Encoding strategies for information-theoretic complexity measures in thermography-based rheumatoid arthritis detection

Rheumatoid arthritis (RA) remains a condition in which complementary, non-invasive assessment tools are actively explored. While previous thermography studies have focused mainly on temperature dynamics or texture features, the diagnostic value of information-theoretic complexity measures is still not well understood. This study evaluates three such measures, Lempel–Ziv complexity (LZC), permutation complexity (PC), and belief permutation entropy (BPE), for distinguishing RA patients from healthy individuals, with emphasis on the impact of different symbolic encoding strategies under no-cooling and cooling conditions. A dataset of 477 hand thermograms (291 healthy controls, 186 RA patients) was analyzed using four encoding schemes: binary, slope-direction, zero-crossing, and multilevel thresholding. All statistical conclusions were assessed at the subject level using median aggregation per participant, with multiplicity-adjusted testing on protocol-matched cohorts to avoid within-subject dependence and availability bias. The primary endpoint was subject-level discrimination quantified by effect size and ROC–AUC. Results indicate that the diagnostic utility of complexity measures in hand thermography strongly depends on both encoding choices and the acquisition protocol. Under no-cooling conditions, several LZC variants and PC showed statistically significant but small group differences after BH-FDR correction ( | d | ≈ 0 . 23 − 0 . 29 ; A U C ≈ 0 . 57 − 0 . 58 ). Under cooling, most LZC- and PC-based effects were attenuated and yielded lower discriminative performance than BPE in the primary subject-level analysis. In contrast, BPE became the strongest discriminator, reaching a large effect size ( d ≈ 0 . 80 , BH-FDR p < 1 0 − 5 ) and stable ROC–AUC ( ≈ 0 . 71 ). Overall, the results show that encoding strategy is a major determinant of complexity-based thermographic discrimination, while BPE provides a robust tie-aware ordinal descriptor under thermal stress.