Table 1.

Summary of updating methods. ${\gamma }_0+{\gamma }_1^T\mathbf{X}$ is the prior odds from original risk model R_X for X = (X₁, …X_p)^T. LR_ind = P(Z|Y = 1)/P(Z|Y = 0),LR_dep = P(Z|Y=1,X)/P(Z|Y = 0,X), which is estimated separately (LR-separate) or jointly (LR-joint). Only “Logistic new” and CML, assuming that the covariate distributions in the population used to estimate R_X and the population used to update the model are the same, estimate the parameters in equation (5) corresponding to the correct model.

Method	Study type	log (posterior odds) =	Assumes independence of X and Z	Nr. of parameters estimated for
				Z binary	Z continuous
Logistic new	cohort	$\mu +{\beta }_{\mathbf{X}}^T\mathbf{X}+{\beta }_{z}Z$	No	p+2	p+2
LR-joint		${\gamma }_0+{\gamma }_1^T\mathbf{X}+log({\mathit{\text{LR}}}_{\mathit{\text{dep}}})$	No	p+2	p+3
LR-separate		$${\gamma }_0+{\gamma }_1^T\mathbf{X}+log({\mathit{\text{LR}}}_{\mathit{\text{dep}}})$$	No	2(p+1)	2(p+1)+2
LR-ind		${\gamma }_0+{\gamma }_1^T\mathbf{X}+log({\mathit{\text{LR}}}_{\mathit{\text{ind}}})$	Yes	2	4
LR-offset		${\gamma }_0+{\gamma }_1^T\mathbf{X}+{\delta }_0+{\delta }_{1}Z$	Yes	2	2
LR-shrink		${\gamma }_0+{\gamma }_1^T\mathbf{X}+\theta log({\mathit{\text{LR}}}_{\mathit{\text{ind}}})$	No	3	5
Logistic new	case-control	${\mu }^{\ast }+{\beta }_{\mathbf{X}}^T\mathbf{X}+{\beta }_{Z}Z$	No	p+3	p+3
LR-offset		${\gamma }_1^T\mathbf{X}+{\delta }_0^{\ast }+{\delta }_{1}Z$	Yes	3	3
LR-shrink		${\gamma }_1^T\mathbf{X}+{\theta }_0^{\ast }+{\theta }_{1}log({\mathit{\text{LR}}}_{\mathit{\text{ind}}})$	No	5	7
CML			No	p+2	p+2

p: number of old risk factors