Metaregressão
Juan Pablo Edwards
24/10/2014
dados## id prod ctrl_sev dis_pres b0 b1 b0.SE
## 1 2012_1 2642.3 42.500 h 2898.667 -7.585391 7.085634
## 2 2012_2 3135.0 36.250 h 3927.859 -24.477332 6.810604
## 3 2012_3 2492.7 41.250 h 3251.704 -16.110989 7.418998
## 4 2012_4 2957.8 30.625 h 3445.446 -4.364499 3.941473
## 5 2012_6 3744.0 27.000 l 4218.295 -9.249662 7.425488
## 6 2012_7 2992.5 44.750 h 3610.327 -7.228888 2.185961
## 7 2012_8 3400.0 47.750 h 3848.940 -12.178492 6.589507
## 8 2013_1 3493.4 40.000 h 3882.550 -4.588254 4.537889
## 9 2013_10 2550.1 45.675 h 3330.020 -36.060893 5.574162
## 10 2013_12 1208.4 29.500 l 1969.408 -13.027761 6.169600
## 11 2013_3 2499.7 26.500 l 3751.011 -23.093483 2.966246
## 12 2013_5 2833.9 22.250 l 4249.448 -35.079457 5.220999
## 13 2013_8 2728.7 48.500 h 3617.205 -17.593282 2.909147
## 14 2013_9 1284.3 41.125 h 1603.815 -15.716396 5.834118
## 15 2014_1 3633.9 28.125 l 3883.763 -10.744523 3.000276
## 16 2014_10 1770.0 29.350 l 4118.405 -60.802565 8.080833
## 17 2014_11 2151.7 51.250 h 2740.186 -34.516343 11.252236
## 18 2014_12 1486.0 18.500 l 2428.840 -49.601622 9.013081
## 19 2014_14 2084.0 33.250 h 3670.118 -45.800428 11.329478
## 20 2014_15 3034.9 12.475 l 4281.515 -80.603137 25.597768
## 21 2014_16 2205.8 20.100 l 3005.912 -28.396429 5.929205
## 22 2014_2 3345.1 41.050 h 3541.663 -5.668744 2.877861
## 23 2014_5 3102.9 11.000 l 3920.497 -52.275505 14.465461
## 24 2014_6 3819.4 18.000 l 3828.731 -6.238477 4.140976
## 25 2014_8 3790.0 24.750 l 4559.966 -55.480689 11.510726
## 26 2014_9 3750.0 12.375 l 4584.237 -49.166246 7.341558
## b1.SE
## 1 252.10767
## 2 201.26204
## 3 227.57640
## 4 86.87648
## 5 129.15512
## 6 68.90476
## 7 223.06366
## 8 123.84894
## 9 57.07209
## 10 72.30311
## 11 100.48090
## 12 149.42064
## 13 76.17176
## 14 81.44291
## 15 46.69593
## 16 269.20942
## 17 90.36883
## 18 92.18541
## 19 184.75890
## 20 143.58791
## 21 92.13784
## 22 93.80435
## 23 156.75904
## 24 75.97199
## 25 84.68645
## 26 74.38404Ajuste dos modelos aleatorios
# Coeficiente angular "b1"
b1.rand = rma.uni(b1, sei = b1.SE, method="ML",data= dados)
b1.rand ##
## Random-Effects Model (k = 26; tau^2 estimator: ML)
##
## tau^2 (estimated amount of total heterogeneity): 0 (SE = 1796.5955)
## tau (square root of estimated tau^2 value): 0
## I^2 (total heterogeneity / total variability): 0.00%
## H^2 (total variability / sampling variability): 1.00
##
## Test for Heterogeneity:
## Q(df = 25) = 0.9855, p-val = 1.0000
##
## Model Results:
##
## estimate se zval pval ci.lb ci.ub
## -23.4449 18.0504 -1.2989 0.1940 -58.8229 11.9332
##
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1forest (b1.rand, slab = dados$id)
# Intercepto "b0"
b0.rand = rma.uni(b0, sei = b0.SE, method="ML",data= dados)
b0.rand##
## Random-Effects Model (k = 26; tau^2 estimator: ML)
##
## tau^2 (estimated amount of total heterogeneity): 526163.7940 (SE = 145952.4837)
## tau (square root of estimated tau^2 value): 725.3715
## I^2 (total heterogeneity / total variability): 100.00%
## H^2 (total variability / sampling variability): 22636.30
##
## Test for Heterogeneity:
## Q(df = 25) = 310552.4724, p-val < .0001
##
## Model Results:
##
## estimate se zval pval ci.lb ci.ub
## 3544.9057 142.2672 24.9172 <.0001 3266.0671 3823.7444 ***
##
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1forest (b0.rand, slab = dados$id)
Incluindo uma variavel moderadora qualitativa: pressão de doença (severidade no tratamento controle, low=10-30% ou high >30%)
# Intercepto
b0.dis_press = rma.uni(b0, sei = b0.SE, mods = ~ factor(dis_pres), method = "ML", data = dados) ; b0.dis_press##
## Mixed-Effects Model (k = 26; tau^2 estimator: ML)
##
## tau^2 (estimated amount of residual heterogeneity): 482551.2729 (SE = 133856.5455)
## tau (square root of estimated tau^2 value): 694.6591
## I^2 (residual heterogeneity / unaccounted variability): 99.99%
## H^2 (unaccounted variability / sampling variability): 19846.09
## R^2 (amount of heterogeneity accounted for): 8.29%
##
## Test for Residual Heterogeneity:
## QE(df = 24) = 294354.4848, p-val < .0001
##
## Test of Moderators (coefficient(s) 2):
## QM(df = 1) = 2.3502, p-val = 0.1253
##
## Model Results:
##
## se zval pval ci.lb
## intrcpt 3336.0465 192.6726 17.3146 <.0001 2958.4152
## factor(dis_pres)l 417.7388 272.4890 1.5330 0.1253 -116.3298
## ci.ub
## intrcpt 3713.6778 ***
## factor(dis_pres)l 951.8074
##
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1# Coeficiente angular
b1.dis_press = rma.uni(b1, sei = b1.SE, mods = ~ factor(dis_pres), method = "ML", data = dados); b1.dis_press##
## Mixed-Effects Model (k = 26; tau^2 estimator: ML)
##
## tau^2 (estimated amount of residual heterogeneity): 0 (SE = 1796.5955)
## tau (square root of estimated tau^2 value): 0
## I^2 (residual heterogeneity / unaccounted variability): 0.00%
## H^2 (unaccounted variability / sampling variability): 1.00
## R^2 (amount of heterogeneity accounted for): NA%
##
## Test for Residual Heterogeneity:
## QE(df = 24) = 0.9369, p-val = 1.0000
##
## Test of Moderators (coefficient(s) 2):
## QM(df = 1) = 0.0486, p-val = 0.8256
##
## Model Results:
##
## se zval pval ci.lb ci.ub
## intrcpt -19.0544 26.8836 -0.7088 0.4785 -71.7452 33.6364
## factor(dis_pres)l -7.9946 36.2767 -0.2204 0.8256 -79.0955 63.1064
##
## intrcpt
## factor(dis_pres)l
##
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1Incluindo a variavel moderadora pressao de doença como qualitativa: pressão de doença (severidade no tratamento controle)
b0.ctrl_sev = rma.uni(b0, sei = b0.SE, mods = ~ ctrl_sev, method = "ML", data = dados); b0.ctrl_sev ##
## Mixed-Effects Model (k = 26; tau^2 estimator: ML)
##
## tau^2 (estimated amount of residual heterogeneity): 463589.0701 (SE = 128597.3762)
## tau (square root of estimated tau^2 value): 680.8738
## I^2 (residual heterogeneity / unaccounted variability): 99.99%
## H^2 (unaccounted variability / sampling variability): 19139.34
## R^2 (amount of heterogeneity accounted for): 11.89%
##
## Test for Residual Heterogeneity:
## QE(df = 24) = 295796.2067, p-val < .0001
##
## Test of Moderators (coefficient(s) 2):
## QM(df = 1) = 3.5101, p-val = 0.0610
##
## Model Results:
##
## se zval pval ci.lb ci.ub
## intrcpt 4214.7707 381.6675 11.0430 <.0001 3466.7162 4962.8252 ***
## ctrl_sev -21.1384 11.2826 -1.8735 0.0610 -43.2519 0.9751 .
##
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1b1.ctrl_sev = rma.uni(b1, sei = b1.SE, mods = ~ ctrl_sev, method = "ML", data = dados); b0.ctrl_sev##
## Mixed-Effects Model (k = 26; tau^2 estimator: ML)
##
## tau^2 (estimated amount of residual heterogeneity): 463589.0701 (SE = 128597.3762)
## tau (square root of estimated tau^2 value): 680.8738
## I^2 (residual heterogeneity / unaccounted variability): 99.99%
## H^2 (unaccounted variability / sampling variability): 19139.34
## R^2 (amount of heterogeneity accounted for): 11.89%
##
## Test for Residual Heterogeneity:
## QE(df = 24) = 295796.2067, p-val < .0001
##
## Test of Moderators (coefficient(s) 2):
## QM(df = 1) = 3.5101, p-val = 0.0610
##
## Model Results:
##
## se zval pval ci.lb ci.ub
## intrcpt 4214.7707 381.6675 11.0430 <.0001 3466.7162 4962.8252 ***
## ctrl_sev -21.1384 11.2826 -1.8735 0.0610 -43.2519 0.9751 .
##
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1