C Appendix C: Supplementary tables

Table C.1: Descriptive statistics of the assigned dose levels for 13 studies included in a dose–response meta-analysis between red meat consumption (g per day) and bladder cancer risk.
ID Referent Min P25 Median P75 Max
1 8.6 8.6 30.0 51.4 77.1 102.9
2 34.6 34.6 50.3 65.5 83.2 106.7
3 7.8 7.8 19.5 34.1 51.5 71.7
4 28.9 28.9 63.2 92.8 193.9 442.7
5 17.3 17.3 38.0 55.8 76.6 112.1
6 6.0 6.0 24.4 42.9 77.1 111.4
7 85.5 85.5 122.9 160.3 230.2 300.2
8 17.1 17.1 43.1 64.2 83.0 101.9
9 34.4 34.4 63.8 90.8 122.7 171.8
10 8.0 0.0 8.0 17.1 51.4 102.9
11 8.0 0.0 8.0 17.1 51.4 102.9
13 8.6 8.6 30.0 51.4 77.1 102.9
14 51.4 51.4 68.6 85.7 102.9 120.0
Table C.2: AIC for the study-specific second-degree fractional polynomials with power terms specified by \(p\) in a dose–response meta-analysis between red meat consumption (g per day) and bladder cancer risk. The last row reports the power term corresponding to the lowest AIC.
p 1 2 3 4 5 6 7 8 9 10 11 13 14
(-2, -2) 1.12 -3.66 -1.88 -4.04 -4.29 -0.71 1.76 -2.7 -3.43 -3.5 -1.8 2.38 -0.37
(-2, -1) 1.12 -3.66 -2.17 -3.98 -4.56 -0.71 1.76 -2.71 -3.8 -3.67 -1.43 2.38 -0.37
(-2, -0.5) 1.12 -3.65 -2.3 -3.94 -4.71 -0.71 1.76 -2.71 -3.97 -3.75 -1.2 2.38 -0.37
(-2, 0) 1.12 -3.65 -2.41 -3.91 -4.88 -0.71 1.76 -2.71 -4.14 -3.8 -0.95 2.38 -0.37
(-2, 0.5) 1.12 -3.64 -2.47 -3.88 -5.04 -0.71 1.76 -2.72 -4.28 -3.8 -0.7 2.38 -0.37
(-2, 1) 1.12 -3.62 -2.48 -3.85 -5.21 -0.71 1.76 -2.73 -4.39 -3.73 -0.47 2.38 -0.37
(-2, 2) 1.12 -3.6 -2.39 -3.83 -5.5 -0.71 1.76 -2.74 -4.51 -3.39 -0.14 2.38 -0.37
(-2, 3) 1.12 -3.56 -2.19 -3.82 -5.74 -0.71 1.76 -2.75 -4.52 -3.1 0 2.38 -0.37
(-1, -1) 1.12 -3.65 -2.33 -3.89 -4.77 -0.71 1.76 -2.71 -4.07 -3.87 -0.82 2.38 -0.37
(-1, -0.5) 1.12 -3.64 -2.39 -3.84 -4.9 -0.71 1.76 -2.71 -4.19 -3.94 -0.45 2.38 -0.37
(-1, 0) 1.12 -3.63 -2.45 -3.79 -5.04 -0.71 1.76 -2.71 -4.31 -3.95 -0.06 2.38 -0.37
(-1, 0.5) 1.12 -3.62 -2.48 -3.74 -5.18 -0.71 1.76 -2.71 -4.41 -3.85 0.32 2.38 -0.37
(-1, 1) 1.12 -3.61 -2.48 -3.7 -5.32 -0.71 1.76 -2.71 -4.47 -3.63 0.63 2.38 -0.37
(-1, 2) 1.12 -3.58 -2.43 -3.65 -5.57 -0.71 1.76 -2.72 -4.53 -3.01 1 2.38 -0.37
(-1, 3) 1.12 -3.56 -2.32 -3.63 -5.78 -0.71 1.76 -2.73 -4.5 -2.6 1.13 2.38 -0.37
(-0.5, -0.5) 1.12 -3.63 -2.43 -3.78 -5.01 -0.71 1.76 -2.71 -4.3 -3.98 -0.01 2.38 -0.37
(-0.5, 0) 1.12 -3.63 -2.46 -3.72 -5.13 -0.71 1.76 -2.71 -4.39 -3.92 0.44 2.38 -0.37
(-0.5, 0.5) 1.12 -3.61 -2.48 -3.66 -5.26 -0.71 1.76 -2.71 -4.46 -3.72 0.82 2.38 -0.37
(-0.5, 1) 1.12 -3.6 -2.48 -3.6 -5.38 -0.71 1.76 -2.71 -4.51 -3.4 1.11 2.38 -0.37
(-0.5, 2) 1.12 -3.58 -2.45 -3.53 -5.61 -0.71 1.76 -2.71 -4.53 -2.69 1.39 2.38 -0.37
(-0.5, 3) 1.12 -3.55 -2.38 -3.5 -5.81 -0.71 1.76 -2.71 -4.48 -2.32 1.46 2.38 -0.37
(0, 0) 1.12 -3.62 -2.48 -3.64 -5.24 -0.71 1.76 -2.7 -4.45 -3.76 0.89 2.38 -0.37
(0, 0.5) 1.12 -3.61 -2.48 -3.56 -5.35 -0.71 1.76 -2.7 -4.5 -3.45 1.23 2.38 -0.37
(0, 1) 1.12 -3.59 -2.48 -3.49 -5.46 -0.71 1.76 -2.7 -4.53 -3.05 1.45 2.38 -0.37
(0, 2) 1.12 -3.57 -2.47 -3.39 -5.67 -0.71 1.76 -2.69 -4.52 -2.39 1.61 2.38 -0.37
(0, 3) 1.12 -3.54 -2.43 -3.34 -5.84 -0.71 1.76 -2.69 -4.45 -2.15 1.63 2.38 -0.37
(0.5, 0.5) 1.12 -3.6 -2.48 -3.46 -5.44 -0.71 1.76 -2.7 -4.53 -3.07 1.49 2.38 -0.37
(0.5, 1) 1.12 -3.58 -2.48 -3.37 -5.54 -0.71 1.76 -2.69 -4.54 -2.67 1.63 2.38 -0.37
(0.5, 2) 1.12 -3.56 -2.48 -3.23 -5.72 -0.71 1.76 -2.67 -4.5 -2.21 1.7 2.38 -0.37
(0.5, 3) 1.12 -3.54 -2.47 -3.16 -5.88 -0.71 1.76 -2.66 -4.42 -2.14 1.7 2.38 -0.37
(1, 1) 1.12 -3.57 -2.48 -3.25 -5.62 -0.71 1.76 -2.68 -4.53 -2.37 1.7 2.38 -0.37
(1, 2) 1.12 -3.55 -2.48 -3.07 -5.78 -0.71 1.76 -2.65 -4.47 -2.17 1.73 2.38 -0.37
(1, 3) 1.12 -3.53 -2.48 -2.97 -5.92 -0.71 1.76 -2.63 -4.38 -2.24 1.73 2.38 -0.37
(2, 2) 1.12 -3.54 -2.48 -2.8 -5.9 -0.71 1.76 -2.6 -4.38 -2.33 1.74 2.38 -0.37
(2, 3) 1.12 -3.52 -2.46 -2.62 -6.01 -0.71 1.76 -2.55 -4.28 -2.54 1.73 2.38 -0.37
(3, 3) 1.12 -3.52 -2.4 -2.38 -6.09 -0.71 1.76 -2.46 -4.19 -2.78 1.73 2.38 -0.37
Best p -2, -2 -2, -2 0.5, 0.5 -2, -2 3, 3 -2, -2 -2, -2 -2, 3 0.5, 1 -0.5, -0.5 -2, -2 -2, -2 -2, -2
Table C.3: Conditional predicted coefficients for quadratic curves in 12 studies on the association between coffee consumption (cups/day) and all-cause mortality based on a one-stage (os) and two-stage (ts) approach.
ID \(\hat \beta_{1\textrm{os}}\) \(\hat \beta_{2\textrm{os}}\) \(\hat \beta_{1\textrm{ts}}\) \(\hat \beta_{2\textrm{ts}}\)
2 -0.043 0.002 -0.074 0.005
4 -0.125 0.015 -0.112 0.013
5 -0.077 0.007 -0.094 0.009
6 -0.060 0.005 -0.080 0.006
7 -0.012 -0.003 -0.050 0.000
10 -0.140 0.018 -0.115 0.013
11 -0.159 0.021 -0.118 0.014
16 -0.028 -0.001 -0.074 0.005
17 -0.134 0.017 -0.132 0.017
18 -0.082 0.008 -0.101 0.010
28 0.032 -0.011
29 -0.019 -0.002