Mixed-model nlme fit to 13C Breath Data

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

Usage

nlme_fit(
  data,
  dose = 100,
  start = list(m = 30, k = 1/100, beta = 2),
  sample_minutes = 15
)

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 to insert dummy columns for patient_id and group if the data are distinct, and report an error if not. At least 2 records are required for a population fit, but 10 or more are recommended to obtain a stable result.

dose

Dose of acetate or octanoate. Currently, only one common dose for all records is supported. The dose only affects parameter m of the fit; all important t50-parameters are unaffected by the dose.

start

Optional start values. In most case, the default values are good enough to achieve convergence, but slightly different values for beta (between 1 and 2.5) can save a non-convergent run.

sample_minutes

When the mean sampling interval is < sampleMinutes, data are subsampled using a spline algorithm by function subsample_data. See the graphical output of plot.breathtestfit for an example where too densely sampled data of one patients were subsampled for the fit.

Value

A list of class ("breathtestnlmefit" "breathtestfit") with elements

coef

Estimated parameters in a key-value format with columns patient_id, group, parameter, stat, method and value. Parameter stat currently always has value "estimate". Confidence intervals will be added later, so do not take for granted that all parameters are estimates. Has an attribute AIC which can be retrieved by the S3-function AIC.

data

The data effectively fitted. If points are to closely sampled in the input, e.g. with BreathId devices, data are subsampled before fitting.

See also

Base methods coef, plot, print; methods from package broom: tidy, augment.

Examples

d = simulate_breathtest_data(n_records = 3, noise = 0.7, seed = 4712)
data = cleanup_data(d$data)
fit = nlme_fit(data)
plot(fit) # calls plot.breathtestfit

options(digits = 3)
library(dplyr)
cf = coef(fit)
# The coefficients are in long key-value format
cf
#> # A tibble: 24 × 5
#>    patient_id group parameter method                      value
#>    <chr>      <chr> <chr>     <chr>                       <dbl>
#>  1 rec_01     A     m         exp_beta                 44.8    
#>  2 rec_01     A     k         exp_beta                  0.00833
#>  3 rec_01     A     beta      exp_beta                  1.52   
#>  4 rec_01     A     t50       bluck_coward             16.3    
#>  5 rec_01     A     t50       maes_ghoos              120.     
#>  6 rec_01     A     t50       maes_ghoos_scintigraphy  48.4    
#>  7 rec_01     A     tlag      bluck_coward            -33.3    
#>  8 rec_01     A     tlag      maes_ghoos               49.9    
#>  9 rec_02     A     m         exp_beta                 40.0    
#> 10 rec_02     A     k         exp_beta                  0.0122 
#> # ℹ 14 more rows
# AIC can be extracted
AIC(fit)
#> [1] 133
# Reformat the coefficients to wide format and compare 
# with the expected coefficients from the simulation 
# in d$record.
cf %>%
  filter(grepl("m|k|beta", parameter )) %>%
  select(-method, -group) %>%
  tidyr::spread(parameter, value) %>%
  inner_join(d$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        44  44.8    1.46     1.52 0.00817 0.00833
#> 2 rec_02        39  40.0    2.73     2.77 0.0124  0.0122 
#> 3 rec_03        42  35.2    2.20     2.55 0.00722 0.00907