Component, Dose, and Time Network Meta-Analysis with Dose-Dependent Interactions

Bayesian component model-based network meta-analysis for treatment combinations with explicit component dose-response and dose-dependent interaction surfaces. The main interface fits single-timepoint arm-level networks with continuous or binary outcomes, any number of components, additive, bilinear, or saturating pairwise interactions, study-level random effects, and prediction at unobserved dose combinations. A stage-one longitudinal interface fits a two-component exponential time-course model with a bilinear interaction on the asymptote. Estimation uses 'Stan' through 'cmdstanr' or 'rstan'. Methods are described in Welton et al. (2009) , Mawdsley et al. (2016) , Wicha et al. (2017) , and Pedder et al. (2019) .

cdtmbnma

cdtmbnma is an R source package for Bayesian component, dose, and time model-based network meta-analysis with dose-dependent interaction surfaces.

The core model fits arm-level component-dose networks. Each treatment arm is represented by a dose vector, where zero means the component is absent. The model estimates component Emax dose-response curves and, when the data identify them, pairwise dose-dependent interaction surfaces. It supports continuous outcomes with known arm standard errors and binary outcomes through a binomial-logit likelihood.

The package also includes a stage-one longitudinal model for repeated arm means: a two-component exponential time-course model with a bilinear interaction on the long-term asymptote.

Contents

• cdt_data() prepares single-timepoint arm-level data for Stan.
• cdt_fit() fits the single-timepoint model.
• cdtmbnma() is a one-call wrapper around cdt_data() and cdt_fit().
• cdt_time_data() and cdt_time_fit() prepare and fit the two-component longitudinal model.
• predict(), summary(), coef(), and plot() methods are provided.
• sacval_example() reads the sacubitril/valsartan blood-pressure dose plane.
• antihtn_factorial_template() and copd_bgf_template() read structured extraction templates included with the package.

Installation

A Stan backend is required to fit models. cmdstanr is recommended.

install.packages("posterior")
install.packages("cmdstanr", repos = c("https://stan-dev.r-universe.dev", getOption("repos")))
cmdstanr::install_cmdstan()

install.packages("remotes")
remotes::install_local("cdtmbnma_0.2.1.tar.gz", build_vignettes = TRUE)

rstan can be used instead of cmdstanr by installing rstan and calling cdt_fit(..., backend = "rstan") or cdt_time_fit(..., backend = "rstan").

Quick start: single-timepoint dose plane

library(cdtmbnma)

sv <- sacval_example()

sv_design <- cdt_data(
  sv,
  study = "study",
  components = c("d_sac", "d_val"),
  outcome = "continuous",
  y = "y",
  se = "se",
  dstar = c(d_sac = 200, d_val = 320)
)

fit <- cdt_fit(
  sv_design,
  interaction = "bilinear",
  chains = 4,
  iter_warmup = 1000,
  iter_sampling = 1000,
  seed = 1
)

summary(fit)
coef(fit)
plot(fit)
predict(fit, data.frame(d_sac = 100, d_val = 160))

For a binary outcome, use outcome = "binary" and supply events and n_binary instead of y and se.

Interaction surfaces

For component doses d_c and d_c', the single-timepoint model has three options.

The additive model uses no interaction:

cdt_fit(design, interaction = "none")

The bilinear model adds one parameter per component pair:

[ \psi_{cc'}(d_c, d_{c'}) = \eta_{cc'} \left(\frac{d_c}{d_c^\star}\right) \left(\frac{d_{c'}}{d_{c'}^\star}\right). ]

The saturating general pharmacodynamic interaction surface is:

[ \psi_{cc'}(d_c, d_{c'}) = \mathrm{INT}{cc'} \frac{d_c}{\kappa_c + d_c} \frac{d{c'}}{\kappa_{c'} + d_{c'}}. ]

Both surfaces are centred on additivity. They vanish whenever either component is absent.

Quick start: two-component time-course model

long_dat <- data.frame(
  study = rep("trial1", 6),
  arm = rep(c("placebo", "A", "AB"), each = 2),
  week = rep(c(4, 8), 3),
  dose_A = rep(c(0, 10, 10), each = 2),
  dose_B = rep(c(0, 0, 20), each = 2),
  y = c(0, 0, -1, -2, -2, -3),
  se = rep(1, 6)
)

time_design <- cdt_time_data(
  long_dat,
  study = "study",
  arm = "arm",
  time = "week",
  components = c("dose_A", "dose_B"),
  y = "y",
  se = "se",
  dstar = c(dose_A = 10, dose_B = 20)
)

# fit_time <- cdt_time_fit(time_design)

The time-course interface is intentionally narrower than the main interface: two components, continuous outcomes, exponential time-course, and a bilinear interaction on the long-term asymptote.

Notes on interpretation

The null is additivity on the modelled scale: mean difference for continuous outcomes and log odds for binary outcomes. A favourable interaction relative to that additive component model is a statistical interaction on the chosen scale; it is not automatically equivalent to Bliss independence, Loewe additivity, or a pharmacological mechanism.

The interaction surface is identifiable only for component pairs that co-occur in at least one arm. If no component pair co-occurs, cdt_fit() falls back to the additive model.