[R-meta] High heterogeneity and publication bias in mean difference meta-analysis
Martin Lobo
m|obo4370 @end|ng |rom hotm@||@com
Tue Jun 28 15:43:59 CEST 2022
Hi everyone,
I recently asked about doing a mean difference meta-analysis where I had 3 different measurements, cm3, mm, and cm2. They told me to carry out a stratified meta-analysis, although I did not understand why a meta-analysis of standardized differences could not work, carry out the stratification by the 3 measures.
The problem that I have found is the high heterogeneity and the asymmetry in the funnel plot. Although one group has k=5 and another k=2, so I have not evaluated the publication bias, in the third group with k=14 the bias is positive. Could this be due to the high heterogeneity? How should I report the results?
I copy to show the results with prediction interval. Sensitivity analysis works fine. The study of influence gives that 3 studies are influential. The study of out-liers is very rare, there are about 8 studies with out-liers.
Number of studies combined: k = 5
MD 95%-CI z p-value
Fixed effect model 0.0050 [ -0.0869; 0.0969] 0.11 0.9149
Random effects model 10.4453 [ 1.7681; 19.1224] 2.36 0.0183
Prediction interval [-20.2018; 41.0923]
Quantifying heterogeneity:
tau^2 = 73.1374 [18.7590; >829.7896]; tau = 8.5520 [4.3312; >28.8061]
I^2 = 95.3% [91.7%; 97.4%]; H = 4.63 [3.47; 6.17]
Test of heterogeneity:
Q d.f. p-value
85.63 4 < 0.0001
Number of studies combined: k = 14
MD 95%-CI z p-value
Fixed effect model 0.1997 [0.1724; 0.2270] 14.33 < 0.0001
Random effects model 1.0164 [0.7829; 1.2499] 8.53 < 0.0001
Prediction interval [0.1733; 1.8595]
Quantifying heterogeneity:
tau^2 = 0.1355 [0.2216; 2.3742]; tau = 0.3682 [0.4708; 1.5409]
I^2 = 95.6% [94.0%; 96.8%]; H = 4.78 [4.08; 5.60]
Test of heterogeneity:
Q d.f. p-value
296.49 13 < 0.0001
Leave-One-Out Analysis (Sorted by I2)
-----------------------------------
Effect LLCI ULCI I2
Omitting Lima-Mart�nez b et al. (2014)20** 0.197 0.169 0.224 0.948
Omitting Bacaks�z et al. (2014)21 0.190 0.163 0.218 0.948
Omitting Bulbul et al. (2013)19 0.186 0.159 0.214 0.953
Omitting Lima-Mart�nez a et al. (2014)20** 0.198 0.171 0.225 0.956
Omitting Temiz et al. (2015)24 0.197 0.169 0.224 0.957
Omitting Resorlu et al. (2015)25 0.197 0.170 0.224 0.957
Omitting Uysal et al. (2016)28 0.196 0.169 0.223 0.957
Omitting Surucu et al. (2019)31 0.228 0.197 0.258 0.957
Omitting Fatma et al. (2015)26 0.198 0.171 0.225 0.958
Omitting Demir et al. (2021)32 0.197 0.170 0.225 0.958
Omitting Ekmen et al. (2021)34 0.287 0.233 0.341 0.958
Omitting Saha et al. (2022)36 0.197 0.170 0.224 0.958
Omitting Akyildiz et al. (2014)23 0.199 0.172 0.226 0.959
Omitting Girisha et al. (2021)35 0.199 0.171 0.226 0.959
Influence Diagnostics
-------------------
rstudent dffits cook.d cov.r QE.del hat weight infl
Omitting Bulbul et al. (2013)19 6.454 0.967 0.935 1.022 254.847 0.022 2.197 *
Omitting Lima-Mart�nez a et al. (2014)20** 4.884 0.112 0.013 1.001 272.639 0.001 0.053
Omitting Lima-Mart�nez b et al. (2014)20** 8.065 0.220 0.048 1.001 231.453 0.001 0.074
Omitting Bacaks�z et al. (2014)21 8.224 0.673 0.453 1.007 228.868 0.007 0.666
Omitting Akyildiz et al. (2014)23 1.913 0.046 0.002 1.001 292.834 0.001 0.059
Omitting Temiz et al. (2015)24 4.413 0.209 0.044 1.002 277.024 0.002 0.223
Omitting Resorlu et al. (2015)25 3.895 0.189 0.036 1.002 281.326 0.002 0.234
Omitting Fatma et al. (2015)26 2.921 0.119 0.014 1.002 287.960 0.002 0.165
Omitting Uysal et al. (2016)28 4.402 0.262 0.069 1.004 277.113 0.004 0.354
Omitting Surucu et al. (2019)31 -4.157 -2.012 4.049 1.234 279.212 0.190 18.982 *
Omitting Demir et al. (2021)32 2.847 0.179 0.032 1.004 288.390 0.004 0.395
Omitting Ekmen et al. (2021)34 -3.656 -6.268 39.288 3.939 283.129 0.746 74.615 *
Omitting Girisha et al. (2021)35 0.618 0.076 0.006 1.015 296.113 0.015 1.480
Omitting Saha et al. (2022)36 2.809 0.200 0.040 1.005 288.604 0.005 0.504
Baujat Diagnostics (sorted by Heterogeneity Contribution)
-------------------------------------------------------
HetContrib InfluenceEffectSize
Omitting Bacaks�z et al. (2014)21 67.176 0.450
Omitting Lima-Mart�nez b et al. (2014)20** 64.994 0.048
Omitting Bulbul et al. (2013)19 40.733 0.915
Omitting Lima-Mart�nez a et al. (2014)20** 23.843 0.013
Omitting Temiz et al. (2015)24 19.428 0.043
Omitting Uysal et al. (2016)28 19.313 0.069
Omitting Resorlu et al. (2015)25 15.133 0.036
Omitting Surucu et al. (2019)31 14.002 3.281
Omitting Fatma et al. (2015)26 8.520 0.014
Omitting Demir et al. (2021)32 8.073 0.032
Omitting Saha et al. (2022)36 7.851 0.040
Omitting Akyildiz et al. (2014)23 3.659 0.002
Omitting Ekmen et al. (2021)34 3.393 9.973
Omitting Girisha et al. (2021)35 0.376 0.006
Bulbul et al. (2013)19 0.8000 [ 0.6157; 0.9843] 6.4
Lima-Mart�nez a et al. (2014)20** 3.1700 [ 1.9778; 4.3622] 2.5
Lima-Mart�nez b et al. (2014)20** 4.3200 [ 3.3183; 5.3217] 3.1
Bacaksiz et al. (2014)21 1.6000 [ 1.2651; 1.9349] 5.9
Akyildiz et al. (2014)23 1.3000 [ 0.1726; 2.4274] 2.7
Temiz et al. (2015)24 1.5000 [ 0.9218; 2.0782] 4.8
Resorlu et al. (2015)25 1.3200 [ 0.7556; 1.8844] 4.9
Fatma et al. (2015)26 1.2000 [ 0.5284; 1.8716] 4.4
Uysal et al. (2016)28 1.2300 [ 0.7705; 1.6895] 5.4
Surucu et al. (2019)31 0.0800 [ 0.0173; 0.1427] 6.6
Demir et al. (2021)32 0.8300 [ 0.3952; 1.2648] 5.5
Ekmen et al. (2021)34 0.1700 [ 0.1384; 0.2016] 6.7
Girisha et al. (2021)35 0.2700 [ 0.0454; 0.4946] 6.3
Saha et al. (2022)36 0.7500 [ 0.3651; 1.1349] 5.7
Filled: Uysal et al. (2016)28 -0.8789 [-1.3384; -0.4194] 5.4
Filled: Akyildiz et al. (2014)23 -0.9489 [-2.0763; 0.1785] 2.7
Filled: Resorlu et al. (2015)25 -0.9689 [-1.5333; -0.4045] 4.9
Filled: Temiz et al. (2015)24 -1.1489 [-1.7271; -0.5707] 4.8
Filled: Bacaksiz et al. (2014)21 -1.2489 [-1.5837; -0.9140] 5.9
Filled: Lima-Mart�nez a et al. (2014)20** -2.8189 [-4.0111; -1.6266] 2.5
Filled: Lima-Mart�nez b et al. (2014)20** -3.9689 [-4.9706; -2.9672] 3.1
Number of studies combined: k = 21 (with 7 added studies)
MD 95%-CI z p-value
Random effects model 0.3282 [ 0.0886; 0.5678] 2.68 0.0073
Prediction interval [-0.6951; 1.3515]
Quantifying heterogeneity:
tau^2 = 0.2241 [0.4633; 3.3918]; tau = 0.4734 [0.6807; 1.8417]
I^2 = 96.1% [95.1%; 97.0%]; H = 5.09 [4.51; 5.76]
Test of heterogeneity:
Q d.f. p-value
519.01 20 < 0.0001
I have used the random effects model due to the great heterogeneity. In principle I could say that in the group k=5, future studies might not find an increase in volume because the prediction interval is negative to positive. In the K=14 group, future studies would give in the same direction, not being able to specify the mean value. This is correct?
Should I not analyze biases due to high heterogeneity?
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Lorenzo Mart�n Lobo MTSAC, FACC, FESC
Especialista Jerarquizado en Cardiolog�a
Jefe de Dpto Enf. Cardiovasculares y Cardiometabolismo Hospital Militar Campo de Mayo.
Jefe de Cardiolog�a Hospital Militar Campo de Mayo
Ex Jefe de Unidad Coronaria Hospital Militar Campo de Mayo
Miembro Titular de la Sociedad Argentina de Cardiolog�a
Fellow American College of Cardiology
Fellow European Society of Cardiology
Ex Miembro del Area de Investigaci�n de la SAC
Ex Director del Consejo de Aterosclerosis y Trombosis de la SAC
Miembro Asesor del Consejo de Aterosclerosis y Trombosis de la SAC
Ex Director del Consejo de Epidemiolog�a y Prevenci�n Cardiovascular de la SAC
Miembro Asesor del Consejo de Epidemiolog�a y Prevenci�n Cardiovascular de la SAC
Experto en Lipidos de la Sociedad Argentina de Lipidos.
Miembro de la Sociedad Argentina de Lipidos.
Instructor de ACLS de la American Heart Association
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