Cervical Cancer Case Study

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Cervical Cancer Case Study

• Presented by
• University of Guelph

Baktiar Hasan Mark Kane Melanie
Laframboise Michael Maschio Andy Quigley
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Objectives

• To determine an appropriate model for the
  prediction of recurrence of cervical cancer
• To classify future patients on their risk of
  recurrence of cervical cancer

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Cervical Cancer Data Set

• The original data set included 905 cases
• Patients were removed from the data set if they
  had ANY of the following
• Were NOT free of the disease after surgery
• ? 845 Cases remain

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Modeling Methods

• Mixture Model with Accelerated Failure time
• Peng and Debham (1998)
• Cox Proportional Hazard Model
• Latent Variable Model
• Bayesian Survival Analysis
• Seltman, Greenhouse, and Wassserman (2001)
• Chen, Ibrahim, and Sinha (1999)

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Mixture model

• The model we chose for modeling time to
  recurrence is a mixture model of the form
• S(t)pSu(t) (1-p)
• F(t)pFu(t)
• Benefits
• Allows for cure rate
• Covariates can be incorporated into survival time
  Su(t) AND\OR cure rate 1-p

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Mixture Model (Cont)

• The model can be fit using a S-plus library
  (GFCURE) written by Peng.
• Further details about the library and the model
  can be found in Peng et al. (1998) and Maller and
  Zhou (1996).
• It should be mentioned that we found an error in
  the S-plus library written by Peng. The
  function pred.gfcure has a small error which can
  cause the program to crash or produce incorrect
  predicted values in some situations.

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Immunes and Sufficient Follow up

• Maller and Zhou (1996) suggest tests to examine
  the hypotheses of
• Presence of immunes in the data set
• Sufficient follow up time
• In the data set, it was found that immunes were
  present and there was not strong evidence to
  suggest that follow up time was insufficient

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Missing Covariates

• It was noticed that a large proportion of the
  cases (40) had at least one covariate with a
  missing value
• Various methods to handle this situation include
• Ignoring cases with missing covariate data
• Maximum Likelihood MethodsChen and Ibrahim (2001)

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Missing Covariates (Cont)

• We chose to perform variable selection on only
  the cases that contain no missing covariates
  (n534).
• BIAS introduced ???
• CHECK compare distributions of covariates in
  full and reduced data sets
• NO significant bias was introduced

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Distribution

• A variety of distributions were considered for
  modeling recurrence time including Weibull,
  gamma, lognormal, log-logistic, extended
  generalized gamma and generalized F.
• From comparing the distributions using AIC for
  the above models, there was little improvement
  from fitting a distribution with 3 or 4
  parameters versus a 2 parameter distribution.
• Of the 2 parameter distributions considered the
  Weibull distribution surfaced as the best
  distribution in terms of likelihood and
  prediction of the cure rate.

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Variable Selection

• Stepwise variable selection was performed using
  the 534 patients previously mentioned AIC was
  used as the entering criterion.
• Variables were allowed to enter both the cure
  rate portion of the model and survival time
  portion of the model.
• The final model chosen uses the explanatory
  variables pelvis lymph node involvement
  (PELLYMPH) and size of tumor (SIZE) to model the
  survival time of uncured patients and uses
  Capillary Lymphatic Spaces (CLS) and depth of
  tumor (MAXDEPTH) to predict cure rate.

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Variable Selection (Cont)

• It should be noted that CLS was modeled as a
  continuous variable rather than discrete because
  twice the difference of log likelihoods from
  modeling CLS as continuous versus discrete is
  0.017.
• Interactions of the significant covariates in the
  chosen model were also considered, but were found
  to be non-significant.

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Chosen Model
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Interpretation of the Model

• The negative coefficient of PELLYMPH indicates
  that uncured patients found positive for pelvis
  lymph node involvement will have a lower
  recurrence time than patients found negative for
  pelvis lymph node involvement .
• The coefficient of SIZE is also negative, which
  means that for uncured patients, larger tumor
  size corresponds to quicker recurrence of cancer.
• The positive value of CLS in the cure rate
  portion of the model indicates that patients with
  a positive prognosis have a higher probability of
  recurrence.
• The coefficient of MAXDEPTH is also positive,
  indicating that patients with a large tumor depth
  have a higher probability of recurrence.

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Model Validation

• In order to determine how well the chosen model
  will predict future patients, the data was
  randomly split into two subsets.
• Since it is not known if a patient who did not
  relapse was cured or censored it is not possible
  to compare the predicted probability of
  recurrence with the actual probability of
  recurrence.
• A graphical method was utilized for determining
  how well the predicted probabilities performed.

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Model Validation (Cont)

• The graphical method involved predicting the
  probability of recurrence before time ti (F(t))
  for a number of chosen times.
• This prediction is smoothed against recurrence,
  which is 1 if recurrence occurred before time ti
  or 0 if recurrence has not occurred before time
  ti
• A criticism of this graphical method is that it
  is possible for a patient with a survival time
  less than ti but no recurrence to have a
  recurrence between their censored survival time
  and ti so they should have been coded as a 1 not
  a zero for the graph.

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Classification

• The second objective is to classify patients into
  3 groups Low relapse, Moderate relapse, and High
  relapse.
• We classified patients based on their estimated
  cure rate from the final model previously
  mentioned.
• Low relapse estimated cure rate 94
• Moderate relapse 84 lt estimated cure rate lt 94
• High relapse estimated cure rate 84

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Conclusions

• We found that the attributes Capillary Lymphatic
  Spaces and depth of tumor are important for
  predicting the probability of relapse and pelvis
  lymph node involvement and size of tumor are
  important for predicting the survival time of
  uncured patients.
• We used these attributes in a Weibull mixture
  model to classify patients according to their
  risk of recurrence.

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References

• Chen, M., and Ibrahim, J. (2001), Maximum
  likelihood methods for cure rate models with
  missing covariates Biometrics, 57, 43-52.
• Chen, M., Ibrahim, J., and Sinha, D. (1999), A
  new bayesian model for survival data with a
  surviving fraction JASA, 94, 909-919.
• Maller, R., and Zhou, X. (1996), Survival
  Analysis with Long-Term Survivors. Toronto John
  Wiley Sons.
• Peng, Y., Dear, K., and Debham, J. (1998), A
  generalized F mixture model for cure rate
  estimation Statistics in Medicine, 17, 813-830.
• Seltman, H., Greenhouse, J., and Wasserman, L.
  (2001), Bayesian model selection analysis of
  a survival model with a surviving function
  Statistics in Medicine 20, 1681-1691.