estimating survival data from published kaplan-meier … · estimating survival data from published...

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)