We certainly agree on the mentioned advantages and disadvantages of observational studies and on the strengths of combining findings from randomised trials with those of observational studies.
Further, we agree on the possibility of the suggested analyses with ‘switch to’ and ‘add on’ as two separate outcomes. We chose the combined outcome measure as using two separate outcome measures (in addition to hospitalisation as an outcome measure) would decrease the statistical power to a low level in some of the analyses. In addition, one of the advantages of using the combined outcome measure is that the results may turn out to be more clear to guide clinical decisions on whether to use lithium or valproate in long-term treatment of bipolar disorder following a number of clinical situations (depression, mania, mixed episode or remission).
Propensity score matching (or other ways of introducing propensity score in the analysis Reference D'Agostino1 ) is a viable alternative to the approach based on multiple Cox regression models used in our paper. However, much experience (e.g. Sturmer et al Reference Sturmer, Joshi, Glynn, Avorn, Rothman and Schneeweiss2 ) suggests that the results thus obtained would not tend to be substantially different. The limiting factor seems to be the available amount of covariate information.
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