# MedStat Stutter

## Phantasies of a physicist fallen among physicians

### Pairwise differences in cross-over design

November 8, 2016, 11:13 am

A colleague asked me how to present the results of a study in gastric emptying. As you have seen multiple time here, the emptying time t50 is the target variable. But read on even if you work with blood pressure (also often misused as example), rehabilitation, or pharmacology. The methods are the sa...

### Multiple indexing with Stan

August 27, 2016, 8:56 pm

## Summary

volume ~ normal(
v0[record] .* (1+ kappa[record] .* (minute ./ tempt[record])) .*
exp(-minute ./ tempt[record]), sigma);

## Fitting gastric emptying time series

Gastric volume times serie measured by MRI techniques can have an initial volume overshoot due to secretion. To estimate half-times and the degree of overshoot, the author of this blog has introduced the linexp function [@Fruehauf2011] with three parameters to complement the power exponential function used in earlier research [@Elashoff1982, @Elashoff1983b] with scintigraphic data.

linexp:

v = v0* (1+t*kappa/tempt)*exp(-t/t_{empt})

### 13C Breath test: Population Fit and Bayesian Models

August 13, 2016, 4:07 pm

## Summary

Time series from 13C breath test recordings are used as a surrogate indicator for gastric emptying. Gastric emptying half time t50 is computed by fitting the series with an exponential beta or a Gamma function. Often, records are too short to obtain stable estimates of the trailing part. One can easily get unrealistic emptying times when single curves are fitted (Ghoos et al. (1993), Maes et al. (1998)).

Population methods can come to the rescue. When these fail, Bayesian methods provide a robust approach to non-linear curve fitting.

Zipped source files and data

### Box-Cox Transformations for linexp fits

August 1, 2016, 11:03 am

The coefficients of linexp fits to gastric emptying curves are generally used in mixed-models to analyze group and meal difference. The distribution of the extracted parameters is often highly skewed, so before using linear models or estimates of reference ranges with functions in package referenceInterval or Hmisc, a transformation might be required.

From a large corpus of gastric emptying curves analyzed with nonlinear fits of the linexp function, the following recommendations for transformation were obtained using the boxcox and the logtrans function in package MASS: