4.5 Specification of Prior Distributions

4.5.1 Fitting Priors

We extend the fitting prior in (4.8) to the partial borrowing power prior approach formally proposed in [6] and [10]. The partial borrowing power prior is that the historical data are borrowed only through the common parameters shared in the model for the historical data and the current data. Thus, the strength of the historical data is borrowed only through the common parameters. The fitting prior for open , gamma comma theta , close under the meta-regression survival model in (4.3) is given by
pi super open f close end super . open . gamma comma theta vertical line , d sub 0 , comma , eh sub 0 . close . proportional to . left brace . integral . product , from , k equals 1 , to , k sub 0 , of . product , from , j equals , x sub 01 k end sub , to , x sub 02 k end sub , of . left brace . e x p the set . nu sub 0 comma j plus 1 comma k end sub the set . gamma sub 0 , plus , gamma sub 1 , j plus , theta sub 0 k end sub end set end set . .
(4.10)
where ...

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