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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

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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

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

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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

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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

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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

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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

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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

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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

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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)

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ALTERNATIVE META-ANALYSES

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RESULTS: Cost-Effectiveness Plane

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RESULTS: CE Acceptability Curve

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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

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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

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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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