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Using Weibull Model to Predict the Future: ATAC Trial. Anna Osmukhina, PhD Principal Statistician, AstraZeneca 15 April 2010. Survival Analysis. Rate. Example: Exponential Time to Event. Constant hazard. Overall Survival. No disease. Randomization. Death. Events in Early Breast Cancer.

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using weibull model to predict the future atac trial

Using Weibull Model to Predict the Future: ATAC Trial

Anna Osmukhina, PhD

Principal Statistician, AstraZeneca

15 April 2010

events in early breast cancer

Overall Survival

No disease

Randomization

Death

Events in Early Breast Cancer

Disease-Free-Survival: time from randomization

to first recurrence or death

Initial treatment: surgery, chemotherapy, radiotherapy

No disease

No disease

New lesions

Recurrence

a little bit of history tamoxifen
A Little Bit of History: Tamoxifen
  • “Tamoxifen for early breast cancer: an overview of the randomised trials “
    • Early Breast Cancer Trialists' Collaborative Group
      • The Lancet, V 351, 1998, pp 1451-67
  • Meta-analysis of 55 trials, ~37000 women
  • In women with hormone receptor +-ve disease, tamoxifen 5 years 
    • Recurrence  43%
    • Death (any cause)  23%
atac trial
ATAC Trial
  • Anastrozole, Tamoxifen, Alone or in Combination
  • >9000 early breast cancer patients;
  • 5 years of treatment + 5 years follow up
  • Analyses:
    • 2001: Major analysis (DFS event-driven)
    • 2004: Treatment completion
    • 2007: 5+2
    • (2009)
atac results by 2004 hormone receptor positive subgroup
ATAC Results by 2004(Hormone Receptor Positive Subgroup)

* Cox proportional hazards model: semi-parametric

**Rothman approach

weibull distribution for survival analysis
Weibull Distribution for Survival Analysis

Constant hazard

“Accelerated failure time”

Rate

Scale (Shape)

weibull time to event
Weibull Time to Event

Accelerated hazard

weibull time to event1
Weibull Time to Event

Decelerated hazard

weibull distribution in sas proc lifereg
Weibull Distribution in SAS PROC LIFEREG

covariates

Rates in ith individual:

predictions using weibull model
Predictions Using Weibull Model

Individual patient data so far

EXPLORE

BUILD

Future data for each patient

x1000

SIMULATE

Weibull model

fitting weibull model
Fitting Weibull Model
  • SAS PROC LIFEREG
  • Model events using baseline characteristics
    • Demography
    • Disease characteristics
  • Version 1: separately for each treatment
  • Version 2: treatment arms combined
predictions using weibull distribution
Predictions Using Weibull Distribution

Individual patient data so far

EXPLORE

BUILD

Future data for each patient

x1000

SIMULATE

Weibull model

future assumptions 3 scenarios
Future Assumptions: 3 Scenarios
  • Optimistic: Trend continues
  • Middle: no difference from now on
      • Conditional HR=1.0
  • Pessimistic: “A” worse from now on
    • Conditional HR=1.1
  • Very optimistic (for OS only)
    • Conditional HR = 0.9
predictions using weibull distribution1
Predictions Using Weibull Distribution

Individual patient data so far

EXPLORE

BUILD

Future data for each patient

x1000

ANALYZE

SIMULATE

Weibull model

1000 versions of the study future/ scenario

Future assumptions

revisiting fitting weibull model
Revisiting: Fitting Weibull Model
  • Model events using baseline characteristics
    • Demography
    • Disease characteristics
predictions using weibull distribution2
Predictions Using Weibull Distribution

Individual patient data so far

EXPLORE

BUILD

Future data for each patient

x1000

ANALYZE

SIMULATE

Weibull model

1000 versions of the study future/ scenario

Future assumptions

revisiting fitting weibull model1
Revisiting: Fitting Weibull Model
  • Model events using baseline characteristics
    • Demography
    • Disease characteristics
  • Model discontinuation with time-dependent covariate: (time</>5 years)
future event prediction
Future Event Prediction

Good

Bad

Overestimated number of new events

Is as good as assumptions

More parameters = More assumptions (correct or not)?

Adjusting for emergent risk factors?

  • Good HR (CI) estimates
    • Thanks to mature data?
  • Individual risk factors
  • Scenarios, complex questions
  • Describe/manage expectations
  • Complex models
    • Loss to follow up, administrative censoring
references
References
  • Early Breast Cancer Trialists' Collaborative Group
    • Lancet 1998; 351: 1451-67
  • ATAC trialists’ group
    • Lancet 2002; 359: 2131–39
    • Lancet 2005; 365: 60–62
    • Lancet Oncol 2008; 9: 45–53
  • Carroll K, “On the use and utility of the Weibull model in the analysis of survival data”
    • Controlled Clinical Trials 24 (2003) 682–701
  • Rothman M, “Design and analysis of non-inferiority mortality trials in oncology”
    • Statist. Med. 2003; 22:239–264