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Analysis of dietary interventions. A simple payoff matrix for display of comparative dietary trials.

Feinman RD, Fine EJ, Volek JS - Nutr J (2008)

Bottom Line: Probability of outcome can be calculated from the fraction of matrix elements corresponding to specified conditions.The method has the advantage of emphasizing differences and providing the maximum amount of information.In a test case in which a cross-over study had been performed the matrix derived from theoretical paired comparisons (treating the data as two parallel studies) was consistent with the results from the actual pairing in the cross-over.

View Article: PubMed Central - HTML - PubMed

Affiliation: Department of Biochemistry, State University of New York Downstate Medical Center, Brooklyn, New York, USA. rfeinman@downstate.edu

ABSTRACT

Objective: To provide a simple method for presentation of data in comparative dietary trials.

Methods: Individual data from each diet are ranked and all possible paired comparisons are made and displayed in a pay-off matrix which can be color-coded according to the magnitude of the differences between the two diets. Probability of outcome can be calculated from the fraction of matrix elements corresponding to specified conditions. The method has the advantage of emphasizing differences and providing the maximum amount of information.

Results: The method was tested with values from the literature and allows intuitive sense of the comparative effectiveness of the two diets. In a test case in which a cross-over study had been performed the matrix derived from theoretical paired comparisons (treating the data as two parallel studies) was consistent with the results from the actual pairing in the cross-over.

Conclusion: The matrix method is a simple way of providing access to the differences between dietary trials. It exaggerates differences but can be used in combination with group statistics that, conversely, provide reliability at the expense of detailed information.

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Payoff matrix for dietary comparisons. Matrices show (theoretical) paired comparisons: Weight loss (in kg) for each individual in the VLCKD is shown in rank order across the top of the matrix (X-axis). Weight loss for the LF is shown down the side of the matrix (X-axis). Each matrix element shows the difference between the value for the VLCKD (column) and the value for the LF (row):VLCKD-LF. Positive values indicate more weight loss for the VLCKD value than the LF, negative values indicate the reverse. Data are from reference [3] in which subjects were assigned to two diets with roughly similar caloric levels (VLCKD: 1855 kcal/d; LF: 1550 kcal/d) differing in nutrient composition: VLCKD = %carbohydrate:fat:protein = ~9:63:28, LF, ~58:22:20. After a fixed period (50 days for men; 30 days for women) subjects switched to the other diet. Data in the matrices are for performance in each phase. In the cross-over data, weight loss for each subject from the LF phase is subtracted from weight loss in the VLCKD phase (regardless of which came first in the experiment) and displayed in rank order.  Color-coding as indicated in the figure.
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Figure 1: Payoff matrix for dietary comparisons. Matrices show (theoretical) paired comparisons: Weight loss (in kg) for each individual in the VLCKD is shown in rank order across the top of the matrix (X-axis). Weight loss for the LF is shown down the side of the matrix (X-axis). Each matrix element shows the difference between the value for the VLCKD (column) and the value for the LF (row):VLCKD-LF. Positive values indicate more weight loss for the VLCKD value than the LF, negative values indicate the reverse. Data are from reference [3] in which subjects were assigned to two diets with roughly similar caloric levels (VLCKD: 1855 kcal/d; LF: 1550 kcal/d) differing in nutrient composition: VLCKD = %carbohydrate:fat:protein = ~9:63:28, LF, ~58:22:20. After a fixed period (50 days for men; 30 days for women) subjects switched to the other diet. Data in the matrices are for performance in each phase. In the cross-over data, weight loss for each subject from the LF phase is subtracted from weight loss in the VLCKD phase (regardless of which came first in the experiment) and displayed in rank order. Color-coding as indicated in the figure.

Mentions: The matrix shown in Figure 1 represents the differences in all responses for the two diets (regardless of order). The horizontal row across the top of the matrix shows the individual values for weight loss on the VLCKD, while the vertical column on the left shows individual weight losses on LF. The matrix elements are the differences between the two diets, that is, the column value minus the row value. Positive values indicate that the VLCKD did better than the low fat. Examination of the color coding of the matrix shows that, consistent with the mean responses, there is a clear choice of the VLCKD. The actual probability predicted by the theoretical pairing shown in Table 1 are calculated from the total number of matrix elements for each condition divided by the total.


Analysis of dietary interventions. A simple payoff matrix for display of comparative dietary trials.

Feinman RD, Fine EJ, Volek JS - Nutr J (2008)

Payoff matrix for dietary comparisons. Matrices show (theoretical) paired comparisons: Weight loss (in kg) for each individual in the VLCKD is shown in rank order across the top of the matrix (X-axis). Weight loss for the LF is shown down the side of the matrix (X-axis). Each matrix element shows the difference between the value for the VLCKD (column) and the value for the LF (row):VLCKD-LF. Positive values indicate more weight loss for the VLCKD value than the LF, negative values indicate the reverse. Data are from reference [3] in which subjects were assigned to two diets with roughly similar caloric levels (VLCKD: 1855 kcal/d; LF: 1550 kcal/d) differing in nutrient composition: VLCKD = %carbohydrate:fat:protein = ~9:63:28, LF, ~58:22:20. After a fixed period (50 days for men; 30 days for women) subjects switched to the other diet. Data in the matrices are for performance in each phase. In the cross-over data, weight loss for each subject from the LF phase is subtracted from weight loss in the VLCKD phase (regardless of which came first in the experiment) and displayed in rank order.  Color-coding as indicated in the figure.
© Copyright Policy - open-access
Related In: Results  -  Collection

License
Show All Figures
getmorefigures.php?uid=PMC2543038&req=5

Figure 1: Payoff matrix for dietary comparisons. Matrices show (theoretical) paired comparisons: Weight loss (in kg) for each individual in the VLCKD is shown in rank order across the top of the matrix (X-axis). Weight loss for the LF is shown down the side of the matrix (X-axis). Each matrix element shows the difference between the value for the VLCKD (column) and the value for the LF (row):VLCKD-LF. Positive values indicate more weight loss for the VLCKD value than the LF, negative values indicate the reverse. Data are from reference [3] in which subjects were assigned to two diets with roughly similar caloric levels (VLCKD: 1855 kcal/d; LF: 1550 kcal/d) differing in nutrient composition: VLCKD = %carbohydrate:fat:protein = ~9:63:28, LF, ~58:22:20. After a fixed period (50 days for men; 30 days for women) subjects switched to the other diet. Data in the matrices are for performance in each phase. In the cross-over data, weight loss for each subject from the LF phase is subtracted from weight loss in the VLCKD phase (regardless of which came first in the experiment) and displayed in rank order. Color-coding as indicated in the figure.
Mentions: The matrix shown in Figure 1 represents the differences in all responses for the two diets (regardless of order). The horizontal row across the top of the matrix shows the individual values for weight loss on the VLCKD, while the vertical column on the left shows individual weight losses on LF. The matrix elements are the differences between the two diets, that is, the column value minus the row value. Positive values indicate that the VLCKD did better than the low fat. Examination of the color coding of the matrix shows that, consistent with the mean responses, there is a clear choice of the VLCKD. The actual probability predicted by the theoretical pairing shown in Table 1 are calculated from the total number of matrix elements for each condition divided by the total.

Bottom Line: Probability of outcome can be calculated from the fraction of matrix elements corresponding to specified conditions.The method has the advantage of emphasizing differences and providing the maximum amount of information.In a test case in which a cross-over study had been performed the matrix derived from theoretical paired comparisons (treating the data as two parallel studies) was consistent with the results from the actual pairing in the cross-over.

View Article: PubMed Central - HTML - PubMed

Affiliation: Department of Biochemistry, State University of New York Downstate Medical Center, Brooklyn, New York, USA. rfeinman@downstate.edu

ABSTRACT

Objective: To provide a simple method for presentation of data in comparative dietary trials.

Methods: Individual data from each diet are ranked and all possible paired comparisons are made and displayed in a pay-off matrix which can be color-coded according to the magnitude of the differences between the two diets. Probability of outcome can be calculated from the fraction of matrix elements corresponding to specified conditions. The method has the advantage of emphasizing differences and providing the maximum amount of information.

Results: The method was tested with values from the literature and allows intuitive sense of the comparative effectiveness of the two diets. In a test case in which a cross-over study had been performed the matrix derived from theoretical paired comparisons (treating the data as two parallel studies) was consistent with the results from the actual pairing in the cross-over.

Conclusion: The matrix method is a simple way of providing access to the differences between dietary trials. It exaggerates differences but can be used in combination with group statistics that, conversely, provide reliability at the expense of detailed information.

Show MeSH