| run_model {rnmamod} | R Documentation |
Perform Bayesian pairwise or network meta-analysis
Description
Performs a one-stage pairwise or network meta-analysis while addressing aggregate binary or continuous missing participant outcome data via the pattern-mixture model.
Usage
run_model(
data,
measure,
model,
assumption,
heter_prior,
mean_misspar,
var_misspar,
D,
ref,
base_risk,
n_chains,
n_iter,
n_burnin,
n_thin,
inits = NULL
)
Arguments
data |
A data-frame of the one-trial-per-row format with arm-level data. See 'Format' for the specification of the columns. |
measure |
Character string indicating the effect measure. For a binary
outcome, the following can be considered: |
model |
Character string indicating the analysis model with values
|
assumption |
Character string indicating the structure of the
informative missingness parameter.
Set |
heter_prior |
A list of three elements with the following order:
1) a character string indicating the distribution with
(currently available) values |
mean_misspar |
A scalar or numeric vector of two numeric values for the
mean of the normal distribution of the informative missingness parameter
(see 'Details'). The default argument is 0 and corresponds to the
missing-at-random assumption.
See also 'Details' in |
var_misspar |
A positive non-zero number for the variance of the
normal distribution of the informative missingness parameter.
When the |
D |
A binary number for the direction of the outcome.
Set |
ref |
An integer specifying the reference intervention. The number
should match the intervention identifier under element t in
|
base_risk |
A scalar, a vector of length three with elements sorted in
ascending order, or a matrix with two columns and number of rows equal to
the number of relevant trials. In the case of a scalar or vector, the
elements should be in the interval (0, 1) (see 'Details'). If
|
n_chains |
Positive integer specifying the number of chains for the
MCMC sampling; an argument of the |
n_iter |
Positive integer specifying the number of Markov chains for the
MCMC sampling; an argument of the |
n_burnin |
Positive integer specifying the number of iterations to
discard at the beginning of the MCMC sampling; an argument of the
|
n_thin |
Positive integer specifying the thinning rate for the
MCMC sampling; an argument of the |
inits |
A list with the initial values for the parameters; an argument
of the |
Format
The columns of the data-frame in the argument data refer
to the following elements for a continuous outcome:
| t | An intervention identifier in each arm. |
| y | The observed mean value of the outcome in each arm. |
| sd | The observed standard deviation of the outcome in each arm. |
| m | The number of missing participant outcome data in each arm. |
| n | The number of randomised participants in each arm. |
For a binary outcome, the columns of the data-frame in the argument
data refer to the following elements:
| t | An intervention identifier in each arm. |
| r | The observed number of events of the outcome in each arm. |
| m | The number of missing participant outcome data in each arm. |
| n | The number of randomised participants in each arm. |
The number of rows in data equals the number of collected trials.
Each element appears in data as many times as the maximum number of
interventions compared in a trial of the dataset.
In pairwise meta-analysis, the maximum number of arms is inherently two.
The same holds for a network meta-analysis without multi-arm trials.
In the case of network meta-analysis with multi-arm trials, the maximum
number of arms exceeds two. See 'Examples' that illustrates the structure
of data for a network with a maximum number of four arms.
It is not a prerequisite of run_model that the multi-arm trials
appear at the bottom of the dataset.
Details
The model runs in JAGS and the progress of the simulation
appears on the R console. The output of run_model is used as an S3
object by other functions of the package to be processed further and
provide an end-user-ready output.
The data_preparation function is called to prepare the data
for the Bayesian analysis. data_preparation creates the
pseudo-data-frames m_new, and I, that have the same
dimensions with the element N. m_new takes the zero
value for the observed trial-arms with unreported missing participant
outcome data (i.e., m equals NA for the corresponding
trial-arms), the same value with m for the observed trial-arms with
reported missing participant outcome data, and NA for the unobserved
trial-arms. I is a dummy pseudo-data-frame and takes the value one
for the observed trial-arms with reported missing participant outcome data,
the zero value for the observed trial-arms with unreported missing
participant outcome data (i.e., m_new equals zero for the
corresponding trial-arms), and NA for the unobserved trial-arms.
Thus, I indicates whether missing participant outcome data have been
collected for the observed trial-arms. If the user has not defined the
element m in data, m_new and I take the zero
value for all observed trial-arms to indicate that no missing participant
outcome data have been collected for the analysed outcome. See 'Details' in
data_preparation.
Furthermore, data_preparation sorts the interventions across
the arms of each trial in an ascending order and correspondingly the
remaining elements in data (see 'Format').
data_preparation considers the first column in t as
being the control arm for every trial. Thus, this sorting ensures that
interventions with a lower identifier are consistently treated as the
control arm in each trial. This case is relevant in non-star-shaped
networks.
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.
To perform a Bayesian pairwise or network meta-analysis, the
prepare_model function is called which contains the WinBUGS
code as written by Dias et al. (2013a) for binomial and normal likelihood to
analyse aggregate binary and continuous outcome data, respectively.
prepare_model uses the consistency model (as described in
Lu and Ades (2006)) to estimate all possible comparisons in the network.
It also accounts for the multi-arm trials by assigning conditional
univariate normal distributions on the underlying trial-specific effect
size of comparisons with the baseline arm of the multi-arm trial
(Dias et al., 2013a).
The code of Dias et al. (2013a) has been extended to incorporate the
pattern-mixture model to adjust the underlying outcome in each arm of
every trial for missing participant outcome data (Spineli et al., 2021;
Spineli, 2019a; Turner et al., 2015). The assumptions about the
missingness parameter are specified using the arguments mean_misspar
and var_misspar. Specifically, run_model considers the
informative missingness odds ratio in the logarithmic scale for binary
outcome data (Spineli, 2019a; Turner et al., 2015; White et al., 2008), the
informative missingness difference of means when measure is
"MD" or "SMD", and the informative missingness ratio of means
in the logarithmic scale when measure is "ROM"
(Spineli et al., 2021; Mavridis et al., 2015).
When assumption is trial-specific (i.e., "IDE-TRIAL" or
"HIE-TRIAL"), or independent (i.e., "IND-CORR" or
"IND-UNCORR"), only one numeric value can be assigned to
mean_misspar because the same missingness scenario is applied to all
trials and trial-arms of the dataset, respectively. When assumption
is "IDE-ARM" or "HIE-ARM", a maximum of two
different or identical numeric values can be assigned as a
vector to mean_misspars: the first value refers to the experimental
arm, and the second value refers to the control arm of a trial.
In the case of a network, the first value is considered for all
non-reference interventions and the second value is considered for the
reference intervention of the network (i.e., the intervention with
identifier equal to ref). This is necessary to ensure transitivity
in the assumptions for the missingness parameter across the network
(Spineli, 2019b).
When there is at least one trial-arm with unreported missing participant
outcome data (i.e., m equals NA for the corresponding
trial-arms) or when missing participant outcome data have not been
collected for the analysed outcome (i.e., m is missing in
data), run_model assigns the assumption "IND-UNCORR"
to assumption.
Currently, there are no empirically-based prior distributions for the
informative missingness parameters. The user may refer to Spineli (2019),
Turner et al. (2015), Mavridis et al. (2015), and White et al. (2008) to
determine mean_misspar and select a proper value for
var_misspar.
The scalar base_risk refers to a fixed baseline risk for the
selected reference intervention (as specified with ref).
When base_risk is a three-element vector, it refers to a random
baseline risk and the elements should be sorted in ascending order as they
refer to the lower bound, mean value, and upper bound of the 95%
confidence interval for the baseline risk for the selected reference
intervention. The baseline_model function is called to
calculate the mean and variance of the approximately normal distribution of
the logit of an event for ref using these three elements
(Dias et al., 2018). When base_risk is a matrix, it refers to the
predicted baseline risk with first column being the number of events, and
second column being the sample size of the corresponding trials on the
selected reference intervention. Then the baseline_model
function is called that contains the WinBUGS code as written by Dias et al.
(2013b) for the hierarchical baseline model. The posterior mean and
precision of the predictive distribution of the logit of an event
for the selected reference intervention are plugged in the WinBUGS code for
the relative effects model (via the prepare_model function).
The matrix base_risk should not comprise the trials in data
that include the ref, unless justified (Dias et al., 2018).
To obtain unique absolute risks for each intervention, the network
meta-analysis model has been extended to incorporate the transitive risks
framework, namely, an intervention has the same absolute risk regardless of
the comparator intervention(s) in a trial (Spineli et al., 2017).
The absolute risks are a function of the odds ratio (the base-case
effect measure for a binary outcome) and the selected baseline risk for the
reference intervention (ref) (Appendix in Dias et al., 2013a).
We advocate using the odds ratio as an effect measure for its desired
mathematical properties. Then, the relative risk and risk difference can be
obtained as a function of the absolute risks of the corresponding
interventions in the comparison of interest. Hence, regardless of the
selected measure for a binary outcome, run_model performs
pairwise or network meta-analysis based on the odds ratio.
Value
A list of R2jags output on the summaries of the posterior distribution, and the Gelman-Rubin convergence diagnostic (Gelman et al., 1992) of the following monitored parameters for a fixed-effect pairwise meta-analysis:
EM |
The estimated summary effect measure (according to the argument
|
EM_LOR |
The estimated summary odd ratio in the logarithmic scale when
|
dev_o |
The deviance contribution of each trial-arm based on the observed outcome. |
hat_par |
The fitted outcome at each trial-arm. |
phi |
The informative missingness parameter. |
For a fixed-effect network meta-analysis, the output additionally includes:
SUCRA |
The surface under the cumulative ranking curve for each intervention. |
SUCRA_LOR |
The surface under the cumulative ranking curve for each
intervention under the odds ratio effect measure when |
effectiveneness |
The ranking probability of each intervention for every rank. |
For a random-effects pairwise meta-analysis, the output additionally includes the following elements:
EM_pred |
The predicted summary effect measure (according to the
argument |
EM_pred_LOR |
The predicted summary odds ratio in the logarithmic
scale when |
delta |
The estimated trial-specific effect measure (according to the
argument |
tau |
The between-trial standard deviation. |
In network meta-analysis, EM and EM_pred refer to all
possible pairwise comparisons of interventions in the network. Furthermore,
tau is typically assumed to be common for all observed comparisons
in the network. For a multi-arm trial, we estimate a total of T-1
delta for comparisons with the baseline intervention of the trial
(found in the first column of the element t), with T being
the number of interventions in the trial.
Furthermore, the output includes the following elements:
leverage_o |
The leverage for the observed outcome at each trial-arm. |
sign_dev_o |
The sign of the difference between observed and fitted outcome at each trial-arm. |
model_assessment |
A data-frame on the measures of model assessment: deviance information criterion, number of effective parameters, and total residual deviance. |
indic |
The sign of basic parameters in relation to the reference
intervention as specified in argument |
jagsfit |
An object of S3 class |
The run_model function also returns the arguments data,
measure, model, assumption, heter_prior,
mean_misspar, var_misspar, D, ref,
base_risk, n_chains, n_iter, n_burnin,
and n_thin as specified by the user to be inherited by other
functions of the package.
Author(s)
Loukia M. Spineli
References
Cooper NJ, Sutton AJ, Morris D, Ades AE, Welton NJ. Addressing between-study heterogeneity and inconsistency in mixed treatment comparisons: Application to stroke prevention treatments in individuals with non-rheumatic atrial fibrillation. Stat Med 2009;28(14):1861–81. doi: 10.1002/sim.3594
Dias S, Ades AE, Welton NJ, Jansen JP, Sutton AJ. Network Meta-Analysis for Decision Making. Chichester (UK): Wiley; 2018.
Dias S, Sutton AJ, Ades AE, Welton NJ. Evidence synthesis for decision making 2: a generalized linear modeling framework for pairwise and network meta-analysis of randomized controlled trials. Med Decis Making 2013a;33(5):607–17. doi: 10.1177/0272989X12458724
Dias S, Welton NJ, Sutton AJ, Ades AE. Evidence synthesis for decision making 5: the baseline natural history model. Med Decis Making 2013b;33(5):657–70. doi: 10.1177/0272989X13485155
Gelman A, Rubin DB. Inference from iterative simulation using multiple sequences. Stat Sci 1992;7(4):457–72. doi: 10.1214/ss/1177011136
Lu G, Ades AE. Assessing evidence inconsistency in mixed treatment comparisons. J Am Stat Assoc 2006;101:447–59. doi: 10.1198/016214505000001302
Mavridis D, White IR, Higgins JP, Cipriani A, Salanti G. Allowing for uncertainty due to missing continuous outcome data in pairwise and network meta-analysis. Stat Med 2015;34(5):721–41. doi: 10.1002/sim.6365
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 2019a;19(1):86. doi: 10.1186/s12874-019-0731-y
Spineli LM. Modeling missing binary outcome data while preserving transitivity assumption yielded more credible network meta-analysis results. J Clin Epidemiol 2019b;105:19–26. doi: 10.1016/j.jclinepi.2018.09.002
Spineli LM, Brignardello-Petersen R, Heen AF, Achille F, Brandt L, Guyatt GH, et al. Obtaining absolute effect estimates to facilitate shared decision making in the context of multiple-treatment comparisons. Abstracts of the Global Evidence Summit, Cape Town, South Africa. Cochrane Database of Systematic Reviews 2017;9(Suppl 1):18911.
Turner NL, Dias S, Ades AE, Welton NJ. A Bayesian framework to account for uncertainty due to missing binary outcome data in pairwise meta-analysis. Stat Med 2015;34(12):2062–80. doi: 10.1002/sim.6475
White IR, Higgins JP, Wood AM. Allowing for uncertainty due to missing data in meta-analysis–part 1: two-stage methods. Stat Med 2008;27(5):711–27. doi: 10.1002/sim.3008
See Also
autojags,
baseline_model, data_preparation,
heterogeneity_param_prior,
jags,
missingness_param_prior, prepare_model
Examples
data("nma.baker2009")
# Show the first six trials of the dataset
head(nma.baker2009)
# Perform a random-effects network meta-analysis
# Note: Ideally, set 'n_iter' to 10000 and 'n_burnin' to 1000
run_model(data = nma.baker2009,
measure = "OR",
model = "RE",
assumption = "IDE-ARM",
heter_prior = list("halfnormal", 0, 1),
mean_misspar = c(0, 0),
var_misspar = 1,
D = 0,
ref = 1,
n_chains = 3,
n_iter = 1000,
n_burnin = 100,
n_thin = 1)