Performs the Bayesian node-splitting approach of Dias et al. (2010) extended to address aggregate binary and continuous missing participant outcome data via the pattern-mixture model (Spineli et al., 2021; Spineli, 2019). This model offers a local evaluation of the plausibility of the consistency assumption in the network (Dias et al., 2010).
Arguments
- full
- n_chains
Positive integer specifying the number of chains for the MCMC sampling; an argument of the
jagsfunction of the R-package R2jags. The default argument is 2.- n_iter
Positive integer specifying the number of Markov chains for the MCMC sampling; an argument of the
jagsfunction of the R-package R2jags. The default argument is 10000.- n_burnin
Positive integer specifying the number of iterations to discard at the beginning of the MCMC sampling; an argument of the
jagsfunction of the R-package R2jags. The default argument is 1000.- n_thin
Positive integer specifying the thinning rate for the MCMC sampling; an argument of the
jagsfunction of the R-package R2jags. The default argument is 1.- inits
A list with the initial values for the parameters; an argument of the
jagsfunction of the R-package R2jags. The default argument isNULL, and JAGS generates the initial values.
Value
An R2jags output on the summaries of the posterior distribution, and the Gelman-Rubin convergence diagnostic of the following monitored parameters:
- direct
The summary effect measure (according to the argument
measuredefined inrun_model) of each split node based on the corresponding trials.- indirect
The indirect summary effect measure (according to the argument
measuredefined inrun_model) of each split node based on the remaining network after removing (splitting) the corresponding node.- diff
The inconsistency parameter for each split node defined as the difference between the direct and indirect effect of the corresponding split node.
- p_value
The two-sided Bayesian p-value (based on the posterior mean on step(diff)) for each split node defined.
- tau
The between-trial standard deviation after each split node, when the random-effects model has been specified.
Furthermore, the output includes the following element:
- model_assessment
A data-frame on the measures of model assessment after each split node: deviance information criterion, total residual deviance, and number of effective parameters.
Details
run_nodesplit inherits the arguments data,
measure, model, assumption, heter_prior,
mean_misspar, var_misspar, ref, and indic from
run_model (now contained in the argument full).
This prevents specifying a different Bayesian model from that considered
in run_model. Therefore, the user needs first to apply
run_model, and then use run_nodesplit
(see 'Examples').
For a binary outcome, when measure is "RR" (relative risk) or "RD"
(risk difference) in run_model, run_nodesplit
currently performs node-splitting using the odds ratio as effect measure
for being the base-case effect measure in run_model
for a binary outcome (see also 'Details' in run_model).
To perform the Bayesian node-splitting approach, the
prepare_nodesplit function is called which contains the
WinBUGS code as written by Dias et al. (2010) for binomial and normal
likelihood to analyse binary and continuous outcome data, respectively.
prepare_nodesplit has been extended to incorporate the
pattern-mixture model with informative missingness parameters for binary
and continuous outcome data (see 'Details' in run_model).
run_nodesplit runs the Bayesian node-splitting approach in
JAGS. The progress of the simulation appears on the R console. The
number of times run_nodesplit is used appears on the R console as a
text in red and it equals the number of split nodes (see 'Examples').
If there are no split nodes in the network, the execution of the function
will be stopped and an error message will be printed on the R console.
The model is updated until convergence using the
autojags function of the R-package
R2jags with 2 updates and
number of iterations and thinning equal to n_iter and n_thin,
respectively.
run_nodesplit uses the
mtc.nodesplit.comparisons
function of the R-package
gemtc
to obtain automatically the nodes to split based on the decision rule of
van Valkenhoef et al. (2016).
run_nodesplit uses the option (1) in van Valkenhoef et al. (2016)
to parameterise multi-arm trials that contain the node-to-split.
In contrast,
mtc.nodesplit.comparisons
uses the option (3) in van Valkenhoef et al. (2016).
Option (1) keeps the baseline arm of the node-to-split in the corresponding
multi-arms. Option (3) excludes both arms of the node-to-split from the
corresponding multi-arm trials.
The output of run_nodesplit is not end-user-ready.
The nodesplit_plot function inherits the output of
run_nodesplit as an S3 object and processes it further to provide an
end-user-ready output.
run_nodesplit can be used only for a network of interventions.
In the case of two interventions, the execution of the function will
be stopped and an error message will be printed on the R console.
References
Dias S, Welton NJ, Caldwell DM, Ades AE. Checking consistency in mixed treatment comparison meta-analysis. Stat Med 2010;29(7-8):932–44. doi: 10.1002/sim.3767
Gelman A, Rubin DB. Inference from iterative simulation using multiple sequences. Stat Sci 1992;7(4):457–72. doi: 10.1214/ss/1177011136
Spineli LM, Kalyvas C, Papadimitropoulou K. Continuous(ly) missing outcome data in network meta-analysis: a one-stage pattern-mixture model approach. Stat Methods Med Res 2021;30(4):958–75. doi: 10.1177/0962280220983544
Spineli LM. An empirical comparison of Bayesian modelling strategies for missing binary outcome data in network meta-analysis. BMC Med Res Methodol 2019;19(1):86. doi: 10.1186/s12874-019-0731-y
van Valkenhoef G, Dias S, Ades AE, Welton NJ. Automated generation of node-splitting models for assessment of inconsistency in network meta-analysis. Res Synth Methods 2016;7(1):80–93. doi: 10.1002/jrsm.1167
Examples
data("nma.baker2009")
# Read results from 'run_model' (using the default arguments)
res <- readRDS(system.file('extdata/res_baker.rds', package = 'rnmamod'))
# \donttest{
# Run random-effects node-splitting approach
# Note: Ideally, set 'n_iter' to 10000 and 'n_burnin' to 1000
run_nodesplit(full = res,
n_chains = 3,
n_iter = 1000,
n_burnin = 100,
n_thin = 1)
#> JAGS generates initial values for the parameters.
#> 1 out of 8 split nodes
#> Compiling model graph
#> Resolving undeclared variables
#> Allocating nodes
#> Graph information:
#> Observed stochastic nodes: 79
#> Unobserved stochastic nodes: 141
#> Total graph size: 2526
#>
#> Initializing model
#>
#> Updating model for split node 1 until convergence
#> 2 out of 8 split nodes
#> Compiling model graph
#> Resolving undeclared variables
#> Allocating nodes
#> Graph information:
#> Observed stochastic nodes: 79
#> Unobserved stochastic nodes: 141
#> Total graph size: 2526
#>
#> Initializing model
#>
#> Updating model for split node 2 until convergence
#> 3 out of 8 split nodes
#> Compiling model graph
#> Resolving undeclared variables
#> Allocating nodes
#> Graph information:
#> Observed stochastic nodes: 79
#> Unobserved stochastic nodes: 141
#> Total graph size: 2526
#>
#> Initializing model
#>
#> Updating model for split node 3 until convergence
#> 4 out of 8 split nodes
#> Compiling model graph
#> Resolving undeclared variables
#> Allocating nodes
#> Graph information:
#> Observed stochastic nodes: 79
#> Unobserved stochastic nodes: 141
#> Total graph size: 2535
#>
#> Initializing model
#>
#> Updating model for split node 4 until convergence
#> 5 out of 8 split nodes
#> Compiling model graph
#> Resolving undeclared variables
#> Allocating nodes
#> Graph information:
#> Observed stochastic nodes: 79
#> Unobserved stochastic nodes: 141
#> Total graph size: 2535
#>
#> Initializing model
#>
#> Updating model for split node 5 until convergence
#> 6 out of 8 split nodes
#> Compiling model graph
#> Resolving undeclared variables
#> Allocating nodes
#> Graph information:
#> Observed stochastic nodes: 79
#> Unobserved stochastic nodes: 141
#> Total graph size: 2535
#>
#> Initializing model
#>
#> Updating model for split node 6 until convergence
#> 7 out of 8 split nodes
#> Compiling model graph
#> Resolving undeclared variables
#> Allocating nodes
#> Graph information:
#> Observed stochastic nodes: 79
#> Unobserved stochastic nodes: 141
#> Total graph size: 2526
#>
#> Initializing model
#>
#> Updating model for split node 7 until convergence
#> 8 out of 8 split nodes
#> Compiling model graph
#> Resolving undeclared variables
#> Allocating nodes
#> Graph information:
#> Observed stochastic nodes: 79
#> Unobserved stochastic nodes: 141
#> Total graph size: 2531
#>
#> Initializing model
#>
#> Updating model for split node 8 until convergence
#> $direct
#> treat1 treat2 mean sd 2.5% 97.5% Rhat n.eff
#> 1 6 1 -0.3475195 0.2602996 -0.8250056 0.14883633 1.127628 22
#> 2 7 1 -0.6430262 0.2319460 -1.0959832 -0.21210808 1.037831 71
#> 3 8 1 -0.4050210 0.1678153 -0.7639951 -0.08004837 1.021618 140
#> 4 5 4 -0.1899555 0.2080949 -0.6273254 0.19779258 1.015704 190
#> 5 7 4 -0.5709905 0.2112652 -0.9607394 -0.15696131 1.136719 25
#> 6 7 5 -0.3608537 0.2313994 -0.8171038 0.08420671 1.031627 73
#> 7 8 6 -1.5415404 0.6420013 -2.7872876 -0.04214797 1.039615 330
#> 8 8 7 -0.8964306 0.3862680 -1.7145885 -0.15782588 1.247387 13
#>
#> $indirect
#> treat1 treat2 mean sd 2.5% 97.5% Rhat n.eff
#> 1 6 1 1.18185777 1.0172878 -0.4561300 3.06036788 2.138137 5
#> 2 7 1 -0.44282277 0.8149694 -2.0758064 0.86855275 1.081094 31
#> 3 8 1 -1.29301628 0.5283317 -2.2837218 -0.32314054 1.228704 13
#> 4 5 4 -0.67293295 0.3679087 -1.4270310 0.02705463 1.015950 390
#> 5 7 4 -0.18342210 0.1997755 -0.5461401 0.21901942 1.124704 21
#> 6 7 5 -0.39620448 0.2758297 -0.9447325 0.18625857 1.053474 57
#> 7 8 6 -0.06677049 0.2194732 -0.5204410 0.31541549 1.075757 34
#> 8 8 7 -0.02523183 0.1966435 -0.4200616 0.34142787 1.002945 820
#>
#> $diff
#> treat1 treat2 mean sd 2.5% 97.5% Rhat n.eff
#> 1 6 1 -1.52937728 0.9812317 -3.47376423 0.077611225 1.982397 5
#> 2 7 1 -0.20020344 0.7192733 -1.51415053 1.227400009 1.095414 29
#> 3 8 1 0.88799524 0.5463173 -0.04556213 1.899368146 1.213016 14
#> 4 5 4 0.48297748 0.3760610 -0.28218680 1.209727041 1.012588 280
#> 5 7 4 -0.38756835 0.2897400 -0.94496509 0.142615551 1.023809 840
#> 6 7 5 0.03535077 0.3912771 -0.82790747 0.789128152 1.038185 96
#> 7 8 6 -1.47476990 0.6700360 -2.63068712 -0.000297547 1.048805 83
#> 8 8 7 -0.87119878 0.4358669 -1.69174050 0.075655267 1.169309 17
#>
#> $p_value
#> treat1 treat2 p_value
#> 1 6 1 0.06600000
#> 2 7 1 0.73200000
#> 3 8 1 0.06266667
#> 4 5 4 0.21133333
#> 5 7 4 0.14066667
#> 6 7 5 0.84800000
#> 7 8 6 0.05000000
#> 8 8 7 0.05800000
#>
#> $tau
#> treat1 treat2 50% sd 2.5% 97.5% Rhat n.eff
#> 1 6 1 0.1215437 0.08246478 0.0082049142 0.3260568 1.103753 49
#> 2 7 1 0.1405358 0.08750373 0.0147942634 0.3361953 1.086028 34
#> 3 8 1 0.1217684 0.09416532 0.0148473826 0.3615808 1.314259 11
#> 4 5 4 0.1027161 0.08058699 0.0292031041 0.2880754 1.005836 770
#> 5 7 4 0.0870589 0.08095747 0.0006200626 0.2728706 1.389290 11
#> 6 7 5 0.1558986 0.10610953 0.0070656223 0.3937198 1.467487 9
#> 7 8 6 0.1240954 0.07847724 0.0141844211 0.3071928 1.161875 34
#> 8 8 7 0.1575697 0.09560836 0.0068516860 0.3738418 1.155318 35
#>
#> $model
#> [1] "RE"
#>
#> $model_assessment
#> treat1 treat2 deviance DIC pD
#> 1 6 1 53.92127 90.42423 36.50296
#> 2 7 1 54.23491 91.29573 37.06082
#> 3 8 1 53.34470 88.85501 35.51031
#> 4 5 4 53.71467 91.13127 37.41660
#> 5 7 4 54.19413 91.75235 37.55822
#> 6 7 5 54.46978 92.80598 38.33620
#> 7 8 6 52.78928 88.71401 35.92473
#> 8 8 7 54.19800 92.15368 37.95568
#>
#> $n_chains
#> [1] 3
#>
#> $n_iter
#> [1] 1000
#>
#> $n_burnin
#> [1] 100
#>
#> $n_thin
#> [1] 1
#>
#> attr(,"class")
#> [1] "run_nodesplit"
# }