[R-meta] metafor::rma-function: Statistically significant interaction, but increased tau2 – and how to get the slope from the output
Sabrina Mai Nielsen
@@br|n@@m@|@n|e|@en @end|ng |rom reg|onh@dk
Thu Aug 1 20:52:21 CEST 2019
I am having troubles making sense of a REML-based meta-regression with an interaction between a factor and numeric variable, fitted with rma.
In my study, I have included RCTs from 19 meta-analyses to investigate the association between %women in the RCTs and the effect sizes (i.e. logOR).
The slope for %women, without interaction, is not significant (see below, M_REML0, p=0.6858), and I am now investigating the interaction between %women (CF1_Women..IMP) and the ID for the meta-analysis (i.e. if the slope for %women varies in the different meta-analyses).
1) The interaction seem significant when testing for moderators, but the between-trial variation, tau^2, does not decrease as expected. Why is that?
(When I try method="ML" instead of REML, then tau^2 does decrease as expected; see anova(M0,M1) below)
M_REML0 (without interaction), tau^2 = 0.2076
M_REML1 (with an interaction), tau^2 = 0.2127, Test of Moderators (interaction terms) p-val = 0.0044
(see full outputs below)
2) I am in doubt how to get the estimate for the slopes – e.g. for meta-analysis with ID 8.
estimate se zval pval ci.lb ci.ub
intrcpt -0.3567 1.0739 -0.3322 0.7398 -2.4616 1.7481
CF1_Women..IMP 0.0114 0.0139 0.8244 0.4097 -0.0157 0.0386
(...)
CF1_Women..IMP:id8 -0.0718 0.0214 -3.3572 0.0008 -0.1137 -0.0299 ***
(see full output below)
I would think it would be calculated as CF1_Women..IMP + CF1_Women..IMP:id8, i.e. 0.0114 +(-0.0718) = -0.0604 (with corresponding 95%CI of -0.1294 to 0.0087). Is that correct?
Or is the slope for ID 8 simply the estimate reported for CF1_Women..IMP:id8, i.e. (-0.0718, 95%CI -0.1137 to -0.0299)?
I am asking because when I do a meta-regression with only RCTs for ID 8, I get -0.0940 (95%CI -0.1864 to -0.0016; output not shown), which is more similar to the CF1_Women..IMP:id8 estimate.
Also, when I calculate the slopes for all the meta-analysis IDs, none of them are significantly different from 0, despite the interaction term is significant. I guess that is possible, but it makes me doubt the way I calculated the slopes.
Thanks a lot in advance! Your help is very appreciated!
Best,
Sabrina
=======A FEW RELEVANT OUTPUTS=======
> M_REML0<-rma(logOR, logOR.var, mods= ~CF1_Women..IMP + id, method="REML", data=d, btt=2)
> M_REML1<-rma(logOR, logOR.var, mods= ~CF1_Women..IMP * id, method="REML", data=d, btt=c(21:38))
> M_REML0
Mixed-Effects Model (k = 212; tau^2 estimator: REML)
tau^2 (estimated amount of residual heterogeneity): 0.2076 (SE = 0.0357)
tau (square root of estimated tau^2 value): 0.4556
I^2 (residual heterogeneity / unaccounted variability): 66.60%
H^2 (unaccounted variability / sampling variability): 2.99
R^2 (amount of heterogeneity accounted for): 63.70%
Test for Residual Heterogeneity:
QE(df = 192) = 545.9074, p-val < .0001
Test of Moderators (coefficient 2):
QM(df = 1) = 0.1637, p-val = 0.6858
Model Results:
estimate se zval pval ci.lb ci.ub
intrcpt 0.4156 0.3105 1.3383 0.1808 -0.1931 1.0242
CF1_Women..IMP 0.0013 0.0032 0.4046 0.6858 -0.0049 0.0075
id2 0.0672 0.3965 0.1695 0.8654 -0.7099 0.8443
id3 0.5059 0.2521 2.0066 0.0448 0.0117 1.0000 *
id4 0.1753 0.2739 0.6402 0.5221 -0.3615 0.7121
id5 0.2610 0.2558 1.0201 0.3077 -0.2404 0.7624
id6 0.0351 0.2763 0.1272 0.8988 -0.5065 0.5768
id7 0.8416 0.3464 2.4295 0.0151 0.1626 1.5205 *
id8 0.1775 0.2723 0.6519 0.5145 -0.3562 0.7112
id9 -0.3137 0.2684 -1.1690 0.2424 -0.8398 0.2123
id10 -0.8378 0.2723 -3.0765 0.0021 -1.3715 -0.3040 **
id11 0.2878 0.2106 1.3665 0.1718 -0.1250 0.7006
id12 0.1932 0.3449 0.5603 0.5753 -0.4827 0.8692
id13 0.1538 0.2959 0.5199 0.6031 -0.4261 0.7337
id14 -1.0020 0.3432 -2.9195 0.0035 -1.6747 -0.3293 **
id15 -0.6162 0.2739 -2.2497 0.0245 -1.1531 -0.0794 *
id16 -1.5704 0.3394 -4.6269 <.0001 -2.2356 -0.9052 ***
id17 -1.4576 0.2942 -4.9552 <.0001 -2.0341 -0.8811 ***
id18 -0.0457 0.4967 -0.0921 0.9266 -1.0193 0.9278
id19 -0.3440 0.3283 -1.0479 0.2947 -0.9874 0.2994
---
Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
> M_REML1
Mixed-Effects Model (k = 212; tau^2 estimator: REML)
tau^2 (estimated amount of residual heterogeneity): 0.2127 (SE = 0.0378)
tau (square root of estimated tau^2 value): 0.4612
I^2 (residual heterogeneity / unaccounted variability): 67.50%
H^2 (unaccounted variability / sampling variability): 3.08
R^2 (amount of heterogeneity accounted for): 62.80%
Test for Residual Heterogeneity:
QE(df = 174) = 488.8555, p-val < .0001
Test of Moderators (coefficients 21:38):
QM(df = 18) = 37.5693, p-val = 0.0044
Model Results:
estimate se zval pval ci.lb ci.ub
intrcpt -0.3567 1.0739 -0.3322 0.7398 -2.4616 1.7481
CF1_Women..IMP 0.0114 0.0139 0.8244 0.4097 -0.0157 0.0386
id2 8.6017 8.6515 0.9942 0.3201 -8.3549 25.5583
id3 0.7355 1.3494 0.5451 0.5857 -1.9093 3.3804
id4 0.2098 1.2889 0.1628 0.8707 -2.3164 2.7360
id5 1.7079 1.1849 1.4414 0.1495 -0.6144 4.0302
id6 -3.6331 2.2106 -1.6435 0.1003 -7.9658 0.6995
id7 -5.4865 2.7547 -1.9917 0.0464 -10.8857 -0.0874 *
id8 5.2745 1.5782 3.3421 0.0008 2.1812 8.3677 ***
id9 0.4174 1.2215 0.3417 0.7326 -1.9766 2.8114
id10 -0.1295 1.2015 -0.1078 0.9142 -2.4844 2.2253
id11 0.2269 1.7098 0.1327 0.8944 -3.1242 3.5779
id12 -0.7519 2.3333 -0.3222 0.7473 -5.3250 3.8212
id13 -0.0701 3.4723 -0.0202 0.9839 -6.8758 6.7355
id14 -0.1842 2.0870 -0.0882 0.9297 -4.2747 3.9063
id15 0.9002 1.3974 0.6442 0.5194 -1.8386 3.6389
id16 6.4300 7.6265 0.8431 0.3992 -8.5176 21.3776
id17 0.7142 2.1172 0.3373 0.7359 -3.4353 4.8638
id18 -0.4641 1.5171 -0.3059 0.7597 -3.4376 2.5095
id19 1.2194 4.9584 0.2459 0.8057 -8.4989 10.9376
CF1_Women..IMP:id2 -0.1243 0.1269 -0.9795 0.3274 -0.3730 0.1244
CF1_Women..IMP:id3 -0.0026 0.0177 -0.1480 0.8824 -0.0374 0.0322
CF1_Women..IMP:id4 0.0012 0.0174 0.0672 0.9464 -0.0329 0.0353
CF1_Women..IMP:id5 -0.0207 0.0157 -1.3162 0.1881 -0.0515 0.0101
CF1_Women..IMP:id6 0.0533 0.0308 1.7332 0.0831 -0.0070 0.1136 .
CF1_Women..IMP:id7 0.0690 0.0313 2.2031 0.0276 0.0076 0.1304 *
CF1_Women..IMP:id8 -0.0718 0.0214 -3.3572 0.0008 -0.1137 -0.0299 ***
CF1_Women..IMP:id9 -0.0095 0.0162 -0.5858 0.5580 -0.0413 0.0223
CF1_Women..IMP:id10 -0.0092 0.0156 -0.5907 0.5547 -0.0399 0.0214
CF1_Women..IMP:id11 0.0004 0.0217 0.0167 0.9867 -0.0422 0.0430
CF1_Women..IMP:id12 0.0112 0.0290 0.3852 0.7001 -0.0456 0.0679
CF1_Women..IMP:id13 0.0042 0.0496 0.0856 0.9318 -0.0929 0.1014
CF1_Women..IMP:id14 -0.0108 0.0281 -0.3837 0.7012 -0.0658 0.0443
CF1_Women..IMP:id15 -0.0207 0.0186 -1.1133 0.2656 -0.0570 0.0157
CF1_Women..IMP:id16 -0.0834 0.0777 -1.0733 0.2831 -0.2356 0.0689
CF1_Women..IMP:id17 -0.0252 0.0239 -1.0543 0.2918 -0.0721 0.0217
CF1_Women..IMP:id18 0.0186 0.0274 0.6814 0.4956 -0.0350 0.0723
CF1_Women..IMP:id19 -0.0203 0.0637 -0.3189 0.7498 -0.1452 0.1046
---
Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
>
> M0<-rma(logOR, logOR.var, mods= ~CF1_Women..IMP + id, method="ML", data=d)
> M1<-rma(logOR, logOR.var, mods= ~CF1_Women..IMP * id, method="ML", data=d, btt=c(21:38))
> anova(M0,M1)
df AIC BIC AICc logLik LRT pval QE tau^2 R^2
Full 39 515.2691 646.1760 533.4086 -218.6346 488.8555 0.1182
Reduced 21 520.4230 590.9113 525.2862 -239.2115 41.1539 0.0014 545.9074 0.1510 21.75%
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