This vignette illustrates how to perform a one-stage Bayesian
random-effects network meta-analysis with consistency equation using the
`run_model`

function. This function includes arguments to
handle aggregate missing participant outcome data (MOD) in each arm of
every trial via the pattern-mixture model.

We will use the network on pharmacologic interventions for chronic
obstructive pulmonary disease (COPD) from the systematic review of Baker et
al. (2009). This network comprises 21 trials comparing seven
pharmacological interventions with each other and placebo. The
exacerbation of COPD (harmful outcome) is the analysed binary outcome
(see `?nma.baker2009`

).

`run_model`

calls the `jags`

function from the
**R2jags**
package to perform the Bayesian analysis using the BUGS code of Dias and
colleagues (2013).

```
run_model(data = nma.baker2009,
measure = "OR",
heter_prior = list("halfnormal", 0, 1),
D = 0,
n_chains = 3,
n_iter = 10000,
n_burnin = 1000,
n_thin = 1)
```

With only the minimum required arguments, the function adjusts MOD
under the missing-at-random assumption (MAR; by default) via the
informative missingness odds ratio (IMOR) in the logarithmic scale
(White et al. (2008)): The minimum required arguments of
`run_model`

include specifying:

- the dataset (a data-frame with one-trial-per-row format) in
`data`

(see`?data_preparation`

); - the effect measure in
`measure`

(see ‘Arguments’ in`?run_model`

): - the prior distribution for the heterogeneity parameter in
`heter_prior`

(see`?heterogeneity_param_prior`

); - the direction of the outcome in
`D`

(here,`D = 0`

because the outcome is harmful; see, ‘Arguments’ in`?run_model`

) - the number of chains in
`n_chains`

(see ‘Arguments’ in`?run_model`

– also for the subsequent arguments); - the number of iterations in
`n_iter`

; - the number of burn-in in
`n_burnin`

, and - the thinning in
`n_thin`

.

Suppose we decide to use an *empirically-based prior distribution
for the between-trial variance* that aligns with the outcome and
interventions under investigation. We also consider a *hierarchical
structure for the prior normal distribution of the log IMOR that is
specific to the interventions* in the network
(`assumption = "HIE-ARM"`

) (Turner et al., 2015a; Spineli,
2019). We still assume MAR on average with variance of log IMOR equal to
1 (`var_misspar = 1`

) which is also the default argument. In
this case, `run_model`

must be specified as follows:

```
run_model(data = nma.baker2009,
measure = "OR",
model = "RE",
assumption = "HIE-ARM",
heter_prior = list("lognormal", -2.06, 0.438),
mean_misspar = c(0, 0),
var_misspar = 1,
D = 0,
n_chains = 3,
n_iter = 10000,
n_burnin = 1000,
n_thin = 1)
```

The argument `model = "RE"`

refers to the random-effects
model. For the fixed-effect model, use `model = "FE"`

.

`heter_prior = list("lognormal", -2.06, 0.438)`

refers to
‘symptoms reflecting the continuation of condition’ for the
‘pharmacological versus placebo’ comparison-type as elicited by Turner
and colleagues (2015b).

In the argument `mean_misspar = c(0, 0)`

, the first and
second element of the vector refers to the mean log IMOR in the
non-reference interventions and the reference intervention of the
network, respectively – the latter is always the intervention with
identifier equal to 1. Hence, for all non-reference interventions we can
consider **the same** mean log IMOR. See ‘Details’ in
`?missingness_param_prior`

`run_model`

returns **a list of R2jags
output** on the summaries of the posterior distribution, and the
Gelman-Rubin convergence diagnostic of the monitored parameters (see
‘Value’ in `?run_model`

). The output is used as an S3 object
by other functions of the package to be processed further and provide an
end-user-ready output. See, for example, the function
`?league_heatmap`

that creates the league table with the
effect sizes of all possible comparisons in the network.

`run_model`

can also handle a dataset where MOD have not
be extracted or MOD have been extracted for some trials or trial-arms.
For illustrative purposes, we removed the item `m`

from
`nma.baker2009`

to indicate that MOD were not extracted for
this outcome:

```
study t1 t2 t3 t4 r1 r2 r3 r4 n1 n2 n3 n4
1 Llewellyn-Jones, 1996 1 4 NA NA 3 0 NA NA 8 8 NA NA
2 Paggiaro, 1998 1 4 NA NA 51 45 NA NA 139 142 NA NA
3 Mahler, 1999 1 7 NA NA 47 28 NA NA 143 135 NA NA
4 Casaburi, 2000 1 8 NA NA 41 45 NA NA 191 279 NA NA
5 van Noord, 2000 1 7 NA NA 18 11 NA NA 50 47 NA NA
6 Rennard, 2001 1 7 NA NA 41 38 NA NA 135 132 NA NA
```

Using the minimum required arguments, `run_model`

will run
and provide results.

`run_model`

calls the `data_preparation`

function. The latter creates a pseudo-data-frame for the item
`m`

(see ‘Value’ in `?data_preparation`

) that
assigns `NA`

to all trial-arms. `data_preparation`

also creates the pseudo-data-frame `I`

that has the same
dimension with the other items in the dataset, and assigns the zero
value to all trial-arms to indicate that no MOD have been extracted.
Both pseudo-data-frames aim to retain in the dataset the trials without
information on MOD; otherwise, these trials would have been excluded
from the analysis. See ‘Details’ in `?data_preparation`

and
`?run_model`

.

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* 2013;**33**(5):607–617. doi:
10.1177/0272989X12458724

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

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* 2015a;**34**(12):2062–80.
doi:
10.1002/sim.6475

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

Turner RM, Jackson D, Wei Y, Thompson SG, Higgins JPT. Predictive
distributions for between-study heterogeneity and simple methods for
their application in Bayesian meta-analysis. *Stat Med*
2015b;**34**(6):984–98. doi:
10.1002/sim.6381