Meta-Analysis
Copyright ©2013 Baishideng.
World J Meta-Anal. Aug 26, 2013; 1(2): 57-77
Published online Aug 26, 2013. doi: 10.13105/wjma.v1.i2.57
Table 1 Models used to relate risk to dose
logc (RR)=β1d(linear)
loge (RR)=β1d + β2d2(quadratic)
loge (RR)=β1d + β2d2 + β3d3(cubic)
loge (RR)=β1dY(power)
loge (RR)=β1loge (d)(log)
loge (RR)=β1expe (d)(exponential)
loge (RR)=β1loge (1 + Wd)(log-with-baseline)
Table 2 Amount smoked by current smokers (cigarettes per day) - dose-response data
Block: StudyAmount smoked groupings1Mean valuesRRs2
1: AKIBA1-14, 15-24, 25+8.11, 19.19, 34.633.50, 6.10, 19.10 M
2: AKIBA1-14, 15+8.11, 24.093.60, 5.80 M
3: ARCHER1-19, 20, 21+10, 20, 31.833.53, 6.09, 8.52 M
4: AXELSS202043.30
5: BENSHL1-9, 10-19, 20+4.85, 12.73, 26.034.00, 9.05, 10.95 M
6: BEST1-9, 10-20, 21+4.85, 15.92, 31.8310.00, 16.41, 17.31 M
7: BOUCOT1-20, 21-40, 41+13.38, 29.02, 53.3354.09, 78.56, 161.70 M
8: BRETT1-14, 15-24, 25+8.11, 19.19, 34.632.55, 4.25, 8.00 M
9: BROSS1-20, 21+13.38, 31.834.91, 7.20 M
10: BUFFLE1-19, 20, 21+10.20, 31.835.60, 11.84, 22.10 M
11: CEDERL1-7, 8-15, 16+4.29, 11.61, 25.413.40, 7.50, 11.90 M
12: CEDERL1-7, 8-15, 16+4.29, 11.61, 25.412.83, 7.74, 7.56
13: CHANG1-10, 11-20, 21+7.08, 17.67, 31.835.02, 10.60, 8.26
14: CHANG1-10, 11-20, 21+7.08, 17.67, 31.833.03, 4.87, 8.21 M
15: CHOW1-19, 20-29, 30+10, 21.35, 38.3913.88, 21.87, 44.48 M
16: COMSTO1-19, 20-39, 40+10, 22.90, 45.7112.42, 18.16, 24.92 M
17: COMSTO1-19, 20-39, 40+10, 22.90, 45.717.45, 17.35, 13.27
18: CORREA1-20, 21+13.38, 31.839.30, 25.30 M
19: CPSI1-9, 10-19, 20-39, 40+4.85, 12.73, 22.90, 45.714.51, 8.41, 14.30, 17.49 M
20: CPSII1-9, 10-19, 20, 21-39, 40, 41+4.85, 12.73, 20, 26.71, 40, 53.3312.22, 14.52, 21.59, 22.72, 24.14, 45.52 M
21: CPSII1-9, 10-19, 20, 21-39, 40, 41+4.85, 12.73, 20, 26.71, 40, 53.333.89, 8.33, 14.21, 21.40, 19.31, 18.22
22: DARBY1-14, 15-24, 25+8.11, 19.19, 34.6373.47, 95.43, 142.69 M
23: DARBY1-14, 15-24, 25+8.11, 19.19, 34.6315.70, 21.50, 41.62 M
24: DEAN31-12, 13-22, 23+7.65, 18.42, 33.045.46, 7.42, 21.66 M
25: DEAN31-12, 13-22, 23+7.65, 18.42, 33.043.16, 8.42, 24.24 M
26: DEKLER1-14, 15-24, 25+8.11, 19.19, 34.6319.40, 23.00, 32.50 M
27: DOLL21-14, 15-24, 25+8.11, 19.19, 34.635.20, 10.60, 22.40 M
28: DOLL21-14, 15-24, 25+8.11, 19.19, 34.631.29, 6.43, 29.71 M
29: DORANT1-9, 10-19, 20+4.85, 12.73, 26.038.52, 27.22, 36.24 M
30: DORGAN1-19, 20+10, 26.039.13, 20.65 M
31: DORGAN1-19, 20+10, 26.0326.67, 72.46 M
32: DORGAN1-19, 20+10, 26.036.55, 24.13 M
33: DORGAN1-19, 20+10, 26.037.43, 41.43 M
34: DORN1-9, 10-20, 21-39, 40+4.85, 15.92, 26.71, 45.714.02, 9.92, 17.19, 22.75 M
35: ENGELA1-4, 5-9, 10-14, 15-19, 20+2.5, 6.5, 10.88, 15.83, 26.031.40, 4.10, 7.00, 11.00, 15.00 M
36: ENGELA1-4, 5-9, 10-14, 15+2.5, 6.5, 10.88, 24.0912.00, 12.00, 24.00, 26.00
37: ENSTRO1-9, 10-19, 20, 21-39, 40+4.85, 12.73, 20, 26.71, 45.714.74, 7.68, 13.65, 16.08, 19.41 M
38: ENSTRO1-9, 10-19, 20, 21+4.85, 12.73, 20, 31.832.15, 4.31, 9.48, 16.47 M
39: GAO21-19, 20-29, 30+10, 21.35, 38.393.36, 7.54, 10.63 M
40: GILLIS1-14, 15-24, 25-34, 35-49, 50+8.11, 19.19, 28.13, 39, 53.334.50, 7.60, 8.60, 9.70, 7.80
41: HAENSZ1-20, 21+13.38, 31.831.77, 5.15 M
42: HAMMO21-19, 20+10.00, 26.039.15, 10.39 M
43: HAMMON1-9, 10-20, 21-39, 40+4.85, 15.92, 26.71, 45.717.44, 8.42, 17.91, 20.64 M
44: HIRAYA1-9, 10-19, 20+4.85, 12.73, 26.032.06, 4.00, 6.24 M
45: HIRAYA1-9, 10-19, 20+4.85, 12.73, 26.032.25, 2.56, 4.47 M
46: HITOSU1-14, 15-24, 25+8.11, 19.19, 34.632.08, 2.82, 4.68 M
47: HITOSU1-14, 15+8.11, 24.093.11, 3.17 M
48: HOLE1-14, 15-24, 25-34, 35+8.11, 19.19, 28.13, 44.385.47, 8.90, 10.75, 7.49
49: HUMBLE1-19, 20+10, 26.039.20, 24.70 M
50: HUMBLE1-19, 20+10, 26.0311.60, 26.10 M
51: HUMBLE1-19, 20+10, 26.0319.20, 16.00
52: HUMBLE1-19, 20+10, 26.0318.50, 36.90 M
53: KAISE21-19, 20+10, 26.034.47, 10.34 M
54: KAISE21-19, 20+10, 26.037.61, 22.12 M
55: KAISER1-19, 20-40, 41+10, 24.32, 53.336.58, 17.24, 20.91 M
56: KAISER1-19, 20-40, 41+10, 24.32, 53.333.42, 7.98, 12.63 M
57: KANELL1-10, 11-20, 21-35, 36+7.08, 17.67, 26.71, 45.711.71, 7.06, 20.39, 34.22 M
58: KATSOU1-20, 21+13.38, 31.832.26, 7.46 M
59: KAUFMA1-14, 15-24, 25-34, 35-44, 45+8.11, 19.19, 28.13, 39, 53.338.00, 15.00, 28.00, 43.00, 60.00 M
60: KINLEN1-14, 15-24, 25+8.11, 19.19, 34.6310.61, 14.14, 21.74 M
61: KNEKT1-14, 15+8.11, 24.095.00, 12.70 M
62: KOO1-10, 11-20, 21-307.08, 17.67, 25.881.36, 7.29, 1.52
63: LIAW1-10, 11-20, 21+7.08, 17.67, 31.833.10, 3.60, 8.30 M
64: LIDDEL1-19, 20+10, 26.033.33, 5.02 M
65: MACLEN1-9, 10-19, 20-29, 30+4.85, 12.73, 21.35, 38.391.36, 3.41, 4.16, 5.00 M
66: MACLEN1-9, 10-19, 20+4.85, 12.73, 26.030.76, 3.44, 3.84
67: MATOS1-14, 15-24, 25+8.11, 19.19, 34.631.60, 8.00, 15.00 M
68: MIGRAN1-9, 10-19, 20, 21+4.85, 12.73, 20, 31.834.01, 4.24, 5.14, 5.93 M
69: MIGRAN1-9, 10-19, 204.85, 12.73, 204.88, 6.53, 7.48 M
70: MRFITR1-19, 20-39, 40+10, 22.90, 45.7110.86, 50.12, 56.43 M
71: NAM1-24, 25+14.06, 34.636.70, 10.27 M
72: NAM1-24, 25+14.06, 34.639.06, 16.65 M
73: PARKIN1-14, 15+8.11, 24.093.90, 5.20 M
74: PERSH21-9, 10+4.85, 20.905.76, 11.34 M
75: PETO1-14, 15+8.11, 24.095.50, 9.49 M
76: PEZZO21-20, 21-40, 41+13.38, 29.02, 53.338.00, 44.39, 112.13 M
77: PEZZOT1-20, 21-40, 41+13.38, 29.02, 53.337.40, 70.00, 246.50 M
78: PRESCO1-14, 15+8.11, 24.0910.20, 19.96 M
79: PRESCO1-14, 15+8.11, 24.096.36, 10.08 M
80: SEGI21-9, 10-19, 20-29, 30-39, 40+4.85, 12.73, 21.33, 31.07, 45.712.10, 3.10, 3.40, 6.90, 7.90 M
81: SEGI21-9, 10-19, 20+4.85, 12.73, 26.032.90, 1.44, 1.03
82: SHAW1-19, 20+10, 26.036.31, 30.48 M
83: SOBUE1-19, 20-29, 30+10, 21.35, 38.393.52, 4.00, 4.55 M
84: SPEIZE1-4, 5-14, 15-24, 25-34, 35+2.5, 9.42, 19.19, 28.13, 44.382.70, 5.20, 12.60, 15.70, 22.00 M
85: STOCKW1-19, 20-40, 41+10, 24.32, 53.336.67, 14.51, 28.84 M
86: SVENSS1-10, 11-20, 21+7.08, 17.67, 31.834.60, 12.60, 59.00 M
87: TENKAN1-14, 15-24, 25+8.11, 19.19, 34.6315.86, 20.25, 24.97 M
88: TSUGAN1-15, 16-35, 36+9.33, 22.45, 45.710.90, 1.22, 1.66
89: TULINI1-14, 15-24, 25+8.11, 19.19, 34.636.02, 12.00, 27.30 M
90: TULINI1-14, 15-24, 25+8.11, 19.19, 34.638.17, 26.30, 38.70 M
91: TVERDA1-9, 10-19, 20+4.85, 12.73, 26.032.14, 3.32, 6.56 M
92: TVERDA1-9, 20+4.85, 26.034.53, 18.00 M
93: WAKAI1-19, 20-20, 30+10.00, 21.35, 38.391.80, 4.01, 9.19 M
94: WU1-20, 21+13.38, 31.833.25, 8.48 M
95: WYNDE61-10, 11-20, 21-30, 31+7.08, 17.67, 25.88, 43.066.80, 11.16, 17.32, 28.22 M
96: WYNDE61-10, 11-20, 21-30, 31+7.08, 17.67, 25.88, 38.393.75, 11.97, 21.64, 39.14 M
97: YAMAGU1-20, 21+13.38, 31.833.75, 12.14 M
1In some studies, amount smoked is based on cigarette equivalents for cigars and pipes;
2M indicates a strictly monotonic rise in RR with increasing amount smoked.
Table 3 Comparing the suitability of different models relating log RR to amount smoked by current smokers, expressed as d = cigarettes per day/10
ModelParameter value1Fitted coefficient(s) (SE)DevianceDFDeviance explained (%)
Null--24894.5397
Linear: log RR = β1d-β1 = 0.6107 (0.0046)7265.329670.82
Quadratic: log RR = β1d + β2d2-β1 = 1.4121 (0.0130), β2 = -0.1792 (0.0027)2907.399588.32
Cubic: log RR = β1d + β2d2 + β3d3-β1 = 2.1915 (0.0266), β2 = -0.6346 (0.0138), β3 = 0.0633 (0.0019)1779.059492.86
Power: log RR = β1dYY = 0.32β1 = 1.8922 (0.0124)1512.4996
Y = 0.33β1 = 1.8691 (0.0122)1506.1996
Y = 0.34β1 = 1.8457 (0.0121)1506.079693.95
Y = 0.35β1 = 1.8222 (0.0119)1511.9296
Y = 0.36β1 = 1.7986 (0.0118)1523.5496
Y = 0.50β1 = 1.4673 (0.0097)2179.7196
Y = 1.00β1 = 0.6107 (0.0046)7265.3296
Y = 2.00β1 = 0.0969 (0.0010)14739.1996
Log: log RR = β1log d-β1 = 1.2265 (0.0107)11674.709653.10
Exponential: log RR = β1exp d-β1 = 0.0120 (0.0002)19480.219621.75
Log-with-baseline: log RR = β1log (1 + Wd)W = 7.5β1 = 0.8520 (0.0056)1466.2196
W = 7.7β1 = 0.8456 (0.0055)1465.3796
W = 7.9β1 = 0.8394 (0.0054)1464.8896
W = 8.0β1 = 0.8364 (0.0055)1464.7696
W = 8.1β1 = 0.8334 (0.0054)1464.719694.12
W = 8.2β1 = 0.8305 (0.0054)1464.7396
W = 8.3β1 = 0.8277 (0.0054)1464.8296
1Note that we only sought the best-fitting value of Y to two decimal places and of W to one decimal place.
Table 4 Amount smoked by current smokers - observed and fitted lung cancers for the linear, best power and best log-with-baseline model, with β1 fitted separately for each block
Midpoint amount smoked (cigs/d)Observed1Fitted2
Linear modelBest power modelBest log-with-baseline model
< 51249.171023.001297.421173.88
5 to < 102579.622156.312595.372539.78
10 to < 156125.694749.926276.746299.68
15 to < 207940.186678.148009.068156.50
20 to < 3018138.3615724.4517468.9917678.51
30 to < 403858.944106.123743.233701.31
40+7703.888860.428115.777949.95
Never smoked6649.6110947.086738.866745.84
Total54245.4554245.4554245.4554245.45
Fit statistic33792.5365.2956.78
1Observed pseudo-number of lung cancer cases, summed over blocks;
2Fitted pseudo-number of lung cancer cases, summed over blocks. For each study, the fitted number of cases for each block is calculated from the numbers at risk and the fitted RRs by amount smoked, derived from the fitted value of β1;
3Based on summation of (observed-fitted)2/fitted, the summation also including terms for the observed and fitted total numbers of controls (not shown). The statistic can be considered to be approximately chisquared on 12 DF and is significant at P < 0.001 for all three models.
Table 5 Amount smoked by current smokers - fitted values of β1 and SE, and P values for goodness-of-fit tests for the best-fitting power model and log-with-baseline model
Block: StudyLog-with-baseline model1log RR = β1 [1 + (8.10c/10)]
Power model1log RR = β1 [(c/10)0.34]
β1SE β1P (fit)2β1SE β1P (fit)2
1: AKIBA0.65990.0712NS1.48820.1609NS
2: AKIBA0.60990.0660NS1.34450.1453NS
3: ARCHER0.67130.1274NS1.49320.2835NS
4: AXELSS1.32450.2214NS2.97700.4976NS
5: BENSHL0.71330.1169NS1.63370.2688NS
6: BEST0.56780.08240.00001.34830.19480.0001
7: BOUCOT0.83320.2140NS1.74390.4482NS
8: BRETT0.66370.1146NS1.49460.2575NS
9: BROSS0.60900.0735NS1.35140.1634NS
10: BUFFLE0.93490.1040NS2.08100.2313NS
11: CEDERL0.81910.0726NS1.83880.1634NS
12: CEDERL0.76970.0693NS1.68330.1520NS
13: CHANG0.67720.1522NS1.50440.3402NS
14: CHANG0.62550.1165NS1.39370.2595NS
15: CHOW1.00020.1050NS2.21340.2311NS
16: COMSTO0.84970.1552NS1.84910.3399NS
17: COMSTO0.88570.1172NS1.95600.2601NS
18: CORREA0.99450.0483NS2.20520.1069NS
19: CPSI0.83140.03480.00021.82780.07730.0000
20: CPSII0.82620.03310.00001.84670.07390.0000
21: CPSII0.89720.03040.01531.98740.06770.0006
22: DARBY0.81980.12130.00001.90850.27700.0000
23: DARBY1.08790.0841NS2.44340.1879NS
24: DEAN30.82710.07240.00091.89680.16390.0042
25: DEAN30.86170.0801(0.0569)1.91520.17890.0368
26: DEKLER0.57040.1839NS1.31140.4155NS
27: DOLL21.04640.0644(0.0824)2.35310.1443NS
28: DOLL21.10010.1698NS2.44240.37450.0091
29: DORANT1.10820.08670.03222.51830.19720.0270
30: DORGAN0.97280.0937NS2.18140.2101NS
31: DORGAN1.41680.1835NS3.15570.4086NS
32: DORGAN0.96360.0595NS2.14180.1325NS
33: DORGAN1.03590.1844NS2.29760.4094NS
34: DORN0.90240.01710.00012.00990.03810.0000
35: ENGELA1.00830.1270NS2.30430.2995NS
36: ENGELA1.08970.15610.02062.56540.3553NS
37: ENSTRO0.82610.03120.00001.79100.06840.0000
38: ENSTRO0.82290.02520.00001.83680.05640.0000
39: GAO20.70370.1042NS1.55260.2304NS
40: GILLIS0.58110.0729NS1.27040.1614NS
41: HAENSZ0.33820.0805NS0.75630.1796NS
42: HAMMO20.51980.11670.01121.18700.26410.0138
43: HAMMON0.80320.07480.00381.81850.16770.0116
44: HIRAYA0.59740.0337NS1.33740.0756NS
45: HIRAYA0.44240.0501NS0.97290.1100NS
46: HITOSU0.45730.1182NS1.03240.2654NS
47: HITOSU0.49880.1223NS1.09920.2686NS
48: HOLE0.61420.1082NS1.34100.2413NS
49: HUMBLE1.04350.1431NS2.33860.3207NS
50: HUMBLE1.03780.2633NS2.33060.5907NS
51: HUMBLE0.89220.1393NS1.99970.3114NS
52: HUMBLE1.22680.2487NS2.73180.5532NS
53: KAISE20.75990.1018NS1.69910.2278NS
54: KAISE21.00980.1107NS2.25920.2478NS
55: KAISER0.76850.04770.02471.61300.10100.0033
56: KAISER0.68820.0570NS1.49320.1238NS
57: KANELL0.89820.06470.00001.97580.14420
58: KATSOU0.45170.1260NS1.00890.2809NS
59: KAUFMA1.07120.0583NS2.35600.1278NS
60: KINLEN0.60210.06160.00171.38380.13990.0055
61: KNEKT0.86440.1264NS1.96180.2876NS
62: KOO0.43090.1424NS0.92990.3133NS
63: LIAW0.55380.0918NS1.23840.2045NS
64: LIDDEL0.51360.0742NS1.15350.1666NS
65: MACLEN0.49730.1511NS1.08750.3355NS
66: MACLEN0.43010.1161NS0.93500.2577NS
67: MATOS0.83150.1122NS1.83900.2485NS
68: MIGRAN0.45900.1448NS1.05680.3286NS
69: MIGRAN0.72460.2207NS1.65470.4987NS
70: MRFITR0.63820.22250.03381.19840.44610.0152
71: NAM0.68830.0711NS1.51570.1569NS
72: NAM0.84810.0690NS1.88090.1532NS
73: PARKIN0.61290.0554NS1.35560.1222NS
74: PERSH20.84200.03810.00041.90650.08540.0446
75: PETO0.62620.1606NS1.46510.3737NS
76: PEZZO21.36410.12510.00512.97840.27100.0118
77: PEZZOT1.54830.15690.00053.40450.34150.0014
78: PRESCO0.82890.1002(0.0759)1.93050.2318NS
79: PRESCO0.73830.0942NS1.67250.2122NS
80: SEGI20.56790.0991NS1.28490.2208NS
81: SEGI20.15030.1297NS0.35130.2865NS
82: SHAW1.13260.1121NS2.52980.2509NS
83: SOBUE0.40480.0594NS0.88930.1309NS
84: SPEIZE0.87720.0390NS1.95090.0870NS
85: STOCKW0.88220.0096NS1.93830.0210NS
86: SVENSS0.92550.1158NS2.04790.2573NS
87: TENKAN0.62110.10920.00011.44070.24840.0003
88: TSUGAN0.11040.1169NS0.24610.2574NS
89: TULINI1.00190.0901NS2.23940.2008NS
90: TULINI1.24890.0862(0.0728)2.84470.19830.0098
91: TVERDA0.60630.0773NS1.36570.1746NS
92: TVERDA0.93090.1838NS2.12440.4198NS
93: WAKAI0.67760.1099(0.0831)1.50730.2430NS
94: WU0.59160.1017NS1.31830.2263NS
95: WYNDE60.91810.0373NS2.02370.0820NS
96: WYNDE60.97960.03710.01022.17670.08250.0060
97: YAMAGU0.66080.1223NS1.47560.2723NS
1c = cigarettes/d;
2Not significant (NS) indicates P≥ 0.1. P values in the range 0.05 ≤P < 0.1 are shown in brackets.
Table 6 Amount smoked by current smokers - inverse-variance weighted simple regression analyses of β1 based on best-fitting log + baseline model
FactorLevelnβ1 (95% CI)P1RR for 20 cigs/d
All970.83 (0.80-0.86)10.71
SexMale550.79 (0.75-0.84)< 0.059.50
Female340.82 (0.75-0.88)10.21
Combined80.89 (0.84-0.94)12.50
Study typeCase-control490.86 (0.82-0.90)< 0.111.48
Prospective480.80 (0.76-0.85)9.85
ContinentNorth America430.87 (0.84-0.89)< 0.00111.48
Europe320.83 (0.76-0.90)10.65
Asia170.53 (0.45-0.61)4.53
Other50.80 (0.61-0.99)9.80
Publication year2< 1990400.83 (0.79-0.88)< 0.110.71
1990-1994290.77 (0.70-0.84)8.90
1995-1999280.87 (0.82-0.92)11.94
Product3Any product200.75 (0.64-0.85)NS8.36
Cigarettes +/-610.85 (0.81-0.88)11.09
Cigarettes only160.82 (0.74-0.90)10.19
UnexposedNever cigarettes320.83 (0.76-0.90)NS10.49
Never any product650.84 (0.80-0.87)10.76
Grouped midpoint age (yr)< 50140.79 (0.67-0.92)< 0.19.57
50-59620.85 (0.82-0.89)11.35
60+210.79 (0.71-0.84)9.13
Cases in smokers< 100290.67 (0.56-0.78)< 0.0016.72
100 to < 200280.73 (0.64-0.83)8.08
200 to < 500160.76 (0.65-0.87)8.72
500 to < 1000160.80 (0.75-0.86)9.87
1000+80.89 (0.85-0.92)12.42
1Probability values for factor considered, presented as < 0.001, < 0.01, < 0.05, < 0.1 or not significant (NS) (P≥ 0.1);
2Of principal publication for the study;
3Any product = Smokes cigarettes and/or pipes and/or cigars; Cigarettes +/- = Smokes cigarettes with or without other products (pipes, cigars).
Table 7 Duration of smoking by current smokers (yr) - dose-response data
Block: StudyDuration of smoking groupings (yr)Mean valuesRRs1
1: AMANDU0-24, 25+12.66, 41.285.92, 7.02 M
2: BEST1-4, 5-9, 10-14, 15-19, 20-29, 30-39, 40+2.64, 7.02, 12.03, 16.89, 24.03, 33.93, 51.121.60, 2.60, 2.30, 3.20, 4.10, 13.90, 14.20
3: BOUCOT1-39, 40+32.05, 51.1442.40, 89.94 M
4: BUFFLE1-30, 31-40, 41+19.34, 35.56, 48.4914.00, 14.70, 18.15 M
5: CEDERL1-29, 30+23.94, 41.091.80, 7.40 M
6: CEDERL1-29, 30+22.26, 39.471.60, 9.60 M
7: CPSI1-29, 30+23.70, 32.033.83, 6.56 M
8: CPSI1-29, 30-34, 35-39, 40+24.92, 31.91, 36.52, 43.075.58, 13.40, 16.93, 29.61 M
9: CPSI1-29, 30-34, 35-39, 40-44, 45-49, 50+23.57, 32.25, 37.75, 42.03, 46.80, 51.813.11, 6.57, 10.35, 15.21, 21.46, 33.11 M
10: CPSI1-29, 30-34, 35-39, 40-44, 45-49, 50-54, 55-59, 60+10.67, 30.00, 39.00, 42.21, 47.57, 52.05, 56.73, 62.875.46, 6.26, 5.86, 8.22, 12.48, 15.28, 18.86, 28.60
11: CPSI1-29, 30-34, 35-39, 40-44, 45-49, 50-54, 55-59, 60+20.00, 32.00, 37.00, 41.00, 46.25, 51.86, 57.00, 65.032.17, 2.27, 12.66, 3.47, 6.22, 6.31, 12.87, 13.23
12: CPSI1-29, 30+21.86, 31.376.16, 13.80 M
13: CPSI1-29, 30-34, 35-39, 40+23.29, 31.61, 36.72, 43.092.90, 6.91, 8.49, 19.48 M
14: CPSI1-29, 30-34, 35-39, 40-44, 45-49, 50+21.03, 31.92, 37.45, 42.21, 46.65, 52.801.51, 3.71, 4.73, 5.72, 7.78, 14.48 M
15: CPSI1-29, 30-34, 35-39, 40-44, 45-49, 50-54, 55+21.69, 31.38, 37.19, 41.80, 47.14, 51.76, 57.562.30, 3.38, 3.67, 5.81, 7.01, 6.20, 3.32
16: CPSI1-29, 30-34, 35-39, 40-44, 45-49, 50-54, 55+18.00, 30.00, 38.00, 41.75, 46.71, 52.25, 61.540.38, 3.11, 2.72, 3.22, 1.15, 1.85, 3.20
17: CPSII1-29, 30+19.15, 32.133.69, 108.27 M
18: CPSII1-29, 30-34, 35-39, 40+24.92, 31.91, 36.52, 43.077.72, 19.47, 25.01, 36.98 M
19: CPSII1-29, 30-34, 35-39, 40-44, 45-49, 50+23.57, 32.25, 37.75, 42.03, 46.80, 51.8115.51, 17.86, 27.31, 44.71, 50.92, 72.07 M
20: CPSII1-29, 30-34, 35-39, 40-44, 45-49, 50-54, 55-59, 60+10.67, 30.00, 39.00, 42.21, 47.57, 52.05, 56.73, 62.879.97, 11.05, 20.45, 18.59, 24.33, 32.06, 40.43, 45.64
21: CPSII1-29, 30-34, 35-39, 40-44, 45-49, 50-54, 55-59, 60+20.00, 32.00, 37.00, 41.00, 46.25, 51.86, 57.00, 66.097.54, 4.53, 4.37, 16.30, 16.01, 13.40, 18.09, 21.79
22: CPSII1-19, 20+13.93, 24.2310.98, 8.38
23: CPSII1-29, 30-34, 35+23.29, 31.61, 37.818.96, 18.34, 23.32 M
24: CPSII1-29, 30-34, 35-39, 40-44, 45-49, 50+21.03, 31.92, 37.45, 42.22, 46.65, 52.806.50, 13.04, 17.07, 20.56, 23.94, 28.45 M
25: CPSII1-29, 30-34, 35-39, 40-44, 45-49, 50-54, 55+21.69, 31.38, 37.19, 41.80, 47.14, 51.76, 57.566.64, 5.57, 10.19, 12.96, 15.79, 18.75, 19.34
26: CPSII1-29, 30-34, 35-39, 40-44, 45-49, 50-54, 55-59, 60+18.00, 30.00, 38.00, 42.20, 46.71, 52.23, 57.10, 65.063.36, 7.92, 6.31, 8.14, 11.68, 9.45, 9.18, 19.88
27: DEAN21-19, 20+15.09, 38.283.21, 3.84 M
28: DEAN21-19, 20+13.93, 35.850.98, 5.88
29: HUMBLE1-29, 30-39, 40-49, 50+17.18, 34.07, 44.43, 56.6015.45, 17.54, 19.61, 17.27
30: KAISE21-39, 40+23.76, 51.124.86, 15.64 M
31: KAISE21-39, 40+22.73, 48.969.09, 30.41 M
32: KATSOU1-29, 30+14.58, 42.431.29, 7.43 M
33: LIAW1-20, 21-30, 31+14.32, 26.18, 44.790.90, 2.60, 4.70
34: MATOS1-24, 25-39, 40+12.75, 31.16, 50.575.20, 7.40, 10.20 M
35: PEZZO21-35, 36+17.15, 48.8916.25, 26.77 M
1M indicates a strictly monotonic rise in RR with increasing duration of smoking.
Table 8 Comparing the suitability of different models relating log RR to duration of smoking by current smokers, expressed as d = years smoked/10
ModelParameter value1Fitted coefficient(s) (SE)DevianceDFDeviance explained (%)
Null--6161.1135
Linear: log RR = β1d-β1 = 0.5134 (0.0069)672.013489.09
Quadratic: log RR = β1d + β2d2-β1 = 0.6718 (0.0237), β2 = -0.0300 (0.0043)623.203389.88
Cubic: log RR = β1d + β2d2 + β3d3-β1 = 0.6788 (0.0607), β2 = -0.0330 (0.0243), β3 = 0.0003 (0.0025)623.193289.89
Power: log RR = β1dYY = 0.50β1 = 1.1576 (0.0156)682.5634
Y = 0.72β1 = 0.8180 (0.0110)619.3034
Y = 0.73β1 = 0.8049 (0.0108)618.9334
Y = 0.74β1 = 0.7919 (0.0106)618.753489.96
Y = 0.75β1 = 0.7791 (0.0105)618.7634
Y = 0.76β1 = 0.7665 (0.0103)618.9534
Y = 1.00β1 = 0.5134 (0.0069)672.0134
Y = 2.00β1 = 0.0863 (0.0013)1426.4434
Log: log RR = β1log d-β1 = 1.5870 (0.0215)708.963588.49
Exponential: log RR = β1exp dβ1 = 0.0045 (0.0001)4222.013531.47
Log-with-baseline: log RR = β1log (1 + Wd)W = 0.10β1 = 6.4054 (0.0861)629.5834
W = 0.15β1 = 4.6503 (0.0625)623.9934
W = 0.18β1 = 4.0572 (0.0545)622.8234
W = 0.19β1 = 3.9001 (0.0524)622.6934
W = 0.20β1 = 3.7581 (0.0505)622.673489.89
W = 0.21β1 = 3.6293 (0.0488)622.7434
W = 0.22β1 = 3.5117 (0.0472)622.8934
1Note that we only sought the best-fitting value of W and Y to two decimal places.
Table 9 Duration of smoking by current smokers - observed and fitted lung cancers for the linear, best power and best log-with-baseline model, with β1 fitted separately for each block
Midpoint years smokedObserved1Fitted2
Linear modelBest power modelBest log-with-baseline model
< 15109.3689.1093.6191.19
15 to < 30605.64584.79666.12645.42
30 to < 453968.473917.114000.714012.22
45+3493.563573.953499.853499.95
Never smoked2533.972546.032450.692462.20
Total10710.9810710.9810710.9810710.98
Fit statistic328.1425.7024.53
1Observed pseudo-number of lung cancer cases, summed over blocks;
2Fitted pseudo-number of lung cancer cases, summed over blocks. For each study, the fitted number of cases for each block is calculated from the numbers at risk and the fitted RRs by years smoked, derived from the fitted value of β1;
3Based on summation of (observed-fitted)2/fitted, the summation also including terms for the observed and fitted total numbers of controls (not shown). The statistic can be considered to be approximately chisquared distributed on 6 df, and is significant at P < 0.001 for all three models.
Table 10 Duration of smoking by current smokers - fitted values for of β1 and SE, and P values for goodness-of-fit tests for the best-fitting power model and log-with-baseline model
Block: StudyLog-with-baseline model1log RR = β1 [1 + (0.2 yr/10)]
Power model1log RR = β1 (yr/10)0.74
β1SE β1P (fit)2β1SE β1P (fit)2
1: AMANDU1.51140.55040.00300.34540.12100.0046
2: BEST3.71630.4210(0.0548)0.79950.09080.0469
3: BOUCOT6.77311.6574NS1.42350.3482NS
4: BUFFLE4.51410.48880.04660.95700.1029(0.0780)
5: CEDERL3.40440.7166NS0.71470.1512NS
6: CEDERL3.35660.7692NS0.69900.1609NS
7: CPSI3.63861.4531NS0.75300.3009NS
8: CPSI5.72480.4753(0.0947)1.21220.1011(0.0518)
9: CPSI4.80580.20320.00031.01300.04290.0002
10: CPSI3.76810.15570.00020.79760.03280.0010
11: CPSI3.14370.17680.00790.65660.03690.0073
12: CPSI5.13281.5211NS1.05180.3119NS
13: CPSI3.99600.33770.03080.83420.07080.0165
14: CPSI2.85750.1844(0.0637)0.59990.03880.0383
15: CPSI2.63840.18720.00000.55440.03940.0000
16: CPSI1.54430.3346NS0.32380.0702NS
17: CPSII9.54822.46620.01491.94850.51600.0076
18: CPSII6.11600.5675NS1.28740.1199NS
19: CPSII5.99050.3222(0.0749)1.27220.0684(0.0921)
20: CPSII4.59130.19960.00580.97140.04210.0210
21: CPSII3.66040.2069NS0.76450.0432NS
22: CPSII5.10733.0925NS1.10110.6362NS
23: CPSII5.81030.4709NS1.21800.0988NS
24: CPSII4.94980.2256NS1.04610.0476NS
25: CPSII4.10280.1646NS0.86560.0347NS
26: CPSII3.33100.1915NS0.69930.0402NS
27: DEAN22.10380.3399NS0.45150.0723NS
28: DEAN22.91550.6412NS0.59840.1334NS
29: HUMBLE4.27800.28070.00910.90050.05900.0148
30: KAISE23.87580.4357NS0.82020.0922NS
31: KAISE24.78830.5320NS1.01980.1130NS
32: KATSOU2.93050.7339NS0.60310.1527NS
33: LIAW2.42770.4372NS0.50930.0921NS
34: MATOS3.43560.5336NS0.72760.1124NS
35: PEZZO23.30220.52830.00020.72600.11370.0005
1Years smoked;
2Not significant (NS) indicates P≥ 0.1. P values in the range 0.05 ≤P < 0.1 are shown in brackets.
Table 11 Duration of smoking by current smokers - inverse-variance weighted simple regression analyses of β1 based on best-fitting power model
FactorLevelnβ1 (95%CI)P1RR for 30 yr smoked
All350.79 (0.72-0.86)5.94
SexMale180.84 (0.73-0.94)NS6.59
Female150.74 (0.64-0.85)5.35
Combined20.79 (0.45-1.12)5.89
Study typeCase-control70.73 (0.50-0.97)NS5.24
Prospective280.80 (0.72-0.87)6.02
ContinentNorth America270.81 (0.73-0.88)NS6.19
Europe50.55 (0.20-0.90)3.44
Asia10.51 (-0.11-1.13)3.15
Other20.73 (0.19-1.27)5.15
Publication year2< 199080.76 (0.52-0.99)NS5.50
1990-199420.44 (-0.20-1.09)2.73
1995-1999250.80 (0.72-0.88)6.08
Product3Any product40.50 (0.18-0.83)NS3.12
Cigarettes +/-100.86 (0.73-0.98)6.89
Cigarettes only210.78 (0.70-0.87)5.85
UnexposedNever cigarettes190.77 (0.69-0.86)NS5.71
Never any product160.85 (0.71-0.99)6.75
Grouped midpoint age (yr)< 5081.06 (0.78-1.34)< 0.0511.00
50-59130.87 (0.75-0.99)7.04
60+140.73 (0.65-0.82)5.21
Cases in smokers< 100140.62 (0.39-0.84)NS4.01
100 to < 20090.73 (0.59-0.87)5.19
200 to < 50060.78 (0.67-0.89)5.18
500 to < 100050.95 (0.80-1.10)8.58
1000+10.80 (0.59-1.01)6.04
1Probability values for factor considered, presented as < 0.001, < 0.01, < 0.05, < 0.1 or not significant (NS) (P≥ 0.1);
2Of principal publication for the study;
3Any product = Smokes cigarettes and/or pipes and/or cigars; Cigarettes +/- = Smokes cigarettes with or without other products (pipes, cigars).
Table 12 Age of starting to smoke by current smokers (yr) - dose-response data
Block: StudyAge of starting to smoke groupings (yr)Mean valuesRRs1
1: CEDERL< 17, 17-18, 19+13.83, 17.52, 22.456.40, 9.80, 6.50
2: CEDERL< 17, 17-18, 19+14.31, 17.56, 24.320.61, 1.84, 1.99
3: CPSI< 15, 15-19, 20-24, 25+11.98, 16.74, 21.29, 28.4715.00, 9.71, 7.14, 3.43 M
4: CPSI< 15, 15-19, 20-24, 25+11.59, 16.56, 21.00, 30.9018.16, 16.32, 12.00, 5.21 M
5: CPSI< 15, 15-19, 20-24, 25+11.19, 16.61, 21.07, 35.0014.03, 16.60, 8.66, 1.71
6: CPSI< 15, 15-19, 20-24, 25+12.71, 16.88, 21.26, 31.519.00, 5.00, 4.00, 1.50 M
7: CPSI< 20, 20-24, 25+16.02, 20.95, 33.292.59, 3.23, 2.62
8: DEAN3< 15, 15-19, 20-24, 25+11.73, 16.67, 21.19, 29.955.67, 7.01, 6.86, 6.80
9: DEAN3< 15, 15-19, 20-24, 25+12.45, 16.95, 21.15, 32.192.41, 2.90, 2.95, 3.70
10: DORN< 15, 15-19, 20-24, 25+11.63, 16.43, 21.23, 30.8823.42, 16.25, 11.06, 5.18 M
11: DORN< 15, 15-19, 20-24, 25+11.37, 16.81, 20.69, 32.6314.18, 11.31, 7.94, 4.95 M
12: ENGELA< 20, 20-29, 30+15.08, 22.23, 35.107.42, 3.60, 3.79
13: ENGELA< 20, 20-29, 30+15.80, 22.63, 35,8011.29, 8.15, 2.73 M
14: GAO2< 20, 20-29, 30+15.11, 22.17, 35.948.62, 6.44, 2.15 M
15: HIRAYA< 20, 20+14.90, 24.025.71, 4.35 M
16: HIRAYA< 20, 20+15.87, 27.400.78, 2.46
17: LIAW< 21, 21-24, 25+15.70, 21.94, 32.034.60, 5.90, 1.50
18: MATOS< 15, 15-19, 20+11.96, 16.64, 23.4911.30, 8.60, 5.30 M
19: MIGRAN< 16, 16-19, 20+12.60, 17.19, 23.7110.03, 6.93, 7.79
20: MIGRAN< 16, 16-19, 20+12.94, 17.31, 26.177.17, 8.29, 7.98
21: MRFITR< 16, 16-17, 18-19, 20-21, 22-23, 24+12.93, 16.45, 18.31, 20.40, 22.35, 27.7445.91, 67.17, 50.54, 27.09, 60.06, 23.91
22: SEGI2< 20, 20-22, 23+15.28, 20.77, 26.608.21, 5.56, 1.83 M
23: SEGI2< 20, 20-22, 23+14.87, 20.90, 28.968.70, 5.68, 3.56 M
24: SEGI2< 20, 20-22, 23+14.37, 20.59, 30.873.26, 1.70, 1.52 M
25: SVENSS< 19, 19-25, 26+15.04, 21.31, 33.897.82, 13.08, 5.61
26: WAKAI< 20, 20-29, 30+14.91, 22.14, 37.233.69, 4.62, 2.08
27: WU< 19, 19-24, 25+15.06, 20.71, 31.4410.32, 3.57, 1.55 M
1M indicates a strictly monotonic decline in RR with increasing age of starting to smoke.
Table 13 Comparing the suitability of different models relating log RR to age of starting smoke by current smokers, expressed as d = (70-age at start)/10
ModelParameter value1Fitted coefficient(s) (SE)DevianceDFDeviance explained (%)
Null--2145.3027
Linear: log RR = β1d-β1 = 0.3681 (0.0085)276.672687.10
Quadratic: log RR = β1d + β2d2-β1 = 0.1987 (0.0349)251.632588.27
β2 = 0.0318 (0.0064)
Cubic: log RR = β1d + β2d2 + β3d3-β1 = -0.0415 (0.2143)250.342488.33
β2 = 0.1304 (0.0870)
β3 = -0.0100 (0.0088)
Power: log RR = β1dYY = 0.75β1 = 0.5515 (0.0129)316.6926
Y = 1.00β1 = 0.3681 (0.0085)276.6726
Y = 1.42β1 = 0.1825 (0.0042)251.2726
Y = 1.43β1 = 0.1794 (0.0041)251.2426
Y = 1.44β1 = 0.1764 (0.0041)251.232688.29
Y = 1.45β1 = 0.1734 (0.0040)251.2526
Y = 1.46β1 = 0.1705 (0.0039)251.2826
Y = 1.50β1 = 0.1592 (0.0037)251.6726
Y = 2.00β1 = 0.0668 (0.0015)284.0426
Log: log RR = β1log d-β1 = 1.1460 (0.0270)340.232684.14
Exponential: log RR = β1exp d-β1 = 0.0058 (0.0002)852.852660.24
1Note that we only sought the best-fitting value of Y to two decimal places.
Table 14 Age of starting to smoke by current smokers - observed and fitted lung cancers for the linear and best power model, with β1 fitted separately for each block
Age of starting (yr)Observed1Fitted2
Linear modelBest power model
< 161304.921294.481387.73
16 to < 201964.761906.551921.20
20 to < 241227.481266.991216.48
25+2173.902219.262122.14
Never smoked894.41878.20917.92
Total7565.477565.477565.47
Fit statistic34.779.75
1Observed pseudo-number of lung cancer cases, summed over blocks;
2Fitted pseudo-number of lung cancer cases, summed over blocks. For each study, the fitted number of cases for each block is calculated from the numbers at risk and the fitted relative risks for age of starting to smoke, derived from the fitted value of β1;
3Based on summation of (observed-fitted)2/fitted, the summation also including terms for the observed and fitted total numbers of controls (not shown). The statistic can be considered to be approximately chisquared distributed on 6 df and is not significant (P > 0.1) for both models.
Table 15 Age of starting to smoke by current smokers - fitted values of β1 and SE, and P values for goodness-of-fit tests for the linear model and for the best-fitting power model
Block: StudyLinear model1log RR = β1(70 - a)/10
Power model1log RR = β1(70 - a)/101.44
β1SE β1P (fit)2β1SE β1P (fit)2
1: CEDERL0.03850.0082NS0.18280.0394NS
2: CEDERL0.01400.0089NS0.06990.0445NS
3: CPSI0.04610.00410.04900.21670.0188NS
4: CPSI0.05240.0029(0.0959)0.23990.0135(0.0579)
5: CPSI0.05120.00470.01950.24080.02230.0307
6: CPSI0.03010.0036(0.0510)0.14800.0175NS
7: CPSI0.02370.0046NS0.11680.02380.0828
8: DEAN30.03320.0041NS0.14820.01890.0342
9: DEAN30.02090.0039NS0.09600.0187NS
10: DORN0.05490.0037(0.0874)0.25270.0166NS
11: DORN0.04550.0027NS0.20860.0125NS
12: ENGELA0.03600.00370.01090.16820.01710.0269
13: ENGELA0.04420.0045NS0.21860.0221NS
14: GAO20.03940.0066NS0.19090.0318NS
15: HIRAYA0.03170.0022NS0.14970.01040.0288
16: HIRAYA0.02070.0029NS0.10860.0152NS
17: LIAW0.02960.00500.03960.14480.0242(0.0661)
18: MATOS0.04110.0063NS0.19330.0296NS
19: MIGRAN0.03730.0087NS0.16120.0385NS
20: MIGRAN0.04000.0108NS0.18590.0519NS
21: MRFITR0.06860.0237NS0.29310.1055NS
22: SEGI20.04680.0140NS0.23250.0639NS
23: SEGI20.04400.0128NS0.19740.0557NS
24: SEGI20.01920.0109NS0.09450.0500NS
25: SVENSS0.04320.0051NS0.20640.0246NS
26: WAKAI0.02750.0068NS0.12440.0318NS
27: WU0.03480.0063NS0.17410.0305NS
1a = Age of starting to smoke;
2Not significant (NS) indicates P≥ 0.1. P values in the range 0.05 ≤P < 0.1 are shown in brackets.
Table 16 Age of starting to smoke by current smokers - inverse-variance weighted simple regression analyses of β1 based on best-fitting power model
FactorLevelnβ1 (95%CI)P1RR for 15 yr start
All270.18 (0.16-0.20)7.80
SexMale170.19 (0.17-0.21)< 0.059.49
Female90.14 (0.11-0.17)5.14
Combined10.14 (0.04-0.25)5.40
Study typeCase-control100.15 (0.11-0.20)NS5.94
Prospective170.18 (0.16-0.20)8.37
ContinentNorth America90.21 (0.19-0.23)< 0.0111.49
Europe90.16 (0.13-0.19)6.38
Asia80.14 (0.11-0.17)5.17
Other10.19 (0.08-0.31)9.50
Publication year2< 1990110.15 (0.11-0.19)< 0.015.59
1990-199440.14 (0.11-0.17)5.17
1995-1999120.20 (0.18-0.22)10.37
Product3Any product30.17 (0.11-0.24)< 0.057.65
Cigarettes +/-160.19 (0.17-0.21)9.09
Cigarettes only80.13 (0.09-0.17)4.69
UnexposedNever cigarettes40.19 (0.13-0.25)NS9.05
Never any product230.17 (0.15-0.20)7.66
Grouped midpoint age (yr)< 5070.18 (0.13-0.23)NS7.73
50-5990.21 (0.17-0.25)10.98
60+110.17 (0.14-0.19)6.88
Cases in smokers< 100120.14 (0.11-0.17)< 0.0015.09
100 to < 20070.20 (0.16-0.24)9.88
200 to < 50040.17 (0.23-0.20)7.02
500 to < 100030.23 (0.20-0.26)14.57
1000+10.15 (0.11-0.19)5.71
1Probability values for factor considered, presented as < 0.001, < 0.01, < 0.05, < 0.1 or not significant (NS) (P≥ 0.1);
2Of principal publication for the study;
3Any product = Smokes cigarettes and/or pipes and/or cigars; Cigarettes +/- = Smokes cigarettes with or without other products (pipes, cigars).