Bayesian Stan fit to 13C Breath Data

Fits exponential beta curves to 13C breath test series data using Bayesian Stan methods. See https://menne-biomed.de/blog/breath-test-stan/ for a comparison between single curve, mixed-model population and Bayesian methods.

Usage

stan_fit(
  data,
  dose = 100,
  sample_minutes = 15,
  student_t_df = 10,
  chains = 2,
  iter = 1000,
  seed = 4711
)

Arguments

data: Data frame or tibble as created by cleanup_data, with mandatory columns patient_id, group, minute and pdr. It is recommended to run all data through cleanup_data which will insert dummy columns for patient_id and minute if the data are distinct, and report an error if not. It is possible to fit single curves, but this does not make fully use of the stabilization of the estimated t50. Instead of fitting single curves, use a set of 20+ of the typical data in your clinic, and append the data set from the single patient as a mix-in.
dose: Dose of acetate or octanoate. Currently, only one common dose for all records is supported.
sample_minutes: If mean sampling interval is < sampleMinutes, data are subsampled using a spline algorithm
student_t_df: When student_t_df < 10, the student distribution is used to model the residuals. Recommended values to model typical outliers are from 3 to 6. When student_t_df >= 10, the normal distribution is used.
chains: Number of chains for Stan
iter: Number of iterations for each Stan chain
seed: Optional seed for rstan

Value

A list of classes "breathteststanfit" and "breathtestfit" with elements

coef Estimated parameters as data frame in a key-value format with columns patient_id, group, parameter, method and value. Has an attribute AIC.
data The effectively analyzed data. If density of points is too high, e.g. with BreathId devices, data are subsampled before fitting.
stan_fit The Stan fit for use with shinystan::launch_shiny or extraction of chains.

Examples

# This needs some time !!!
library(breathtestcore)
cmdstanr::check_cmdstan_toolchain(fix = TRUE, quiet = TRUE)
#> Warning: The 'fix' argument is deprecated as of CmdStanR 1.0.0 and will be removed in a future release.
library(dplyr, quietly = TRUE, warn.conflicts = FALSE)
d = simulate_breathtest_data(n_records = 3) # default 3 records
data = cleanup_data(d$data)
# Use more than 80 iterations and 4 chains for serious fits
fit = stan_fit(data, chains = 1, iter = 80)
plot(fit) # calls plot.breathtestfit

# Extract coefficients and compare these with those
# used to generate the data
options(digits = 2)
cf = coef(fit)
cf |>
  filter(grepl("m|k|beta", parameter)) |>
  select(-method, -group) |>
  tidyr::spread(parameter, value) |>
  inner_join(d$record, by = "patient_id") |>
  select(
    patient_id,
    m_in = m.y,
    m_out = m.x,
    beta_in = beta.y,
    beta_out = beta.x,
    k_in = k.y,
    k_out = k.x
  )
#> # A tibble: 3 × 7
#>   patient_id  m_in m_out beta_in beta_out    k_in  k_out
#>   <chr>      <dbl> <dbl>   <dbl>    <dbl>   <dbl>  <dbl>
#> 1 rec_01        26  23.6    1.27     1.34 0.00999 0.0115
#> 2 rec_02        43  42.6    1.90     1.91 0.0116  0.0118
#> 3 rec_03        16  16.6    1.90     1.79 0.0129  0.0118
# For a detailed analysis of the fit, use the shinystan library
# shinystan::launch_shinystan(fit$stan_fit)
# \donttest{

# The following plots are somewhat degenerate because
# of the few iterations in stan_fit
library(bayesplot)
#> This is bayesplot version 1.15.0
#> - Online documentation and vignettes at mc-stan.org/bayesplot
#> - bayesplot theme set to bayesplot::theme_default()
#>    * Does _not_ affect other ggplot2 plots
#>    * See ?bayesplot_theme_set for details on theme setting
color_scheme_set("viridisD")
drws = fit$stan_fit$draws(variables = c("beta[1]", "beta[2]", "beta[3]"))
mcmc_dens(drws)

mcmc_hist(fit$stan_fit$draws(variables = c("beta[1]", "beta[2]", "beta[3]")))
#> `stat_bin()` using `bins = 30`. Pick better value `binwidth`.

mcmc_intervals(fit$stan_fit$draws(variables = c("beta[1]", "beta[2]", "beta[3]")))

mcmc_trace(fit$stan_fit$draws(variables = c("beta[1]", "beta[2]", "beta[3]")))

mcmc_areas(fit$stan_fit$draws(variables = c("beta[1]", "beta[2]", "beta[3]")))

# }

Usage

Arguments

Value

See also

Examples