Estimating transition probabilities from a metanalysis
Aurelio Mejia
To estimate transition probabilities for cost-effectiveness models, some authors use this proportion: # of events / total number of patients of the articles included in the meta analysis. What are your thoughts regarding this approach? For example, assume you have a meta analysis that includes 10 articles and they all report the number of deaths over one year in a particular population. The total number of deaths in the 10 articles is 20, and the total number of patients included in the articles is 200. Therefore, one might employ 10% (20/200) as an estimate for the probability of death in a given year.
Comments
I think the best practice (e.g., see http://www.nicedsu.org.uk/Evidence-Synthesis-TSD-series(2391675).htm) is to use a meta-analysis to estimate the treatment effect in the first instance (e.g., the odds ratio of death in one year between the treatment and control arm), and then to separately estimate the baseline (i.e., control arm) natural history (transition probabilities).
It may be that the best estimate for the baseline natural history is the collection of trials included in the meta-analysis, but in some cases it may be more appropriate to look for national datasets, e.g., SEER (for US evaluation of cancer treatment), Office for National Statistics (for UK evaluations). This is particularly the case if the trials come from a number of different settings and the baseline risks appear to vary significantly across the settings.
A simple pooling of the control arms of the different studies will not be appropriate unless they have very similar rates, or if they are all of very similar size. A better approach is probably to perform a random effects meta-analysis of the control arms, e.g.:
Where r_{i0} is the number of events in the control arm of study i, n_{i0} is the number of patients in the control arm of study i. \beta is then the "average" log-odds of the event, and \sigma^2 is the heterogeneity across the trials in the log-odds of the event.
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