Time-to-event data analyses
Differences in methods routinely used by
Regulators and HTA
Anja Schiel, PhD
Statistician / Norwegian Medicines Agency
Disclaimer
The views and opinions expressed in this presentation are
the author's own and do not necessarily reflect the official
position of the Norwegian Medicines Agency or EMA.
Time-to-event, what’s so special?
• We censor patients to allow the use of their information
despite not having observed the event of interest.
• In this situation standard logistic regression is not
appropriate.
• We need to keep in mind that
• Time-to-event must be positive (> 0) and is right skewed
• The probability of surviving past a certain point in time in itself is
important information maybe more than observing the event
• What kind of assumptions we make and which estimators we use
Regulators
• Regulatory decision making is based on median survival
times and HR
The data
..and what we make of it
HTA / Cost-effectiveness analysis
• Less interested in point estimators or the HR, but rather the
area under the curve to allow Markov-modelling
• Models should run with a lifetime horizon to capture all
relevant differences
HTA / Cost-effectiveness analysis
• Less interested in point estimators or the HR, but rather the
area under the curve to allow Markov-modelling
• Models should run with a lifetime horizon to capture all
relevant differences
HTA / Cost-effectiveness analysis
• Less interested in point estimators or the HR, but rather the
area under the curve to allow Markov-modelling
• Models should run with a lifetime horizon to capture all
relevant differences
HTA / Cost-effectiveness analysis
• Less interested in point estimators or the HR, but rather the
area under the curve to allow Markov-modelling
• Models should run with a lifetime horizon to capture all
relevant differences
How to get from this…..
….to this?
Main problems for Regulators and HTAs is
• Decreasing follow-up time, in particular for OS
• Uncertainty with decreasing numbers of subjects at risk
The solution used by the HTAs
• Extrapolation by parametric modelling
• Solves the problem of the median point estimator, we
get mean survival times
• Allows prediction beyond the actual observation time
• Can help with artefacts such as the staircase
phenomenon
The challenge
• Find the appropriate parametric model
• The usual suspects:
•
•
•
•
•
•
Exponential
Weibull
Log-logistic
Log-normal
Gompertz
Generalised gamma
• Proportional hazard model or Accelerated Failure time
model?
The overlooked problem
• The assumption of proportional hazard
• The treatment effect is constant over time in the observed
but also the un-observed period
• This assumption needs to be tested!
• Regulators do not routinely ask for confirmation of the PH
assumption
• HTAs start to request better documentation for the choice of
modelling approach
Keep in mind…
• ….that this is not just a statistical exercise
Biology
Underlying
risk
Choice of
distributions
Fit
Validation /
Plausibility
Best fit
DSU TSD 14
• Simple doesn’t always
work
• More complex but also
more flexible models exist
• There is no wrong or right
by definition
Is this just some sort of voodoo?
• No, it will not make our decisions better, but it will make
them better informed