Results from 26 trials examining the effectiveness of glucose-lowering agents in patients with type 2 diabetes

dat.senn2013

Format

The data frame contains the following columns:

studycharacter(first) author and year of study
ninumericsample size of the study arm
treatmentcharactertreatment given
commentcharacterwhether figures given are based on raw values at outcome or on change from baseline
minumericraw mean or mean change
sdinumericstandard deviation

Details

The dataset includes the results from 26 randomized controlled trials examining the effectiveness of adding various oral glucose-lowering agents to a baseline sulfonylurea therapy in patients with type 2 diabetes. The outcome measured in the studies was either the mean HbA1c level at follow-up or the mean change in HbA1c level from baseline to follow-up. A total of 10 different treatment types were examined in these studies: acarbose, benfluorex, metformin, miglitol, pioglitazone, placebo, rosiglitazone, sitagliptin, sulfonylurea alone, and vildagliptin. One study included three treatment arms (Willms, 1999), while the rest of the studies included two treatment arms (hence, the dataset includes the results from 53 treatment arms).

The data can be used for a network meta-analysis, either using an arm-based or a contrast-based model. See ‘Examples’ below.

Source

Senn, S., Gavini, F., Magrez, D., & Scheen, A. (2013). Issues in performing a network meta-analysis. Statistical Methods in Medical Research, 22(2), 169–189. https://doi.org/10.1177/0962280211432220

References

Law, M., Jackson, D., Turner, R., Rhodes, K., & Viechtbauer, W. (2016). Two new methods to fit models for network meta-analysis with random inconsistency effects. BMC Medical Research Methodology, 16, 87. https://doi.org/10.1186/s12874-016-0184-5

Rücker, G., & Schwarzer, G. (2015). Ranking treatments in frequentist network meta-analysis works without resampling methods. BMC Medical Research Methodology, 15, 58. https://doi.org/10.1186/s12874-015-0060-8

Examples

### copy data into 'dat' and examine data
dat <- dat.senn2013
dat
#>                    study  ni     treatment comment    mi   sdi
#> 1       De Fronzo (1995) 213     metformin  change -1.70 1.459
#> 2       De Fronzo (1995) 209       placebo  change  0.20 1.446
#> 3           Lewin (2007) 431     metformin  change -0.74 1.106
#> 4           Lewin (2007) 144       placebo  change  0.08 1.004
#> 5          Willms (1999)  29     metformin  change -2.50 0.862
#> 6          Willms (1999)  31      acarbose  change -2.30 1.782
#> 7          Willms (1999)  29       placebo  change -1.30 1.831
#> 8        Davidson (2007) 117 rosiglitazone  change -1.20 1.097
#> 9        Davidson (2007) 116       placebo  change  0.14 1.093
#> 10  Wolffenbuttel (1999) 183 rosiglitazone  change -0.90 1.100
#> 11  Wolffenbuttel (1999) 192       placebo  change  0.20 1.110
#> 12         Kipnes (2001) 182  pioglitazone  change -1.20 1.369
#> 13         Kipnes (2001) 181       placebo  change  0.10 1.024
#> 14        Kerenyi (2004) 160 rosiglitazone  change -0.91 0.990
#> 15        Kerenyi (2004) 154       placebo  change -0.14 0.920
#> 16       Hanefeld (2004) 319  pioglitazone     raw  7.61 1.072
#> 17       Hanefeld (2004) 320     metformin     raw  7.45 1.073
#> 18         Derosa (2004)  45  pioglitazone     raw  6.80 0.800
#> 19         Derosa (2004)  42 rosiglitazone     raw  6.70 0.900
#> 20          Baksi (2004) 218 rosiglitazone  change -1.20 1.112
#> 21          Baksi (2004) 233       placebo  change  0.10 1.036
#> 22     Rosenstock (2008)  59 rosiglitazone  change -1.17 1.229
#> 23     Rosenstock (2008)  57       placebo  change -0.08 1.208
#> 24            Zhu (2003) 210 rosiglitazone  change -1.90 1.470
#> 25            Zhu (2003) 105       placebo  change -0.40 1.300
#> 26           Yang (2003) 102 rosiglitazone  change -1.09 1.650
#> 27           Yang (2003)  96     metformin  change -0.95 1.500
#> 28 Vongthavaravat (2002) 164 rosiglitazone  change -1.10 1.559
#> 29 Vongthavaravat (2002) 170  sulfonylurea  change  0.10 0.992
#> 30          Oyama (2008)  41      acarbose  change -0.70 0.800
#> 31          Oyama (2008)  43  sulfonylurea  change -0.30 0.600
#> 32          Costa (1997)  36      acarbose  change -1.10 0.360
#> 33          Costa (1997)  29       placebo  change -0.30 0.700
#> 34      Hermansen (2007) 106   sitagliptin  change -0.30 0.940
#> 35      Hermansen (2007) 106       placebo  change  0.27 0.940
#> 36         Garber (2008) 132  vildagliptin  change -0.63 1.034
#> 37         Garber (2008) 144       placebo  change  0.07 1.080
#> 38           Alex (1998) 291     metformin  change  0.13 1.428
#> 39           Alex (1998) 300  sulfonylurea  change  0.50 1.450
#> 40       Johnston (1994)  68      miglitol  change -0.41 1.072
#> 41       Johnston (1994)  63       placebo  change  0.33 1.032
#> 42      Johnston (1998a)  91      miglitol  change -0.43 0.954
#> 43      Johnston (1998a)  43       placebo  change  0.98 1.311
#> 44            Kim (2007)  57 rosiglitazone  change -1.10 1.341
#> 45            Kim (2007)  56     metformin  change -1.10 1.139
#> 46      Johnston (1998b)  49      miglitol  change -0.12 1.400
#> 47      Johnston (1998b)  34       placebo  change  0.56 1.166
#> 48 Gonzalez-Ortiz (2004)  34     metformin  change -1.30 1.861
#> 49 Gonzalez-Ortiz (2004)  37       placebo  change -0.90 1.803
#> 50         Stucci (1996)  28    benfluorex     raw  8.03 1.290
#> 51         Stucci (1996)  30       placebo     raw  8.26 1.350
#> 52         Moulin (2006) 161    benfluorex  change -0.82 1.028
#> 53         Moulin (2006) 156       placebo  change  0.19 1.374

# \dontrun{

### load metafor package
library(metafor)

### create network graph ('igraph' package must be installed)
library(igraph, warn.conflicts=FALSE)
pairs <- data.frame(do.call(rbind,
   sapply(split(dat$treatment, dat$study), function(x) t(combn(x,2)))), stringsAsFactors=FALSE)
pairs$X1 <- factor(pairs$X1, levels=sort(unique(dat$treatment)))
pairs$X2 <- factor(pairs$X2, levels=sort(unique(dat$treatment)))
tab <- table(pairs[,1], pairs[,2])
tab # adjacency matrix
#>                
#>                 acarbose benfluorex metformin miglitol pioglitazone placebo rosiglitazone sitagliptin
#>   acarbose             0          0         0        0            0       2             0           0
#>   benfluorex           0          0         0        0            0       2             0           0
#>   metformin            1          0         0        0            0       4             0           0
#>   miglitol             0          0         0        0            0       3             0           0
#>   pioglitazone         0          0         1        0            0       1             1           0
#>   placebo              0          0         0        0            0       0             0           0
#>   rosiglitazone        0          0         2        0            0       6             0           0
#>   sitagliptin          0          0         0        0            0       1             0           0
#>   sulfonylurea         0          0         0        0            0       0             0           0
#>   vildagliptin         0          0         0        0            0       1             0           0
#>                
#>                 sulfonylurea vildagliptin
#>   acarbose                 1            0
#>   benfluorex               0            0
#>   metformin                1            0
#>   miglitol                 0            0
#>   pioglitazone             0            0
#>   placebo                  0            0
#>   rosiglitazone            1            0
#>   sitagliptin              0            0
#>   sulfonylurea             0            0
#>   vildagliptin             0            0
g <- graph_from_adjacency_matrix(tab, mode = "plus", weighted=TRUE, diag=FALSE)
plot(g, edge.curved=FALSE, edge.width=E(g)$weight, layout=layout_as_star(g, center="placebo"),
     vertex.size=45, vertex.color="lightgray", vertex.label.color="black", vertex.label.font=2)


### table of studies versus treatments examined
print(addmargins(table(dat$study, dat$treatment)), zero.print="")
#>                        
#>                         acarbose benfluorex metformin miglitol pioglitazone placebo rosiglitazone
#>   Alex (1998)                                       1                                            
#>   Baksi (2004)                                                                    1             1
#>   Costa (1997)                 1                                                  1              
#>   Davidson (2007)                                                                 1             1
#>   De Fronzo (1995)                                  1                             1              
#>   Derosa (2004)                                                           1                     1
#>   Garber (2008)                                                                   1              
#>   Gonzalez-Ortiz (2004)                             1                             1              
#>   Hanefeld (2004)                                   1                     1                      
#>   Hermansen (2007)                                                                1              
#>   Johnston (1994)                                            1                    1              
#>   Johnston (1998a)                                           1                    1              
#>   Johnston (1998b)                                           1                    1              
#>   Kerenyi (2004)                                                                  1             1
#>   Kim (2007)                                        1                                           1
#>   Kipnes (2001)                                                           1       1              
#>   Lewin (2007)                                      1                             1              
#>   Moulin (2006)                           1                                       1              
#>   Oyama (2008)                 1                                                                 
#>   Rosenstock (2008)                                                               1             1
#>   Stucci (1996)                           1                                       1              
#>   Vongthavaravat (2002)                                                                         1
#>   Willms (1999)                1                    1                             1              
#>   Wolffenbuttel (1999)                                                            1             1
#>   Yang (2003)                                       1                                           1
#>   Zhu (2003)                                                                      1             1
#>   Sum                          3          2         8        3            3      19            10
#>                        
#>                         sitagliptin sulfonylurea vildagliptin Sum
#>   Alex (1998)                                  1                2
#>   Baksi (2004)                                                  2
#>   Costa (1997)                                                  2
#>   Davidson (2007)                                               2
#>   De Fronzo (1995)                                              2
#>   Derosa (2004)                                                 2
#>   Garber (2008)                                             1   2
#>   Gonzalez-Ortiz (2004)                                         2
#>   Hanefeld (2004)                                               2
#>   Hermansen (2007)                1                             2
#>   Johnston (1994)                                               2
#>   Johnston (1998a)                                              2
#>   Johnston (1998b)                                              2
#>   Kerenyi (2004)                                                2
#>   Kim (2007)                                                    2
#>   Kipnes (2001)                                                 2
#>   Lewin (2007)                                                  2
#>   Moulin (2006)                                                 2
#>   Oyama (2008)                                 1                2
#>   Rosenstock (2008)                                             2
#>   Stucci (1996)                                                 2
#>   Vongthavaravat (2002)                        1                2
#>   Willms (1999)                                                 3
#>   Wolffenbuttel (1999)                                          2
#>   Yang (2003)                                                   2
#>   Zhu (2003)                                                    2
#>   Sum                             1            3            1  53

### table of frequencies with which treatment pairs were studied
print(as.table(crossprod(table(dat$study, dat$treatment))), zero.print="")
#>                
#>                 acarbose benfluorex metformin miglitol pioglitazone placebo rosiglitazone sitagliptin
#>   acarbose             3                    1                             2                          
#>   benfluorex                      2                                       2                          
#>   metformin            1                    8                     1       4             2            
#>   miglitol                                           3                    3                          
#>   pioglitazone                              1                     3       1             1            
#>   placebo              2          2         4        3            1      19             6           1
#>   rosiglitazone                             2                     1       6            10            
#>   sitagliptin                                                             1                         1
#>   sulfonylurea         1                    1                                           1            
#>   vildagliptin                                                            1                          
#>                
#>                 sulfonylurea vildagliptin
#>   acarbose                 1             
#>   benfluorex                             
#>   metformin                1             
#>   miglitol                               
#>   pioglitazone                           
#>   placebo                               1
#>   rosiglitazone            1             
#>   sitagliptin                            
#>   sulfonylurea             3             
#>   vildagliptin                          1

### add means and sampling variances of the means to the dataset
dat <- escalc(measure="MN", mi=mi, sdi=sdi, ni=ni, data=dat)

### turn treatment variable into factor and set reference level
dat$treatment <- relevel(factor(dat$treatment), ref="placebo")

### add a space before each level (this makes the output a bit more legible)
levels(dat$treatment) <- paste0(" ", levels(dat$treatment))

### network meta-analysis using an arm-based fixed-effects model with fixed study effects
res.fe <- rma.mv(yi, vi, mods = ~ study + treatment - 1, data=dat, slab=paste0(study, treatment))
res.fe
#> 
#> Multivariate Meta-Analysis Model (k = 53; method: REML)
#> 
#> Variance Components: none
#> 
#> Test for Residual Heterogeneity:
#> QE(df = 18) = 96.9841, p-val < .0001
#> 
#> Test of Moderators (coefficients 1:35):
#> QM(df = 35) = 42156.8401, p-val < .0001
#> 
#> Model Results:
#> 
#>                             estimate      se      zval    pval    ci.lb    ci.ub     ​ 
#> studyAlex (1998)              1.0917  0.0866   12.6029  <.0001   0.9219   1.2615  *** 
#> studyBaksi (2004)             0.0560  0.0548    1.0230  0.3063  -0.0513   0.1633      
#> studyCosta (1997)            -0.2775  0.1047   -2.6496  0.0081  -0.4827  -0.0722   ** 
#> studyDavidson (2007)          0.0709  0.0756    0.9377  0.3484  -0.0773   0.2191      
#> studyDe Fronzo (1995)        -0.1932  0.0767   -2.5176  0.0118  -0.3436  -0.0428    * 
#> studyDerosa (2004)            7.8814  0.1041   75.7432  <.0001   7.6774   8.0853  *** 
#> studyGarber (2008)            0.0700  0.0900    0.7778  0.4367  -0.1064   0.2464      
#> studyGonzalez-Ortiz (2004)   -0.5693  0.2189   -2.6004  0.0093  -0.9984  -0.1402   ** 
#> studyHanefeld (2004)          8.6201  0.0724  119.1426  <.0001   8.4783   8.7619  *** 
#> studyHermansen (2007)         0.2700  0.0913    2.9573  0.0031   0.0911   0.4489   ** 
#> studyJohnston (1994)          0.4319  0.1117    3.8667  0.0001   0.2130   0.6509  *** 
#> studyJohnston (1998a)         0.6071  0.1353    4.4877  <.0001   0.3420   0.8723  *** 
#> studyJohnston (1998b)         0.6919  0.1550    4.4642  <.0001   0.3881   0.9957  *** 
#> studyKerenyi (2004)           0.0642  0.0584    1.1008  0.2710  -0.0501   0.1786      
#> studyKim (2007)               0.0512  0.1235    0.4147  0.6783  -0.1908   0.2933      
#> studyKipnes (2001)            0.0158  0.0667    0.2375  0.8123  -0.1149   0.1466      
#> studyLewin (2007)             0.2892  0.0618    4.6804  <.0001   0.1681   0.4103  *** 
#> studyMoulin (2006)            0.1220  0.1051    1.1609  0.2457  -0.0840   0.3280      
#> studyOyama (2008)             0.1352  0.1100    1.2290  0.2191  -0.0804   0.3508      
#> studyRosenstock (2008)       -0.0241  0.1156   -0.2082  0.8351  -0.2507   0.2025      
#> studyStucci (1996)            8.6013  0.1849   46.5307  <.0001   8.2390   8.9636  *** 
#> studyVongthavaravat (2002)    0.4165  0.0954    4.3644  <.0001   0.2295   0.6035  *** 
#> studyWillms (1999)           -1.3878  0.1402   -9.9014  <.0001  -1.6625  -1.1131  *** 
#> studyWolffenbuttel (1999)     0.2502  0.0617    4.0542  <.0001   0.1292   0.3711  *** 
#> studyYang (2003)              0.1396  0.1196    1.1680  0.2428  -0.0947   0.3740      
#> studyZhu (2003)              -0.5819  0.0844   -6.8947  <.0001  -0.7473  -0.4165  *** 
#> treatment acarbose           -0.8273  0.1085   -7.6252  <.0001  -1.0400  -0.6147  *** 
#> treatment benfluorex         -0.9051  0.1271   -7.1211  <.0001  -1.1543  -0.6560  *** 
#> treatment metformin          -1.1140  0.0596  -18.6892  <.0001  -1.2309  -0.9972  *** 
#> treatment miglitol           -0.9438  0.1269   -7.4375  <.0001  -1.1926  -0.6951  *** 
#> treatment pioglitazone       -1.0663  0.0758  -14.0590  <.0001  -1.2149  -0.9176  *** 
#> treatment rosiglitazone      -1.2019  0.0477  -25.2158  <.0001  -1.2953  -1.1084  *** 
#> treatment sitagliptin        -0.5700  0.1291   -4.4145  <.0001  -0.8231  -0.3169  *** 
#> treatment sulfonylurea       -0.4394  0.0915   -4.8041  <.0001  -0.6187  -0.2601  *** 
#> treatment vildagliptin       -0.7000  0.1273   -5.4998  <.0001  -0.9495  -0.4505  *** 
#> 
#> ---
#> Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
#> 

### test if treatment factor as a whole is significant
anova(res.fe, btt="treatment")
#> 
#> Test of Moderators (coefficients 27:35):
#> QM(df = 9) = 1060.3371, p-val < .0001
#> 

### forest plot of the contrast estimates (treatments versus placebos)
forest(tail(coef(res.fe), 9), tail(diag(vcov(res.fe)), 9), slab=levels(dat$treatment)[-1],
       xlim=c(-2.5, 2.0), alim=c(-1.5, 0.5), psize=1, xlab="Estimate", header="Treatment")


### weight matrix for the estimation of the fixed effects (leaving out the study effects)
w <- t(tail(vcov(res.fe) %*% t(model.matrix(res.fe)) %*% weights(res.fe, type="matrix"), 9))
rownames(w) <- res.fe$slab

### create shade plot for the diabetes network with placebo as the reference treatment
### negative values in blue shades, positive values in red shades
cols <- colorRampPalette(c("blue", "gray95", "red"))(9)
heatmap(w, Rowv=NA, Colv=NA, scale="none", margins=c(6,11), col=cols,
        cexRow=.7, cexCol=1, labCol=levels(dat$treatment)[-1])


### network meta-analysis using an arm-based random-effects model with fixed study effects
### by setting rho=1/2, tau^2 reflects the amount of heterogeneity for all treatment comparisons
res.re <- rma.mv(yi, vi, mods = ~ study + treatment - 1, random = ~ treatment | study, rho=1/2,
                 data=dat, slab=paste0(study, treatment))
res.re
#> 
#> Multivariate Meta-Analysis Model (k = 53; method: REML)
#> 
#> Variance Components:
#> 
#> outer factor: study     (nlvls = 26)
#> inner factor: treatment (nlvls = 10)
#> 
#>             estim    sqrt  fixed 
#> tau^2      0.0999  0.3161     no 
#> rho        0.5000            yes 
#> 
#> Test for Residual Heterogeneity:
#> QE(df = 18) = 96.9841, p-val < .0001
#> 
#> Test of Moderators (coefficients 1:35):
#> QM(df = 35) = 2237.5843, p-val < .0001
#> 
#> Model Results:
#> 
#>                             estimate      se     zval    pval    ci.lb    ci.ub     ​ 
#> studyAlex (1998)              1.0880  0.3221   3.3777  0.0007   0.4567   1.7193  *** 
#> studyBaksi (2004)             0.0672  0.2850   0.2357  0.8136  -0.4915   0.6258      
#> studyCosta (1997)            -0.2770  0.3118  -0.8885  0.3743  -0.8881   0.3341      
#> studyDavidson (2007)          0.0869  0.2896   0.2999  0.7643  -0.4808   0.6546      
#> studyDe Fronzo (1995)        -0.1858  0.2924  -0.6355  0.5251  -0.7590   0.3873      
#> studyDerosa (2004)            7.9315  0.3197  24.8072  <.0001   7.3048   8.5581  *** 
#> studyGarber (2008)            0.0700  0.3287   0.2130  0.8313  -0.5742   0.7142      
#> studyGonzalez-Ortiz (2004)   -0.5534  0.3567  -1.5514  0.1208  -1.2526   0.1458      
#> studyHanefeld (2004)          8.6589  0.3139  27.5871  <.0001   8.0437   9.2741  *** 
#> studyHermansen (2007)         0.2700  0.3290   0.8206  0.4119  -0.3749   0.9149      
#> studyJohnston (1994)          0.4349  0.3100   1.4033  0.1605  -0.1726   1.0424      
#> studyJohnston (1998a)         0.7039  0.3228   2.1808  0.0292   0.0713   1.3366    * 
#> studyJohnston (1998b)         0.6949  0.3280   2.1184  0.0341   0.0520   1.3379    * 
#> studyKerenyi (2004)           0.0906  0.2857   0.3170  0.7512  -0.4693   0.6505      
#> studyKim (2007)               0.0782  0.3180   0.2460  0.8057  -0.5450   0.7014      
#> studyKipnes (2001)            0.0180  0.2988   0.0603  0.9519  -0.5676   0.6037      
#> studyLewin (2007)             0.2400  0.2887   0.8314  0.4058  -0.3259   0.8060      
#> studyMoulin (2006)            0.0471  0.3172   0.1484  0.8820  -0.5747   0.6689      
#> studyOyama (2008)             0.1287  0.3461   0.3720  0.7099  -0.5496   0.8071      
#> studyRosenstock (2008)       -0.0081  0.3026  -0.0269  0.9786  -0.6012   0.5849      
#> studyStucci (1996)            8.5150  0.3528  24.1346  <.0001   7.8235   9.2065  *** 
#> studyVongthavaravat (2002)    0.3400  0.3210   1.0594  0.2894  -0.2890   0.9691      
#> studyWillms (1999)           -1.3770  0.3168  -4.3471  <.0001  -1.9978  -0.7561  *** 
#> studyWolffenbuttel (1999)     0.2668  0.2863   0.9316  0.3515  -0.2945   0.8280      
#> studyYang (2003)              0.1614  0.3161   0.5108  0.6095  -0.4581   0.7810      
#> studyZhu (2003)              -0.5392  0.2926  -1.8427  0.0654  -1.1128   0.0343    . 
#> treatment acarbose           -0.8414  0.2384  -3.5288  0.0004  -1.3087  -0.3741  *** 
#> treatment benfluorex         -0.7369  0.2776  -2.6545  0.0079  -1.2810  -0.1928   ** 
#> treatment metformin          -1.1284  0.1494  -7.5528  <.0001  -1.4212  -0.8356  *** 
#> treatment miglitol           -0.9499  0.2253  -4.2170  <.0001  -1.3914  -0.5084  *** 
#> treatment pioglitazone       -1.1294  0.2119  -5.3295  <.0001  -1.5448  -0.7141  *** 
#> treatment rosiglitazone      -1.2337  0.1235  -9.9933  <.0001  -1.4757  -0.9918  *** 
#> treatment sitagliptin        -0.5700  0.3414  -1.6694  0.0950  -1.2392   0.0992    . 
#> treatment sulfonylurea       -0.4175  0.2326  -1.7950  0.0727  -0.8734   0.0384    . 
#> treatment vildagliptin       -0.7000  0.3408  -2.0543  0.0400  -1.3679  -0.0321    * 
#> 
#> ---
#> Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
#> 

### test if treatment factor as a whole is significant
anova(res.re, btt="treatment")
#> 
#> Test of Moderators (coefficients 27:35):
#> QM(df = 9) = 167.9616, p-val < .0001
#> 

### forest plot of the contrast estimates (treatments versus placebos)
forest(tail(coef(res.re), 9), tail(diag(vcov(res.re)), 9), slab=levels(dat$treatment)[-1],
       xlim=c(-3.0, 2.5), alim=c(-1.5, 0.5), psize=1, xlab="Estimate", header="Treatment")


### compute the contribution of each study to the overall Q-test value
qi <- sort(by((resid(res.fe) / sqrt(dat$vi))^2, dat$study, sum))

### check that the values add up
sum(qi)
#> [1] 96.98407
res.fe$QE
#> [1] 96.98407

### plot the values
s <- length(qi)
par(mar=c(5,10,2,1))
plot(qi, 1:s, pch=19, xaxt="n", yaxt="n", xlim=c(0,40), xlab="Chi-Square Contribution", ylab="")
axis(side=1)
axis(side=2, at=1:s, labels=names(qi), las=1, tcl=0)
segments(rep(0,s), 1:s, qi, 1:s)


############################################################################

### restructure dataset to a contrast-based format
dat <- dat.senn2013[c(1,4:2,5:6)] # reorder variables first
dat <- to.wide(dat, study="study", grp="treatment", ref="placebo", grpvars=4:6)
dat
#>                    study comment   treatment.1 ni.1  mi.1 sdi.1   treatment.2 ni.2  mi.2 sdi.2 id
#> 1            Alex (1998)  change     metformin  291  0.13 1.428  sulfonylurea  300  0.50 1.450  1
#> 2           Baksi (2004)  change rosiglitazone  218 -1.20 1.112       placebo  233  0.10 1.036  2
#> 3           Costa (1997)  change      acarbose   36 -1.10 0.360       placebo   29 -0.30 0.700  3
#> 4        Davidson (2007)  change rosiglitazone  117 -1.20 1.097       placebo  116  0.14 1.093  4
#> 5       De Fronzo (1995)  change     metformin  213 -1.70 1.459       placebo  209  0.20 1.446  5
#> 6          Derosa (2004)     raw  pioglitazone   45  6.80 0.800 rosiglitazone   42  6.70 0.900  6
#> 7          Garber (2008)  change  vildagliptin  132 -0.63 1.034       placebo  144  0.07 1.080  7
#> 8  Gonzalez-Ortiz (2004)  change     metformin   34 -1.30 1.861       placebo   37 -0.90 1.803  8
#> 9        Hanefeld (2004)     raw     metformin  320  7.45 1.073  pioglitazone  319  7.61 1.072  9
#> 10      Hermansen (2007)  change   sitagliptin  106 -0.30 0.940       placebo  106  0.27 0.940 10
#> 11       Johnston (1994)  change      miglitol   68 -0.41 1.072       placebo   63  0.33 1.032 11
#> 12      Johnston (1998a)  change      miglitol   91 -0.43 0.954       placebo   43  0.98 1.311 12
#> 13      Johnston (1998b)  change      miglitol   49 -0.12 1.400       placebo   34  0.56 1.166 13
#> 14        Kerenyi (2004)  change rosiglitazone  160 -0.91 0.990       placebo  154 -0.14 0.920 14
#> 15            Kim (2007)  change     metformin   56 -1.10 1.139 rosiglitazone   57 -1.10 1.341 15
#> 16         Kipnes (2001)  change  pioglitazone  182 -1.20 1.369       placebo  181  0.10 1.024 16
#> 17          Lewin (2007)  change     metformin  431 -0.74 1.106       placebo  144  0.08 1.004 17
#> 18         Moulin (2006)  change    benfluorex  161 -0.82 1.028       placebo  156  0.19 1.374 18
#> 19          Oyama (2008)  change      acarbose   41 -0.70 0.800  sulfonylurea   43 -0.30 0.600 19
#> 20     Rosenstock (2008)  change rosiglitazone   59 -1.17 1.229       placebo   57 -0.08 1.208 20
#> 21         Stucci (1996)     raw    benfluorex   28  8.03 1.290       placebo   30  8.26 1.350 21
#> 22 Vongthavaravat (2002)  change rosiglitazone  164 -1.10 1.559  sulfonylurea  170  0.10 0.992 22
#> 23         Willms (1999)  change      acarbose   31 -2.30 1.782       placebo   29 -1.30 1.831 23
#> 24         Willms (1999)  change     metformin   29 -2.50 0.862       placebo   29 -1.30 1.831 24
#> 25  Wolffenbuttel (1999)  change rosiglitazone  183 -0.90 1.100       placebo  192  0.20 1.110 25
#> 26           Yang (2003)  change     metformin   96 -0.95 1.500 rosiglitazone  102 -1.09 1.650 26
#> 27            Zhu (2003)  change rosiglitazone  210 -1.90 1.470       placebo  105 -0.40 1.300 27
#>     comp   design
#> 1  me-su    me-su
#> 2  ro-pl    ro-pl
#> 3  ac-pl    ac-pl
#> 4  ro-pl    ro-pl
#> 5  me-pl    me-pl
#> 6  pi-ro    pi-ro
#> 7  vi-pl    vi-pl
#> 8  me-pl    me-pl
#> 9  me-pi    me-pi
#> 10 si-pl    si-pl
#> 11 mi-pl    mi-pl
#> 12 mi-pl    mi-pl
#> 13 mi-pl    mi-pl
#> 14 ro-pl    ro-pl
#> 15 me-ro    me-ro
#> 16 pi-pl    pi-pl
#> 17 me-pl    me-pl
#> 18 be-pl    be-pl
#> 19 ac-su    ac-su
#> 20 ro-pl    ro-pl
#> 21 be-pl    be-pl
#> 22 ro-su    ro-su
#> 23 ac-pl ac-me-pl
#> 24 me-pl ac-me-pl
#> 25 ro-pl    ro-pl
#> 26 me-ro    me-ro
#> 27 ro-pl    ro-pl

### calculate mean difference and corresponding sampling variance for each treatment comparison
dat <- escalc(measure="MD", m1i=mi.1, sd1i=sdi.1, n1i=ni.1,
                            m2i=mi.2, sd2i=sdi.2, n2i=ni.2, data=dat)
dat
#> 
#>                    study comment   treatment.1 ni.1  mi.1 sdi.1   treatment.2 ni.2  mi.2 sdi.2 id 
#> 1            Alex (1998)  change     metformin  291  0.13 1.428  sulfonylurea  300  0.50 1.450  1 
#> 2           Baksi (2004)  change rosiglitazone  218 -1.20 1.112       placebo  233  0.10 1.036  2 
#> 3           Costa (1997)  change      acarbose   36 -1.10 0.360       placebo   29 -0.30 0.700  3 
#> 4        Davidson (2007)  change rosiglitazone  117 -1.20 1.097       placebo  116  0.14 1.093  4 
#> 5       De Fronzo (1995)  change     metformin  213 -1.70 1.459       placebo  209  0.20 1.446  5 
#> 6          Derosa (2004)     raw  pioglitazone   45  6.80 0.800 rosiglitazone   42  6.70 0.900  6 
#> 7          Garber (2008)  change  vildagliptin  132 -0.63 1.034       placebo  144  0.07 1.080  7 
#> 8  Gonzalez-Ortiz (2004)  change     metformin   34 -1.30 1.861       placebo   37 -0.90 1.803  8 
#> 9        Hanefeld (2004)     raw     metformin  320  7.45 1.073  pioglitazone  319  7.61 1.072  9 
#> 10      Hermansen (2007)  change   sitagliptin  106 -0.30 0.940       placebo  106  0.27 0.940 10 
#> 11       Johnston (1994)  change      miglitol   68 -0.41 1.072       placebo   63  0.33 1.032 11 
#> 12      Johnston (1998a)  change      miglitol   91 -0.43 0.954       placebo   43  0.98 1.311 12 
#> 13      Johnston (1998b)  change      miglitol   49 -0.12 1.400       placebo   34  0.56 1.166 13 
#> 14        Kerenyi (2004)  change rosiglitazone  160 -0.91 0.990       placebo  154 -0.14 0.920 14 
#> 15            Kim (2007)  change     metformin   56 -1.10 1.139 rosiglitazone   57 -1.10 1.341 15 
#> 16         Kipnes (2001)  change  pioglitazone  182 -1.20 1.369       placebo  181  0.10 1.024 16 
#> 17          Lewin (2007)  change     metformin  431 -0.74 1.106       placebo  144  0.08 1.004 17 
#> 18         Moulin (2006)  change    benfluorex  161 -0.82 1.028       placebo  156  0.19 1.374 18 
#> 19          Oyama (2008)  change      acarbose   41 -0.70 0.800  sulfonylurea   43 -0.30 0.600 19 
#> 20     Rosenstock (2008)  change rosiglitazone   59 -1.17 1.229       placebo   57 -0.08 1.208 20 
#> 21         Stucci (1996)     raw    benfluorex   28  8.03 1.290       placebo   30  8.26 1.350 21 
#> 22 Vongthavaravat (2002)  change rosiglitazone  164 -1.10 1.559  sulfonylurea  170  0.10 0.992 22 
#> 23         Willms (1999)  change      acarbose   31 -2.30 1.782       placebo   29 -1.30 1.831 23 
#> 24         Willms (1999)  change     metformin   29 -2.50 0.862       placebo   29 -1.30 1.831 24 
#> 25  Wolffenbuttel (1999)  change rosiglitazone  183 -0.90 1.100       placebo  192  0.20 1.110 25 
#> 26           Yang (2003)  change     metformin   96 -0.95 1.500 rosiglitazone  102 -1.09 1.650 26 
#> 27            Zhu (2003)  change rosiglitazone  210 -1.90 1.470       placebo  105 -0.40 1.300 27 
#>     comp   design      yi     vi 
#> 1  me-su    me-su -0.3700 0.0140 
#> 2  ro-pl    ro-pl -1.3000 0.0103 
#> 3  ac-pl    ac-pl -0.8000 0.0205 
#> 4  ro-pl    ro-pl -1.3400 0.0206 
#> 5  me-pl    me-pl -1.9000 0.0200 
#> 6  pi-ro    pi-ro  0.1000 0.0335 
#> 7  vi-pl    vi-pl -0.7000 0.0162 
#> 8  me-pl    me-pl -0.4000 0.1897 
#> 9  me-pi    me-pi -0.1600 0.0072 
#> 10 si-pl    si-pl -0.5700 0.0167 
#> 11 mi-pl    mi-pl -0.7400 0.0338 
#> 12 mi-pl    mi-pl -1.4100 0.0500 
#> 13 mi-pl    mi-pl -0.6800 0.0800 
#> 14 ro-pl    ro-pl -0.7700 0.0116 
#> 15 me-ro    me-ro  0.0000 0.0547 
#> 16 pi-pl    pi-pl -1.3000 0.0161 
#> 17 me-pl    me-pl -0.8200 0.0098 
#> 18 be-pl    be-pl -1.0100 0.0187 
#> 19 ac-su    ac-su -0.4000 0.0240 
#> 20 ro-pl    ro-pl -1.0900 0.0512 
#> 21 be-pl    be-pl -0.2300 0.1202 
#> 22 ro-su    ro-su -1.2000 0.0206 
#> 23 ac-pl ac-me-pl -1.0000 0.2180 
#> 24 me-pl ac-me-pl -1.2000 0.1412 
#> 25 ro-pl    ro-pl -1.1000 0.0130 
#> 26 me-ro    me-ro  0.1400 0.0501 
#> 27 ro-pl    ro-pl -1.5000 0.0264 
#> 

### calculate the variance-covariance matrix of the mean differences for the multitreatment studies
calc.v <- function(x) {
   v <- matrix(x$sdi.2[1]^2 / x$ni.2[1], nrow=nrow(x), ncol=nrow(x))
   diag(v) <- x$vi
   v
}
V <- bldiag(lapply(split(dat, dat$study), calc.v))

### add contrast matrix to dataset
dat <- contrmat(dat, grp1="treatment.1", grp2="treatment.2")
dat
#> 
#>                    study comment   treatment.1 ni.1  mi.1 sdi.1   treatment.2 ni.2  mi.2 sdi.2 id 
#> 1            Alex (1998)  change     metformin  291  0.13 1.428  sulfonylurea  300  0.50 1.450  1 
#> 2           Baksi (2004)  change rosiglitazone  218 -1.20 1.112       placebo  233  0.10 1.036  2 
#> 3           Costa (1997)  change      acarbose   36 -1.10 0.360       placebo   29 -0.30 0.700  3 
#> 4        Davidson (2007)  change rosiglitazone  117 -1.20 1.097       placebo  116  0.14 1.093  4 
#> 5       De Fronzo (1995)  change     metformin  213 -1.70 1.459       placebo  209  0.20 1.446  5 
#> 6          Derosa (2004)     raw  pioglitazone   45  6.80 0.800 rosiglitazone   42  6.70 0.900  6 
#> 7          Garber (2008)  change  vildagliptin  132 -0.63 1.034       placebo  144  0.07 1.080  7 
#> 8  Gonzalez-Ortiz (2004)  change     metformin   34 -1.30 1.861       placebo   37 -0.90 1.803  8 
#> 9        Hanefeld (2004)     raw     metformin  320  7.45 1.073  pioglitazone  319  7.61 1.072  9 
#> 10      Hermansen (2007)  change   sitagliptin  106 -0.30 0.940       placebo  106  0.27 0.940 10 
#> 11       Johnston (1994)  change      miglitol   68 -0.41 1.072       placebo   63  0.33 1.032 11 
#> 12      Johnston (1998a)  change      miglitol   91 -0.43 0.954       placebo   43  0.98 1.311 12 
#> 13      Johnston (1998b)  change      miglitol   49 -0.12 1.400       placebo   34  0.56 1.166 13 
#> 14        Kerenyi (2004)  change rosiglitazone  160 -0.91 0.990       placebo  154 -0.14 0.920 14 
#> 15            Kim (2007)  change     metformin   56 -1.10 1.139 rosiglitazone   57 -1.10 1.341 15 
#> 16         Kipnes (2001)  change  pioglitazone  182 -1.20 1.369       placebo  181  0.10 1.024 16 
#> 17          Lewin (2007)  change     metformin  431 -0.74 1.106       placebo  144  0.08 1.004 17 
#> 18         Moulin (2006)  change    benfluorex  161 -0.82 1.028       placebo  156  0.19 1.374 18 
#> 19          Oyama (2008)  change      acarbose   41 -0.70 0.800  sulfonylurea   43 -0.30 0.600 19 
#> 20     Rosenstock (2008)  change rosiglitazone   59 -1.17 1.229       placebo   57 -0.08 1.208 20 
#> 21         Stucci (1996)     raw    benfluorex   28  8.03 1.290       placebo   30  8.26 1.350 21 
#> 22 Vongthavaravat (2002)  change rosiglitazone  164 -1.10 1.559  sulfonylurea  170  0.10 0.992 22 
#> 23         Willms (1999)  change      acarbose   31 -2.30 1.782       placebo   29 -1.30 1.831 23 
#> 24         Willms (1999)  change     metformin   29 -2.50 0.862       placebo   29 -1.30 1.831 24 
#> 25  Wolffenbuttel (1999)  change rosiglitazone  183 -0.90 1.100       placebo  192  0.20 1.110 25 
#> 26           Yang (2003)  change     metformin   96 -0.95 1.500 rosiglitazone  102 -1.09 1.650 26 
#> 27            Zhu (2003)  change rosiglitazone  210 -1.90 1.470       placebo  105 -0.40 1.300 27 
#>     comp   design      yi     vi acarbose benfluorex metformin miglitol pioglitazone rosiglitazone 
#> 1  me-su    me-su -0.3700 0.0140        0          0         1        0            0             0 
#> 2  ro-pl    ro-pl -1.3000 0.0103        0          0         0        0            0             1 
#> 3  ac-pl    ac-pl -0.8000 0.0205        1          0         0        0            0             0 
#> 4  ro-pl    ro-pl -1.3400 0.0206        0          0         0        0            0             1 
#> 5  me-pl    me-pl -1.9000 0.0200        0          0         1        0            0             0 
#> 6  pi-ro    pi-ro  0.1000 0.0335        0          0         0        0            1            -1 
#> 7  vi-pl    vi-pl -0.7000 0.0162        0          0         0        0            0             0 
#> 8  me-pl    me-pl -0.4000 0.1897        0          0         1        0            0             0 
#> 9  me-pi    me-pi -0.1600 0.0072        0          0         1        0           -1             0 
#> 10 si-pl    si-pl -0.5700 0.0167        0          0         0        0            0             0 
#> 11 mi-pl    mi-pl -0.7400 0.0338        0          0         0        1            0             0 
#> 12 mi-pl    mi-pl -1.4100 0.0500        0          0         0        1            0             0 
#> 13 mi-pl    mi-pl -0.6800 0.0800        0          0         0        1            0             0 
#> 14 ro-pl    ro-pl -0.7700 0.0116        0          0         0        0            0             1 
#> 15 me-ro    me-ro  0.0000 0.0547        0          0         1        0            0            -1 
#> 16 pi-pl    pi-pl -1.3000 0.0161        0          0         0        0            1             0 
#> 17 me-pl    me-pl -0.8200 0.0098        0          0         1        0            0             0 
#> 18 be-pl    be-pl -1.0100 0.0187        0          1         0        0            0             0 
#> 19 ac-su    ac-su -0.4000 0.0240        1          0         0        0            0             0 
#> 20 ro-pl    ro-pl -1.0900 0.0512        0          0         0        0            0             1 
#> 21 be-pl    be-pl -0.2300 0.1202        0          1         0        0            0             0 
#> 22 ro-su    ro-su -1.2000 0.0206        0          0         0        0            0             1 
#> 23 ac-pl ac-me-pl -1.0000 0.2180        1          0         0        0            0             0 
#> 24 me-pl ac-me-pl -1.2000 0.1412        0          0         1        0            0             0 
#> 25 ro-pl    ro-pl -1.1000 0.0130        0          0         0        0            0             1 
#> 26 me-ro    me-ro  0.1400 0.0501        0          0         1        0            0            -1 
#> 27 ro-pl    ro-pl -1.5000 0.0264        0          0         0        0            0             1 
#>    sitagliptin sulfonylurea vildagliptin placebo 
#> 1            0           -1            0       0 
#> 2            0            0            0      -1 
#> 3            0            0            0      -1 
#> 4            0            0            0      -1 
#> 5            0            0            0      -1 
#> 6            0            0            0       0 
#> 7            0            0            1      -1 
#> 8            0            0            0      -1 
#> 9            0            0            0       0 
#> 10           1            0            0      -1 
#> 11           0            0            0      -1 
#> 12           0            0            0      -1 
#> 13           0            0            0      -1 
#> 14           0            0            0      -1 
#> 15           0            0            0       0 
#> 16           0            0            0      -1 
#> 17           0            0            0      -1 
#> 18           0            0            0      -1 
#> 19           0           -1            0       0 
#> 20           0            0            0      -1 
#> 21           0            0            0      -1 
#> 22           0           -1            0       0 
#> 23           0            0            0      -1 
#> 24           0            0            0      -1 
#> 25           0            0            0      -1 
#> 26           0            0            0       0 
#> 27           0            0            0      -1 
#> 

### network meta-analysis using a contrast-based random-effects model
### by setting rho=1/2, tau^2 reflects the amount of heterogeneity for all treatment comparisons
### the treatment left out (placebo) becomes the reference level for the treatment comparisons
res <- rma.mv(yi, V, mods = ~ acarbose + benfluorex + metformin + miglitol + pioglitazone +
                              rosiglitazone + sitagliptin + sulfonylurea + vildagliptin - 1,
              random = ~ comp | study, rho=1/2, data=dat)
res
#> 
#> Multivariate Meta-Analysis Model (k = 27; method: REML)
#> 
#> Variance Components:
#> 
#> outer factor: study (nlvls = 26)
#> inner factor: comp  (nlvls = 14)
#> 
#>             estim    sqrt  fixed 
#> tau^2      0.0999  0.3161     no 
#> rho        0.5000            yes 
#> 
#> Test for Residual Heterogeneity:
#> QE(df = 18) = 96.9841, p-val < .0001
#> 
#> Test of Moderators (coefficients 1:9):
#> QM(df = 9) = 167.9616, p-val < .0001
#> 
#> Model Results:
#> 
#>                estimate      se     zval    pval    ci.lb    ci.ub     ​ 
#> acarbose        -0.8414  0.2384  -3.5288  0.0004  -1.3087  -0.3741  *** 
#> benfluorex      -0.7369  0.2776  -2.6545  0.0079  -1.2810  -0.1928   ** 
#> metformin       -1.1284  0.1494  -7.5528  <.0001  -1.4212  -0.8356  *** 
#> miglitol        -0.9499  0.2253  -4.2170  <.0001  -1.3914  -0.5084  *** 
#> pioglitazone    -1.1294  0.2119  -5.3295  <.0001  -1.5448  -0.7141  *** 
#> rosiglitazone   -1.2337  0.1235  -9.9933  <.0001  -1.4757  -0.9918  *** 
#> sitagliptin     -0.5700  0.3414  -1.6694  0.0950  -1.2392   0.0992    . 
#> sulfonylurea    -0.4175  0.2326  -1.7950  0.0727  -0.8734   0.0384    . 
#> vildagliptin    -0.7000  0.3408  -2.0543  0.0400  -1.3679  -0.0321    * 
#> 
#> ---
#> Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
#> 

### forest plot of the contrast estimates (treatments versus placebos)
forest(coef(res), diag(vcov(res)), slab=names(coef(res)), order="obs",
       xlim=c(-3.0, 2.5), alim=c(-1.5, 0.5), psize=1, xlab="Estimate", header="Treatment")


### estimate all pairwise differences between treatments
contr <- data.frame(t(combn(names(coef(res)), 2)))
contr <- contrmat(contr, "X1", "X2", last="vildagliptin")
rownames(contr) <- paste(contr$X1, "-", contr$X2)
contr <- as.matrix(contr[-c(1:2)])
sav <- predict(res, newmods=contr)
sav[["slab"]] <- rownames(contr)
sav
#> 
#>                                 pred     se   ci.lb   ci.ub   pi.lb   pi.ub 
#> acarbose - benfluorex        -0.1045 0.3659 -0.8217  0.6128 -1.0522  0.8433 
#> acarbose - metformin          0.2870 0.2504 -0.2037  0.7778 -0.5033  1.0774 
#> acarbose - miglitol           0.1085 0.3280 -0.5344  0.7514 -0.7843  1.0013 
#> acarbose - pioglitazone       0.2880 0.3054 -0.3105  0.8866 -0.5734  1.1495 
#> acarbose - rosiglitazone      0.3924 0.2526 -0.1026  0.8874 -0.4006  1.1854 
#> acarbose - sitagliptin       -0.2714 0.4165 -1.0876  0.5449 -1.2961  0.7534 
#> acarbose - sulfonylurea      -0.4238 0.2568 -0.9273  0.0796 -1.2221  0.3744 
#> acarbose - vildagliptin      -0.1414 0.4159 -0.9565  0.6738 -1.1652  0.8825 
#> benfluorex - metformin        0.3915 0.3153 -0.2264  1.0094 -0.4835  1.2665 
#> benfluorex - miglitol         0.2130 0.3575 -0.4877  0.9137 -0.7223  1.1483 
#> benfluorex - pioglitazone     0.3925 0.3492 -0.2920  1.0770 -0.5307  1.3157 
#> benfluorex - rosiglitazone    0.4968 0.3038 -0.0986  1.0923 -0.3625  1.3561 
#> benfluorex - sitagliptin     -0.1669 0.4401 -1.0294  0.6956 -1.2288  0.8950 
#> benfluorex - sulfonylurea    -0.3194 0.3622 -1.0292  0.3905 -1.2616  0.6228 
#> benfluorex - vildagliptin    -0.0369 0.4395 -0.8983  0.8245 -1.0980  1.0242 
#> metformin - miglitol         -0.1785 0.2703 -0.7083  0.3513 -0.9937  0.6366 
#> metformin - pioglitazone      0.0010 0.2176 -0.4254  0.4274 -0.7511  0.7531 
#> metformin - rosiglitazone     0.1053 0.1600 -0.2082  0.4189 -0.5890  0.7997 
#> metformin - sitagliptin      -0.5584 0.3727 -1.2889  0.1721 -1.5162  0.3994 
#> metformin - sulfonylurea     -0.7109 0.2272 -1.1561 -0.2656 -1.4738  0.0521 
#> metformin - vildagliptin     -0.4284 0.3721 -1.1576  0.3008 -1.3853  0.5285 
#> miglitol - pioglitazone       0.1795 0.3093 -0.4266  0.7857 -0.6872  1.0463 
#> miglitol - rosiglitazone      0.2839 0.2569 -0.2196  0.7873 -0.5144  1.0822 
#> miglitol - sitagliptin       -0.3799 0.4091 -1.1816  0.4218 -1.3931  0.6333 
#> miglitol - sulfonylurea      -0.5324 0.3238 -1.1670  0.1023 -1.4193  0.3545 
#> miglitol - vildagliptin      -0.2499 0.4085 -1.0505  0.5507 -1.2622  0.7624 
#> pioglitazone - rosiglitazone  0.1043 0.2163 -0.3196  0.5283 -0.6464  0.8550 
#> pioglitazone - sitagliptin   -0.5594 0.4019 -1.3470  0.2282 -1.5615  0.4427 
#> pioglitazone - sulfonylurea  -0.7119 0.2914 -1.2831 -0.1407 -1.5545  0.1308 
#> pioglitazone - vildagliptin  -0.4294 0.4013 -1.2159  0.3571 -1.4306  0.5718 
#> rosiglitazone - sitagliptin  -0.6637 0.3631 -1.3754  0.0479 -1.6073  0.2798 
#> rosiglitazone - sulfonylurea -0.8162 0.2290 -1.2651 -0.3674 -1.5813 -0.0512 
#> rosiglitazone - vildagliptin -0.5337 0.3624 -1.2441  0.1766 -1.4763  0.4088 
#> sitagliptin - sulfonylurea   -0.1525 0.4132 -0.9622  0.6573 -1.1720  0.8671 
#> sitagliptin - vildagliptin    0.1300 0.4824 -0.8155  1.0755 -1.0004  1.2604 
#> sulfonylurea - vildagliptin   0.2825 0.4126 -0.5262  1.0911 -0.7362  1.3012 
#> 

### fit random inconsistency effects model (see Law et al., 2016)
inc <- rma.mv(yi, V, mods = ~ acarbose + benfluorex + metformin + miglitol + pioglitazone +
                              rosiglitazone + sitagliptin + sulfonylurea + vildagliptin - 1,
              random = list(~ comp | study, ~ comp | design), rho=1/2, phi=1/2, data=dat)
inc
#> 
#> Multivariate Meta-Analysis Model (k = 27; method: REML)
#> 
#> Variance Components:
#> 
#> outer factor: study (nlvls = 26)
#> inner factor: comp  (nlvls = 14)
#> 
#>             estim    sqrt  fixed 
#> tau^2      0.0999  0.3161     no 
#> rho        0.5000            yes 
#> 
#> outer factor: design (nlvls = 15)
#> inner factor: comp   (nlvls = 14)
#> 
#>             estim    sqrt  fixed 
#> gamma^2    0.0000  0.0000     no 
#> phi        0.5000            yes 
#> 
#> Test for Residual Heterogeneity:
#> QE(df = 18) = 96.9841, p-val < .0001
#> 
#> Test of Moderators (coefficients 1:9):
#> QM(df = 9) = 167.9616, p-val < .0001
#> 
#> Model Results:
#> 
#>                estimate      se     zval    pval    ci.lb    ci.ub     ​ 
#> acarbose        -0.8414  0.2384  -3.5288  0.0004  -1.3087  -0.3741  *** 
#> benfluorex      -0.7369  0.2776  -2.6545  0.0079  -1.2810  -0.1928   ** 
#> metformin       -1.1284  0.1494  -7.5528  <.0001  -1.4212  -0.8356  *** 
#> miglitol        -0.9499  0.2253  -4.2170  <.0001  -1.3914  -0.5084  *** 
#> pioglitazone    -1.1294  0.2119  -5.3295  <.0001  -1.5448  -0.7141  *** 
#> rosiglitazone   -1.2337  0.1235  -9.9933  <.0001  -1.4757  -0.9918  *** 
#> sitagliptin     -0.5700  0.3414  -1.6694  0.0950  -1.2392   0.0992    . 
#> sulfonylurea    -0.4175  0.2326  -1.7950  0.0727  -0.8734   0.0384    . 
#> vildagliptin    -0.7000  0.3408  -2.0543  0.0400  -1.3679  -0.0321    * 
#> 
#> ---
#> Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
#> 

############################################################################

### compute P-scores (see Rücker & Schwarzer, 2015)
contr <- data.frame(t(combn(c(names(coef(res)),"placebo"), 2))) # add 'placebo' to contrast matrix
contr <- contrmat(contr, "X1", "X2", last="placebo", append=FALSE)
b <- c(coef(res),0) # add 0 for 'placebo' (the reference treatment)
vb <- bldiag(vcov(res),0) # add 0 row/column for 'placebo' (the reference treatment)
pvals <- apply(contr, 1, function(x) pnorm((x%*%b) / sqrt(t(x)%*%vb%*%x)))
tab <- vec2mat(pvals, corr=FALSE)
tab[upper.tri(tab)] <- t((1 - tab)[upper.tri(tab)])
rownames(tab) <- colnames(tab) <- colnames(contr)
round(tab, 2) # like Table 2 in the article
#>               acarbose benfluorex metformin miglitol pioglitazone rosiglitazone sitagliptin
#> acarbose            NA       0.61      0.13     0.37         0.17          0.06        0.74
#> benfluorex        0.39         NA      0.11     0.28         0.13          0.05        0.65
#> metformin         0.87       0.89        NA     0.75         0.50          0.26        0.93
#> miglitol          0.63       0.72      0.25       NA         0.28          0.13        0.82
#> pioglitazone      0.83       0.87      0.50     0.72           NA          0.31        0.92
#> rosiglitazone     0.94       0.95      0.74     0.87         0.69            NA        0.97
#> sitagliptin       0.26       0.35      0.07     0.18         0.08          0.03          NA
#> sulfonylurea      0.05       0.19      0.00     0.05         0.01          0.00        0.36
#> vildagliptin      0.37       0.47      0.12     0.27         0.14          0.07        0.61
#> placebo           0.00       0.00      0.00     0.00         0.00          0.00        0.05
#>               sulfonylurea vildagliptin placebo
#> acarbose              0.95         0.63    1.00
#> benfluorex            0.81         0.53    1.00
#> metformin             1.00         0.88    1.00
#> miglitol              0.95         0.73    1.00
#> pioglitazone          0.99         0.86    1.00
#> rosiglitazone         1.00         0.93    1.00
#> sitagliptin           0.64         0.39    0.95
#> sulfonylurea            NA         0.25    0.96
#> vildagliptin          0.75           NA    0.98
#> placebo               0.04         0.02      NA
cbind(pscore=round(sort(apply(tab, 1, mean, na.rm=TRUE), decreasing=TRUE), 3))
#>               pscore
#> rosiglitazone  0.898
#> metformin      0.786
#> pioglitazone   0.778
#> miglitol       0.614
#> acarbose       0.519
#> benfluorex     0.438
#> vildagliptin   0.420
#> sitagliptin    0.329
#> sulfonylurea   0.207
#> placebo        0.012

# note: the values are slightly different from the ones given in Table 3 of Rücker and
# Schwarzer (2015) since model 'res' above is fitted using REML estimation while the
# results shown in the article are based on the 'netmeta' package, which uses a DL-type
# estimator for the amount of heterogeneity by default

############################################################################

# }