Perform network meta-analysis

Run the model

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.

Using all arguments

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

The output

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.

No or partially extracted missing participant outcome data

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.