Terms and diagram of prevalence methodology

Deductive Ceiling The 1st and 2nd reports involve the same 60,000 population. The 2nd report adds approximately 40,000 to that population.  Of this 100,000, there were 25 molecular hits above the clinical cutoff point. Because it is impossible for a slice to be larger than the pie it is cut out of, neither report can have more than 25 molecular hits above the clinical cutoff. I refer to this deductive fact, and to the number 25, as the “deductive ceiling.”  We use this to give the 1st report the best footing mathematically possible during its reconciliation with the 2nd report. In these equations, we are only concerned with the limit of possibility: 25. So for the sake of simplifying the matter to a clear deductive equation, I will sometimes speak of this maximum 25 as if an estimate. This allows us to work with a fixed number, instead of a cumbersome range of numbers. Later in the report we will deal with actual estimates.
Deductive Floor Conversely, because the 1st report had a total number of 100 molecular hits, there could not be less than 75 such hits below the clinical cutoff. That is, if the maximum number of hits above the cutoff is 25, then that leaves 100 – 25 = 75 minimum hits below the cutoff.  I refer to this as the “deductive floor.” For the sake of simplifying the matter to a clear deductive equation, I will sometimes speak of this minimum 75 as if it were an estimate. This allows us to work with a fixed number, instead of a range. Later in the report we will deal with actual estimates.
DLCN Dutch Lipid Clinic Network criteria: If I use the terms “clinical,” I refer to the DLCN clinical scoring system as used by the authors of the reports in question. I might write, “above the clinical detection point” or “above the clinical cutoff point.” By this I mean a passing score, according to the authors, using the DLCN system: ”Definite and Probable.”  If I say “above the clinical cutoff” or “above the detection point,” I refer to the higher scores, and not necessarily to the order of rows in a given table. For example, the authors provide a table where the higher scores are actually set in the lower rows of a table. These would be nonetheless “above” the DLCN cutoff pointmeaning they have sufficiently high scores to be regarded as having “FH.”They look like they might have FH.  The clinical test is used in contradistinction to a molecular test: those who look like they might carry a mutation versus those who are confirmed to carry a mutation. Damgaard found that of those who scored in the top two DLCN categories, 50% were nonetheless not found to carry a mutation. 
FH Familial (inherited) Hypercholesterolemia. Also known as Heterozygous FH (HeFH). Strictly speaking it is determined by mutations in the LDL receptor (LDLR). Around 2,000 different LDLR mutations have been discovered. Thus, there is a “spectrum” of FH LDLR mutations.  However, clinically, other diseases and environmental factors can have the same outward appearance (same “phenotype”). This permits an ambiguity which sometimes leaves FH as a kind of umbrella-term under which other diseases and environmental factors co-exist. As with most linguistic ambiguities, this confusion is a cultural reality. However, even among professionals and experts, this dual use of the term has been exploited by the industry.
Non-FH Nonfamilial (non-inherited) Hypercholesterolemia
FDB Familial Defective Apolipoprotein B100. This is a mutation in a different location: from the molecular perspective, FH refers to the receptor and FDB refers to the ligand (APOB). FDB is generally milder than FH and is rare outside of European ancestry. Unlike FH, there are not a wide variety of harmful FDB mutations. They are almost always R3500Q and R3500W.  And in any event, within the data used by the authors there is no “spectrum” for FDB beyond R3500Q and R3500W. 
ADH Autosomal Dominant Hypercholesterolemia is the true umbrella term under which FH and FDB are distinctive constituents. While the ambiguity inherent in a clinical use of “FH” conceals the molecular nature of its constituents, “ADH” clarifies those constituents at the molecular level.  Given that FH is an inherited disease, where the mutations are the key point, responsible treatment demands a careful distinction between the terms FH and FDB … which the authors of the Authoritative report do not make. Rather these authors skip over expert definition and exploit the confusion by avoiding the use of “ADH” as a term in the entire Authoritative report. (There are other molecular constituents under this umbrella; however, they do not play a role in the mathematical and logical abuses that I outline in my analysis.)
Genotype “All or part of the genetic constitution of an individual or group” ~ Merriam-Webster’s
Phenotype “The visible properties of an organism that are produced by the interaction of the genotype and the environment.” ~ Merriam-Webster’s 
Spectrum As it applies to the 2nd report, the set of known, distinct mutations within FH and/or FDB.
Proband Sometimes referred to as an “index patient.”  A single member of a family is isolated. For example, if related grandparents, parents, and children all have FH, only one of them will be counted as a proband.  There are two key sets of mutation carriers. In my analysis, probands should be understood in the context of the mutation spectrum. For mathematical purposes, Top4 probands would be a distinct set from the Top4 mutation hits among the general population. Although problematic, the authors think of these two sets of numbers as parallel, where the distribution of probands within the spectrum is symmetrical to the distribution of mutation hits within the general population. For example, if the 55 Top4 probands make up 38.7% of the 142 probands in the entire spectrum, then we should carry that same proportion over and treat the 174 Top4 mutation hits within the Copenhagen population as 38.7% of the total prevalence. With this, the authors derive total prevalence: 174 ÷ .387 = 450. (See illustration below.)
Top4 This is my usage and specific to my analysis. By this I refer to the four most frequently occurring mutations within FH and FDB combined, according to their use in the 1st and 2nd reports. This term works in two distinct contexts: it can refer to probands within the spectrum but also to mutation carriers in the general population study. For example, in the 2nd report, there were 55 probands with Top4 mutations within the spectrum and there were 174 carriers of Top4 mutations within the Copenhagen population sample.  See illustration below and here.
209 or 184 clinical results When I refer to 209 or the adjusted 184 as clinical results, I refer to the number of clinical hits after excluding Top4 carriers. An estimated 15 are shared between both samples, and because we include them in the 100 Top4 molecular, we will leave them out of the Clinical total, so as not to count them twice. 309 – 100 Top4 molecular = 209 results clinical results, I.E., after excluding Top4. See pages here and here.
Ex-Top4 This is my usage and specific to my analysis.  The Top4 probands are calculated by the 2nd report to be 38.7% of total probands within the mutation spectrum. The authors then carry over this proportion to the population study: they calculate the total mutation carriers by dividing the Top4 mutation carriers by .387. I use “Ex-Top4” to refer, not to the total of mutation carriers (or probands), but only to that portion which is counterpart to the Top4. (Total carriers – Top4 carriers = Ex-Top4 carriers … or, Total Probands – Top4 probands = Ex-Top4 probands.) See illustration below and here.  Importantly, according to the authors’ data, all Ex-Top4 are FH LDLR, and there are no FDB APOB included.
Top3 After removing FDB APOB from the Top4, only the three most frequent mutations remain and they are all FH LDLR.