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Power and sample size determination for the group comparison of patient-reported outcomes with Rasch family models.

Blanchin M, Hardouin JB, Guillemin F, Falissard B, Sébille V - PLoS ONE (2013)

Bottom Line: Preliminary developments have been proposed for sample size and power determination for the comparison of PRO in cross-sectional studies comparing two groups of patients when an IRT model is intended to be used for analysis.The objective of this work was to validate these developments in a large number of situations reflecting real-life studies.At the design stage, the questionnaire used to measure the intended PRO should be carefully chosen in relation to the studied population.

View Article: PubMed Central - PubMed

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

ABSTRACT

Background: Patient-reported outcomes (PRO) that comprise all self-reported measures by the patient are important as endpoint in clinical trials and epidemiological studies. Models from the Item Response Theory (IRT) are increasingly used to analyze these particular outcomes that bring into play a latent variable as these outcomes cannot be directly observed. Preliminary developments have been proposed for sample size and power determination for the comparison of PRO in cross-sectional studies comparing two groups of patients when an IRT model is intended to be used for analysis. The objective of this work was to validate these developments in a large number of situations reflecting real-life studies.

Methodology: The method to determine the power relies on the characteristics of the latent trait and of the questionnaire (distribution of the items), the difference between the latent variable mean in each group and the variance of this difference estimated using Cramer-Rao bound. Different scenarios were considered to evaluate the impact of the characteristics of the questionnaire and of the variance of the latent trait on performances of the Cramer-Rao method. The power obtained using Cramer-Rao method was compared to simulations.

Principal findings: Powers achieved with the Cramer-Rao method were close to powers obtained from simulations when the questionnaire was suitable for the studied population. Nevertheless, we have shown an underestimation of power with the Cramer-Rao method when the questionnaire was less suitable for the population. Besides, the Cramer-Rao method stays valid whatever the values of the variance of the latent trait.

Conclusions: The Cramer-Rao method is adequate to determine the power of a test of group effect at design stage for two-group comparison studies including patient-reported outcomes in health sciences. At the design stage, the questionnaire used to measure the intended PRO should be carefully chosen in relation to the studied population.

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Distributions of items and latent variable for  and .Vertical lines: values of the difficulties of the items.
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pone-0057279-g001: Distributions of items and latent variable for and .Vertical lines: values of the difficulties of the items.

Mentions: To study the impact of the values of the item difficulties, the distribution of items could vary in two different ways according to the regularity of the spacing of the items and the gap between the mean of the latent variable and the mean of the items distribution. To obtain item difficulties that are quite regularly spaced, their values are set to the percentiles of a determined probability distribution. The normal distribution is used with the same mean and variance as the latent trait distribution. The questionnaire will therefore estimate the patients levels of quality of life with the same accuracy whatever the level of quality of life on the continuum of the latent trait as shown on Figure 1 (subfigure A). To obtain irregularly spaced item difficulties, an equiprobable mixture of two gaussian distributions was used. When the spacing is irregular, the estimates of the patients levels, of quality of life for example, will be more precise when difficulties are close to each other than when they are far apart from each other. We can see on Figure 1 (subfigure B) that the quality of life levels around −1 will be estimated more precisely than quality of life levels between −0.5 and 0.5. The case of irregular spacing of item difficulties is probably more encountered in practice than regular spacing.


Power and sample size determination for the group comparison of patient-reported outcomes with Rasch family models.

Blanchin M, Hardouin JB, Guillemin F, Falissard B, Sébille V - PLoS ONE (2013)

Distributions of items and latent variable for  and .Vertical lines: values of the difficulties of the items.
© Copyright Policy
Related In: Results  -  Collection

Show All Figures
getmorefigures.php?uid=PMC3585387&req=5

pone-0057279-g001: Distributions of items and latent variable for and .Vertical lines: values of the difficulties of the items.
Mentions: To study the impact of the values of the item difficulties, the distribution of items could vary in two different ways according to the regularity of the spacing of the items and the gap between the mean of the latent variable and the mean of the items distribution. To obtain item difficulties that are quite regularly spaced, their values are set to the percentiles of a determined probability distribution. The normal distribution is used with the same mean and variance as the latent trait distribution. The questionnaire will therefore estimate the patients levels of quality of life with the same accuracy whatever the level of quality of life on the continuum of the latent trait as shown on Figure 1 (subfigure A). To obtain irregularly spaced item difficulties, an equiprobable mixture of two gaussian distributions was used. When the spacing is irregular, the estimates of the patients levels, of quality of life for example, will be more precise when difficulties are close to each other than when they are far apart from each other. We can see on Figure 1 (subfigure B) that the quality of life levels around −1 will be estimated more precisely than quality of life levels between −0.5 and 0.5. The case of irregular spacing of item difficulties is probably more encountered in practice than regular spacing.

Bottom Line: Preliminary developments have been proposed for sample size and power determination for the comparison of PRO in cross-sectional studies comparing two groups of patients when an IRT model is intended to be used for analysis.The objective of this work was to validate these developments in a large number of situations reflecting real-life studies.At the design stage, the questionnaire used to measure the intended PRO should be carefully chosen in relation to the studied population.

View Article: PubMed Central - PubMed

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

ABSTRACT

Background: Patient-reported outcomes (PRO) that comprise all self-reported measures by the patient are important as endpoint in clinical trials and epidemiological studies. Models from the Item Response Theory (IRT) are increasingly used to analyze these particular outcomes that bring into play a latent variable as these outcomes cannot be directly observed. Preliminary developments have been proposed for sample size and power determination for the comparison of PRO in cross-sectional studies comparing two groups of patients when an IRT model is intended to be used for analysis. The objective of this work was to validate these developments in a large number of situations reflecting real-life studies.

Methodology: The method to determine the power relies on the characteristics of the latent trait and of the questionnaire (distribution of the items), the difference between the latent variable mean in each group and the variance of this difference estimated using Cramer-Rao bound. Different scenarios were considered to evaluate the impact of the characteristics of the questionnaire and of the variance of the latent trait on performances of the Cramer-Rao method. The power obtained using Cramer-Rao method was compared to simulations.

Principal findings: Powers achieved with the Cramer-Rao method were close to powers obtained from simulations when the questionnaire was suitable for the studied population. Nevertheless, we have shown an underestimation of power with the Cramer-Rao method when the questionnaire was less suitable for the population. Besides, the Cramer-Rao method stays valid whatever the values of the variance of the latent trait.

Conclusions: The Cramer-Rao method is adequate to determine the power of a test of group effect at design stage for two-group comparison studies including patient-reported outcomes in health sciences. At the design stage, the questionnaire used to measure the intended PRO should be carefully chosen in relation to the studied population.

Show MeSH