# METHODOLOGY FOR META- ANALYSIS OF TIME TO EVENT TYPE OUTCOMES TO INFORM ECONOMIC EVALUATIONS Nicola Cooper, Alex Sutton, Keith Abrams Department of Health.

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METHODOLOGY FOR META- ANALYSIS OF TIME TO EVENT TYPE OUTCOMES TO INFORM ECONOMIC EVALUATIONS Nicola Cooper, Alex Sutton, Keith Abrams Department of Health Sciences, University of Leicester, UK XI Cochrane Colloquium Barcelona, 26-31 st October 2003

In clinical studies with time to event data as the principal outcome, median time to event usually reported. However, for economic evaluations the statistic of interest is the mean => Area under survival curve (i.e. provides best estimate of expected time to an event ) Often mean time to an event can NOT be determined from observed data alone due to right- censoring (i.e. actual time to an event for some individuals unknown either due to loss of follow-up or event not incurred by end of study) BACKGROUND

PROBLEM: Mean undefined Last observation censored => mean undefined Trt 1 Trt 2

Determine how best to use time to event data for the purpose of economic evaluation. i.e. how to estimate mean time to an event (& associated uncertainty) in the presence of right-censoring: 1) using published summary statistics 2) using individual patient data OBJECTIVE

ESTIMATING THE MEAN FROM SUMMARY STATISTICS Often only median time to an event reported. BUT for economic evaluation need mean time From median only – a exponential distribution can be assumed to estimate the mean From survival curve may be possible to derive individual patient data (IPD) Mean = 1/ Var = 1/ 2

ESTIMATING MEAN FROM IPD Restricted mean: If longest time censored use: Censored time as event (biased underestimate) Maximum feasible time as event (biased overestimate) Maximum feasible time Censored time

ESTIMATING MEAN FROM IPD Extrapolation outside of the observation period by fitting parametric survival distributions (e.g. Weibull, exponential). Exponentially extending the survival curve to zero

EXAMPLE Use of Neuraminidase Inhibitors (NIs) to treat influenza in otherwise healthy adults 3 published trials comparing NIs to standard care Main outcome: Time to symptoms alleviated Meta-analysis to obtain a pooled estimate of the absolute mean difference in time to symptoms alleviated between NIs and standard care to inform an economic evaluation

EXAMPLE Turner D, Wailoo A, Nicholson K, Cooper N, Sutton A and Abrams K. Systematic review and economic decision modelling for the prevention and treatment of influenza A and B. Health Technology Assessment Report. 2003. Same as above

COMPARISON OF M-As USING ALTERNATIVE APPROACHES TO ESTIMATE MEAN 1.Restricted mean – Assume event occurs at time of censoring (IPD) 2.Restricted mean – Assume event occurs at maximum feasible value (IPD) 3.Extrapolation beyond data applying an exponential distribution (IPD) 4.Exponential distribution assumption (summary)

ALTERNATIVE META-ANALYSES

RESULTS: Cost-Effectiveness Plane

RESULTS: CE Acceptability Curve

CONCLUSIONS Inferences dont change in this example but estimates of the mean (and associated uncertainty) do – therefore this may be a critical issue for other applications. Problematic even if IPD available – i.e. still do not know the correct answer if the last value is right-censored Sensitivity analysis would seem the best way to proceed

Combining the data from different trials – Could use different distributional assumptions to estimate the mean for different trials and different arms of the same trial? Model averaging? FURTHER ISSUES

Neymark N, Adriaenssen I., Gorlia T, Caleo S and Bolla M. Estimating survival gain for economic evaluations with survival time as principal endpoint A cost- effectiveness analysis of adding early hormonal therapy to radiotherapy in patients with locally advanced prostate cancer. Health Economics. 2002; 11(3)233-248. Turner D, Wailoo A, Nicholson K, Cooper N, Sutton A and Abrams K. Systematic review and economic decision modelling for the prevention and treatment of influenza A and B. Health Technology Assessment Report. 2003. REFERENCES

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