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D. Kennedy, Y. Li, K. Kennedy, H.-C. Hsu, D. Jethwani; Parametric vs. Non-Parametric Analysis to Assess Ocular Protection Index (OPI) in Cross-Over Designs. Invest. Ophthalmol. Vis. Sci. 2010;51(13):3361.
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Parametric and non-parametric methods were applied to OPI data from a three-visit, three-treatment ophthalmic cross-over study to determine which method is better at identifying statistically significant differences. The OPI response variable is the primary endpoint and it is often positively skewed. Traditionally, parametric analysis methods are requested to be used for the primary analysis. It is clear that the parametric model assumptions (i.e., normally distributed data) are not entirely valid when analyzing OPI data. Therefore, other more appropriate analysis methods (e.g., non-parametric) can potentially improve the ability to identify statistically significant differences.
The results from the study were originally analyzed using two parametric methods: a repeated measures analysis was performed adjusting period and sequence using a mixed model, and a two sample t-test making pairwise comparisons at each of the individual visits. Two non-parametric analyses were run post-hoc: an overall non-parametric analysis adjusting for period, and a basic non-parametric analysis with Hodges-Lehmann type estimator. Resultant P-values were compared to determine if the non-parametric methods perform equivalently or better than the parametric.
Pairwise comparisons were performed among two active treatments, Drug C and Drug K, and one placebo. For both the per protocol (PP) and intent-to-treat (ITT) populations, more statistically significant differences resulted when using the non-parametric methods. Furthermore, both non-parametric methods produced very similar results.
Non-parametric methods, when applied to OPI data in cross-over designs, have a greater ability to identify statistically significant pairwise comparisons when compared to parametric methods. These methods do not require any distributional assumptions. Therefore, model assumption validity is relaxed. Furthermore, both non-parametric methods produced consistent results.
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