Incorporating published univariable associations in diagnostic and prognostic modeling

A Debray, Thomas P; Koffijberg, Hendrik; Lu, Difei; Vergouwe, Yvonne; Steyerberg, Ewout W; M Moons, Karel G

doi:10.1186/1471-2288-12-121

BMC Medical Research Methodology

Table 2 Results simulation study

From: Incorporating published univariable associations in diagnostic and prognostic modeling

				No meta-analysis			Greenland/Steyerberg				Improved adaptation method			Improved adaptation method
							adaptation method			(no prior)				(weakly informative prior)
N _I	N _L	σ _h	ρ(x ₁, x ₂)	PB	MSE	coverage	PB	MSE	coverage	(*)	PB	MSE	coverage	PB	MSE	coverage
100	500	0	0	15.07%	0.613	89.0%	8.87%	0.219	89.2%	8	1.3 e+12%	1.8 e+23	97.8%	-1.98%	0.065	89.6%
200	500	0	0	6.58%	0.186	90.0%	2.34%	0.063	90.8%	1	18.13%	3.671	94.4%	-1.44%	0.043	89.0%
500	500	0	0	3.65%	0.061	90.4%	1.00%	0.024	90.0%	0	2.21%	0.026	91.0%	-0.54%	0.021	89.0%
1000	500	0	0	1.31%	0.028	90.2%	0.84%	0.014	91.2%	0	1.34%	0.014	90.6%	-0.11%	0.013	90.0%
100	500	0	0.50	20.39%	0.888	91.2%	5.75%	0.166	94.4%	7	-80.77%	3.9 e+04	98.4%	1.41%	0.048	96.2%
200	500	0	0.50	8.22%	0.226	91.0%	1.63%	0.037	93.0%	0	4.55%	0.091	94.2%	0.32%	0.031	93.6%
500	500	0	0.50	1.89%	0.073	87.6%	0.45%	0.019	92.2%	0	0.89%	0.020	90.8%	-0.32%	0.019	91.4%
1000	500	0	0.50	0.88%	0.031	92.2%	0.33%	0.011	93.8%	0	0.55%	0.012	92.8%	-0.19%	0.011	93.8%
100	500	0.20	0	10.89%	0.440	92.4%	5.17%	0.140	90.4%	8	-3.7 e+02%	5.6 e+04	98.0%	-4.02%	0.056	89.8%
200	500	0.20	0	6.54%	0.177	92.0%	3.81%	0.060	91.6%	1	-11.08%	0.801	95.6%	-0.18%	0.039	91.6%
500	500	0.20	0	1.23%	0.049	93.8%	0.34%	0.024	92.2%	0	1.53%	0.026	92.2%	-1.13%	0.022	90.8%
1000	500	0.20	0	0.94%	0.029	89.2%	0.89%	0.017	90.4%	0	1.42%	0.018	90.4%	0.02%	0.016	89.8%
100	2000	0	0	47.95%	4.9 e+01	93.2%	37.63%	4.3 e+01	86.2%	21	1.6 e+12%	1.5 e+23	98.2%	-1.09%	0.058	89.6%
200	2000	0	0	5.60%	0.184	90.2%	3.31%	0.058	89.8%	1	54.36%	2.1 e+02	94.2%	-0.12%	0.036	88.2%
500	2000	0	0	2.36%	0.064	87.2%	1.10%	0.017	89.2%	0	2.31%	0.020	91.4%	-0.07%	0.015	88.8%
1000	2000	0	0	1.17%	0.027	90.0%	0.58%	0.009	90.2%	0	1.16%	0.010	89.2%	-0.03%	0.009	87.4%
100	2000	0	0.50	20.05%	0.856	89.6%	5.68%	0.139	92.0%	11	3.5 e+12%	1.3 e+23	98.4%	1.67%	0.045	95.4%
200	2000	0	0.50	6.99%	0.206	90.8%	2.67%	0.035	92.2%	1	5.94%	0.120	93.8%	2.02%	0.029	92.2%
500	2000	0	0.50	2.44%	0.063	90.8%	0.75%	0.011	92.8%	0	1.18%	0.011	92.0%	0.45%	0.010	92.2%
1000	2000	0	0.50	1.62%	0.032	89.4%	0.26%	0.007	91.6%	0	0.45%	0.007	91.6%	0.02%	0.007	91.4%
100	2000	0.20	0	16.17%	0.654	92.6%	7.67%	0.201	89.8%	16	1.5 e+03%	3.9 e+04	98.2%	-2.66%	0.046	91.0%
200	2000	0.20	0	6.63%	0.177	93.0%	3.74%	0.057	89.2%	1	13.89%	0.754	94.8%	0.26%	0.037	88.8%
500	2000	0.20	0	2.33%	0.056	92.8%	1.23%	0.021	89.6%	0	2.46%	0.023	89.4%	-0.08%	0.019	88.6%
1000	2000	0.20	0	2.02%	0.027	92.2%	1.07%	0.014	87.4%	0	1.62%	0.015	86.6%	0.37%	0.013	85.8%

Simulation results for the situation in which an IPD of N _I subjects is available and the literature associations are based on 4 studies of N _L subjects each. Between-study heterogeneity of literature associations is parameterized by σ _h. Correlation between the predictor variables x ₁ and x ₂ is indicated by ρ(x ₁, x ₂). The following statistics of ${\hat{β}}_{1}$ are presented: percentage bias (PB), Mean Squared Error (MSE) and coverage of the 90% confidence interval (coverage). We also assessed how often the Greenland/Steyerberg adaptation method estimated a negative variance for ${\hat{β}}_{1}$ (*).

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ISSN: 1471-2288

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