Using Weibull Model to Predict the Future: ATAC Trial Anna Osmukhina, PhD Principal Statistician, AstraZeneca 15 April 2010

Survival Analysis NameFormulaExample: exponential distribution Time to event random variable Probability density function Cumulative distribution function Survival function Hazard function 4/15/20102 Rate

Example: Exponential Time to Event 4/15/20103 Constant hazard

Events in Early Breast Cancer Randomization Death Overall Survival No disease Disease-Free-Survival: time from randomization to first recurrence or death No disease New lesions Recurrence No disease Initial treatment: surgery, chemotherapy, radiotherapy 4/15/20104

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 Meta-analysis of 55 trials, ~37000 women In women with hormone receptor +-ve disease, tamoxifen  5 years  – Recurrence  43% – Death (any cause)  23% 4/15/20105

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) 4/15/20106

Presenting the Results: KM Plot for DFS, /15/20107

ATAC Results by 2004 (Hormone Receptor Positive Subgroup) Analysis data cut off date EndpointAnalysis results*Comment Hazard ratio, A/T (95% CI )P-value 29 June 2001DFS0.78 (0.65, 0.93)0.005Superior OSNot reportedNR 31 March 2004DFS0.83 (0.73, 0.95)0.005Superior OS0.97 (0.83, 1.14)Not sigNon-inferior** * Cox proportional hazards model: semi-parametric **Rothman approach 4/15/20108

Questions About the Future 2001 DFS: superiority 2004 DFS: superiority OS: Non- inferiority 2007 DFS: Keep? OS: Gain superiority? Lose NI? 4/15/20109

Weibull Distribution for Survival Analysis NameFormulaExponential distribution Weibull distribution TTE random variable PDF Survival function Hazard function 4/15/ Constant hazard “Accelerated failure time” Rate Scale (Shape)

Exponential Time to Event 4/15/ Constant hazard

Weibull Time to Event 4/15/ Accelerated hazard

Weibull Time to Event 4/15/ Decelerated hazard

Weibull Distribution in SAS PROC LIFEREG NameFormulaWeibull distribution TTE random variable PDF Survival function Hazard function 4/15/ Rates in i th individual: covariates

Questions About the Future 2001 DFS: superiority 2004 DFS: superiority OS: Non- inferiority 2007 DFS: Keep? OS: Gain superiority? Lose NI? 4/15/201015

Predictions Using Weibull Model Future data for each patient x1000 Individual patient data so far Weibull model SIMULATE 4/15/ EXPLORE

Fit Weibull Model to the Data So Far 4/15/201017

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 4/15/201018

Weibull Models for the Data So Far 4/15/201019

Predictions Using Weibull Distribution Future data for each patient x1000 Individual patient data so far Weibull model SIMULATE EXPLORE 4/15/201020

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 4/15/201021

Predictions Using Weibull Distribution Future data for each patient x1000 Individual patient data so far Weibull model SIMULATE Future assumptions ANALYZE 4/15/ versions of the study future/ scenario EXPLORE

Predicting the Future, 31 March 2004 EndpointScenarioTotal events, simulated mean HR, A/T (95% CI) DFSNow (0.73, 0.95) 3 years later: Optimistic (0.75, 0.92) 3 years later: Middle (0.80, 0.98) 3 years later: Pessimistic (0.82, 1.02) OSNow (0.83, 1.14) 3 years later: Very Optimistic (0.83, 1.07) 3 years later: Middle (0.87, 1.11) 3 years later: Pessimistic (0.90, 1.15) 4/15/201023

Another Way to Look at It EndpointScenarioProbability of… SuperiorityNon-inferiority (Rothman) Inferiority DFSNow (2004)100%Not useful0% 3 years later: Optimistic99.4%Not useful<0.1% 3 years later: Middle71.5%Not useful<0.1% 3 years later: Pessimistic29.9%Not useful<0.1% OSNow (2004)0%100%0% 3 years later: Very Optimistic5.5%99.2%<0.1% 3 years later: Middle0.6%89.7%<0.1% 3 years later: Pessimistic<0.1%66.0%0.2% 4/15/201024

Predictions About the Future 2001 DFS: superiority 2004 DFS: superiority OS: Non- inferiority 2007 DFS: Likely to keep superiority OS: Superiority very unlikely; Likely to keep NI 4/15/201025

So, How Did That Work Out? EndpointScenarioTotal events, simulated mean HR, A/T (95% CI) DFSNow (0.73, 0.95) 3 years later: Optimistic (0.75, 0.92) 3 years later: Middle (0.80, 0.98) 3 years later: Pessimistic (0.82, 1.02) 3 years later: Actual ( ) OSNow (0.83, 1.14) 3 years later: Very Optimistic (0.83, 1.07) 3 years later: Middle (0.87, 1.11) 3 years later: Pessimistic (0.90, 1.15) 3 years later: Actual ( ) 4/15/201026

Revisiting: Fitting Weibull Model Model events using baseline characteristics – Demography – Disease characteristics 4/15/201027

Side Note: Loss to Follow Up 4/15/201028

Predictions Using Weibull Distribution Future data for each patient x1000 Individual patient data so far Weibull model SIMULATE Future assumptions ANALYZE 4/15/ versions of the study future/ scenario EXPLORE

Revisiting: Fitting Weibull Model Model events using baseline characteristics – Demography – Disease characteristics Model discontinuation with time-dependent covariate: (time 5 years) 4/15/201030

Future Event Prediction Good 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 Bad Overestimated number of new events Is as good as assumptions – More parameters = More assumptions (correct or not)? Adjusting for emergent risk factors? 4/15/201031

References Early Breast Cancer Trialists' Collaborative Group – Lancet 1998; 351: 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 4/15/201032