Let’s return to the leveraged denominator, and see what numbers we come up with if we hold to correct mathematics. If we treat each disease separately, we see that of the 55 Top4 probands in the spectrum 36 were FH and 19 were FDB. We see that the 19 FDB probands in the spectrum and the 111 FDB mutation hits in the general population had only R3500Q and R3500W mutations. Practically speaking, these two mutations constitute the total spectrum for FDB. Other mutations are extremely rare. Here are three of the same authors in the Authoritative report. (R3500Q = Arg3500Gln )
And here are two of the same authors again. (R3500Q = Arg3500Gln)
In the studies used in the 2nd report, no other mutations were included in the FDB APOB spectrum. We have the whole pie, and so there is no missing slice to calculate. As an exercise, however, we would remain consistent by filling out the equation: 19 probands found ÷ a total of 19 probands in the whole FDB APOB spectrum = 1. Now there were 111 FDB APOB found in the general population. So we divide 111 by 1 and arrive at total of 111 FDB APOB. Again, we do not have to account for a remainder. There is nothing like an “Ex-Top4” when it comes to FDB APOB. All Ex-Top4 belong to the FH LDLRspectrum. So from the population of 98,000 we divide by the 111 FDB APOB found, and our FDB prevalence is 1:883.
This leaves us with the FH LDLR spectrum. Specifically referring to Denmark and the molecular results in Brusgaard’s study, 53 different LDLR mutations were found. Because there are more LDLRmutations in the spectrum besides the three most frequent, we will calculate the remaining proportion of the spectrum. But we will subtract the FDB APOB probands from the total probands because we are only calculating a ratio for FH LDLR. So 36 probands ÷ 123 total probands in the LDLR spectrum (not 142) = .2927. That gives us a total of 215 in the general population, representing the 63 carriers of the three most frequent mutations plus the remaining 152 carriers of the other LDLR mutations ((63 ÷ .2927 = 215 total and 215 – 63 = 152).
Without leveraging the denominators prevalence approaches established rates.
In the table on the right, we can see that across the board the prevalence numbers are significantly higher for the leveraged denominators. In the middle column, we calculate with the unleveraged denominators, while otherwise using the reports’ own sets of numbers. We arrive at very different conclusions. Prevalence, without leveraging the denominator, returns to estimates established by previous scientists. Here are the elements to the full calculation, broken down into the ADH constituents: FH LDLR and FDB APOB.
The traditional FH LDLR prevalence is 1:500. Using the authors’ own data, I come up with 1:456. That’s only about 10% off. For FDB, the prevalence is held by established scientists to be 1:1000. The authors’ numbers, without inflating the denominator, come in at 1:883. With leveraging, it is 1:118.
No Symmetry of proportion
Note that these corrected numbers are not reversible either. “Top-down” and “bottom-up” calculations do not match up. Beginning with the total 174 and dividing by .387, I end with a prevalence of 218. However, breaking down my calculations into FH and FDB separately, adjusting the ratio accordingly, I end with a prevalence of 301. This is more evidence of asymmetry. (See this page and this page.) A symmetry of proportion between the spectrum and the results in the general population just does not exist. No one’s math is leakproof with the information provided.
 In the 2nd report, it is unclear whether the authors lumped R3500Q with R3500W together or not. Supplementary Table 2 suggests that they did. Table 3 suggests that they did not. However, the difference would be negligible. One of the supporting sources for the 2nd report, Brusgaard, listed 2 mutation types for APOB, where R3500Q proband hits to R3500W proband hits were 40 to 1, and where only 1 R3500W mutation was found. If the authors’ only targeted R3500Q, then when factoring in the remainder of the spectrum the number used for division would be: 40÷41=.976. The difference in results would be negligible. Total results (IE, not distilled into probands) were 75 hits for R3500Q, and only 1 hit for R3500W, that’s 75 R3500Q of a total 76 APOB mutations found. No other harmful APOB mutations were found besides these two.
 The text in Brusgaard, et al, uses the number 54 as the total of all mutation types found. In Brusgaard’s report, I manually counted 55 on Table 2, 53 of which were LDLR.
 Note that without the FDB here, we are no longer talking about the Top4 as we did before, since we have subtracted out one of the elements from the Top4. We are now working with the three most frequent FH LDLR mutations.