale 2.28 0.23 1.87 2.78

95% CI

Exponential Model Prognostic Groups

PELLYMPH CLS 1 or 2 HISTOLOGY (SCC) SIZE>3 cm Rate/Pyr P(Survival=2) P(Survival=5)

High RiskY Y Y Y 0.497 0.37 0.08N Y N Y 0.336 0.51 0.19Y Y N Y 0.237 0.62 0.31Y N Y Y 0.135 0.76 0.51N Y Y Y 0.125 0.78 0.54N N N Y 0.092 0.83 0.63Y Y Y N 0.073 0.86 0.69 *

Medium RiskN Y N N 0.049 0.91 0.78Y Y N N 0.035 0.93 0.84N N Y Y 0.034 0.93 0.84

Low RiskY N Y N 0.020 0.96 0.91N Y Y N 0.018 0.96 0.91N N N N 0.013 0.97 0.94Y N N N 0.009 0.98 0.95N N Y N 0.005 0.99 0.98 *

* see plot

Log-normal Model Prognostic GroupsPELLYMPH CLS 1 or 2 HISTOLOGY (SCC) SIZE>3 cm Rate/Pyr P(Survival=2) P(Survival=5)

High RiskY Y Y Y 0.197 0.51 0.36N Y N Y 0.161 0.57 0.41Y Y N Y 0.394 0.36 0.22Y N Y Y 0.077 0.76 0.61N Y Y Y 0.090 0.72 0.57N N N Y 0.066 0.79 0.66Y Y N N 0.071 0.77 0.64

Medium RiskN Y N N 0.038 0.90 0.81Y Y Y N 0.044 0.88 0.78N N Y Y 0.041 0.89 0.79

Low RiskY N Y N 0.021 0.97 0.92N Y Y N 0.024 0.96 0.90N N N N 0.019 0.97 0.94Y N N N 0.033 0.92 0.84N N Y N 0.012 0.99 0.97

Comparison of Prognostic Groups

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

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.

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

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)