marginal_effects {multinma}

Marginal treatment effects

Description

Generate population-average marginal treatment effects. These are formed from population-average absolute predictions, so this function is a wrapper around predict.stan_nma().

Usage

marginal_effects(
  object,
  ...,
  mtype = c("difference", "ratio", "link"),
  all_contrasts = FALSE,
  trt_ref = NULL,
  probs = c(0.025, 0.25, 0.5, 0.75, 0.975),
  predictive_distribution = FALSE,
  summary = TRUE
)

Arguments

object

A stan_nma object created by nma().

...

Arguments passed to predict.stan_nma(), for example to specify the covariate distribution and baseline risk for a target population, e.g. newdata, baseline, and related arguments. For survival outcomes, type can also be specified to determine the quantity from which to form a marginal effect. For example, type = "hazard" with mtype = "ratio" produces marginal hazard ratios, type = "median" with mtype = "difference" produces marginal median survival time differences, and so on.

mtype

The type of marginal effect to construct from the average absolute effects, either "difference" (the default) for a difference of absolute effects such as a risk difference, "ratio" for a ratio of absolute effects such as a risk ratio, or "link" for a difference on the scale of the link function used in fitting the model such as a marginal log odds ratio.

all_contrasts

Logical, generate estimates for all contrasts (TRUE), or just the "basic" contrasts against the network reference treatment (FALSE)? Default FALSE.

trt_ref

Reference treatment to construct relative effects against, if all_contrasts = FALSE. By default, relative effects will be against the network reference treatment. Coerced to character string.

probs

Numeric vector of quantiles of interest to present in computed summary, default c(0.025, 0.25, 0.5, 0.75, 0.975)

predictive_distribution

Logical, when a random effects model has been fitted, should the predictive distribution for marginal effects in a new study be returned? Default FALSE.

summary

Logical, calculate posterior summaries? Default TRUE.

Value

A nma_summary object if summary = TRUE, otherwise a list containing a 3D MCMC array of samples and (for regression models) a data frame of study information.

Examples

## Smoking cessation

# Run smoking RE NMA example if not already available
if (!exists("smk_fit_RE")) example("example_smk_re", run.donttest = TRUE)


# Marginal risk difference in each study population in the network
marginal_effects(smk_fit_RE, mtype = "difference")

# Since there are no covariates in the model, the marginal and conditional
# (log) odds ratios here coincide
marginal_effects(smk_fit_RE, mtype = "link")
relative_effects(smk_fit_RE)

# Marginal risk differences in a population with 67 observed events out of
# 566 individuals on No Intervention, corresponding to a Beta(67, 566 - 67)
# distribution on the baseline probability of response
(smk_rd_RE <- marginal_effects(smk_fit_RE,
                               baseline = distr(qbeta, 67, 566 - 67),
                               baseline_type = "response",
                               mtype = "difference"))
plot(smk_rd_RE)


## Plaque psoriasis ML-NMR

# Run plaque psoriasis ML-NMR example if not already available
if (!exists("pso_fit")) example("example_pso_mlnmr", run.donttest = TRUE)


# Population-average marginal probit differences in each study in the network
(pso_marg <- marginal_effects(pso_fit, mtype = "link"))
plot(pso_marg, ref_line = c(0, 1))

# Population-average marginal probit differences in a new target population,
# with means and SDs or proportions given by
new_agd_int <- data.frame(
  bsa_mean = 0.6,
  bsa_sd = 0.3,
  prevsys = 0.1,
  psa = 0.2,
  weight_mean = 10,
  weight_sd = 1,
  durnpso_mean = 3,
  durnpso_sd = 1
)

# We need to add integration points to this data frame of new data
# We use the weighted mean correlation matrix computed from the IPD studies
new_agd_int <- add_integration(new_agd_int,
                               durnpso = distr(qgamma, mean = durnpso_mean, sd = durnpso_sd),
                               prevsys = distr(qbern, prob = prevsys),
                               bsa = distr(qlogitnorm, mean = bsa_mean, sd = bsa_sd),
                               weight = distr(qgamma, mean = weight_mean, sd = weight_sd),
                               psa = distr(qbern, prob = psa),
                               cor = pso_net$int_cor,
                               n_int = 64)

# Population-average marginal probit differences of achieving PASI 75 in this
# target population, given a Normal(-1.75, 0.08^2) distribution on the
# baseline probit-probability of response on Placebo (at the reference levels
# of the covariates), are given by
(pso_marg_new <- marginal_effects(pso_fit,
                                  mtype = "link",
                                  newdata = new_agd_int,
                                  baseline = distr(qnorm, -1.75, 0.08)))
plot(pso_marg_new)


## Progression free survival with newly-diagnosed multiple myeloma

# Run newly-diagnosed multiple myeloma example if not already available
if (!exists("ndmm_fit")) example("example_ndmm", run.donttest = TRUE)


# We can produce a range of marginal effects from models with survival
# outcomes, specified with the mtype and type arguments. For example:

# Marginal survival probability difference at 5 years, all contrasts
marginal_effects(ndmm_fit, type = "survival", mtype = "difference",
                 times = 5, all_contrasts = TRUE)

# Marginal difference in RMST up to 5 years
marginal_effects(ndmm_fit, type = "rmst", mtype = "difference", times = 5)

# Marginal median survival time ratios
marginal_effects(ndmm_fit, type = "median", mtype = "ratio")

# Marginal log hazard ratios
# With no covariates in the model, these are constant over time and study
# populations, and are equal to the log hazard ratios from relative_effects()
plot(marginal_effects(ndmm_fit, type = "hazard", mtype = "link"),
     # The hazard is infinite at t=0 in some studies, giving undefined logHRs at t=0
     na.rm = TRUE)

# The NDMM vignette demonstrates the production of time-varying marginal
# hazard ratios from a ML-NMR model that includes covariates, see
# `vignette("example_ndmm")`

# Marginal survival difference over time
plot(marginal_effects(ndmm_fit, type = "survival", mtype = "difference"))