Probability density from Eq. (8) for randomly oriented prolate ellipsoids with major radius c and minor radius a as shown in the figure. The vertical line corresponds to the diameter for a sphere with the volume π/6. Each curve diverges at its upper bound but is finite at the lower bound.
For randomly oriented prolate ellipsoids with given c/a ratios, (a) the mean RECIST d and (b) its standard deviation. The probability distribution is given in Eq. (8) and plotted in Fig. 1. See Eq. (5) for the oblate case.
Logarithm (base 10) of RECIST diameter in millimeters vs logarithm of volume in cubic millimeters for 5000 ellipsoids with random orientations, sizes, and a:b:c ratios restricted between 1 and ɛ. Upper lines are best fit; lower lines correspond to spheres.
Logarithm of RECIST diameter in millimeters vs logarithm of volume in cubic millimeters for (a) liver malignoma (Ref. 18) and (b) nasopharyngeal carcinoma (Ref. 19). Upper lines are best fit; lower lines correspond to spheres. In (a), black points correspond to baseline data and green points correspond to follow up data.
Probability densities of residuals of the fits in Fig 3.for ɛ = 1.1, 2, and 16, and a histogram of empirical data from Heußel et al. (Ref. 18). Normal distributions with the same standard deviations are plotted with dashed lines.
(a) Probabilities of two sampled ellipsoids with random orientations, random a:b:c ratios, and random volumes, to have the relationship V2 > V1 given the ratio of their measured RECIST diameters. Curves are plotted in order for ɛ = 1.1, 1.5, 2, 4, 8, 16, and 8000. Horizontal lines represent the 5% and 95% probabilities. Vertical lines represent the RECIST criteria for PR and PD. The full range of Δ in this plot represents 1/2 ≤ d 2/d 1 ≤ 2. (b) Probabilities for all pairs of tumors measured in a previous study of liver malignoma (Ref. 18) fit to ɛ = 5 of the series in (a). (c) Relative frequencies of observed malignoma pairs with (left) V2 < V1 and (right) V2 > V1.
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