*2.5. Statistical Analysis*

Descriptive and longitudinal statistics was performed on the R free software version 3.5.1 (02-07-2018). The longitudinal nonparametric analysis on marginal bone levels was implemented on the ld.f1 function within the package nparLD. This non-parametric method exhibits a competitive performance for small sample sizes and outliers. In the per-implant analysis, the ANOVA-type statistic (ATS) was calculated for the global alternatives with 'time' as the fixed su-plot factor. A *p* value < 0.05 has been used as a cut-off for significance and a robust analysis of variance and a Spearman's correlation

coefficient has been performed. A further mixed effect model (function lmer within package lme4) was used to control for crossed random effects posed by patients contributing with more than one implant. This formula expects that there is going to be multiple responses per patient, and these responses will depend on each subject's baseline level. This effectively resolved the non-independence that stemmed from having multiple responses by the same subject.

### **3. Results**
