MBNMAtime: Package Overview

Hugo Pedder

2023-10-14

Introduction

This vignette demonstrates how to use MBNMAtime to perform meta-analysis of studies with multiple follow-up measurements in order to account for time-course relationships within single or multiple treatment comparisons. This can be performed by conducting Model-Based (Network) Meta-Analysis (MBNMA) to pool relative treatment effects. MBNMA models therefore estimate treatment effects over time (e.g. days, weeks, months).

Including all available follow-up measurements within a study makes use of all the available evidence in a way that maintains connectivity between treatments and explains how the response of the treatment changes over time, thus accounting for heterogeneity and inconsistency that may be present from “lumping” together different time points in a standard Network Meta-Analysis (NMA). All models and analyses are implemented in a Bayesian framework, following an extension of the standard NMA methodology presented by (Lu and Ades 2004) and are run in JAGS (version 4.3.1 or later is required if using R version >= 4.2 with Windows Operating Systems) (JAGS Computer Program 2017). For full details of time-course MBNMA methodology see Pedder et al. (2019), and a simulation study exploring the statistical properties of the method is reported in Pedder et al. (2020).

MBNMAtime provides a complete set of functions that allow for meta-analysis of longitudinal time-course data and plotting of a number of informative graphics. Functions are provided for ranking, prediction, and for assessing consistency when modelling using relative effects. The package allows for flexible modelling of either relative or absolute effects interchangeably on different time-course parameters within the same analysis, whilst providing a straightforward syntax with which to define these models.

This package has been developed alongside MBNMAdose, a package that allows users to perform dose-response MBNMA to allow for modelling of dose-response relationships between different agents within a network. However, they should not be loaded into R at the same time as there are a number of functions with shared names that perform similar tasks yet are specific to dealing with either time-course or dose-response data.

Within the vignettes, some models have not been evaluated, or have been run with fewer iterations than would be necessary to achieve convergence and produce valid results in practice. This has been done to speed up computation and rendering of the vignettes.

Workflow within the package

Functions within MBNMAtime follow a clear pattern of use:

  1. Load your data into the correct format using mb.network() (Exploring the data
  2. Specify a suitable time-course function and analyse your data using mb.run() (Performing a time-course MBNMA
  3. Test for consistency using functions like mb.nodesplit() (Checking for consistency
  4. Examine model outputs, such as relative effects, forest plots and treatment rankings (Model outputs
  5. Use your model to make predictions or estimate treatment effects at specific time-points using predict() (Predictions

At each of these stages there are a number of informative graphs that can be generated to help understand the data and make decisions regarding model fitting.

Datasets Included in the Package

Pain relief in osteoarthritis

osteopain is from a systematic review of treatments for pain in osteoarthritis, used previously in Pedder et al. (2019). The outcome is pain measured on a continuous scale, and aggregate data responses correspond to the mean WOMAC pain score at different follow-up times. The dataset includes 30 Randomised-Controlled Trials (RCTs), comparing 29 different treatments (including placebo). osteopain is a data frame in long format (one row per time point, arm and study), with the variables studyID, time, y, se, treatment and arm.

studyID time y se treatment arm treatname
Baerwald 2010 0 6.55 0.09 Pl_0 1 Placebo_0
Baerwald 2010 2 5.40 0.09 Pl_0 1 Placebo_0
Baerwald 2010 6 4.97 0.10 Pl_0 1 Placebo_0
Baerwald 2010 13 4.75 0.11 Pl_0 1 Placebo_0
Baerwald 2010 0 6.40 0.13 Na_1000 2 Naproxen_1000
Baerwald 2010 2 4.03 0.13 Na_1000 2 Naproxen_1000

Alogliptin for lowering blood glucose concentration in type II diabetes

alog_pcfb is from a systematic review of Randomised-Controlled Trials (RCTs) comparing different doses of alogliptin with placebo (Langford et al. 2016). The systematic review was simply performed and was intended to provide data to illustrate a statistical methodology rather than for clinical inference. Alogliptin is a treatment aimed at reducing blood glucose concentration in type II diabetes. The outcome is continuous, and aggregate data responses correspond to the mean change in HbA1c from baseline to follow-up in studies of at least 12 weeks follow-up. The dataset includes 14 Randomised-Controlled Trials (RCTs), comparing 5 different doses of alogliptin with placebo (6 different treatments in total). alog_pcfb is a data frame in long format (one row per time point, arm and study), with the variables studyID, clinicaltrialGov_ID, agent, dose, treatment, time, y, se, and N.

studyID clinicaltrialGov_ID agent dose treatment time y se n
1 NCT01263470 alogliptin 0.00 placebo 2 0.00 0.02 75
1 NCT01263470 alogliptin 6.25 alog_6.25 2 -0.16 0.02 79
1 NCT01263470 alogliptin 12.50 alog_12.5 2 -0.17 0.02 84
1 NCT01263470 alogliptin 25.00 alog_25 2 -0.16 0.02 79
1 NCT01263470 alogliptin 50.00 alog_50 2 -0.15 0.02 79
1 NCT01263470 alogliptin 0.00 placebo 4 -0.01 0.04 75

Tiotropium, Aclidinium and Placebo for maintenance treatment of moderate to severe chronic obstructive pulmonary disease

A dataset from a systematic review of Randomised-Controlled Trials (RCTs) for maintenance treatment of moderate to severe chronic obstructive pulmonary disease (COPD) (Karabis et al. 2013). Data are extracted from (Tallarita, De lorio, and Baio 2019). SEs were imputed for three studies, and number of patients randomised were imputed for one study (LAS 39) in which they were missing, using the median standard deviation calculated from other studies in the dataset. The outcome is trough Forced Expiratory Volume in 1 second (FEV1), measured in litres and reported in each study arm as mean change from baseline to follow-up. The dataset includes 13 RCTs, comparing 2 treatments (Tiotropium and Aclidinium) and placebo. copd is a data frame in long format (one row per observation, arm and study), with the variables studyID, time, y, se, treatment, and n.

studyID time y se treatment n
ACCORD I 1 -0.01 0.01 Placebo 187
ACCORD I 4 -0.01 0.01 Placebo 187
ACCORD I 8 -0.01 0.01 Placebo 187
ACCORD I 12 -0.02 0.01 Placebo 187
ACCORD I 1 0.10 0.01 Aclidinium 190
ACCORD I 4 0.11 0.01 Aclidinium 190

Body weight reduction in obesity patients

obesityBW_CFB is from a systematic review of pharmacological treatments for obesity. The outcome measured is change from baseline in body weight (kg) at different follow-up times. 35 RCTs are included that investigate 26 different treatments (16 agents/agent combinations compared at different doses). obesityBW_CFB is a dataset in long format (one row per time point, arm and study), with the variables studyID, time, y, se, N, treatment, arm, treatname, agent and class.

class is the class of a particular agent (e.g. Lipase inhibitor)

studyID time y se n treatment treatname agent class
27 Apfelbaum 1999 4 -1.00 0.39 78 plac placebo placebo Placebo
28 Apfelbaum 1999 4 -1.59 0.38 81 sibu_10MG sibutramine 10MG sibutramine SNRI
29 Apfelbaum 1999 9 -1.59 0.40 78 plac placebo placebo Placebo
30 Apfelbaum 1999 9 -3.01 0.39 81 sibu_10MG sibutramine 10MG sibutramine SNRI
31 Apfelbaum 1999 13 -2.25 0.41 78 plac placebo placebo Placebo
32 Apfelbaum 1999 13 -4.76 0.40 81 sibu_10MG sibutramine 10MG sibutramine SNRI

Serum uric acid concentration in gout

goutSUA_CFB is from a systematic review of interventions for lowering Serum Uric Acid (SUA) concentration in patients with gout [not published previously]. The outcome is continuous, and aggregate data responses correspond to the mean change from baseline in SUA in mg/dL at different follow-up times. The dataset includes 28 RCTs, comparing 41 treatments (8 agents compared at different doses). goutSUA_CFB is a data frame in long format (one row per arm and study), with the variables studyID, time, y, se, treatment, arm, class and treatname.

studyID time y se treatment treatname class
1102 1 0.07 0.25 RDEA_100 RDEA594_100 RDEA
1102 1 0.02 0.18 RDEA_200 RDEA594_200 RDEA
1102 1 0.06 0.25 RDEA_400 RDEA594_400 RDEA
1102 2 -0.53 0.25 RDEA_100 RDEA594_100 RDEA
1102 2 -1.37 0.18 RDEA_200 RDEA594_200 RDEA
1102 2 -1.73 0.25 RDEA_400 RDEA594_400 RDEA

References

JAGS Computer Program. 2017. https://mcmc-jags.sourceforge.io/.
Karabis, A., L. Lindner, M. Mocarski, E. Huisman, and A. Greening. 2013. “Comparative Efficacy of Aclidinium Versus Glycopyrronium and Tiotropium, as Maintenance Treatment of Moderate to Severe COPD Patients: A Systematic Review and Network Meta-Analysis.” Journal Article. Int J Chron Obstruct Pulmon Dis 8: 405–23. https://doi.org/10.2147/COPD.S48967.
Langford, O., J. K. Aronson, G. van Valkenhoef, and R. J. Stevens. 2016. “Methods for Meta-Analysis of Pharmacodynamic Dose-Response Data with Application to Multi-Arm Studies of Alogliptin.” Journal Article. Stat Methods Med Res. https://doi.org/10.1177/0962280216637093.
Lu, G., and A. E. Ades. 2004. “Combination of Direct and Indirect Evidence in Mixed Treatment Comparisons.” Journal Article. Stat Med 23 (20): 3105–24. https://doi.org/10.1002/sim.1875.
Pedder, H., M. Boucher, S. Dias, M. Bennetts, and N. J. Welton. 2020. “Performance of Model-Based Network Meta-Analysis (MBNMA) of Time-Course Relationships: A Simulation Study.” Journal Article. Research Synthesis Methods 11 (5): 678–97. https://doi.org/10.1002/jrsm.1432.
Pedder, H., S. Dias, M. Bennetts, M. Boucher, and N. J. Welton. 2019. “Modelling Time-Course Relationships with Multiple Treatments: Model-Based Network Meta-Analysis for Continuous Summary Outcomes.” Journal Article. Res Synth Methods 10 (2): 267–86.
Tallarita, M., M. De lorio, and G. Baio. 2019. “A Comparative Review of Network Meta-Analysis Models in Longitudinal Randomized Controlled Trial.” Journal Article. Statistics in Medicine 38 (16): 3053–72. https://doi.org/10.1002/sim.8169.