t50_bluck_coward {breathtestcore} | R Documentation |

Uses Newton's method to solve the self-corrected Bluck-Coward equation for 1/2 to compute the half-emptying time t_50.

See also equation G(n,t) in

Bluck LJC, Jackson S, Vlasakakis G, Mander A (2011) Bayesian hierarchical methods to interpret the 13C-octanoic acid breath test for gastric emptying. Digestion 83_96-107, page 98.

t50_bluck_coward(cf)

`cf` |
Named vector of coefficients; only |

Time where value is 1/2 of the maximum, i.e. t_50 or t_1/2 in minutes; in the publication by Bluck et al, the parameter is called t_1/2(in).

# From table 3 and 4 in Bluck et al.; values for \code{k} and \code{beta} # (nls, bayesian) are entered and checked against the tabulated values of # t_{1/2(in)}. # Most errors are small, but there are some outliers; errors in paper table? # Parameters and Bluck et al. results: # table 3 of Bluck et al. cf3 = data.frame( method = rep(c("nls", "bayesian")), group = rep(c("lean", "obese"),each=2), k = c(0.576,0.606,0.529,0.608), beta = c(5.24, 5.79, 5.95, 7.54), t12 = c(3.67, 3.63, 4.23, 3.99), t12in = c(2.076, 2.110, 2.422, 2.466), tlag = c(2.88, 2.88, 3.34, 3.26), tlagin = c(1.632, 1.724, 1.92, 2.101) ) cf3 = dplyr::mutate(cf3, t50_maes_ghoos = t50_maes_ghoos(cf3), t50_bluck_coward = t50_bluck_coward(cf3), tlag_maes_ghoos = tlag_maes_ghoos(cf3), tlag_bluck_coward = tlag_bluck_coward(cf3), err_t50_maes_ghoos = round(100*(t50_maes_ghoos-t12)/t12, 2), err_t50_bluck_coward = round(100*(t50_bluck_coward-t12in)/t12in, 2), err_lag_maes = round(100*(tlag_maes_ghoos-tlag)/tlag,2), err_lag_bluck_coward = round(100*(tlag_bluck_coward-tlagin)/tlagin,2) ) cf3 # table 4 # there are large differences for mj3, both using the bayesian (26%) # and the nls method (16%). The other data are within the expected limits cf4 = data.frame( method = rep(c("nls", "bayesian"),each=3), group = rep(c("mj1", "mj2", "mj3")), k = c(0.585, 0.437, 0.380, 0.588, 0.418, 0.361), beta=c(4.35, 4.08, 4.44, 4.49, 4.30, 4.29), t12 = c(3.39, 4.25, 4.82, 3.40, 4.61, 5.09), t12in = c(1.77, 2.16, 2.19, 1.81, 2.34, 2.43), tlag = c(2.56, 3.17, 3.39, 2.58, 3.40, 3.62), tlagin = c(1.30, 1.53, 1.33, 1.35, 1.65, 1.57) ) cf4 = dplyr::mutate(cf4, t50_maes_ghoos = t50_maes_ghoos(cf4), t50_bluck_coward = t50_bluck_coward(cf4), tlag_maes_ghoos = tlag_maes_ghoos(cf4), tlag_bluck_coward = tlag_bluck_coward(cf4), err_t50_maes_ghoos = unlist(round(100*(t50_maes_ghoos-t12)/t12)), err_t50_bluck_coward = round(100*(t50_bluck_coward-t12in)/t12in,2), err_lag_maes = round(100*(tlag_maes_ghoos-tlag)/tlag,2), err_lag_bluck_coward = round(100*(tlag_bluck_coward-tlagin)/tlagin,2) ) cf4

[Package *breathtestcore* version 0.8.1 Index]