Incorporating published univariable associations in diagnostic and prognostic modeling

Table 3 Calculation of adapted associations in the application

	Female sex	MI	CHF	Ischemia
Adaptation ${\hat{μ}}_{δ}$ ; ${\hat{σ}}_{δ}^{2}$
Greenland/Steyerberg Adapt. method	0.02; 0.13	-0.76; 0.07	-0.74; 0.05	-0.72; 0.08
Improved Adapt. method (no prior)	0.04; 0.39	-0.69; 0.15	-0.67; 0.16	-0.72; 0.41
Improved Adapt. method (weakly informative prior)	0.05; 0.12	-0.65; 0.07	-0.63, 0.05	-0.67; 0.11
Univariable association ${\hat{μ}}_{u}$ ; ${\hat{σ}}_{u}^{2}$
Greenland/Steyerberg Adapt. method	0.35; 0.03	1.02; 0.07	1.58; 0.12	1.52; 0.10
Improved Adapt. method (no prior)	0.35; 0.03	1.02; 0.07	1.58; 0.12	1.52; 0.10
Improved Adapt. method (weakly informative prior)	0.34; 0.03	1.00; 0.07	1.52; 0.11	1.48; 0.09
Multivariable association ${\hat{μ}}_{m}$ ; ${\hat{σ}}_{m}^{2}$
No meta-analysis	0.30; 0.75	0.74; 0.32	1.04; 0.35	0.99; 0.38
Greenland/Steyerberg Adapt. method	0.36; 0.16	0.26; 0.14	0.84; 0.17	0.80; 0.18
Improved Adapt. method (no prior)	0.38; 0.42	0.33; 0.22	0.91; 0.28	0.80; 0.51
Improved Adapt. method (weakly informative prior)	0.39; 0.15	0.35; 0.14	0.90; 0.16	0.81; 0.21

Illustration of the adaptation (Adapt.) methods for four independent associations for predicting peri-operative mortality (in-hospital or within 30 days) after elective abdominal aortic aneurysm surgery. The following estimates are presented: adaptation from univariable to multivariable association (with mean ${\hat{μ}}_{δ}$ and variance ${\hat{σ}}_{δ}^{2}$ ), summary of univariable associations from the literature and IPD (with mean ${\hat{μ}}_{u}$ and variance ${\hat{σ}}_{u}^{2}$ ) and adapted multivariable association (with mean ${\hat{μ}}_{m}$ and variance ${\hat{σ}}_{m}^{2}$ ). Multivariable estimates were obtained through independent adaptation of the corresponding univariable associations, and are adjusted for the following variables: female sex, age in decades, history of myocardial infarction (MI), congestive heart failure (CHF), ischemia on electrocardiogram, renal co-morbidity and lung co-morbidity.

ISSN: 1471-2288