One in twenty five carried what one in twenty five hundred had

# Self-authored for the EML case corpus (no external origin). A screening planner
# reads that a recessive condition affects one person in 2500 and reasons that
# its carriers - people with a single copy of the gene - must be rare as well,
# a handful in a town of 10000, not worth a carrier screen. How common the
# carriers really are is computed below.
#
# The reasoning is careful. The rate of one in 2500 is accurate; the condition
# really is recessive, needing two copies; carriers really do have one; and the
# intent is exactly 'how many carriers are there'.
#
# An affected person needs a copy from each parent, so the rate of the condition
# is the square of the gene's frequency: one in 2500 means the gene is one copy
# in 50. A carrier needs only one, and that happens about twice in every 50
# people - so in 10000 people there are 4 affected and 392 carriers, 98 carriers
# for every affected person, and 980 of every 1000 copies of the gene sit in
# people who show nothing.

2500 => people_per_affected_person
50 => gene_copies_per_variant_copy
10000 => people_in_the_town

gene_copies_per_variant_copy * gene_copies_per_variant_copy => square_of_the_gene_rarity
int(people_in_the_town / people_per_affected_person) => affected_in_the_town
int(2 * (gene_copies_per_variant_copy - 1) * people_in_the_town / (gene_copies_per_variant_copy * gene_copies_per_variant_copy)) => carriers_in_the_town
int(carriers_in_the_town / affected_in_the_town) => carriers_per_affected_person
int(people_in_the_town / carriers_in_the_town) => one_person_in_this_many_is_a_carrier
carriers_in_the_town + 2 * affected_in_the_town => copies_in_the_town
int(carriers_in_the_town * 1000 / copies_in_the_town) => copies_carried_silently_per_mille

"condition                       : 1 person in " + str(people_per_affected_person) ^0
"gene, one copy in               : " + str(gene_copies_per_variant_copy) + ", since " + str(gene_copies_per_variant_copy) + " squared is " + str(square_of_the_gene_rarity) ^0
"" ^0
"town                            : " + str(people_in_the_town) + " people" ^0
"affected                        : " + str(affected_in_the_town) ^0
"carriers                        : " + str(carriers_in_the_town) + ", one person in " + str(one_person_in_this_many_is_a_carrier) ^0
"carriers per affected person    : " + str(carriers_per_affected_person) ^0
"copies of the gene in the town  : " + str(copies_in_the_town) + ", " + str(copies_carried_silently_per_mille) + " per mille of them in carriers" ^0
"" ^0

# ---- what the planner verified ----

"the rare-means-rare reasoning" ^0
"  rate : 1 in " + str(people_per_affected_person) + ", accurate" ^0
"  inheritance : recessive, two copies needed" ^0
"  carriers : people with one copy" ^0
"  intent : how many carriers are there" ^0
"  facts wrong : 0" ^0
"  verdict : A RARE CONDITION HAS RARE CARRIERS" ^0
"" ^0
"  taking the rate from a sound source is the part done right" ^0
"  here, and it is why " + str(affected_in_the_town) + " affected people in " + str(people_in_the_town) + " is exactly what" ^0
"  the town has" ^0
"" ^0

# ---- how common the carriers are ----

"two copies against one" ^0
"  what an affected person needs : a copy from each parent, so the" ^0
"    rate is the gene's frequency squared" ^0
"  what one in " + str(people_per_affected_person) + " says about the gene : one copy in " + str(gene_copies_per_variant_copy) ^0
"  what a carrier needs : one copy, from either parent, which" ^0
"    happens about twice in every " + str(gene_copies_per_variant_copy) + " people" ^0
"  the town : " + str(carriers_in_the_town) + " carriers against " + str(affected_in_the_town) + " affected, " + str(carriers_per_affected_person) + " to 1" ^0
"  where the gene lives : " + str(copies_carried_silently_per_mille) + " per mille of its copies in people who" ^0
"    show nothing" ^0
"" ^0

# ---- what the planner got ----

"the screening plan" ^0
"  believed : a handful of carriers, not worth a screen" ^0
"  actual : " + str(carriers_in_the_town) + " carriers in the town, one person in " + str(one_person_in_this_many_is_a_carrier) ^0
"  is the rate wrong : no; " + str(affected_in_the_town) + " affected in " + str(people_in_the_town) ^0
"  are carriers as rare as the condition : no; the condition is" ^0
"    the square of the gene's rarity, and the carriers are not" ^0
"" ^0

# ---- null control ----

# The same town counted from the gene's frequency instead of by taking the
# carriers to be about as rare as the condition.
4 => nc_carriers_read_as_rare_as_the_condition
392 => nc_carriers_from_the_gene_frequency
388 => nc_carriers_the_square_root_reveals

"null control - count from the gene, not from the condition" ^0
"  carriers, read as rare as the condition : " + str(nc_carriers_read_as_rare_as_the_condition) ^0
"  carriers, from the gene's frequency : " + str(nc_carriers_from_the_gene_frequency) ^0
"  carriers the square root reveals : " + str(nc_carriers_the_square_root_reveals) ^0
"  no rate and no town changed; the rate was traced back to the" ^0
"  gene before the carriers were counted" ^0
"" ^0

# ---- the rule ----

"what an accurate rate of 1 in " + str(people_per_affected_person) + " guarantees" ^0
"  1 person in " + str(people_per_affected_person) + " has two copies : exactly" ^0
"  carriers are about as rare : not addressed; two copies is the" ^0
"    square of the gene's frequency, the gene is one copy in " + str(gene_copies_per_variant_copy) + "," ^0
"    and one person in " + str(one_person_in_this_many_is_a_carrier) + " carries one copy - " + str(carriers_per_affected_person) + " carriers for every" ^0
"    affected person" ^0
"" ^0

"a rare pair is made of common halves; square a small number and it gets much" ^0
"smaller, so a condition that needs two copies hides a gene that is not rare" ^0
"at all" ^0
"" ^0

"The rate is right: " + str(affected_in_the_town) + " affected in " + str(people_in_the_town) + ". But two copies is the square of the" ^0
"gene's frequency, so the gene is one copy in " + str(gene_copies_per_variant_copy) + " and the town holds " + str(carriers_in_the_town) + " carriers," ^0
"" + str(carriers_per_affected_person) + " for every affected person, with " + str(copies_carried_silently_per_mille) + " per mille of the gene's copies in people" ^0
"who show nothing, until the carriers are counted from the gene and not from the condition." ^0

people_per_affected_person = 2500
gene_copies_per_variant_copy = 50
people_in_the_town = 10000
square_of_the_gene_rarity = gene_copies_per_variant_copy * gene_copies_per_variant_copy
affected_in_the_town = int(people_in_the_town / people_per_affected_person)
carriers_in_the_town = int(2 * (gene_copies_per_variant_copy - 1) * people_in_the_town / (gene_copies_per_variant_copy * gene_copies_per_variant_copy))
carriers_per_affected_person = int(carriers_in_the_town / affected_in_the_town)
one_person_in_this_many_is_a_carrier = int(people_in_the_town / carriers_in_the_town)
copies_in_the_town = carriers_in_the_town + 2 * affected_in_the_town
copies_carried_silently_per_mille = int(carriers_in_the_town * 1000 / copies_in_the_town)
print("condition                       : 1 person in " + str(people_per_affected_person))
print("gene, one copy in               : " + str(gene_copies_per_variant_copy) + ", since " + str(gene_copies_per_variant_copy) + " squared is " + str(square_of_the_gene_rarity))
print("")
print("town                            : " + str(people_in_the_town) + " people")
print("affected                        : " + str(affected_in_the_town))
print("carriers                        : " + str(carriers_in_the_town) + ", one person in " + str(one_person_in_this_many_is_a_carrier))
print("carriers per affected person    : " + str(carriers_per_affected_person))
print("copies of the gene in the town  : " + str(copies_in_the_town) + ", " + str(copies_carried_silently_per_mille) + " per mille of them in carriers")
print("")
print("the rare-means-rare reasoning")
print("  rate : 1 in " + str(people_per_affected_person) + ", accurate")
print("  inheritance : recessive, two copies needed")
print("  carriers : people with one copy")
print("  intent : how many carriers are there")
print("  facts wrong : 0")
print("  verdict : A RARE CONDITION HAS RARE CARRIERS")
print("")
print("  taking the rate from a sound source is the part done right")
print("  here, and it is why " + str(affected_in_the_town) + " affected people in " + str(people_in_the_town) + " is exactly what")
print("  the town has")
print("")
print("two copies against one")
print("  what an affected person needs : a copy from each parent, so the")
print("    rate is the gene's frequency squared")
print("  what one in " + str(people_per_affected_person) + " says about the gene : one copy in " + str(gene_copies_per_variant_copy))
print("  what a carrier needs : one copy, from either parent, which")
print("    happens about twice in every " + str(gene_copies_per_variant_copy) + " people")
print("  the town : " + str(carriers_in_the_town) + " carriers against " + str(affected_in_the_town) + " affected, " + str(carriers_per_affected_person) + " to 1")
print("  where the gene lives : " + str(copies_carried_silently_per_mille) + " per mille of its copies in people who")
print("    show nothing")
print("")
print("the screening plan")
print("  believed : a handful of carriers, not worth a screen")
print("  actual : " + str(carriers_in_the_town) + " carriers in the town, one person in " + str(one_person_in_this_many_is_a_carrier))
print("  is the rate wrong : no; " + str(affected_in_the_town) + " affected in " + str(people_in_the_town))
print("  are carriers as rare as the condition : no; the condition is")
print("    the square of the gene's rarity, and the carriers are not")
print("")
nc_carriers_read_as_rare_as_the_condition = 4
nc_carriers_from_the_gene_frequency = 392
nc_carriers_the_square_root_reveals = 388
print("null control - count from the gene, not from the condition")
print("  carriers, read as rare as the condition : " + str(nc_carriers_read_as_rare_as_the_condition))
print("  carriers, from the gene's frequency : " + str(nc_carriers_from_the_gene_frequency))
print("  carriers the square root reveals : " + str(nc_carriers_the_square_root_reveals))
print("  no rate and no town changed; the rate was traced back to the")
print("  gene before the carriers were counted")
print("")
print("what an accurate rate of 1 in " + str(people_per_affected_person) + " guarantees")
print("  1 person in " + str(people_per_affected_person) + " has two copies : exactly")
print("  carriers are about as rare : not addressed; two copies is the")
print("    square of the gene's frequency, the gene is one copy in " + str(gene_copies_per_variant_copy) + ",")
print("    and one person in " + str(one_person_in_this_many_is_a_carrier) + " carries one copy - " + str(carriers_per_affected_person) + " carriers for every")
print("    affected person")
print("")
print("a rare pair is made of common halves; square a small number and it gets much")
print("smaller, so a condition that needs two copies hides a gene that is not rare")
print("at all")
print("")
print("The rate is right: " + str(affected_in_the_town) + " affected in " + str(people_in_the_town) + ". But two copies is the square of the")
print("gene's frequency, so the gene is one copy in " + str(gene_copies_per_variant_copy) + " and the town holds " + str(carriers_in_the_town) + " carriers,")
print("" + str(carriers_per_affected_person) + " for every affected person, with " + str(copies_carried_silently_per_mille) + " per mille of the gene's copies in people")
print("who show nothing, until the carriers are counted from the gene and not from the condition.")

condition                       : 1 person in 2500
gene, one copy in               : 50, since 50 squared is 2500

town                            : 10000 people
affected                        : 4
carriers                        : 392, one person in 25
carriers per affected person    : 98
copies of the gene in the town  : 400, 980 per mille of them in carriers

the rare-means-rare reasoning
  rate : 1 in 2500, accurate
  inheritance : recessive, two copies needed
  carriers : people with one copy
  intent : how many carriers are there
  facts wrong : 0
  verdict : A RARE CONDITION HAS RARE CARRIERS

  taking the rate from a sound source is the part done right
  here, and it is why 4 affected people in 10000 is exactly what
  the town has

two copies against one
  what an affected person needs : a copy from each parent, so the
    rate is the gene's frequency squared
  what one in 2500 says about the gene : one copy in 50
  what a carrier needs : one copy, from either parent, which
    happens about twice in every 50 people
  the town : 392 carriers against 4 affected, 98 to 1
  where the gene lives : 980 per mille of its copies in people who
    show nothing

the screening plan
  believed : a handful of carriers, not worth a screen
  actual : 392 carriers in the town, one person in 25
  is the rate wrong : no; 4 affected in 10000
  are carriers as rare as the condition : no; the condition is
    the square of the gene's rarity, and the carriers are not

null control - count from the gene, not from the condition
  carriers, read as rare as the condition : 4
  carriers, from the gene's frequency : 392
  carriers the square root reveals : 388
  no rate and no town changed; the rate was traced back to the
  gene before the carriers were counted

what an accurate rate of 1 in 2500 guarantees
  1 person in 2500 has two copies : exactly
  carriers are about as rare : not addressed; two copies is the
    square of the gene's frequency, the gene is one copy in 50,
    and one person in 25 carries one copy - 98 carriers for every
    affected person

a rare pair is made of common halves; square a small number and it gets much
smaller, so a condition that needs two copies hides a gene that is not rare
at all

The rate is right: 4 affected in 10000. But two copies is the square of the
gene's frequency, so the gene is one copy in 50 and the town holds 392 carriers,
98 for every affected person, with 980 per mille of the gene's copies in people
who show nothing, until the carriers are counted from the gene and not from the condition.

Trace event types