plot_integration_error function

Plot numerical integration error

For ML-NMR models, plot the estimated numerical integration error over the entire posterior distribution, as the number of integration points increases. See \insertCite methods_paper,Phillippo_thesismultinma for details.

plot_integration_error(
  x,
  ...,
  stat = "violin",
  orientation = c("vertical", "horizontal", "x", "y"),
  show_expected_rate = TRUE
)

Arguments

• x: An object of type stan_mlnmr
• ...: Additional arguments passed to the ggdist plot stat.
• stat: Character string specifying the ggdist plot stat used to summarise the integration error over the posterior. Default is "violin", which is equivalent to "eye" with some cosmetic tweaks.
• orientation: Whether the ggdist geom is drawn horizontally ("horizontal") or vertically ("vertical"), default "vertical"
• show_expected_rate: Logical, show typical convergence rate $1/N$? Default TRUE.

Returns

A ggplot object.

Details

The total number of integration points is set by the n_int

argument to add_integration(), and the intervals at which integration error is estimated are set by the int_thin argument to nma(). The typical convergence rate of Quasi-Monte Carlo integration (as used here) is $1/N$, which by default is displayed on the plot output.

The integration error at each thinning interval $N_thin$ is estimated for each point in the posterior distribution by subtracting the final estimate (using all n_int points) from the estimate using only the first $N_thin$ points.

Note for survival models

This function is not supported for survival/time-to-event models. These do not save cumulative integration points for efficiency reasons (both time and memory).

Examples

## Plaque psoriasis ML-NMR
# Set up plaque psoriasis network combining IPD and AgD
library(dplyr)
pso_ipd <- filter(plaque_psoriasis_ipd,
                  studyc %in% c("UNCOVER-1", "UNCOVER-2", "UNCOVER-3"))

pso_agd <- filter(plaque_psoriasis_agd,
                  studyc == "FIXTURE")

head(pso_ipd)
head(pso_agd)

pso_ipd <- pso_ipd %>%
  mutate(# Variable transformations
    bsa = bsa / 100,
    prevsys = as.numeric(prevsys),
    psa = as.numeric(psa),
    weight = weight / 10,
    durnpso = durnpso / 10,
    # Treatment classes
    trtclass = case_when(trtn == 1 ~ "Placebo",
                         trtn %in% c(2, 3, 5, 6) ~ "IL blocker",
                         trtn == 4 ~ "TNFa blocker"),
    # Check complete cases for covariates of interest
    complete = complete.cases(durnpso, prevsys, bsa, weight, psa)
  )

pso_agd <- pso_agd %>%
  mutate(
    # Variable transformations
    bsa_mean = bsa_mean / 100,
    bsa_sd = bsa_sd / 100,
    prevsys = prevsys / 100,
    psa = psa / 100,
    weight_mean = weight_mean / 10,
    weight_sd = weight_sd / 10,
    durnpso_mean = durnpso_mean / 10,
    durnpso_sd = durnpso_sd / 10,
    # Treatment classes
    trtclass = case_when(trtn == 1 ~ "Placebo",
                         trtn %in% c(2, 3, 5, 6) ~ "IL blocker",
                         trtn == 4 ~ "TNFa blocker")
  )

# Exclude small number of individuals with missing covariates
pso_ipd <- filter(pso_ipd, complete)

pso_net <- combine_network(
  set_ipd(pso_ipd,
          study = studyc,
          trt = trtc,
          r = pasi75,
          trt_class = trtclass),
  set_agd_arm(pso_agd,
              study = studyc,
              trt = trtc,
              r = pasi75_r,
              n = pasi75_n,
              trt_class = trtclass)
)

# Print network details
pso_net

# Add integration points to the network
pso_net <- add_integration(pso_net,
  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),
  n_int = 64)

# Fit the ML-NMR model
pso_fit <- nma(pso_net, 
               trt_effects = "fixed",
               link = "probit",
               likelihood = "bernoulli2",
               regression = ~(durnpso + prevsys + bsa + weight + psa)*.trt,
               class_interactions = "common",
               prior_intercept = normal(scale = 10),
               prior_trt = normal(scale = 10),
               prior_reg = normal(scale = 10),
               init_r = 0.1,
               QR = TRUE,
               # Set the thinning factor for saving the cumulative results
               # (This also sets int_check = FALSE)
               int_thin = 8)
pso_fit


plot_integration_error(pso_fit)