A neutral comparison of statistical methods for analyzing longitudinally measured ordinal outcomes in rare diseases

Abstract

Ordinal data in a repeated measures design of a crossover study for rare diseases usually do not allow for the use of standard parametric methods, and hence, nonparametric methods should be considered instead. However, only limited simulation studies in settings with small sample sizes exist. Therefore, starting from an Epidermolysis Bullosa simplex trial with the above‐mentioned design, a rank‐based approach using the R package nparLD and different generalized pairwise comparisons (GPC) methods were compared impartially in a simulation study. The results revealed that there was not one single best method for this particular design, because a trade‐off exists between achieving high power, accounting for period effects, and for missing data. Specifically, nparLD as well as the unmatched GPC approaches do not address crossover aspects, and the univariate GPC variants partly ignore the longitudinal information. The matched GPC approaches, on the other hand, take the crossover effect into account in the sense of incorporating the within‐subject association. Overall, the prioritized unmatched GPC method achieved the highest power in the simulation scenarios, although this may be due to the specified prioritization. The rank‐based approach yielded good power even at a sample size of , whereas the matched GPC method could not control the type I error.

How to Analyze Continuous and Discrete Repeated Measures in Small-Sample Cross-Over Trials?

“…Ignoring the cross‐over design in the unmatched GPC, however, leads to asymptotically valid results (Konietschke & Pauly, 2012) and controls the type I error better in sample sizes <15 subjects. GPC has an obvious interpretable treatment effect measure, results in a single analysis rather than a per treatment period analysis and can be easily extended to multivariate outcomes, for example, combining pain, pruritus, and/or quality of life to the blister count outcome (Geroldinger et al., 2023).…”

Istore: a project on innovative statistical methodologies to improve rare diseases clinical trials in limited populations

“…The non-prioritized GPC evaluates each of the outcomes in all possible pairs [ 76 , 82 ], following the idea of the non-parametric O’Brien test [ 83 ]. Additionally, extensions to longitudinal outcomes [ 84 ] and for N-of-1 trials [ 85 ] are available. Covariate adjustment in GPC is feasible through stratification [ 86 ], although in small samples the stratum size needs careful attention.…”

Statistical recommendations for count, binary, and ordinal data in rare disease cross-over trials

“…3 in Sect. “ Discussion ” and see Geroldinger et al [ 14 ] and Verbeeck et al [ 33 ]). The parameters of these distributions were chosen such that the expected values (shift effects) corresponded to clinically meaningful effects.…”

“…Additionally, the blister counts as well as the VAS scores for pain and pruritus were considered as secondary outcome variables (see [ 35 ] for more details). Since these outcomes are measured on different scales (binary for the primary outcome and metric/count as well as ordinal for the secondary outcomes), recommendations for these three types of outcomes will be derived from previously conducted simulation studies [ 14 , 33 ]. Moreover, in each of these two methodological papers, a real life data example was also described, using the original study data of Wally et al[ 35 ].…”

“…For the count outcome the raw blister counts were used. Finally, the binary outcome was created based on an indicator for a 40% reduction compared to baseline (for details regarding the respective simulation setup, see Geroldinger et al [ 14 ] and Verbeeck et al [ 33 ]).…”