estimating survival data from published kaplan-meier … · estimating survival data from published...
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Estimating survival data from published Kaplan-Meier curves:
A comparison of methods
Matthew Taylor, Lily Lewis (YHEC), Richard Perry, Ann Yellowlees, Kelly
Fleetwood and Teresa Barata (Quantics)
Why do we need a parametric survival curve?
• Mathematical convenience • e.g. to run sensitivity analysis, apply hazard ratios from an mixed
treatment comparison
• May need to extrapolate from survival curve • e.g. for estimating the ICER (incremental cost effectiveness ratio)
Estimating parameters from Kaplan-Meier curves
Estimating parameters from Kaplan-Meier curves
Estimating parameters from Kaplan-Meier curves
Estimating parameters from Kaplan-Meier curves
Problems with the least squares approach
• Parameters will depend too much on the tail of the curve • Therefore reduced precision
• No estimate of parameter variance • Cannot put a confidence interval on a hazard ratio
• Cannot undertake appropriate probabilistic sensitivity analysis (PSA)
Estimating parameters from Kaplan-Meier curves
Estimating parameters from Kaplan-Meier curves
Estimating IPD from Kaplan-Meier charts
• Hoyle & Henley 2011 • If only the survival curve, then the method of Parmar 1998 is adopted
(assumes constant censoring)
• If numbers at risk are available, then assumes that censoring is constant between the numbers at risk time intervals
• Guyot et al. 2012 • Can use survival curve only, or with the numbers of events, number at
risk, or both
• Assumes that censoring is constant between the numbers at risk time intervals
Our aim is…
• To compare each methods and assess its:
• Ability to fit an appropriate curve to the original data
• Ability to measure the precision of each estimate (i.e. reflect the uncertainty of the original data)
Methods
Model
Alive Dead
Parameters
• Fixed, one-off drug cost = £5,000 • Background cost per month = £500 • Utility = 0.85 • Cost and quality discounting = 3.5% per annum
• These parameters and the specific survival curves lead to
an expected ICER of £20,000
Two models – Weibull first
Two models – then a loglogistic
Simulations Simulations: Hypothetical trial data #1 of 5000
Simulations Simulations: Hypothetical trial data #2 of 5000
Simulations Simulations: Hypothetical trial data #3 of 5000
For each simulation (i.e. each unique ‘trial’)…
• We use several methods to recreate IPD data and fit distributions (using AIC to select the ‘best’ fit) • Guyot all data (Guyot ALL) • Guyot numbers at risk (Guyot NAR) • Guyot number of events (Guyot NOE) • Guyot survival curve only (Guyot SC) • Hoyle & Henley numbers at risk (Hoyle NAR) • Hoyle & Henley survival curve only (Hoyle SC) • Nonlinear least squares (NLS) • Actual simulation individual patient data (IPD)
Results
Survival model parameter estimates: Iteration #1
Survival model parameter estimates: Iteration #1
Survival model parameter estimates: Iteration #1
Survival model parameter estimates: Iteration #1
Survival model parameter estimates: Iterations #1-#10
Survival model parameter estimates: All iterations
Survival model parameter estimates: All combinations
Survival model variance estimates: Results
Choice of curve bias (when Weibull was simulated)
Choice of curve bias (when log-log was simulated)
ICER estimates: Results
Recommendations
Recommendations based on data availability
• If you have: survival curve + numbers at risk • Then use: Hoyle and Henley 2011
• If you have: Survival curve + number of events • Then use: Guyot et al 2012
• If you only have: Survival curve • Then use: Guyot et al 2012 • (NLS is pretty accurate but does not provide uncertainty
for individual estimates)