Node-splitting model for testing consistency at the treatment level using MBNMA
mbnma.nodesplit.RdSplits contributions for a given set of treatment comparisons into direct and indirect evidence. A discrepancy between the two suggests that the consistency assumption required for NMA and MBNMA may violated.
Arguments
- network
An object of class
mbnma.network.- fun
An object of
class("dosefun")that specifies a functional form to be assigned to the dose-response. See Details.- method
Can take either
"common"or"random"to indicate whether relative effects should be modelled with between-study heterogeneity or not (see details).- comparisons
A matrix specifying the comparisons to be split (one row per comparison). The matrix must have two columns indicating each treatment for each comparison. Values can either be character (corresponding to the treatment names given in
network) or numeric (corresponding to treatment codes within thenetwork- note that these may change ifdrop.discon = TRUE).- incldr
A boolean object indicating whether or not to allow for indirect evidence contributions via the dose-response relationship. This can be used when node-splitting in dose-response MBNMA to allow for a greater number of potential loops in which to check for consistency.
- ...
Arguments to be sent to
ggplot2::ggplot()orforestplot::forestplot()- x
An object of
class("nodesplit")- plot.type
A character string that can take the value of
"forest"to plot forest plots or"density"to plot posterior density plots.
Value
Plots the desired graph if plot.type="forest" and plots and returns an object
of class(c("gg", "ggplot")) if plot.type="density".
Details
The S3 method plot() on an nodesplit object generates either
forest plots of posterior medians and 95\% credible intervals, or density plots
of posterior densities for direct and indirect evidence.
Functions
plot(nodesplit): Plot outputs from treatment-level nodesplit MBNMA models
Examples
# \donttest{
# Using the triptans data
network <- mbnma.network(triptans)
#> Values for `agent` with dose = 0 have been recoded to `Placebo`
#> agent is being recoded to enforce sequential numbering
split <- mbnma.nodesplit(network, fun=demax(), likelihood = "binomial", link="logit",
method="common")
#>
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#> Compiling model graph
#> Resolving undeclared variables
#> Allocating nodes
#> Graph information:
#> Observed stochastic nodes: 182
#> Unobserved stochastic nodes: 84
#> Total graph size: 3684
#>
#> Initializing model
#>
#> [1] "Comparison 1/20"
#> [1] "Calculating nodesplit for: zolmitriptan_1 vs almotriptan_1"
#> Compiling model graph
#> Resolving undeclared variables
#> Allocating nodes
#> Graph information:
#> Observed stochastic nodes: 182
#> Unobserved stochastic nodes: 85
#> Total graph size: 3898
#>
#> Initializing model
#>
#> [1] "Comparison 2/20"
#> [1] "Calculating nodesplit for: rizatriptan_1 vs sumatriptan_1"
#> Compiling model graph
#> Resolving undeclared variables
#> Allocating nodes
#> Graph information:
#> Observed stochastic nodes: 182
#> Unobserved stochastic nodes: 85
#> Total graph size: 3898
#>
#> Initializing model
#>
#> [1] "Comparison 3/20"
#> [1] "Calculating nodesplit for: almotriptan_1 vs sumatriptan_1"
#> Compiling model graph
#> Resolving undeclared variables
#> Allocating nodes
#> Graph information:
#> Observed stochastic nodes: 182
#> Unobserved stochastic nodes: 85
#> Total graph size: 3898
#>
#> Initializing model
#>
#> [1] "Comparison 4/20"
#> [1] "Calculating nodesplit for: rizatriptan_0.5 vs sumatriptan_0.5"
#> Compiling model graph
#> Resolving undeclared variables
#> Allocating nodes
#> Graph information:
#> Observed stochastic nodes: 182
#> Unobserved stochastic nodes: 85
#> Total graph size: 3900
#>
#> Initializing model
#>
#> [1] "Comparison 5/20"
#> [1] "Calculating nodesplit for: rizatriptan_0.25 vs Placebo_0"
#> Compiling model graph
#> Resolving undeclared variables
#> Allocating nodes
#> Graph information:
#> Observed stochastic nodes: 182
#> Unobserved stochastic nodes: 85
#> Total graph size: 3896
#>
#> Initializing model
#>
#> [1] "Comparison 6/20"
#> [1] "Calculating nodesplit for: naratriptan_2 vs Placebo_0"
#> Compiling model graph
#> Resolving undeclared variables
#> Allocating nodes
#> Graph information:
#> Observed stochastic nodes: 182
#> Unobserved stochastic nodes: 85
#> Total graph size: 3896
#>
#> Initializing model
#>
#> [1] "Comparison 7/20"
#> [1] "Calculating nodesplit for: naratriptan_1 vs Placebo_0"
#> Compiling model graph
#> Resolving undeclared variables
#> Allocating nodes
#> Graph information:
#> Observed stochastic nodes: 182
#> Unobserved stochastic nodes: 85
#> Total graph size: 3896
#>
#> Initializing model
#>
#> [1] "Comparison 8/20"
#> [1] "Calculating nodesplit for: zolmitriptan_10 vs Placebo_0"
#> Compiling model graph
#> Resolving undeclared variables
#> Allocating nodes
#> Graph information:
#> Observed stochastic nodes: 182
#> Unobserved stochastic nodes: 85
#> Total graph size: 3896
#>
#> Initializing model
#>
#> [1] "Comparison 9/20"
#> [1] "Calculating nodesplit for: zolmitriptan_4 vs Placebo_0"
#> Compiling model graph
#> Resolving undeclared variables
#> Allocating nodes
#> Graph information:
#> Observed stochastic nodes: 182
#> Unobserved stochastic nodes: 85
#> Total graph size: 3896
#>
#> Initializing model
#>
#> [1] "Comparison 10/20"
#> [1] "Calculating nodesplit for: zolmitriptan_2 vs Placebo_0"
#> Compiling model graph
#> Resolving undeclared variables
#> Allocating nodes
#> Graph information:
#> Observed stochastic nodes: 182
#> Unobserved stochastic nodes: 85
#> Total graph size: 3896
#>
#> Initializing model
#>
#> [1] "Comparison 11/20"
#> [1] "Calculating nodesplit for: zolmitriptan_0.4 vs Placebo_0"
#> Compiling model graph
#> Resolving undeclared variables
#> Allocating nodes
#> Graph information:
#> Observed stochastic nodes: 182
#> Unobserved stochastic nodes: 85
#> Total graph size: 3896
#>
#> Initializing model
#>
#> [1] "Comparison 12/20"
#> [1] "Calculating nodesplit for: almotriptan_2 vs Placebo_0"
#> Compiling model graph
#> Resolving undeclared variables
#> Allocating nodes
#> Graph information:
#> Observed stochastic nodes: 182
#> Unobserved stochastic nodes: 85
#> Total graph size: 3896
#>
#> Initializing model
#>
#> [1] "Comparison 13/20"
#> [1] "Calculating nodesplit for: almotriptan_0.5 vs Placebo_0"
#> Compiling model graph
#> Resolving undeclared variables
#> Allocating nodes
#> Graph information:
#> Observed stochastic nodes: 182
#> Unobserved stochastic nodes: 85
#> Total graph size: 3896
#>
#> Initializing model
#>
#> [1] "Comparison 14/20"
#> [1] "Calculating nodesplit for: frovatriptan_2 vs Placebo_0"
#> Compiling model graph
#> Resolving undeclared variables
#> Allocating nodes
#> Graph information:
#> Observed stochastic nodes: 182
#> Unobserved stochastic nodes: 85
#> Total graph size: 3896
#>
#> Initializing model
#>
#> [1] "Comparison 15/20"
#> [1] "Calculating nodesplit for: frovatriptan_1 vs Placebo_0"
#> Compiling model graph
#> Resolving undeclared variables
#> Allocating nodes
#> Graph information:
#> Observed stochastic nodes: 182
#> Unobserved stochastic nodes: 85
#> Total graph size: 3896
#>
#> Initializing model
#>
#> [1] "Comparison 16/20"
#> [1] "Calculating nodesplit for: sumatriptan_2 vs Placebo_0"
#> Compiling model graph
#> Resolving undeclared variables
#> Allocating nodes
#> Graph information:
#> Observed stochastic nodes: 182
#> Unobserved stochastic nodes: 85
#> Total graph size: 3896
#>
#> Initializing model
#>
#> [1] "Comparison 17/20"
#> [1] "Calculating nodesplit for: sumatriptan_1.7 vs Placebo_0"
#> Compiling model graph
#> Resolving undeclared variables
#> Allocating nodes
#> Graph information:
#> Observed stochastic nodes: 182
#> Unobserved stochastic nodes: 85
#> Total graph size: 3896
#>
#> Initializing model
#>
#> [1] "Comparison 18/20"
#> [1] "Calculating nodesplit for: eletriptan_2 vs Placebo_0"
#> Compiling model graph
#> Resolving undeclared variables
#> Allocating nodes
#> Graph information:
#> Observed stochastic nodes: 182
#> Unobserved stochastic nodes: 85
#> Total graph size: 3896
#>
#> Initializing model
#>
#> [1] "Comparison 19/20"
#> [1] "Calculating nodesplit for: eletriptan_1 vs Placebo_0"
#> Compiling model graph
#> Resolving undeclared variables
#> Allocating nodes
#> Graph information:
#> Observed stochastic nodes: 182
#> Unobserved stochastic nodes: 85
#> Total graph size: 3896
#>
#> Initializing model
#>
#> [1] "Comparison 20/20"
#> [1] "Calculating nodesplit for: eletriptan_0.5 vs Placebo_0"
#> Compiling model graph
#> Resolving undeclared variables
#> Allocating nodes
#> Graph information:
#> Observed stochastic nodes: 182
#> Unobserved stochastic nodes: 85
#> Total graph size: 3896
#>
#> Initializing model
#>
#### To perform nodesplit on selected comparisons ####
# Check for closed loops of treatments with independent evidence sources
# Including indirect evidence via the dose-response relationship
loops <- inconsistency.loops(network$data.ab, incldr=TRUE)
#>
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# This...
single.split <- mbnma.nodesplit(network, fun=dexp(), likelihood = "binomial", link="logit",
method="random", comparisons=rbind(c("sumatriptan_1", "almotriptan_1")))
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#> Compiling model graph
#> Resolving undeclared variables
#> Allocating nodes
#> Graph information:
#> Observed stochastic nodes: 182
#> Unobserved stochastic nodes: 190
#> Total graph size: 4087
#>
#> Initializing model
#>
#> [1] "Comparison 1/1"
#> [1] "Calculating nodesplit for: almotriptan_1 vs sumatriptan_1"
#> Compiling model graph
#> Resolving undeclared variables
#> Allocating nodes
#> Graph information:
#> Observed stochastic nodes: 182
#> Unobserved stochastic nodes: 191
#> Total graph size: 4334
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#> Initializing model
#>
#...is the same as...
single.split <- mbnma.nodesplit(network, fun=dexp(), likelihood = "binomial", link="logit",
method="random", comparisons=rbind(c(6, 12)))
#>
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#> Compiling model graph
#> Resolving undeclared variables
#> Allocating nodes
#> Graph information:
#> Observed stochastic nodes: 182
#> Unobserved stochastic nodes: 190
#> Total graph size: 4087
#>
#> Initializing model
#>
#> [1] "Comparison 1/1"
#> [1] "Calculating nodesplit for: almotriptan_1 vs sumatriptan_1"
#> Compiling model graph
#> Resolving undeclared variables
#> Allocating nodes
#> Graph information:
#> Observed stochastic nodes: 182
#> Unobserved stochastic nodes: 191
#> Total graph size: 4334
#>
#> Initializing model
#>
# Plot results
plot(split, plot.type="density") # Plot density plots of posterior densities
plot(split, txt_gp=forestplot::fpTxtGp(cex=0.5)) # Plot forest plots (with smaller label size)
# Print and summarise results
print(split)
#> ========================================
#> Node-splitting analysis of inconsistency
#> ========================================
#> |Comparison | p-value| Median| 2.5%| 97.5%|
#> |:----------------------------------|-------:|------:|------:|------:|
#> |zolmitriptan_1 vs almotriptan_1 | 0.187| | | |
#> |-> direct | | 0.116| -0.147| 0.380|
#> |-> indirect | | 0.439| 0.231| 0.647|
#> |-> MBNMA | | 0.296| 0.116| 0.466|
#> | | | | | |
#> |rizatriptan_1 vs sumatriptan_1 | 0.090| | | |
#> |-> direct | | 0.199| -0.058| 0.447|
#> |-> indirect | | 0.545| 0.391| 0.697|
#> |-> MBNMA | | 0.446| 0.313| 0.578|
#> | | | | | |
#> |almotriptan_1 vs sumatriptan_1 | 0.061| | | |
#> |-> direct | | -0.402| -0.676| -0.118|
#> |-> indirect | | 0.109| -0.132| 0.314|
#> |-> MBNMA | | 0.206| 0.028| 0.363|
#> | | | | | |
#> |rizatriptan_0.5 vs sumatriptan_0.5 | 0.394| | | |
#> |-> direct | | 0.285| 0.023| 0.549|
#> |-> indirect | | -0.016| -0.237| 0.376|
#> |-> MBNMA | | 0.034| -0.107| 0.154|
#> | | | | | |
#> |rizatriptan_0.25 vs Placebo_0 | 0.275| | | |
#> |-> direct | | 0.094| -0.818| 0.862|
#> |-> indirect | | 0.394| 0.353| 0.794|
#> |-> MBNMA | | 0.391| 0.354| 0.453|
#> | | | | | |
#> |naratriptan_2 vs Placebo_0 | 0.692| | | |
#> |-> direct | | 0.828| 0.265| 1.386|
#> |-> indirect | | 1.078| 0.456| 1.665|
#> |-> MBNMA | | 0.936| 0.509| 1.336|
#> | | | | | |
#> |naratriptan_1 vs Placebo_0 | 0.630| | | |
#> |-> direct | | 0.560| 0.248| 0.876|
#> |-> indirect | | 0.409| 0.127| 0.703|
#> |-> MBNMA | | 0.473| 0.259| 0.676|
#> | | | | | |
#> |zolmitriptan_10 vs Placebo_0 | 0.438| | | |
#> |-> direct | | 2.680| 1.447| 3.991|
#> |-> indirect | | 1.944| 1.401| 2.718|
#> |-> MBNMA | | 2.051| 1.464| 2.742|
#> | | | | | |
#> |zolmitriptan_4 vs Placebo_0 | 0.558| | | |
#> |-> direct | | 1.795| 1.367| 2.192|
#> |-> indirect | | 2.070| 1.594| 2.537|
#> |-> MBNMA | | 1.817| 1.400| 2.237|
#> | | | | | |
#> |zolmitriptan_2 vs Placebo_0 | 0.787| | | |
#> |-> direct | | 1.566| 1.250| 1.884|
#> |-> indirect | | 1.562| 1.344| 1.763|
#> |-> MBNMA | | 1.528| 1.296| 1.744|
#> | | | | | |
#> |zolmitriptan_0.4 vs Placebo_0 | 0.360| | | |
#> |-> direct | | 0.807| 0.000| 1.602|
#> |-> indirect | | 0.665| 0.529| 0.885|
#> |-> MBNMA | | 0.683| 0.534| 0.931|
#> | | | | | |
#> |almotriptan_2 vs Placebo_0 | 0.059| | | |
#> |-> direct | | 1.362| 1.064| 1.649|
#> |-> indirect | | 1.912| 1.632| 2.196|
#> |-> MBNMA | | 1.590| 1.276| 1.850|
#> | | | | | |
#> |almotriptan_0.5 vs Placebo_0 | 0.756| | | |
#> |-> direct | | 0.517| 0.178| 0.855|
#> |-> indirect | | 0.507| 0.349| 0.732|
#> |-> MBNMA | | 0.445| 0.367| 0.661|
#> | | | | | |
#> |frovatriptan_2 vs Placebo_0 | 0.122| | | |
#> |-> direct | | 1.383| 0.794| 1.939|
#> |-> indirect | | 2.298| 1.715| 2.919|
#> |-> MBNMA | | 1.831| 1.356| 2.321|
#> | | | | | |
#> |frovatriptan_1 vs Placebo_0 | 0.111| | | |
#> |-> direct | | 1.200| 0.899| 1.511|
#> |-> indirect | | 0.698| 0.408| 1.003|
#> |-> MBNMA | | 0.933| 0.689| 1.192|
#> | | | | | |
#> |sumatriptan_2 vs Placebo_0 | 0.241| | | |
#> |-> direct | | 1.351| 1.244| 1.468|
#> |-> indirect | | 1.924| 1.230| 2.169|
#> |-> MBNMA | | 1.381| 1.277| 1.483|
#> | | | | | |
#> |sumatriptan_1.7 vs Placebo_0 | 0.209| | | |
#> |-> direct | | 1.099| 0.802| 1.402|
#> |-> indirect | | 1.333| 1.237| 1.428|
#> |-> MBNMA | | 1.314| 1.220| 1.407|
#> | | | | | |
#> |eletriptan_2 vs Placebo_0 | 0.000| | | |
#> |-> direct | | 1.947| 1.777| 2.119|
#> |-> indirect | | 3.341| 3.065| 3.610|
#> |-> MBNMA | | 2.021| 1.846| 2.198|
#> | | | | | |
#> |eletriptan_1 vs Placebo_0 | 0.264| | | |
#> |-> direct | | 1.653| 1.504| 1.814|
#> |-> indirect | | 1.003| 0.892| 1.707|
#> |-> MBNMA | | 1.683| 1.547| 1.827|
#> | | | | | |
#> |eletriptan_0.5 vs Placebo_0 | 0.374| | | |
#> |-> direct | | 1.132| 0.886| 1.374|
#> |-> indirect | | 1.334| 1.153| 1.562|
#> |-> MBNMA | | 1.265| 1.106| 1.435|
#> | | | | | |
summary(split) # Generate a data frame of summary results
#> Comparison Evidence Median 2.5% 97.5% p.value
#> 1 zolmitriptan_1 vs almotriptan_1 Direct 0.116 -0.147 0.380 0.187
#> 2 zolmitriptan_1 vs almotriptan_1 Indirect 0.439 0.231 0.647 0.187
#> 3 zolmitriptan_1 vs almotriptan_1 MBNMA 0.296 0.116 0.466 0.187
#> 4 rizatriptan_1 vs sumatriptan_1 Direct 0.199 -0.058 0.447 0.090
#> 5 rizatriptan_1 vs sumatriptan_1 Indirect 0.545 0.391 0.697 0.090
#> 6 rizatriptan_1 vs sumatriptan_1 MBNMA 0.446 0.313 0.578 0.090
#> 7 almotriptan_1 vs sumatriptan_1 Direct -0.402 -0.676 -0.118 0.061
#> 8 almotriptan_1 vs sumatriptan_1 Indirect 0.109 -0.132 0.314 0.061
#> 9 almotriptan_1 vs sumatriptan_1 MBNMA 0.206 0.028 0.363 0.061
#> 10 rizatriptan_0.5 vs sumatriptan_0.5 Direct 0.285 0.023 0.549 0.394
#> 11 rizatriptan_0.5 vs sumatriptan_0.5 Indirect -0.016 -0.237 0.376 0.394
#> 12 rizatriptan_0.5 vs sumatriptan_0.5 MBNMA 0.034 -0.107 0.154 0.394
#> 13 rizatriptan_0.25 vs Placebo_0 Direct 0.094 -0.818 0.862 0.275
#> 14 rizatriptan_0.25 vs Placebo_0 Indirect 0.394 0.353 0.794 0.275
#> 15 rizatriptan_0.25 vs Placebo_0 MBNMA 0.391 0.354 0.453 0.275
#> 16 naratriptan_2 vs Placebo_0 Direct 0.828 0.265 1.386 0.692
#> 17 naratriptan_2 vs Placebo_0 Indirect 1.078 0.456 1.665 0.692
#> 18 naratriptan_2 vs Placebo_0 MBNMA 0.936 0.509 1.336 0.692
#> 19 naratriptan_1 vs Placebo_0 Direct 0.560 0.248 0.876 0.630
#> 20 naratriptan_1 vs Placebo_0 Indirect 0.409 0.127 0.703 0.630
#> 21 naratriptan_1 vs Placebo_0 MBNMA 0.473 0.259 0.676 0.630
#> 22 zolmitriptan_10 vs Placebo_0 Direct 2.680 1.447 3.991 0.438
#> 23 zolmitriptan_10 vs Placebo_0 Indirect 1.944 1.401 2.718 0.438
#> 24 zolmitriptan_10 vs Placebo_0 MBNMA 2.051 1.464 2.742 0.438
#> 25 zolmitriptan_4 vs Placebo_0 Direct 1.795 1.367 2.192 0.558
#> 26 zolmitriptan_4 vs Placebo_0 Indirect 2.070 1.594 2.537 0.558
#> 27 zolmitriptan_4 vs Placebo_0 MBNMA 1.817 1.400 2.237 0.558
#> 28 zolmitriptan_2 vs Placebo_0 Direct 1.566 1.250 1.884 0.787
#> 29 zolmitriptan_2 vs Placebo_0 Indirect 1.562 1.344 1.763 0.787
#> 30 zolmitriptan_2 vs Placebo_0 MBNMA 1.528 1.296 1.744 0.787
#> 31 zolmitriptan_0.4 vs Placebo_0 Direct 0.807 0.000 1.602 0.360
#> 32 zolmitriptan_0.4 vs Placebo_0 Indirect 0.665 0.529 0.885 0.360
#> 33 zolmitriptan_0.4 vs Placebo_0 MBNMA 0.683 0.534 0.931 0.360
#> 34 almotriptan_2 vs Placebo_0 Direct 1.362 1.064 1.649 0.059
#> 35 almotriptan_2 vs Placebo_0 Indirect 1.912 1.632 2.196 0.059
#> 36 almotriptan_2 vs Placebo_0 MBNMA 1.590 1.276 1.850 0.059
#> 37 almotriptan_0.5 vs Placebo_0 Direct 0.517 0.178 0.855 0.756
#> 38 almotriptan_0.5 vs Placebo_0 Indirect 0.507 0.349 0.732 0.756
#> 39 almotriptan_0.5 vs Placebo_0 MBNMA 0.445 0.367 0.661 0.756
#> 40 frovatriptan_2 vs Placebo_0 Direct 1.383 0.794 1.939 0.122
#> 41 frovatriptan_2 vs Placebo_0 Indirect 2.298 1.715 2.919 0.122
#> 42 frovatriptan_2 vs Placebo_0 MBNMA 1.831 1.356 2.321 0.122
#> 43 frovatriptan_1 vs Placebo_0 Direct 1.200 0.899 1.511 0.111
#> 44 frovatriptan_1 vs Placebo_0 Indirect 0.698 0.408 1.003 0.111
#> 45 frovatriptan_1 vs Placebo_0 MBNMA 0.933 0.689 1.192 0.111
#> 46 sumatriptan_2 vs Placebo_0 Direct 1.351 1.244 1.468 0.241
#> 47 sumatriptan_2 vs Placebo_0 Indirect 1.924 1.230 2.169 0.241
#> 48 sumatriptan_2 vs Placebo_0 MBNMA 1.381 1.277 1.483 0.241
#> 49 sumatriptan_1.7 vs Placebo_0 Direct 1.099 0.802 1.402 0.209
#> 50 sumatriptan_1.7 vs Placebo_0 Indirect 1.333 1.237 1.428 0.209
#> 51 sumatriptan_1.7 vs Placebo_0 MBNMA 1.314 1.220 1.407 0.209
#> 52 eletriptan_2 vs Placebo_0 Direct 1.947 1.777 2.119 0.000
#> 53 eletriptan_2 vs Placebo_0 Indirect 3.341 3.065 3.610 0.000
#> 54 eletriptan_2 vs Placebo_0 MBNMA 2.021 1.846 2.198 0.000
#> 55 eletriptan_1 vs Placebo_0 Direct 1.653 1.504 1.814 0.264
#> 56 eletriptan_1 vs Placebo_0 Indirect 1.003 0.892 1.707 0.264
#> 57 eletriptan_1 vs Placebo_0 MBNMA 1.683 1.547 1.827 0.264
#> 58 eletriptan_0.5 vs Placebo_0 Direct 1.132 0.886 1.374 0.374
#> 59 eletriptan_0.5 vs Placebo_0 Indirect 1.334 1.153 1.562 0.374
#> 60 eletriptan_0.5 vs Placebo_0 MBNMA 1.265 1.106 1.435 0.374
# }