Statistical analysis

For all statistical analyses, a p-value <0.05 was considered statistically significant.

8.14.1. Descriptive statistics

Demographic and clinical characteristics of patients in papers I-III were presented using mean value (standard deviation (SD)) for normally distributed variables, median (interquartile range (IQR)) for variables with skewed distribution and n (%) for

categorical variables. The mean value is the average value of all measurements. SD is a measure for variation between sample measurements and is calculated by the square root of the sample variance. The median value is the middle value of all

measurements. IQR is also a measure of variation between sample measurements, it is calculated by the difference between the 75^th percentile and 25^th percentile. The 25^th percentile or first quartile is defined as the value where one forth or 25% of all measurements are below the value similarly, the 75^th percentile or third quartile is the value where 25% of the measurements are above the value.

Concentrations are often presented as log concentrations which implies that each concentration value differs by a constant, making the values equally spaced from each other and thus the distribution less skewed. In paper I, mucosal 5-ASA concentrations in the different 5-ASA formulation groups were presented as geometric mean (95%

confidence interval (CI)). The geometric mean is applied to find the mean value on a logarithmic scale and calculating the value back to the original scale. The geometric mean is calculated by the antilogarithm of log x. The 95% CI is defined as a calculated interval which will contain the true parameter in 95% of all random samples obtained from a reference population.

8.14.2. Parametric tests

Parametric tests depend on normal distribution of variables.

The Independent Samples t Test or two-sample independent t Test tests if there is a statistical difference between the means of two groups. The test requires samples and

groups to be independent of each other. Independent Samples t Test was applied in paper II and III.

One-way Analysis of variance (ANOVA) is applied to determine if the means of two or more groups are different, the test requires variables to follow normal distribution and have the same variance. The ANOVA F test tests if the overall mean between for example three groups are different, it is important to notice that if the test shows a statistical difference, we still do not know which mean is different. ANOVA was applied in paper I.

8.14.3. Non-parametric tests

Non-parametric tests are applied when the sample size is small, or the variable is not normally distributed, or a combination of the two. The advantage of non-parametric tests are that they do not depend on normal distribution, however if the data is truly normally distributed, some statistical power will be lost by using a non-parametric test.

The Mann Whitney U test is the non-parametric analogue to the two-sample independent t test, and it is used to compare the means of two groups. The test is based on ranks of observation, meaning that each observational value from the two groups is replaced by a rank and the test calculated based on the rank sum. The Kruskal-Wallis test is analogous to the Mann Whitney U test and allows comparisons between more than two groups. We applied the Mann Whitney U test in paper I-III and Kruskal Wallis test in paper I.

The Chi-square test or X² test is a non-parametric test which is applied to test for associations between two categorical variables. Chi-square test is based on the arrangement of a contingency table and computation of the observed and expected count in each cell. The null hypothesis is that the expected and observed values are not significantly different. The Chi-square test require that the expected values are not too low; not more than 1/5 of cells can have an expected value <5 and no cell can have an expected value of <1. If the expected values of some cells are low, a Fisher-Exact test should be performed. The Chi-square test was performed in paper I-III, and Fisher-Exact test was performed in paper II and III.

8.14.4. Multilevel linear mixed model

Multilevel linear mixed model or linear mixed-effect models are suitable for datasets with repeated measurements, missing data and datasets with an unbalanced data structure. The multilevel linear mixed model is an extension of standard linear regression where hierarchical data structure (repeated measurements, for instance) are taken into account.

In paper I, we had repeated 5-ASA concentration measurements at different locations in the distal colon within each patient, also the number of measurements at the different locations were not the same (two samples at 10 cm, one at 25 cm and two at 40 cm proximal of the anal verge), which made the multilevel mixed linear model suitable. 5-ASA formulation and biopsy location were included in the model as fixed factors, whereas subject was defined as a random factor to account for the dependency of the repeated measurements (10, 25 and 40 cm) and order of observation (two samples at 10 cm and 40 cm and one sample at 25 cm). An interaction term between 5-ASA formulation and location was included in the model to test whether the difference in mean 5-ASA concentration by location differed between 5-ASA formulations, and conversely, whether the difference in mean values between 5-ASA formulations differed by location.