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Table 1 Input and estimated parameters in Approach I

From: Impact of correlation of predictors on discrimination of risk models in development and external populations

Population Input parameters Estimated parameters
ρ Normal (μ, σ) Adjusted OR Cases Controls SD of β 0+ ∑β i X i AUC
  ρ (μ, σ) ρ (μ, σ)   
A 0.2 μ: (0, 0); \( \sigma \): (1, 1) (1.5, 1.5) 0.17 μ: (0.37, 0.35); \( \sigma \): (0.97, 0.97) 0.17 μ: (-0.09, -0.09); \( \sigma \): (0.98, 0.98) 0.61 0.663
B -0.1 ,, ,, -0.12 μ: (0.27, 0.28); \( \sigma \): (0.98, 0.98) -0.12 μ: (-0.07, -0.07); \( \sigma \): (0.99, 0.99) 0.54 0.645
C - 0.2 ,, ,, -0.22 μ: (0.26, 0.24); \( \sigma \): (0.99, 0.99) -0.22 μ: (-0.06, -0.06) \( \sigma \): (0.99, 0.99) 0.51 0.639
D 0.1 ,, ,, 0.07 μ: (0.33, 0.33) \( \sigma \): (0.99, 0.99) 0.07 μ: (-0.08, -0.08) \( \sigma \): (0.99, 0.99) 0.59 0.660
E 0.4 ,, ,, 0.37 μ: (0.42, 0.42) \( \sigma \): (0.97, 0.97) 0.37 μ: (-0.10, -0.10) \( \sigma \): (0.98, 0.98) 0.67 0.676
F 0.2 ,, (1.5, 1.2) 0.18 μ: (0.34, 0.20) \( \sigma \): (0.98, 0.98) 0.19 μ: (-0.08, -0.05) \( \sigma \): (0.99, 0.99) 0.47 0.629
G ,, ,, (1.2, 1.2) 0.19 μ: (0.16, 0.17) \( \sigma \): (1, 1) 0.19 μ: (-0.04, -0.04) \( \sigma \): (1, 1) 0.27 0.575
H ,, ,, (1.5, 3) 0.10 μ: (0.41, 0.76) \( \sigma \): (0.97, 0.97) 0.14 μ: (-0.10, -0.19) \( \sigma \): (0.98, 0.98) 1.25 0.789
I ,, ,, (0.8, 0.8) 0.20 μ: (-0.20, -0.20) \( \sigma \): (1, 1) 0.19 μ: (0.05, 0.05) \( \sigma \): (0.99, 0.99) 0.33 0.593
J -0.1 ,, (1.5, 0.8) -0.09 μ: (0.37, -0.20); \( \sigma \): (0.99, 0.99) -0.08 μ: (-0.08, 0.05); \( \sigma \): (0.98, 0.98) 0.49 0.632
K 0.2 ,, ,, 0.21 μ: (0.28, -0.11) \( \sigma \): (0.99, 0.99) 0.21 μ: (-0.07, 0.03) \( \sigma \): (0.99, 0.99) 0.42 0.616
L 0.4 ,, ,, 0.40 μ: (0.24, -0.05); \( \sigma \): (0.99, 0.99) 0.41 μ: (-0.06, 0.01); \( \sigma \): (0.99, 0.99) 0.37 0.603
M ,, Mean: (0, 0); SD: (1, 3) (1.5, 1.5) 0.10 μ: (0.41, 2.47) \( \sigma \): (0.97, 0.97) 0.14 μ: (-0.10, -0.62) \( \sigma \): (0.98, 0.98) 1.37 0.804
N - 0.2 ,, ,, -0.25 μ: (0.11, 2.25) \( \sigma \): (1, 1) -0.24 μ: (-0.03, -0.56) \( \sigma \): (1, 1) 1.21 0.781
O 0.1 ,, ,, 0.01 μ: (0.34, 2.38) \( \sigma \): (0.98, 0.98) 0.04 μ: (-0.08, -0.59) \( \sigma \): (0.99, 0.99) 1.31 0.795
P 0.4 ,, ,, 0.30 μ: (0.56, 2.56) \( \sigma \): (0.94, 0.94) 0.33 μ: (-0.14, -0.63) \( \sigma \): (0.96, 0.96) 1.42 0.810
  1. In each population, a disease prevalence of 20% was used
  2. Population ‘A’ is considered as reference population; all other populations are compared w.r.t ‘A’
  3. SD standard deviation, OR odds ratio
  4. ρ: Pearson correlation between two continuous predictors
  5. A risk factor X ~ Normal (μ, σ) implies ‘X’ follows a normal distribution with mean μ and variance σ 2
  6. In Approach I, the adjusted ORs were pre-specified and thus considered as input parameters
  7. Numbers are rounded to two decimals except for AUC estimates