# FH LDLR and FDB APOB prevalence, without leveraging the denominator

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.