Gut Transit in ICU Trauma Patients (Biostatistics)

Problem

M.Sc. project for the Statistics & Machine Learning module (SRH University, winter term 2025/26). Critically ill patients often can’t tolerate tube feeding, and slow gut motility is a suspected cause. The goal was to replicate the statistics of a published clinical study: do mechanically ventilated trauma patients have slower gastric emptying and small-bowel transit than healthy people?

Data

The public Smart Pill dataset from Rauch et al. (2012, Journal of Critical Care): 95 participants and 22 variables. 8 critically ill trauma patients and 87 healthy volunteers each swallowed a wireless capsule that records pH, pressure and temperature on its way through the gut. The outcomes are gastric emptying (GE), small-bowel (SB) and whole-gut transit times in hours.

Before comparing transit times, I checked that the two groups are comparable. They don’t differ significantly in gender, age, height or weight.

Four panels comparing the groups at baseline. Gender: 75% male among patients vs 55% among volunteers, chi-square p = .279. Box plots of age, height and weight overlap, with t-test p-values of .508, .252 and .578. — Baseline balance: no significant differences in gender, age, height or weight.

Approach

Classified the variables (nominal, ratio, interval, count) to choose suitable tests.
Baseline balance: t-tests and Mann–Whitney U for age, height and weight; χ² and Fisher’s exact test for gender.
Primary outcomes: Shapiro–Wilk normality checks, then Welch’s t-test vs Mann–Whitney U, with a Bonferroni-corrected α = 0.025 for the two primary outcomes and rank-biserial effect sizes.
Odds ratio for delayed gastric emptying (Haldane–Anscombe correction for a zero cell), one-way ANOVA and Kruskal–Wallis by gender and race.
Distribution fitting (Normal, Exponential, Gamma, Log-normal) with Kolmogorov–Smirnov tests.
Pearson vs Spearman correlation, and a multiple regression for SB time with heteroscedasticity-robust (HC3) standard errors.
Did the analysis first in JASP, then rebuilt it as a reproducible Python notebook.

The transit times are strongly right-skewed and fail the normality test, which is why the main comparison uses the rank-based Mann–Whitney test, not a t-test.

Histograms of gastric emptying and small-bowel transit time for each group. Both are right-skewed; Shapiro–Wilk rejects normality for gastric emptying in both groups and for small-bowel transit in healthy volunteers. — Right-skewed transit times: Shapiro–Wilk rejects normality, so non-parametric tests are used.

Left: histogram of healthy volunteers' gastric emptying with four fitted curves; the normal is rejected (KS p < .001) and the log-normal fits best (KS p = .428). Right: Q–Q plot against the log-normal, close to the diagonal except for three long values. — Distribution fitting for healthy volunteers: the normal is rejected, the log-normal fits best.

Results

Outcome	Critically ill (median)	Healthy (median)	Mann–Whitney p
Gastric emptying	13.9 h	3.0 h	< .001
Small-bowel transit	6.7 h	3.8 h	.010
Whole-gut transit	240 h	28.5 h	< .001

All 7 patients with a measurement had delayed gastric emptying (OR = 15.4, 95% CI 0.9–277).
Welch’s t-test missed the gastric-emptying difference (p = .076) because a few extreme values inflate the variance. The rank-based test found it clearly.
Gender has no effect on gastric emptying (ANOVA p = .40). The difference comes from the group.

Box plots of gastric emptying by gender, split by group, on a log scale. Within both men and women, the critically ill patients take far longer than the volunteers. ANOVA for gender p = .402. — Within each gender, patients are much slower than volunteers: group, not gender, drives the difference.

Pearson vs Spearman changes the conclusion. Pooled over both groups, the Pearson correlation between GE and SB time is r = 0.57, but Spearman’s ρ is only 0.04. In healthy volunteers there is no relationship at all. The apparent link comes from a few patients who are extreme on both variables.

Two correlation heatmaps for age, height, weight and the three transit times. Pearson shows GE–SB 0.56 and GE–WG 0.73; Spearman shows GE–SB 0.04 and GE–WG 0.40. — Pearson (left) vs Spearman (right): the strong GE–SB correlation disappears with ranks.

Scatter plots of small-bowel vs gastric emptying time. Healthy volunteers (n = 83): no relationship, r = 0.13, p = .258. Critically ill (n = 7): r = 0.80, p = .030, driven by two patients with very long gastric emptying. — Within the healthy group, GE and SB time are unrelated. The patient trend rests on 7 points.

The multiple regression tells the same story. GE time looks like a strong predictor of SB time (p < .001), but with robust standard errors the effect is no longer significant (p = .125).

Coefficient plot for SB time regressed on GE time, age, weight and group, R² = 0.33. Only GE time has a confidence interval above zero (OLS p < .001), but its robust p-value is .125. Age, weight and group are not significant. — Regression coefficients with 95% CIs. GE time is significant with ordinary but not robust (HC3) errors.

What I learned

Check the assumptions before choosing a test. With skewed data and tiny groups, the “standard” t-test gives the wrong answer.
Robust methods can change the conclusion, not just the decimals. Reporting both versions is more honest than reporting only the one that looks best.
A significant result from 8 patients is still a pilot result. Confidence intervals show that better than p-values do.