Voxel-wise topographical correlation (r) of the PD, MSA and PSP-related brain networks.

*<p>p<0.05 after Bonferroni correction for multiple comparisons (3 comparisons: p<0.0167).</p><p>The p-value is empirically calculated based on the rank of r²-value in 1,000 simulations.</p

Regional differences of two covariance patterns.

<p>(<b>A</b>) Standard SPM analysis with paired t-test design for ON vs. OFF medication with 15 PD patients. (<b>B</b>) The PDRP derived from USA (off-medication) was subtracted from the PDRP derived from South Korea (on-medication). The resulting difference map is z-scored. Only the voxels that were reliable in permutation test were shown (p<0.05, 1,000 permutation). The topography of within-subject differences in medication status (A) was significantly correlated with between-group network differences (B) (r = 0.4228, p<0.001). Likewise, key regions of hypometabolism (e.g., M1, cingulate, cerebellum, putamen) and hypermetabolism (e.g., precuneus) were similarly shown.</p

Voxel-wise topographical correlation (r) of the PDRPs from 4 different countries.

*<p>p<0.05 after Bonferroni correction for multiple comparisons (6 comparisons: p<0.00833).</p><p>The p-value is empirically calculated based on the rank of r²-value in 1,000 simulations.</p

The result of multiple regression: |r| = MI^*b1+Z^*B.

*<p>The lowest AIC value.</p><p>r: topographical correlation (Pearson’s correlation of the voxel weights of the two simulated patterns; MI: global Moran’s I; b1: coefficient of multiple regression of avgMI; Z: random effects dummy variables for 300 volume-pairs; B: coefficient for random effects; se: standard error of b1; AIC: Akaike Information Criteria for the whole model fit.</p

Schematic diagram of the simulation study.

<p>The stimulation was conducted to determine the Window size of Moran’s I that best reflected the inflated topological correlation of the two simulated networks. (<b>A</b>) 300 pseudo-random volume-pairs were generated, then box filters were applied to each volume with six different kernel sizes (3×3×3, 7×7×7, 11×11×11, 15×15×15, 19×19×19, 23×23×23). Then, the global Moran’s I of 1800 volume-pairs (300 original volume-pairs×6 different box filters) was estimated with varying window (W) size (3×3, 9×9, 15×15, 21×21, 27×27, 33×33, 45×45, 51×51, 57×57). The volume-pairs were then vector-transformed and tested for voxel-by-voxel Pearson’s correlation (topographical correlation). Multiple regression was utilized to test if the global Moran’s I significantly predicted the box-filtering-induced elevation of topographical correlation. The window size of the Moran’s I (W) that gave the best prediction of the topographical correlation from the global Moran’s I was identified using AIC. (<b>B–D</b>) The inflated topographical correlation was observed regardless of the W of Moran’s I while the best prediction resulted when the W of Moran’s I was 51 (lowest AIC).</p

Reported percentage of New York City adults infected with COVID-19 versus percentage calculated from our and other reported IFR values prior to May 7, 2020.

As shown in the inset, the predicted maximum and minimum percent of the population in New York City infected with COVID-19 is within the range determined from random adult serological testing [42, 43]. For comparison, we plotted the percentage infected using the IFR values in Table 1.</p

CFR_crude(t) and CFR_closedcase(t) versus time for Germany.

The bottom curve (red) shows CFRcrude(t) plotted versus day after outbreak. The top curve (blue) shows the same for CFRclosedcase(t). CFRcrude(t) increases over this period from a value of 0.12% to a value of 4.36%. It is seen that CFRclosedcase(t) converges to the projected true of CFRcrude earlier than the CFRcrude(t) curve itself.</p

Plots of reported CFR_crude(t) and closed case CFR_crude(t) for Australia, Austria, Iceland, Israel, New Zealand, and South Korea.

Shown below are plots of the reported closed case CFRcrude(t) curve and reported CFRcrude(t) curve for Austria, Australia, Iceland, Israel, New Zealand, and South Korea. The dashed gray line is the value which the closed case CFR(t) has converged to. As for Germany (Fig 1), it is seen that the reported closed case CFR(t) curve converges to a near constant value before the CFRcrude(t) curve. We found (Fig 2, S2 Fig), that for all countries we examined that the converged value of the closed case CFR was close to the optimum for predicting the CFRcrude(t) curve, consistent with it being a good approximation of the true corrected CFR for each country. (PDF)</p

Simulated closed case CFR curves for Germany and South Korea.

In order to understand the basis of the early convergence of the closed case CFR we performed simulations of its time course using cases per day of from Germany and South Korea. Less information is available about the recovery distribution function than the fatality distribution function (fR). Based on the study of SARS by Ghani and coworkers fR is substantially less skewed than FD [1]. This finding is consistent with the reports from early data obtained in China for COVID-19 by Bi et al. and Verity et al. who also found that the median of the fR was several days later than for fD [2, 3]. We assessed the impact of the time to recovery distribution function by simulated the closed case CFR curve using the optimum fR (median 14 days, logSD 0.50) to calculate ND(t) and fR distributions with logSD = 0.25 and median values of 14 days, 16 days, and 18 days. For input data we used the number cases per day for Germany and South Korea. The corrected CFR for each country was used in the simulations. Below we show the simulated closed case CFR curves for Germany and South Korea. Also plotted is the simulated crude CFR curve for each country. It is seen that for all of the recovery distributions evaluated the closed case CFR initially overshoots the corrected CFR value and then converges to it. The smallest overshoot and fastest convergence was for when fR had the same median value as fD. In all cases the CFRcrude curve took longer to converge than the closed case CFR curve, consistent with the reported data from Germany and South Korea (Fig 1 and S1 Fig). The decay portion of the closed case CFR curve for South Korea was consistent with a fR median of 16 days while for Germany a 14-day median better predicted the rapid convergence to the corrected CFR values. The reported initial rise in the closed case CFR for both countries was less well predicted by the simulations, potentially due to differences in the criteria for recovery early in the outbreaks. (PDF)</p

Comparison of age specific IFR coefficients from the present study with serological testing studies internationally [44] and a comprehensive analysis of results from NYC [25] To facilitate comparison, we calculated a 0–64 group mean value for Yang et al. [25] and a 0–69 mean value for Seoane [44] by averaging their reported age sub group IFR values and weighting by percentage of each subgroup of the total infected population.

Comparison of age specific IFR coefficients from the present study with serological testing studies internationally [44] and a comprehensive analysis of results from NYC [25] To facilitate comparison, we calculated a 0–64 group mean value for Yang et al. [25] and a 0–69 mean value for Seoane [44] by averaging their reported age sub group IFR values and weighting by percentage of each subgroup of the total infected population.</p