# MBNMAdose: Package Overview

#### Hugo Pedder

#### 2024-04-18

## Introduction

This vignette demonstrates how to use `MBNMAdose` to perform Model-Based Network Meta-Analysis (MBNMA) of studies with multiple doses of different agents by accounting for the dose-response relationship. This can connect disconnected networks via the dose-response relationship and the placebo response, improve precision of estimated effects and allow interpolation/extrapolation of predicted response based on the dose-response relationship.

Modelling the dose-response relationship also avoids the “lumping” of different doses of an agent which is often done in Network Meta-Analysis (NMA) and can introduce additional heterogeneity or inconsistency. 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 4.3.0 or later is required) (2017). For full details of dose-response MBNMA methodology see Mawdsley et al. (2016). Throughout this vignette we refer to a treatment as a specific dose or a specific agent

This package has been developed alongside `MBNMAtime`, a package that allows users to perform time-course MBNMA to incorporate multiple time points within different studies. 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.

### Workflow within the package

Functions within `MBNMAdose` follow a clear pattern of use:

1. Load your data into the correct format using `mbnma.network()` and explore potential relationships (Exploring the data
2. Perform a dose-response MBNMA using `mbnma.run()` (Performing a dose-response MBNMA. Modelling of effect modifying covariates is also possibly using Network Meta-Regression.
3. Test for consistency at the treatment-level using functions like `nma.nodesplit()` and `nma.run()` (Checking for consistency
4. Examine model outputs, such as relative effects, forest plots and treatment rankings (Model outputs
5. Use your model to predict responses using `predict()` (Predictions

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

## Datasets Included in the Package

### Triptans for migraine pain relief

`triptans` is from a systematic review of interventions for pain relief in migraine (Thorlund et al. 2014). The outcome is binary, and represents (as aggregate data) the number of participants who were headache-free at 2 hours. Data are from patients who had had at least one migraine attack, who were not lost to follow-up, and who did not violate the trial protocol. The dataset includes 70 Randomised-Controlled Trials (RCTs), comparing 7 triptans with placebo. Doses are standardised as relative to a “common” dose, and in total there are 23 different treatments (combination of dose and agent). `triptans` is a data frame in long format (one row per arm and study), with the variables `studyID`, `AuthorYear`, `N`, `r`, `dose` and `agent`.

studyID | AuthorYear | n | r | dose | agent
--- | --- | --- | --- | --- | ---
1 | Tfelt-Hansen P 2006 | 22 | 6 | 0 | placebo
1 | Tfelt-Hansen P 2006 | 30 | 14 | 1 | sumatriptan
2 | Goadsby PJ 2007 | 467 | 213 | 1 | almotriptan
2 | Goadsby PJ 2007 | 472 | 229 | 1 | zolmitriptan
3 | Tuchman M2006 | 160 | 15 | 0 | placebo
3 | Tuchman M2006 | 174 | 48 | 1 | zolmitriptan

### Biologics for treatment of moderate-to-severe psoriasis

There are 3 psoriasis datasets from a systematic review of RCTs comparing biologics at different doses and placebo (Warren et al. 2019). Each dataset contains a different binary outcome, all based on the number of patients experiencing degrees of improvement on the Psoriasis Area and Severity Index (PASI) measured at 12 weeks follow-up. Each dataset contains information on the number of participants who achieved \(\geq75\%\) (`psoriasis75`), \(\geq90\%\) (`psoriasis90`), or \(100\%\) (`psoriasis100`).

### Selective Serotonin Reuptake Inhibitors (SSRIs) for major depression

`ssri` is from a systematic review examining the efficacy of different doses of SSRI antidepressant drugs and placebo (Furukawa et al. 2019). The response to treatment is defined as a 50% reduction in depressive symptoms after 8 weeks (4-12 week range) follow-up. The dataset includes 60 RCTs comparing 5 different SSRIs with placebo.

    kable(head(ssri), digits = 2)

studyID | bias | age | weeks | agent | dose | n | r
--- | --- | --- | --- | --- | --- | --- | ---
1 | Moderate risk | 43.0 | 6 | placebo | 0 | 149 | 69
1 | Moderate risk | 42.9 | 6 | fluoxetine | 20 | 137 | 77
2 | Low risk | 41.2 | 6 | placebo | 0 | 137 | 63
2 | Low risk | 40.9 | 6 | paroxetine | 20 | 138 | 74
7 | Low risk | 41.6 | 6 | placebo | 0 | 158 | 91
7 | Low risk | 41.3 | 6 | fluoxetine | 20 | 148 | 89

### Interventions for Serum Uric Acid (SUA) reduction in gout

`gout` 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 2 weeks follow-up. The dataset includes 10 Randomised-Controlled Trials (RCTs), comparing 5 different agents, and placebo. Data for one agent (RDEA) arises from an RCT that is not placebo-controlled, and so is not connected to the network directly. In total there were 19 different treatments (combination of dose and agent). `gout` is a data frame in long format (one row per arm and study), with the variables `studyID`, `y`, `se`, `agent` and `dose`.

| studyID | y | se | agent | dose
--- | --- | --- | --- | --- | ---
4 | 1102 | -0.53 | 0.25 | RDEA | 100
5 | 1102 | -1.37 | 0.18 | RDEA | 200
6 | 1102 | -1.73 | 0.25 | RDEA | 400
53 | 2001 | -6.82 | 0.06 | Febu | 240
54 | 2001 | 0.15 | 0.04 | Plac | 0
92 | 2003 | -3.43 | 0.03 | Allo | 300

### Interventions for pain relief in osteoarthritis

`osteopain` is from a systematic review of interventions for pain relief in osteoarthritis, used previously in Pedder et al. (2019). The outcome is continuous, and aggregate data responses correspond to the mean WOMAC pain score at 2 weeks follow-up. The dataset includes 18 Randomised-Controlled Trials (RCTs), comparing 8 different agents with placebo. In total there were 26 different treatments (combination of dose and agent). The active treatments can also be grouped into 3 different classes, within which they have similar mechanisms of action. `osteopain_2wkabs` is a data frame in long format (one row per arm and study), with the variables `studyID`, `agent`, `dose`, `class`, `y`, `se`, and `N`.

| studyID | agent | dose | class | y | se | n
--- | --- | --- | --- | --- | --- | --- | ---
13 | 1 | Placebo | 0 | Placebo | 6.26 | 0.23 | 60
14 | 1 | Etoricoxib | 10 | Cox2Inhib | 5.08 | 0.16 | 114
15 | 1 | Etoricoxib | 30 | Cox2Inhib | 4.42 | 0.17 | 102
16 | 1 | Etoricoxib | 5 | Cox2Inhib | 5.34 | 0.16 | 117
17 | 1 | Etoricoxib | 60 | Cox2Inhib | 3.62 | 0.17 | 112
18 | 1 | Etoricoxib | 90 | Cox2Inhib | 4.08 | 0.17 | 112

### 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 RCTs, comparing 5 different doses of alogliptin with placebo, leading to 6 different treatments (combination of dose and agent) within the network. `alog_pcfb` is a data frame in long format (one row per arm and study), with the variables `studyID`, `agent`, `dose`, `y`, `se`, and `N`.

studyID | agent | dose | y | se | n
--- | --- | --- | --- | --- | ---
NCT01263470 | alogliptin | 0.00 | 0.06 | 0.05 | 75
NCT01263470 | alogliptin | 6.25 | -0.51 | 0.08 | 79
NCT01263470 | alogliptin | 12.50 | -0.70 | 0.06 | 84
NCT01263470 | alogliptin | 25.00 | -0.76 | 0.06 | 79
NCT01263470 | alogliptin | 50.00 | -0.82 | 0.05 | 79
NCT00286455 | alogliptin | 0.00 | -0.13 | 0.08 | 63

### Wound closure methods for reducing Surgical Site Infection (SSI)

`ssi_closure` is from a systematic review examining the efficacy of different wound closure methods to reduce Surgical Site Infections (SSI). The outcome is binary and represents the number of patients who experienced a SSI. The dataset includes 129 RCTs comparing 16 different interventions in 6 classes. This dataset is primarily used to illustrate how `MBNMAdose` can be used to perform different types of network meta-analysis without dose-response information. It is in long format (one row per study arm) and includes the variables `studyID`, `Year`, `n`, `r`, `trt` and `class`.

studyID | Year | r | n | trt | class
--- | --- | --- | --- | --- | ---
Chughtai2000_51 | 2000 | 9 | 81 | Suture-absorbable | Suture
Chughtai2000_51 | 2000 | 9 | 81 | Clips | Clips
Johnson1997_52 | 1997 | 24 | 258 | Suture–monofilament | Suture
Johnson1997_52 | 1997 | 23 | 258 | Staples | Staples
Mullen1999_53 | 1999 | 3 | 40 | Suture | Suture
Mullen1999_53 | 1999 | 6 | 40 | Staples | Staples

## References

Furukawa, T. A., A. Cipriani, P. J. Cowen, S. Leucht, M. Egger, and G. Salanti. 2019. “Optimal Dose of Selective Serotonin Reuptake Inhibitors, Venlafaxine, and Mirtazapine in Major Depression: A Systematic Review and Dose-Response Meta-Analysis.” Journal Article. Lancet Psychiatry 6: 601–9.
JAGS Computer Program. 2017. https://mcmc-jags.sourceforge.io/.
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.
Mawdsley, D., M. Bennetts, S. Dias, M. Boucher, and N. J. Welton. 2016. “Model-Based Network Meta-Analysis: A Framework for Evidence Synthesis of Clinical Trial Data.” Journal Article. CPT Pharmacometrics Syst Pharmacol 5 (8): 393–401. https://doi.org/10.1002/psp4.12091.
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.
Thorlund, K., E. J. Mills, P. Wu, E. P. Ramos, A. Chatterjee, E. Druyts, and P. J. Godsby. 2014. “Comparative Efficacy of Triptans for the Abortive Treatment of Migraine: A Multiple Treatment Comparison Meta-Analysis.” Journal Article. Cephalagia. https://doi.org/10.1177/0333102413508661.
Warren, R. B., M. Gooderham, R. Burge, B. Zhu, D. Amato, K. H. Liu, D. Shrom, J. Guo, A. Brnabic, and A. Blauvelt. 2019. “Comparison of Cumulative Clinical Benefits of Biologics for the Treatment of Psoriasis over 16 Weeks: Results from a Network Meta-Analysis.” Journal Article. J Am Acad Dermatol 82 (5): 1138–49.