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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)

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.

View Article: PubMed Central - PubMed

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.

No MeSH data available.


Power estimated with Raschpower as a function of the standard deviation of the item distribution (), the group effect (γ) and the gap between the means of the normal distributions (a) for a sample size per groupNg=200, a number of itemsJ=7 and a variance of the latent variable. Overlaid curves represent different values of a, .
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Fig4: Power estimated with Raschpower as a function of the standard deviation of the item distribution (), the group effect (γ) and the gap between the means of the normal distributions (a) for a sample size per groupNg=200, a number of itemsJ=7 and a variance of the latent variable. Overlaid curves represent different values of a, .

Mentions: Table 2 shows the power estimated with Raschpower for some values of the sample size per group (Ng), the group effect (γ), the variance of the item distribution and the gap between the means of the two normal distributions (a) when the variance of the latent variable =1 and the number of items J=7. The results for all the values of the sample size, the group effect, the variance of the item distribution and the gap between the means of the two normal distributions and values for the variance of the latent variable equals to 0.25, 0.5, 1, 2, 4 or 9 and for the number of item equals to 3, 9 or 15 respectively are presented in Additional file 2. The impact of a misspecification of the item difficulties was the same whatever the values of the number of items (J), the sample size per group (Ng) and the variance of the latent trait (results not shown). In general, the estimated power remains stable or shows a very little decrease when the variance of the item distribution or the gap between the means of the two normal distributions a increases. It seems that a misspecification of the item difficulties regarding their overall pattern (change in a, Figure 2) or their dispersion (change in , Figure 1) has no or very little impact on the power. In some extreme cases, where the gap between the means of the two normal distributions is high and the variance of the item distribution is high compared to the variance of the latent trait, a small decrease of the power is observed. An illustration of this effect is presented in Figure 4. We can observe that the power for γ=0.5 decreases when the variance of the item distribution increases and that the curves are no more overlaid for . In this case, the power decreases more for high values of a. In fact, for γ=0.5, Ng=200 and J=7 the power without misspecification is estimated at 83.5% whereas the power is estimated at 78.3% in case of a high misspecification which results however in a decrease of power of only 5.2%.Table 2


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)

Power estimated with Raschpower as a function of the standard deviation of the item distribution (), the group effect (γ) and the gap between the means of the normal distributions (a) for a sample size per groupNg=200, a number of itemsJ=7 and a variance of the latent variable. Overlaid curves represent different values of a, .
© Copyright Policy - open-access
Related In: Results  -  Collection

License 1 - License 2
Show All Figures
getmorefigures.php?uid=PMC4373307&req=5

Fig4: Power estimated with Raschpower as a function of the standard deviation of the item distribution (), the group effect (γ) and the gap between the means of the normal distributions (a) for a sample size per groupNg=200, a number of itemsJ=7 and a variance of the latent variable. Overlaid curves represent different values of a, .
Mentions: Table 2 shows the power estimated with Raschpower for some values of the sample size per group (Ng), the group effect (γ), the variance of the item distribution and the gap between the means of the two normal distributions (a) when the variance of the latent variable =1 and the number of items J=7. The results for all the values of the sample size, the group effect, the variance of the item distribution and the gap between the means of the two normal distributions and values for the variance of the latent variable equals to 0.25, 0.5, 1, 2, 4 or 9 and for the number of item equals to 3, 9 or 15 respectively are presented in Additional file 2. The impact of a misspecification of the item difficulties was the same whatever the values of the number of items (J), the sample size per group (Ng) and the variance of the latent trait (results not shown). In general, the estimated power remains stable or shows a very little decrease when the variance of the item distribution or the gap between the means of the two normal distributions a increases. It seems that a misspecification of the item difficulties regarding their overall pattern (change in a, Figure 2) or their dispersion (change in , Figure 1) has no or very little impact on the power. In some extreme cases, where the gap between the means of the two normal distributions is high and the variance of the item distribution is high compared to the variance of the latent trait, a small decrease of the power is observed. An illustration of this effect is presented in Figure 4. We can observe that the power for γ=0.5 decreases when the variance of the item distribution increases and that the curves are no more overlaid for . In this case, the power decreases more for high values of a. In fact, for γ=0.5, Ng=200 and J=7 the power without misspecification is estimated at 83.5% whereas the power is estimated at 78.3% in case of a high misspecification which results however in a decrease of power of only 5.2%.Table 2

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.

View Article: PubMed Central - PubMed

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.

No MeSH data available.