Power and sample size determination for the group comparison of patient-reported outcomes using the Rasch model: impact of a misspecification of the parameters.

Blanchin M, Guilleux A, Perrot B, Bonnaud-Antignac A, Hardouin JB, Sébille V - BMC Med Res Methodol (2015)

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Fig3: Power estimated with Raschpower as a function of the standard deviation of the latent variable and the number of items (J) for 50 patients per group and a group effect=0.5 (Figure a), 100 patients per group and a group effect=0.8 (Figure b), 200 patients per group and a group effect=0.5 (Figure c), for 300 patients per group and a group effect=0.2 (Figure d) or 500 patients per group and a group effect=0.2 (Figure e).
Mentions: Table 1 shows the power estimated with Raschpower for some values of the variance of the latent variable , the number of items (J), the group effect (γ) and the sample size per group (Ng). The results for all values of the parameters are presented in Additional file 1. As expected, the estimated power increases with the number of items, the group effect and the sample size. For most of the cases as represented in Figure 3(a), (d) and (e), the estimated power decreases when the variance of the latent trait increases. As a consequence, an underestimation of the variance will lead to an overestimation of the power at the design stage and finally to an underpowered study. The loss of power, corresponding to the decrease between the expected power and the observed power, due to an underestimation of the variance is the highest for small values of the variance and high values of J. For example, for J=15, Ng=300 and γ=0.2, the power is estimated at 89.5% for and at 75.7% for . So, an underestimation of 0.25 of the variance of the latent variable in this example leads to a decrease of 13.8% of the power of the test of group effect. On the opposite, the power is estimated at 20.6% for and at 17.6% for under the same conditions. Therefore, an underestimation of 1 of the variance of the latent variable in this case leads to a decrease of power of only 3.0%.Table 1

Bottom Line: The power of the test of the group effect estimated with Raschpower remains stable or shows a very little decrease whatever the values of the item parameters.A misspecification of the item difficulties regarding their overall pattern or their dispersion seems to have no or very little impact on the power of the test of the group effect.In contrast, a misspecification of the variance of the latent variable can have a strong impact as an underestimation of the variance will lead in some cases to an overestimation of the power at the design stage and may result in an underpowered study.

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Affiliation: EA 4275, Biostatistics, Pharmacoepidemiology and Subjective Measures in Health Sciences, University of Nantes, 1 rue, Gaston Veil, 44000, Nantes, France. myriam.blanchin@univ-nantes.fr.

ABSTRACT

Background: Patient-reported outcomes (PRO) are important as endpoints in clinical trials and epidemiological studies. Guidelines for the development of PRO instruments and analysis of PRO data have emphasized the need to report methods used for sample size planning. The Raschpower procedure has been proposed for sample size and power determination for the comparison of PROs in cross-sectional studies comparing two groups of patients when an item reponse model, the Rasch model, is intended to be used for analysis. The power determination of the test of the group effect using Raschpower requires several parameters to be fixed at the planning stage including the item parameters and the variance of the latent variable. Wrong choices regarding these parameters can impact the expected power and the planned sample size to a greater or lesser extent depending on the magnitude of the erroneous assumptions.

Methods: The impact of a misspecification of the variance of the latent variable or of the item parameters on the determination of the power using the Raschpower procedure was investigated through the comparison of the estimations of the power in different situations.

Results: The power of the test of the group effect estimated with Raschpower remains stable or shows a very little decrease whatever the values of the item parameters. For most of the cases, the estimated power decreases when the variance of the latent trait increases. As a consequence, an underestimation of this variance will lead to an overestimation of the power of the group effect.

Conclusion: A misspecification of the item difficulties regarding their overall pattern or their dispersion seems to have no or very little impact on the power of the test of the group effect. In contrast, a misspecification of the variance of the latent variable can have a strong impact as an underestimation of the variance will lead in some cases to an overestimation of the power at the design stage and may result in an underpowered study.

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