Figure 1.
Logarithmic modeling and linear regression modeling.
A generic structure of logarithmic (A) and linear regression (B) modeling is given in a simple formula (independent variable = days from onset). MMSE: Mini-Mental State Examination; Ln: natural logarithm. ΔMMSE indicates change in MMSE scores between Day A and Day B. X can be calculated with this formula.
Figure 2.
Plots of actual MMSE scores (filled symbols) from early-phase group data (A) and actual (filled symbols) and predicted MMSE scores (open symbols) from a representative subject (B) are shown. In A, the middle line in the box: median; the ends of the box: interquartile range of the median; the bars: ranges of data distribution; asterisk: P<0.0001 in the Wilcoxon signed-rank test. The MMSE score increased significantly over the 3 sets of assessment (Friedman's test, P<0.0001). In B, the pattern of increase in the predicted values that were derived from the logarithmic model formula was similar to the pattern from the MMSE scores of the representative subject that were actually obtained. However, linear regression modeling overestimated the prediction of cognitive recovery to a greater degree compared with the logarithmic approach. MMSE: Mini-Mental State Examination.
Table 1.
Baseline Characteristics of the Study Group.
Figure 3.
Scatterplots showing the relations between MMSE scores actually obtained and predicted MMSE scores.
Predicted and actual MMSE scores at the third (open symbols) and fourth (filled symbols) sets of assessment by logarithmic model (A) and linear regression model (B). Logarithmic regression modeling estimated prediction of cognitive recovery to a more accurate degree than did the linear approach (logarithmic modeling, third set of assessments: R2 = 0.676, P<0.0001, fourth set of assessments: R2 = 0.521, P<0.0001; linear regression modeling, third set of assessments: R2 = 0.598, P<0.0001, fourth set of assessments: R2 = 0.370, P<0.0001).
Table 2.
Profile of Recovery on Mini-Mental State Examination.