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{{draft task|Probability and statistics}}
 
In epidemiology, retrospective analyses have well-known limitations compared to prospective studies.
 
One such limitation is the occurenceoccurrence of __selection<em>selection bias__bias</em> in the choice of subjects between treated
and untreated groups about whom the data is collected. For example, a treatment may have only been
given to persons who were less severely ill, which would bias the results in favor of such subjects
Line 12:
retrospective study is the topic of this task.
 
The genuine, historical example (only partially approximated in this task) is of a study done of persons who, over a course of 180
of 180 days, may or may not have become infected with Covid-19. Prior to becoming ill, these subjects may or may not have taken an available medication, which was actually taken on a particular schedule not used here, but is approximated by stating the medication was taken in doses of 3, 6, or 9 mg daily. The historical study then divided its subjects into three groups based on their cumulative dosage of the study medication:
may not have taken an available medication, which was usually taken in doses of 3, 6, or 9 mg daily.
This retrospective study divided its subjects into three groups based on their cumulative dosage of the
study medication:
 
::* Group UNTREATED were those who did not take the study medication at all before they got Covid-19, including those who exited the study period without Covid-19 and having never taken the study medication.
including those who exited the study period without Covid-19 and having never taken the study medication.
 
::* Group IRREGULAR is those who took the study medication but whose cumulative dose was less than a certain amount (approximated for our purposes as 100 mg) before they either came down with Covid-19 during the study or the study period ended.
before they either came down with Covid-19 during the study or the study period ended.
 
::* Group REGULAR is those who took (our approximation is >= 100 mg) of the study medication either before thaythey came down with Covid-19 or took >= 100 mg by the end of the study and never became infected during the study.
Covid-19 or took >= 100 mg by the end of the study and never became infected during the study.
 
<br />
: Assumptions for the study:
;Assumptions for the study simulation programming task:
::* Daily risk of getting Covid-19 infection for each subject was 0.1% per day, or 18% over the 180 cumulative days of the study.
 
cumulative days of the study.
* The probability of starting treatment medication for anyone not already taking it was 0.5% per day. For those who started medication, the chance of continuing the treatment was increased 50-fold to 25% each day, since most who started the medication continued to take it to some extent.
:: The probability of starting treatment medication for anyone not already taking it was 0.5% per day.
For those who started medication, the chance of continuing the treatment was increased 50-fold to 25%
each day, since most who started the medication continied to take it to some extent.
:: Study dose per day is random between 3, 6 and 9 mg. The daily cumulative dosage is used to determine
the group the subject is in, unless a subject develops Covid-19. If a subject was diagnosed with Covid-19,
their group at the time of that diagnosis is used in the statistical analysis of that group.
* Study dose per day is random between the approximation for the simulation of 3, 6 and 9 mg. The daily cumulative dosage is used to determine the group the subject is in, unless a subject develops Covid-19. If a subject was diagnosed with Covid-19, their group at the time of that diagnosis is used in the statistical analysis of that group.
 
;Task:
 
* Create a simulation of the subjects, keeping track of their medication dosages, group membership, and Covid-19 status during the study.
Covid-19 status during the study.
* Use at least 1000 subjects in the simulation over the 180 days (historically, the study size was 80,000).
* Statistics used are to be the Kruscal statistic for the analysis of multiple groups, with the boolean
study outcome variable whether the subject got Covid-19 during the study period, analyzed versus category.
* You should get a statistical result highly favoring the REGULAR group.
; Stretch task: show monthly outcomes.
 
A* noteUse regardingat outcome:least Note1000 thatsubjects byin the simulation designover allthe subjects180 mustdays have(historically, anthe IDENTICALstudy risk,size thatwas is80,000).
 
0.1 per cent or p = 0.001 per day, of developing Covid-19. Because of the design, any statistical differences
* Statistics used are to be the Kruskal statistic for the analysis of multiple groups, with the boolean study outcome variable whether the subject got Covid-19 during the study period, analyzed versus category. If the programming language does not have a statistical package for such a test, calculation of the Kruskal H statistic may be used, since any values of H over about 50 are considered very highly indicative of significant group difference. A description of that test is found at [[wp:Kruskal%E2%80%93Wallis_one-way_analysis_of_variance|Kruskal-Wallis test]].
between the groups CANNOT come from an influence of the treatment on that risk, but must come from some other
 
feature of the study design.
* You should get a statistical result highly favoring the REGULAR group.
 
 
;Stretch task
* Show monthly outcomes.
 
 
A note regarding outcome: Note that by simulation design all subjects must have an IDENTICAL risk, that is 0.1 per cent or p = 0.001 per day, of developing Covid-19. Because of the design, any statistical differences between the groups CANNOT come from an influence of the treatment on that risk, but must come from some other feature of the study design.
 
;See also:
:;*[[httpswp://en.wikipedia.org/wiki/Selection_bias|Wikipedia - Selection Bias]]
:;*[[httpswp://en.wikipedia.org/wiki/Retrospective_cohort_study |Wikipedia entry on- retrospectiveRetrospective studies]]
:;*[[https://health.ucdavis.edu/ctsc/area/Resource_Library/documents/Challenges-of-Retrospective-Observational-Studies_8March2017_Kim.pdf UCDavis (pdf) Challenges in Retrospective studies]]
<br /><br /><br />
 
 
=={{header|Julia}}==
<syntaxhighlight lang="julia">using HypothesisTests
 
@enum TreatmentClass Untreated Irregular Regular
 
mutable struct Subject
cum_dose::Float64
treatment_class::TreatmentClass
had_covid::Bool
end
 
function update!(subjects::Vector{Subject}, pcovid = 0.001, pstart = 0.005, pdosing = 0.25, drange = 3:3:9)
for subj in subjects
if subj.had_covid
continue
elseif rand() < pcovid
subj.had_covid = true
elseif subj.cum_dose > 0 && rand() <= pdosing || subj.cum_dose == 0 && rand() <= pstart
subj.cum_dose += rand(drange)
subj.treatment_class =
subj.cum_dose == 0 ? Untreated : subj.cum_dose >= 100 ? Regular : Irregular
end
end
end
 
function run_study(N = 10_000, duration = 180)
population = [Subject(0.0, Untreated, false) for _ in 1:N]
unt, unt_covid, irr, irr_covid, reg, reg_covid = 0, 0, 0, 0, 0, 0
println("Population size $N, daily infection risk 0.1%")
for day in 1:duration
update!(population)
if day % 30 == 0
println("\nDay $day:")
unt = count(s -> s.treatment_class == Untreated, population)
unt_covid = count(s -> (s.treatment_class == Untreated) && s.had_covid, population)
println("Untreated: N = $unt, with infection = $unt_covid")
irr = count(s -> s.treatment_class == Irregular, population)
irr_covid = count(s -> (s.treatment_class == Irregular) && s.had_covid, population)
println("Irregular Use: N = $irr, with infection = $irr_covid")
reg = count(s -> s.treatment_class == Regular, population)
reg_covid = count(s -> (s.treatment_class == Regular) && s.had_covid, population)
println("Regular Use: N = $reg, with infection = $reg_covid")
end
if day == 90
println("\nAt midpoint, Infection case percentages are:")
println(" Untreated : ", Float16(100 * unt_covid / unt))
println(" Irregulars: ", Float16(100 * irr_covid / irr))
println(" Regulars : ", Float16(100 * reg_covid / reg))
end
end
println("\nAt study end, Infection case percentages are:")
println(" Untreated : ", Float16(100 * unt_covid / unt), " of group size of $unt")
println(" Irregulars: ", Float16(100 * irr_covid / irr), " of group size of $irr")
println(" Regulars : ", Float16(100 * reg_covid / reg), " of group size of $reg")
untreated = [s.had_covid for s in population if s.treatment_class == Untreated]
irregular = [s.had_covid for s in population if s.treatment_class == Irregular]
regular = [s.had_covid for s in population if s.treatment_class == Regular]
println("\n\n Final statistics:\n")
@show KruskalWallisTest(untreated, irregular, regular)
end
 
run_study()
</syntaxhighlight>{{out}}
<pre>
Population size 10000, daily infection risk 0.1%
 
Day 30:
Untreated: N = 8633, with infection = 288
Irregular Use: N = 1367, with infection = 21
Regular Use: N = 0, with infection = 0
 
Day 60:
Untreated: N = 7513, with infection = 519
Irregular Use: N = 2325, with infection = 79
Regular Use: N = 162, with infection = 2
 
Day 90:
Untreated: N = 6559, with infection = 692
Irregular Use: N = 2362, with infection = 159
Regular Use: N = 1079, with infection = 24
 
At midpoint, Infection case percentages are:
Untreated : 10.55
Irregulars: 6.73
Regulars : 2.225
 
Day 120:
Untreated: N = 5794, with infection = 845
Irregular Use: N = 2071, with infection = 221
Regular Use: N = 2135, with infection = 72
 
Day 150:
Untreated: N = 5115, with infection = 987
Irregular Use: N = 1835, with infection = 266
Regular Use: N = 3050, with infection = 156
 
Day 180:
Untreated: N = 4538, with infection = 1106
Irregular Use: N = 1654, with infection = 302
Regular Use: N = 3808, with infection = 263
 
At study end, Infection case percentages are:
Untreated : 24.38 of group size of 4538
Irregulars: 18.27 of group size of 1654
Regulars : 6.906 of group size of 3808
 
 
Final statistics:
 
KruskalWallisTest(untreated, irregular, regular) = Kruskal-Wallis rank sum test (chi-square approximation)
-------------------------------------------------------
Population details:
parameter of interest: Location parameters
value under h_0: "all equal"
point estimate: NaN
 
Test summary:
outcome with 95% confidence: reject h_0
one-sided p-value: <1e-99
 
Details:
number of observation in each group: [4538, 1654, 3808]
χ²-statistic: 457.179
rank sums: [2.44308e7, 8.39891e6, 1.71753e7]
degrees of freedom: 2
adjustment for ties: 0.417533
 
Kruskal-Wallis rank sum test (chi-square approximation)
-------------------------------------------------------
Population details:
parameter of interest: Location parameters
value under h_0: "all equal"
point estimate: NaN
 
Test summary:
outcome with 95% confidence: reject h_0
one-sided p-value: <1e-99
 
Details:
number of observation in each group: [4538, 1654, 3808]
χ²-statistic: 457.179
rank sums: [2.44308e7, 8.39891e6, 1.71753e7]
degrees of freedom: 2
adjustment for ties: 0.417533
</pre>
 
=={{header|Nim}}==
{{trans|Python}}
{{trans|Wren}}
<syntaxhighlight lang="Nim">import std/[algorithm, math, random, sequtils, strformat, sugar]
 
type
 
TreatmentClass {.pure.} = enum Untreated, Irregular, Regular
 
Subject = object
cumDose: float
category: TreatmentClass
hadCovid: bool
 
const DoseForRegular = 100
 
func categorize(subject: var Subject) =
## Set treatment category based on cumulative treatment taken.
subject.category = if subject.cumDose == 0: Untreated
elif subject.cumDose >= DoseForRegular: Regular
else: Irregular
 
proc update(subject: var Subject; pCovid = 0.001;
pStart = 0.005; pDosing = 0.25; doses = @[3, 6, 9]) =
## Daily update on the subject to check for infection and randomly dose.
if not subject.hadCovid:
if rand(1.0) < pCovid:
subject.hadCovid = true
elif (subject.cumDose == 0 and rand(1.0) < pStart) or
(subject.cumDose > 0 and rand(1.0) < pDosing):
subject.cumDose += sample(doses).toFloat
subject.categorize()
 
func kruskalWallis(a, b, c: seq[bool]): float =
 
# Aggregate and sort.
let s = sorted(a & b & c)
# Find rank of first occurrence of "true".
let ix = s.find(true) + 1
# Calculate average ranks for "false" and "true".
let n = s.len
let arf = ix / 2
let art = (ix + n) / 2
# Calculate sum of ranks for each list.
let sra = sum(a.mapIt(if it: art else: arf))
let srb = sum(b.mapIt(if it: art else: arf))
let src = sum(c.mapIt(if it: art else: arf))
# Calculate H.
result = 12 / (n * (n + 1)) * (sra * sra / a.len.toFloat + srb * srb / b.len.toFloat +
src * src / c.len.toFloat) - 3 * float(n + 1)
 
proc runStudy(numSubjects = 1000; duration = 180; interval= 30) =
## Run the study using the population of size "numSubjects" for "duration" days.
var population = newSeqWith(numSubjects, Subject())
var unt, untCovid, irr, irrCovid, reg, regCovid = 0
echo &"Total subjects: {num_subjects}"
 
for day in 1..duration:
for subj in population.mitems:
subj.update()
 
if day mod interval == 0:
echo &"\nDay {day}:"
unt = population.countIt(it.category == Untreated)
untCovid = population.countIt(it.category == Untreated and it.hadCovid)
echo &"Untreated: N = {unt}, with infection = {untCovid}"
irr = population.countIt(it.category == IRREGULAR)
irrCovid = population.countIt(it.category == IRREGULAR and it.hadCovid)
echo &"Irregular Use: N = {irr}, with infection = {irrCovid}"
reg = population.countIt(it.category == REGULAR)
regCovid = population.countIt(it.category == REGULAR and it.hadCovid)
echo &"Regular Use: N = {reg}, with infection = {reg_covid}"
 
if day == duration div 2:
echo "\nAt midpoint, infection case percentages are:"
echo " Untreated : ", 100 * untCovid / unt
echo " Irregulars: ", 100 * irrCovid / irr
echo " Regulars : ", 100 * regCovid / reg
 
echo "\nAt study end, infection case percentages are:"
echo &" Untreated : {100 * untCovid / unt} of group size of {unt}"
echo &" Irregulars: {100 * irrCovid / irr} of group size of {irr}"
echo &" Regulars : {100 * regCovid / reg} of group size of {reg}"
let untreated = collect:
for s in population:
if s.category == Untreated:
s.hadCovid
let irregular = collect:
for s in population:
if s.category == Irregular:
s.hadCovid
let regular = collect:
for s in population:
if s.category == Regular:
s.hadCovid
echo "\nFinal statistics: ", kruskalWallis(untreated, irregular, regular)
 
randomize()
runStudy(10_000)
</syntaxhighlight>
 
{{out}}
<pre>Total subjects: 10000
 
Day 30:
Untreated: N = 8619, with infection = 283
Irregular Use: N = 1379, with infection = 27
Regular Use: N = 2, with infection = 0
 
Day 60:
Untreated: N = 7480, with infection = 498
Irregular Use: N = 2362, with infection = 77
Regular Use: N = 158, with infection = 3
 
Day 90:
Untreated: N = 6479, with infection = 712
Irregular Use: N = 2440, with infection = 151
Regular Use: N = 1081, with infection = 24
 
At midpoint, infection case percentages are:
Untreated : 10.98935020836549
Irregulars: 6.188524590163935
Regulars : 2.220166512488436
 
Day 120:
Untreated: N = 5655, with infection = 873
Irregular Use: N = 2199, with infection = 210
Regular Use: N = 2146, with infection = 70
 
Day 150:
Untreated: N = 4998, with infection = 1007
Irregular Use: N = 1910, with infection = 257
Regular Use: N = 3092, with infection = 135
 
Day 180:
Untreated: N = 4479, with infection = 1122
Irregular Use: N = 1575, with infection = 302
Regular Use: N = 3946, with infection = 232
 
At study end, infection case percentages are:
Untreated : 25.05023442732753 of group size of 4479
Irregulars: 19.17460317460317 of group size of 1575
Regulars : 5.879371515458693 of group size of 3946
 
Final statistics: 235.1089104422972
</pre>
 
=={{header|Perl}}==
{{trans|Raku}}
<syntaxhighlight lang="perl" line>use v5.036;
use List::AllUtils <sum0 indexes firstidx>;
use enum qw<False True UNTREATED REGULAR IRREGULAR>;
use constant DOSE_FOR_REGULAR => 100;
 
my ($nSubjects,$duration,$interval) = (10000, 180, 30);
my (@dosage) = (0) x $nSubjects;
my (@category) = (UNTREATED) x $nSubjects;
my (@hadcovid) = (False) x $nSubjects;
 
sub update {
my $pCovid = 1e-3;
my $pStartTreatment = 5e-3;
my $pRedose = 1/4;
my @dRange = <3 6 9>;
for my $i (0 .. $nSubjects-1) {
unless ($hadcovid[$i]) {
if (rand() < $pCovid) {
$hadcovid[$i] = True
} else {
my $dose = $dosage[$i];
if ($dose==0 && rand() < $pStartTreatment or $dose > 0 && rand() < $pRedose) {
$dosage[$i] = $dose += $dRange[3*rand()];
$category[$i] = ($dose > DOSE_FOR_REGULAR) ? REGULAR : IRREGULAR
}
}
}
}
}
 
sub kruskal (@sets) {
my @ranked = sort @{$sets[0]}, @{$sets[1]}, @{$sets[2]};
my $n = @ranked;
my @sr = (0) x @sets;
my $ix = firstidx { $_ == 1 } @ranked;
my ($arf,$art) = ($ix/2, ($ix+$n)/2);
 
for my $i (0..2) {
$sr[$i] += $_ ? $art : $arf for @{$sets[$i]}
}
 
my $H = sum0 map { my $s = $sr[$_]; $s**2 / @{$sets[$_]} } 0..$#sr;
12/($n*($n+1)) * $H - 3 * ($n + 1)
}
 
my($unt,$irr,$reg,$hunt,$hirr,$hreg,@sunt,@sirr,@sreg);
my $midpoint = int $duration / 2;
 
say "Total subjects: $nSubjects\n";
 
for my $day (1 .. $duration) {
update();
if (0 == $day % $interval or $day == $duration or $day == $midpoint) {
@sunt = @hadcovid[ indexes { $_ == UNTREATED } @category];
@sirr = @hadcovid[ indexes { $_ == IRREGULAR } @category];
@sreg = @hadcovid[ indexes { $_ == REGULAR } @category];
( $unt, $irr, $reg) = (scalar(@sunt), scalar(@sirr), scalar(@sreg));
($hunt,$hirr,$hreg) = ( sum0(@sunt), sum0(@sirr), sum0(@sreg));
}
 
if (0 == $day % $interval) {
printf "Day %d:\n", $day;
printf "Untreated: N = %4d, with infection = %4d\n", $unt,$hunt;
printf "Irregular Use: N = %4d, with infection = %4d\n", $irr,$hirr;
printf "Regular Use: N = %4d, with infection = %4d\n\n",$reg,$hreg;
}
 
if ($day == $midpoint or $day == $duration) {
my $stage = $day == $midpoint ? 'midpoint' : 'study end';
printf "At $stage, Infection case percentages are:\n";
printf " Untreated : %6.2f\n", 100*$hunt/$unt;
printf " Irregulars: %6.2f\n", 100*$hirr/$irr;
printf " Regulars : %6.2f\n\n", 100*$hreg/$reg;
}
}
 
printf "Final statistics: H = %.2f\n", kruskal ( \@sunt, \@sirr, \@sreg );
 
</syntaxhighlight>
{{out}}
<pre>Total subjects: 10000
 
Day 30:
Untreated: N = 8640, with infection = 283
Irregular Use: N = 1360, with infection = 18
Regular Use: N = 0, with infection = 0
 
Day 60:
Untreated: N = 7499, with infection = 532
Irregular Use: N = 2338, with infection = 75
Regular Use: N = 163, with infection = 1
 
Day 90:
Untreated: N = 6537, with infection = 709
Irregular Use: N = 2382, with infection = 144
Regular Use: N = 1081, with infection = 12
 
At midpoint, Infection case percentages are:
Untreated : 10.85
Irregulars: 6.05
Regulars : 1.11
 
Day 120:
Untreated: N = 5739, with infection = 855
Irregular Use: N = 2102, with infection = 216
Regular Use: N = 2159, with infection = 52
 
Day 150:
Untreated: N = 5091, with infection = 1012
Irregular Use: N = 1792, with infection = 270
Regular Use: N = 3117, with infection = 134
 
Day 180:
Untreated: N = 4468, with infection = 1126
Irregular Use: N = 1669, with infection = 315
Regular Use: N = 3863, with infection = 243
 
At study end, Infection case percentages are:
Untreated : 25.20
Irregulars: 18.87
Regulars : 6.29
 
Final statistics: H = 218.74</pre>
 
=={{header|Phix}}==
{{trans|Wren}}
<!--<syntaxhighlight lang="phix">(phixonline)-->
<span style="color: #008080;">with</span> <span style="color: #008080;">javascript_semantics</span>
<span style="color: #004080;">sequence</span> <span style="color: #000000;">dosage</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">category</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">hadcovid</span>
<span style="color: #008080;">enum</span> <span style="color: #000000;">UNTREATED</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">REGULAR</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">IRREGULAR</span>
<span style="color: #008080;">constant</span> <span style="color: #000000;">DOSE_FOR_REGULAR</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">100</span>
<span style="color: #008080;">procedure</span> <span style="color: #000000;">update</span><span style="color: #0000FF;">(</span><span style="color: #004080;">atom</span> <span style="color: #000000;">pCovid</span><span style="color: #0000FF;">=</span><span style="color: #000000;">0.001</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">pStartTreatment</span><span style="color: #0000FF;">=</span><span style="color: #000000;">0.005</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">pRedose</span><span style="color: #0000FF;">=</span><span style="color: #000000;">0.25</span><span style="color: #0000FF;">,</span> <span style="color: #004080;">sequence</span> <span style="color: #000000;">dRange</span><span style="color: #0000FF;">={</span><span style="color: #000000;">3</span><span style="color: #0000FF;">,</span><span style="color: #000000;">6</span><span style="color: #0000FF;">,</span><span style="color: #000000;">9</span><span style="color: #0000FF;">})</span>
<span style="color: #008080;">for</span> <span style="color: #000000;">i</span><span style="color: #0000FF;">=</span><span style="color: #000000;">1</span> <span style="color: #008080;">to</span> <span style="color: #7060A8;">length</span><span style="color: #0000FF;">(</span><span style="color: #000000;">dosage</span><span style="color: #0000FF;">)</span> <span style="color: #008080;">do</span>
<span style="color: #008080;">if</span> <span style="color: #008080;">not</span> <span style="color: #000000;">hadcovid</span><span style="color: #0000FF;">[</span><span style="color: #000000;">i</span><span style="color: #0000FF;">]</span> <span style="color: #008080;">then</span>
<span style="color: #008080;">if</span> <span style="color: #7060A8;">rnd</span><span style="color: #0000FF;">()<</span><span style="color: #000000;">pCovid</span> <span style="color: #008080;">then</span>
<span style="color: #000000;">hadcovid</span><span style="color: #0000FF;">[</span><span style="color: #000000;">i</span><span style="color: #0000FF;">]</span> <span style="color: #0000FF;">=</span> <span style="color: #004600;">true</span>
<span style="color: #008080;">else</span>
<span style="color: #004080;">atom</span> <span style="color: #000000;">dose</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">dosage</span><span style="color: #0000FF;">[</span><span style="color: #000000;">i</span><span style="color: #0000FF;">]</span>
<span style="color: #008080;">if</span> <span style="color: #0000FF;">(</span><span style="color: #000000;">dose</span><span style="color: #0000FF;">=</span><span style="color: #000000;">0</span> <span style="color: #008080;">and</span> <span style="color: #7060A8;">rnd</span><span style="color: #0000FF;">()<</span><span style="color: #000000;">pStartTreatment</span><span style="color: #0000FF;">)</span>
<span style="color: #008080;">or</span> <span style="color: #0000FF;">(</span><span style="color: #000000;">dose</span><span style="color: #0000FF;">></span><span style="color: #000000;">0</span> <span style="color: #008080;">and</span> <span style="color: #7060A8;">rnd</span><span style="color: #0000FF;">()<</span><span style="color: #000000;">pRedose</span><span style="color: #0000FF;">)</span> <span style="color: #008080;">then</span>
<span style="color: #000000;">dose</span> <span style="color: #0000FF;">+=</span> <span style="color: #000000;">dRange</span><span style="color: #0000FF;">[</span><span style="color: #7060A8;">rand</span><span style="color: #0000FF;">(</span><span style="color: #7060A8;">length</span><span style="color: #0000FF;">(</span><span style="color: #000000;">dRange</span><span style="color: #0000FF;">))]</span>
<span style="color: #000000;">dosage</span><span style="color: #0000FF;">[</span><span style="color: #000000;">i</span><span style="color: #0000FF;">]</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">dose</span>
<span style="color: #000000;">category</span><span style="color: #0000FF;">[</span><span style="color: #000000;">i</span><span style="color: #0000FF;">]</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">iff</span><span style="color: #0000FF;">(</span><span style="color: #000000;">dose</span><span style="color: #0000FF;">></span><span style="color: #000000;">DOSE_FOR_REGULAR</span><span style="color: #0000FF;">?</span><span style="color: #000000;">REGULAR</span><span style="color: #0000FF;">:</span><span style="color: #000000;">IRREGULAR</span><span style="color: #0000FF;">)</span>
<span style="color: #008080;">end</span> <span style="color: #008080;">if</span>
<span style="color: #008080;">end</span> <span style="color: #008080;">if</span>
<span style="color: #008080;">end</span> <span style="color: #008080;">if</span>
<span style="color: #008080;">end</span> <span style="color: #008080;">for</span>
<span style="color: #008080;">end</span> <span style="color: #008080;">procedure</span>
<span style="color: #008080;">function</span> <span style="color: #000000;">kruskal</span><span style="color: #0000FF;">(</span><span style="color: #004080;">sequence</span> <span style="color: #000000;">sets</span><span style="color: #0000FF;">)</span>
<span style="color: #004080;">sequence</span> <span style="color: #000000;">ranked</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">sort</span><span style="color: #0000FF;">(</span><span style="color: #7060A8;">flatten</span><span style="color: #0000FF;">(</span><span style="color: #000000;">sets</span><span style="color: #0000FF;">)),</span>
<span style="color: #000000;">sr</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">repeat</span><span style="color: #0000FF;">(</span><span style="color: #000000;">0</span><span style="color: #0000FF;">,</span><span style="color: #7060A8;">length</span><span style="color: #0000FF;">(</span><span style="color: #000000;">sets</span><span style="color: #0000FF;">))</span>
<span style="color: #004080;">integer</span> <span style="color: #000000;">ix</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">find</span><span style="color: #0000FF;">(</span><span style="color: #004600;">true</span><span style="color: #0000FF;">,</span><span style="color: #000000;">ranked</span><span style="color: #0000FF;">),</span>
<span style="color: #000000;">n</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">length</span><span style="color: #0000FF;">(</span><span style="color: #000000;">ranked</span><span style="color: #0000FF;">)</span>
<span style="color: #004080;">atom</span> <span style="color: #000000;">arf</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">ix</span><span style="color: #0000FF;">/</span><span style="color: #000000;">2</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">art</span> <span style="color: #0000FF;">=</span> <span style="color: #0000FF;">(</span><span style="color: #000000;">ix</span><span style="color: #0000FF;">+</span><span style="color: #000000;">n</span><span style="color: #0000FF;">)/</span><span style="color: #000000;">2</span>
<span style="color: #008080;">for</span> <span style="color: #000000;">i</span><span style="color: #0000FF;">,</span><span style="color: #000000;">set</span> <span style="color: #008080;">in</span> <span style="color: #000000;">sets</span> <span style="color: #008080;">do</span>
<span style="color: #008080;">for</span> <span style="color: #000000;">b</span> <span style="color: #008080;">in</span> <span style="color: #000000;">set</span> <span style="color: #008080;">do</span>
<span style="color: #000000;">sr</span><span style="color: #0000FF;">[</span><span style="color: #000000;">i</span><span style="color: #0000FF;">]</span> <span style="color: #0000FF;">+=</span> <span style="color: #7060A8;">iff</span><span style="color: #0000FF;">(</span><span style="color: #000000;">b</span><span style="color: #0000FF;">?</span><span style="color: #000000;">art</span><span style="color: #0000FF;">:</span><span style="color: #000000;">arf</span><span style="color: #0000FF;">)</span>
<span style="color: #008080;">end</span> <span style="color: #008080;">for</span>
<span style="color: #008080;">end</span> <span style="color: #008080;">for</span>
<span style="color: #004080;">atom</span> <span style="color: #000000;">H</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">0</span>
<span style="color: #008080;">for</span> <span style="color: #000000;">i</span><span style="color: #0000FF;">,</span><span style="color: #000000;">s</span> <span style="color: #008080;">in</span> <span style="color: #000000;">sr</span> <span style="color: #008080;">do</span>
<span style="color: #000000;">H</span> <span style="color: #0000FF;">+=</span> <span style="color: #000000;">s</span><span style="color: #0000FF;">*</span><span style="color: #000000;">s</span><span style="color: #0000FF;">/</span><span style="color: #7060A8;">length</span><span style="color: #0000FF;">(</span><span style="color: #000000;">sets</span><span style="color: #0000FF;">[</span><span style="color: #000000;">i</span><span style="color: #0000FF;">])</span>
<span style="color: #008080;">end</span> <span style="color: #008080;">for</span>
<span style="color: #000000;">H</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">12</span><span style="color: #0000FF;">/(</span><span style="color: #000000;">n</span><span style="color: #0000FF;">*(</span><span style="color: #000000;">n</span><span style="color: #0000FF;">+</span><span style="color: #000000;">1</span><span style="color: #0000FF;">))</span> <span style="color: #0000FF;">*</span> <span style="color: #000000;">H</span> <span style="color: #0000FF;">-</span> <span style="color: #000000;">3</span> <span style="color: #0000FF;">*</span> <span style="color: #0000FF;">(</span><span style="color: #000000;">n</span> <span style="color: #0000FF;">+</span> <span style="color: #000000;">1</span><span style="color: #0000FF;">)</span>
<span style="color: #008080;">return</span> <span style="color: #000000;">H</span>
<span style="color: #008080;">end</span> <span style="color: #008080;">function</span>
<span style="color: #008080;">procedure</span> <span style="color: #000000;">run_study</span><span style="color: #0000FF;">(</span><span style="color: #004080;">integer</span> <span style="color: #000000;">nSubjects</span><span style="color: #0000FF;">=</span><span style="color: #000000;">10000</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">duration</span><span style="color: #0000FF;">=</span><span style="color: #000000;">180</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">interval</span><span style="color: #0000FF;">=</span><span style="color: #000000;">30</span><span style="color: #0000FF;">)</span>
<span style="color: #000000;">dosage</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">repeat</span><span style="color: #0000FF;">(</span><span style="color: #000000;">0</span><span style="color: #0000FF;">,</span><span style="color: #000000;">nSubjects</span><span style="color: #0000FF;">)</span>
<span style="color: #000000;">category</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">repeat</span><span style="color: #0000FF;">(</span><span style="color: #000000;">UNTREATED</span><span style="color: #0000FF;">,</span><span style="color: #000000;">nSubjects</span><span style="color: #0000FF;">)</span>
<span style="color: #000000;">hadcovid</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">repeat</span><span style="color: #0000FF;">(</span><span style="color: #004600;">false</span><span style="color: #0000FF;">,</span><span style="color: #000000;">nSubjects</span><span style="color: #0000FF;">)</span>
<span style="color: #7060A8;">printf</span><span style="color: #0000FF;">(</span><span style="color: #000000;">1</span><span style="color: #0000FF;">,</span><span style="color: #008000;">"Total subjects: %d\n\n"</span><span style="color: #0000FF;">,</span><span style="color: #000000;">nSubjects</span><span style="color: #0000FF;">)</span>
<span style="color: #004080;">sequence</span> <span style="color: #000000;">sunt</span><span style="color: #0000FF;">,</span><span style="color: #000000;">sirr</span><span style="color: #0000FF;">,</span><span style="color: #000000;">sreg</span>
<span style="color: #004080;">integer</span> <span style="color: #000000;">unt</span><span style="color: #0000FF;">,</span><span style="color: #000000;">irr</span><span style="color: #0000FF;">,</span><span style="color: #000000;">reg</span><span style="color: #0000FF;">,</span><span style="color: #000000;">hunt</span><span style="color: #0000FF;">,</span><span style="color: #000000;">hirr</span><span style="color: #0000FF;">,</span><span style="color: #000000;">hreg</span><span style="color: #0000FF;">,</span><span style="color: #000000;">midpoint</span><span style="color: #0000FF;">=</span><span style="color: #7060A8;">floor</span><span style="color: #0000FF;">(</span><span style="color: #000000;">duration</span><span style="color: #0000FF;">/</span><span style="color: #000000;">2</span><span style="color: #0000FF;">)</span>
<span style="color: #008080;">for</span> <span style="color: #000000;">day</span><span style="color: #0000FF;">=</span><span style="color: #000000;">1</span> <span style="color: #008080;">to</span> <span style="color: #000000;">duration</span> <span style="color: #008080;">do</span>
<span style="color: #000000;">update</span><span style="color: #0000FF;">()</span>
<span style="color: #008080;">if</span> <span style="color: #7060A8;">rmdr</span><span style="color: #0000FF;">(</span><span style="color: #000000;">day</span><span style="color: #0000FF;">,</span><span style="color: #000000;">interval</span><span style="color: #0000FF;">)=</span><span style="color: #000000;">0</span> <span style="color: #008080;">or</span> <span style="color: #000000;">day</span><span style="color: #0000FF;">=</span><span style="color: #000000;">duration</span> <span style="color: #008080;">or</span> <span style="color: #000000;">day</span><span style="color: #0000FF;">=</span><span style="color: #000000;">midpoint</span> <span style="color: #008080;">then</span>
<span style="color: #000000;">sunt</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">extract</span><span style="color: #0000FF;">(</span><span style="color: #000000;">hadcovid</span><span style="color: #0000FF;">,</span><span style="color: #7060A8;">find_all</span><span style="color: #0000FF;">(</span><span style="color: #000000;">UNTREATED</span><span style="color: #0000FF;">,</span><span style="color: #000000;">category</span><span style="color: #0000FF;">))</span>
<span style="color: #000000;">sirr</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">extract</span><span style="color: #0000FF;">(</span><span style="color: #000000;">hadcovid</span><span style="color: #0000FF;">,</span><span style="color: #7060A8;">find_all</span><span style="color: #0000FF;">(</span><span style="color: #000000;">IRREGULAR</span><span style="color: #0000FF;">,</span><span style="color: #000000;">category</span><span style="color: #0000FF;">))</span>
<span style="color: #000000;">sreg</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">extract</span><span style="color: #0000FF;">(</span><span style="color: #000000;">hadcovid</span><span style="color: #0000FF;">,</span><span style="color: #7060A8;">find_all</span><span style="color: #0000FF;">(</span><span style="color: #000000;">REGULAR</span><span style="color: #0000FF;">,</span><span style="color: #000000;">category</span><span style="color: #0000FF;">))</span>
<span style="color: #000000;">unt</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">length</span><span style="color: #0000FF;">(</span><span style="color: #000000;">sunt</span><span style="color: #0000FF;">);</span> <span style="color: #000000;">hunt</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">sum</span><span style="color: #0000FF;">(</span><span style="color: #000000;">sunt</span><span style="color: #0000FF;">)</span>
<span style="color: #000000;">irr</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">length</span><span style="color: #0000FF;">(</span><span style="color: #000000;">sirr</span><span style="color: #0000FF;">);</span> <span style="color: #000000;">hirr</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">sum</span><span style="color: #0000FF;">(</span><span style="color: #000000;">sirr</span><span style="color: #0000FF;">)</span>
<span style="color: #000000;">reg</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">length</span><span style="color: #0000FF;">(</span><span style="color: #000000;">sreg</span><span style="color: #0000FF;">);</span> <span style="color: #000000;">hreg</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">sum</span><span style="color: #0000FF;">(</span><span style="color: #000000;">sreg</span><span style="color: #0000FF;">)</span>
<span style="color: #008080;">end</span> <span style="color: #008080;">if</span>
<span style="color: #008080;">if</span> <span style="color: #7060A8;">rmdr</span><span style="color: #0000FF;">(</span><span style="color: #000000;">day</span><span style="color: #0000FF;">,</span><span style="color: #000000;">interval</span><span style="color: #0000FF;">)=</span><span style="color: #000000;">0</span> <span style="color: #008080;">then</span>
<span style="color: #7060A8;">printf</span><span style="color: #0000FF;">(</span><span style="color: #000000;">1</span><span style="color: #0000FF;">,</span><span style="color: #008000;">"Day %d:\n"</span><span style="color: #0000FF;">,</span><span style="color: #000000;">day</span><span style="color: #0000FF;">)</span>
<span style="color: #7060A8;">printf</span><span style="color: #0000FF;">(</span><span style="color: #000000;">1</span><span style="color: #0000FF;">,</span><span style="color: #008000;">"Untreated: N = %d, with infection = %d\n"</span><span style="color: #0000FF;">,{</span><span style="color: #000000;">unt</span><span style="color: #0000FF;">,</span><span style="color: #000000;">hunt</span><span style="color: #0000FF;">})</span>
<span style="color: #7060A8;">printf</span><span style="color: #0000FF;">(</span><span style="color: #000000;">1</span><span style="color: #0000FF;">,</span><span style="color: #008000;">"Irregular Use: N = %d, with infection = %d\n"</span><span style="color: #0000FF;">,{</span><span style="color: #000000;">irr</span><span style="color: #0000FF;">,</span><span style="color: #000000;">hirr</span><span style="color: #0000FF;">})</span>
<span style="color: #7060A8;">printf</span><span style="color: #0000FF;">(</span><span style="color: #000000;">1</span><span style="color: #0000FF;">,</span><span style="color: #008000;">"Regular Use: N = %d, with infection = %d\n\n"</span><span style="color: #0000FF;">,{</span><span style="color: #000000;">reg</span><span style="color: #0000FF;">,</span><span style="color: #000000;">hreg</span><span style="color: #0000FF;">})</span>
<span style="color: #008080;">end</span> <span style="color: #008080;">if</span>
<span style="color: #008080;">if</span> <span style="color: #000000;">day</span><span style="color: #0000FF;">=</span><span style="color: #000000;">midpoint</span> <span style="color: #008080;">then</span>
<span style="color: #7060A8;">printf</span><span style="color: #0000FF;">(</span><span style="color: #000000;">1</span><span style="color: #0000FF;">,</span><span style="color: #008000;">"At midpoint, Infection case percentages are:\n"</span><span style="color: #0000FF;">)</span>
<span style="color: #7060A8;">printf</span><span style="color: #0000FF;">(</span><span style="color: #000000;">1</span><span style="color: #0000FF;">,</span><span style="color: #008000;">" Untreated : %f\n"</span><span style="color: #0000FF;">,</span><span style="color: #000000;">100</span><span style="color: #0000FF;">*</span><span style="color: #000000;">hunt</span><span style="color: #0000FF;">/</span><span style="color: #000000;">unt</span><span style="color: #0000FF;">)</span>
<span style="color: #7060A8;">printf</span><span style="color: #0000FF;">(</span><span style="color: #000000;">1</span><span style="color: #0000FF;">,</span><span style="color: #008000;">" Irregulars: %f\n"</span><span style="color: #0000FF;">,</span><span style="color: #000000;">100</span><span style="color: #0000FF;">*</span><span style="color: #000000;">hirr</span><span style="color: #0000FF;">/</span><span style="color: #000000;">irr</span><span style="color: #0000FF;">)</span>
<span style="color: #7060A8;">printf</span><span style="color: #0000FF;">(</span><span style="color: #000000;">1</span><span style="color: #0000FF;">,</span><span style="color: #008000;">" Regulars : %f\n\n"</span><span style="color: #0000FF;">,</span><span style="color: #000000;">100</span><span style="color: #0000FF;">*</span><span style="color: #000000;">hreg</span><span style="color: #0000FF;">/</span><span style="color: #000000;">reg</span><span style="color: #0000FF;">)</span>
<span style="color: #008080;">end</span> <span style="color: #008080;">if</span>
<span style="color: #008080;">end</span> <span style="color: #008080;">for</span>
<span style="color: #7060A8;">printf</span><span style="color: #0000FF;">(</span><span style="color: #000000;">1</span><span style="color: #0000FF;">,</span><span style="color: #008000;">"At study end, Infection case percentages are:\n"</span><span style="color: #0000FF;">)</span>
<span style="color: #7060A8;">printf</span><span style="color: #0000FF;">(</span><span style="color: #000000;">1</span><span style="color: #0000FF;">,</span><span style="color: #008000;">" Untreated : %f\n"</span><span style="color: #0000FF;">,</span><span style="color: #000000;">100</span><span style="color: #0000FF;">*</span><span style="color: #000000;">hunt</span><span style="color: #0000FF;">/</span><span style="color: #000000;">unt</span><span style="color: #0000FF;">)</span>
<span style="color: #7060A8;">printf</span><span style="color: #0000FF;">(</span><span style="color: #000000;">1</span><span style="color: #0000FF;">,</span><span style="color: #008000;">" Irregulars: %f\n"</span><span style="color: #0000FF;">,</span><span style="color: #000000;">100</span><span style="color: #0000FF;">*</span><span style="color: #000000;">hirr</span><span style="color: #0000FF;">/</span><span style="color: #000000;">irr</span><span style="color: #0000FF;">)</span>
<span style="color: #7060A8;">printf</span><span style="color: #0000FF;">(</span><span style="color: #000000;">1</span><span style="color: #0000FF;">,</span><span style="color: #008000;">" Regulars : %f\n\n"</span><span style="color: #0000FF;">,</span><span style="color: #000000;">100</span><span style="color: #0000FF;">*</span><span style="color: #000000;">hreg</span><span style="color: #0000FF;">/</span><span style="color: #000000;">reg</span><span style="color: #0000FF;">)</span>
<span style="color: #7060A8;">printf</span><span style="color: #0000FF;">(</span><span style="color: #000000;">1</span><span style="color: #0000FF;">,</span><span style="color: #008000;">"Final statistics: H = %f\n"</span><span style="color: #0000FF;">,</span><span style="color: #000000;">kruskal</span><span style="color: #0000FF;">({</span><span style="color: #000000;">sunt</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">sirr</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">sreg</span><span style="color: #0000FF;">}))</span>
<span style="color: #008080;">end</span> <span style="color: #008080;">procedure</span>
<span style="color: #000000;">run_study</span><span style="color: #0000FF;">()</span>
<!--</syntaxhighlight>-->
<small>Aside: the best explanation of the Kruskal-Wallis Test I found was http://www.statisticslectures.com/topics/kruskalwallis/ but I didn't implement anything that I found there.</small>
{{out}}
<pre>
Total subjects: 10000
 
Day 30:
Untreated: N = 8628, with infection = 285
Irregular Use: N = 1372, with infection = 23
Regular Use: N = 0, with infection = 0
 
Day 60:
Untreated: N = 7460, with infection = 518
Irregular Use: N = 2366, with infection = 72
Regular Use: N = 174, with infection = 0
 
Day 90:
Untreated: N = 6497, with infection = 730
Irregular Use: N = 2399, with infection = 151
Regular Use: N = 1104, with infection = 17
 
At midpoint, Infection case percentages are:
Untreated : 11.235955
Irregulars: 6.294289
Regulars : 1.539855
 
Day 120:
Untreated: N = 5709, with infection = 879
Irregular Use: N = 2102, with infection = 220
Regular Use: N = 2189, with infection = 66
 
Day 150:
Untreated: N = 5058, with infection = 1005
Irregular Use: N = 1846, with infection = 273
Regular Use: N = 3096, with infection = 152
 
Day 180:
Untreated: N = 4486, with infection = 1109
Irregular Use: N = 1624, with infection = 315
Regular Use: N = 3890, with infection = 253
 
At study end, Infection case percentages are:
Untreated : 24.721355
Irregulars: 19.396552
Regulars : 6.503856
 
Final statistics: H = 211.421331
</pre>
 
=={{header|Python}}==
Line 147 ⟶ 685:
s.had_covid for s in population if s.category == IRREGULAR]
regular = [s.had_covid for s in population if s.category == REGULAR]
print('\n\n FinalnFinal statistics: ', kruskal(untreated, irregular, regular))
 
 
Line 153 ⟶ 691:
</syntaxhighlight>{{out}}
<pre>
Total subjects: 1,000
 
Day 30:
Untreated: N = 872, with infection = 25
Irregular Use: N = 128, with infection = 2
Regular Use: N = 0, with infection = 0
 
Day 60:
Untreated: N = 755, with infection = 55
Irregular Use: N = 222, with infection = 8
Regular Use: N = 23, with infection = 1
 
Day 90:
Untreated: N = 671, with infection = 70
Irregular Use: N = 219, with infection = 13
Regular Use: N = 110, with infection = 4
 
At midpoint, Infection case percentages are:
Untreated : 10.432190760059612
Irregulars: 5.936073059360731
Regulars : 3.6363636363636362
 
Day 120:
Untreated: N = 600, with infection = 88
Irregular Use: N = 189, with infection = 17
Regular Use: N = 211, with infection = 8
 
Day 150:
Untreated: N = 514, with infection = 108
Irregular Use: N = 194, with infection = 21
Regular Use: N = 292, with infection = 16
 
Day 180:
Untreated: N = 447, with infection = 119
Irregular Use: N = 189, with infection = 26
Regular Use: N = 364, with infection = 26
 
At study end, Infection case percentages are:
Untreated : 26.62192393736018 of group size of 447
Irregulars: 13.756613756613756 of group size of 189
Regulars : 7.142857142857143 of group size of 364
 
Final statistics: KruskalResult(statistic=55.48204323818349, pvalue=8.95833684545873e-13)
</pre>
 
=={{header|Raku}}==
{{trans|Phix}}
<syntaxhighlight lang="raku" line># 20221025 Raku programming solution
 
enum <UNTREATED REGULAR IRREGULAR>;
my \DOSE_FOR_REGULAR = 100;
my ($nSubjects,$duration,$interval) = 10000, 180, 30;
my (@dosage,@category,@hadcovid) := (0,UNTREATED,False)>>.&{($_ xx $nSubjects).Array};
 
sub update($pCovid=1e-3, $pStartTreatment=5e-3, $pRedose=¼, @dRange=<3 6 9>) {
for 0 ..^ @dosage.elems -> \i {
unless @hadcovid[i] {
if rand < $pCovid {
@hadcovid[i] = True
} else {
my $dose = @dosage[i];
if $dose==0 && rand < $pStartTreatment or $dose > 0 && rand < $pRedose {
@dosage[i] = $dose += @dRange.roll;
@category[i] = ($dose > DOSE_FOR_REGULAR) ?? REGULAR !! IRREGULAR
}
}
}
}
}
 
sub kruskal (@sets) {
my $n = ( my @ranked = @sets>>.List.flat.sort ).elems;
my @sr = 0 xx @sets.elems;
my $ix = (@ranked.first: * == True, :k)+1,
my ($arf,$art) = ($ix, $ix+$n) >>/>> 2;
 
for @sets.kv -> \i,@set { for @set -> $b { @sr[i] += $b ?? $art !! $arf } }
 
my $H = [+] @sr.kv.map: -> \i,\s { s*s/@sets[i].elems }
return 12/($n*($n+1)) * $H - 3 * ($n + 1)
}
 
say "Total subjects: $nSubjects\n";
 
my ($midpoint,$unt,$irr,$reg,$hunt,$hirr,$hreg,@sunt,@sirr,@sreg)=$duration div 2;
 
for 1 .. $duration -> \day {
update();
if day %% $interval or day == $duration or day == $midpoint {
@sunt = @hadcovid[ @category.grep: UNTREATED,:k ];
@sirr = @hadcovid[ @category.grep: IRREGULAR,:k ];
@sreg = @hadcovid[ @category.grep: REGULAR, :k ];
($unt,$hunt,$irr,$hirr,$reg,$hreg)=(@sunt,@sirr,@sreg).map:{|(.elems,.sum)}
}
if day %% $interval {
printf "Day %d:\n",day;
printf "Untreated: N = %4d, with infection = %4d\n", $unt,$hunt;
printf "Irregular Use: N = %4d, with infection = %4d\n", $irr,$hirr;
printf "Regular Use: N = %4d, with infection = %4d\n\n",$reg,$hreg
}
if day == $midpoint | $duration {
my $stage = day == $midpoint ?? 'midpoint' !! 'study end';
printf "At $stage, Infection case percentages are:\n";
printf " Untreated : %f\n", 100*$hunt/$unt;
printf " Irregulars: %f\n", 100*$hirr/$irr;
printf " Regulars : %f\n\n",100*$hreg/$reg
}
}
 
printf "Final statistics: H = %f\n", kruskal ( @sunt, @sirr, @sreg )</syntaxhighlight>
{{out}}
<pre>Total subjects: 10000
 
Day 30:
Untreated: N = 8616, with infection = 314
Irregular Use: N = 1383, with infection = 27
Regular Use: N = 1, with infection = 0
 
Day 60:
Untreated: N = 7511, with infection = 561
Irregular Use: N = 2308, with infection = 87
Regular Use: N = 181, with infection = 1
 
Day 90:
Untreated: N = 6571, with infection = 760
Irregular Use: N = 2374, with infection = 141
Regular Use: N = 1055, with infection = 19
 
At midpoint, Infection case percentages are:
Untreated : 11.565972
Irregulars: 5.939343
Regulars : 1.800948
 
Day 120:
Untreated: N = 5757, with infection = 909
Irregular Use: N = 2097, with infection = 189
Regular Use: N = 2146, with infection = 61
 
Day 150:
Untreated: N = 5092, with infection = 1054
Irregular Use: N = 1832, with infection = 238
Regular Use: N = 3076, with infection = 132
 
Day 180:
Untreated: N = 4530, with infection = 1172
Irregular Use: N = 1615, with infection = 282
Regular Use: N = 3855, with infection = 229
 
At study end, Infection case percentages are:
Untreated : 25.871965
Irregulars: 17.461300
Regulars : 5.940337
 
Final statistics: H = 248.419454</pre>
 
=={{header|Wren}}==
{{trans|Python}}
{{libheader|Wren-math}}
<syntaxhighlight lang="wren">import "random" for Random
import "./math" for Nums
 
var Rand = Random.new()
 
var UNTREATED = 0
var IRREGULAR = 1
var REGULAR = 2
var DOSE_FOR_REGULAR = 100
 
/* A subject for the study. */
class Subject {
construct new() {
_cumDose = 0
_category = UNTREATED
_hadCovid = false
_updateCount = 0
}
 
cumDose { _cumDose }
category { _category }
hadCovid { _hadCovid }
updateCount { _updateCount }
 
cumDose(d) { _cumDose = d }
category(c) { _category = c }
hadCovid(h) { _hadCovid = h }
updateCount(u) { _updateCount = u }
 
// Daily update on the subject to check for infection and randomly dose.
update(pCovid, pStartingTreatment, pRedose, dRange) {
if (!_hadCovid) {
if (Rand.float() < pCovid) {
_hadCovid = true
} else if ((_cumDose == 0 && Rand.float() < pStartingTreatment) ||
(_cumDose > 0 && Rand.float() < pRedose)) {
_cumDose = _cumDose + Rand.sample(dRange)
categorize()
}
}
_updateCount = _updateCount + 1
}
 
// Update using default parameters.
update() { update(0.001, 0.005, 0.25, [3, 6, 9]) }
 
// Set treatment category based on cumulative treatment taken.
categorize() {
_category = (_cumDose == 0) ? UNTREATED :
(_cumDose >= DOSE_FOR_REGULAR) ? REGULAR : IRREGULAR
return _category
}
}
 
// a, b and c are assumed to be lists of boolean values.
var kruskal = Fn.new { |a, b, c|
// map the bool values to 1 (true) or 0 (false).
var aa = a.map { |e| e ? 1: 0 }.toList
var bb = b.map { |e| e ? 1: 0 }.toList
var cc = b.map { |e| e ? 1: 0 }.toList
// aggregate and sort them
var ss = (aa + bb + cc).sort()
// find rank of first occurrence of 1
var ix = ss.indexOf(1) + 1
// calculate average ranks for 0 and 1
var arf = (1 + ix - 1) / 2
var n = ss.count
var art = (ix + n) / 2
// calculate sum of ranks for each list
var sra = Nums.sum(a.map { |e| e ? art : arf })
var srb = Nums.sum(b.map { |e| e ? art : arf })
var src = Nums.sum(c.map { |e| e ? art : arf })
// calculate H
var H = 12/(n*(n+1)) * (sra*sra/a.count + srb*srb/b.count + src*src/c.count) - 3 * (n + 1)
return H
}
 
// Run the study using the population of size 'N' for 'duration' days.
var runStudy = Fn.new { |numSubjects, duration, interval|
var population = List.filled(numSubjects, null)
for (i in 0...numSubjects) population[i] = Subject.new()
var unt = 0
var untCovid = 0
var irr = 0
var irrCovid = 0
var reg = 0
var regCovid = 0
System.print("Total subjects: %(numSubjects)")
for (day in 0...duration) {
for (subj in population) subj.update()
if ((day + 1) % interval == 0) {
System.print("\nDay %(day + 1):")
unt = population.count { |s| s.category == UNTREATED }
untCovid = population.count { |s| s.category == UNTREATED && s.hadCovid }
System.print("Untreated: N = %(unt), with infection = %(untCovid)")
irr = population.count { |s| s.category == IRREGULAR }
irrCovid = population.count { |s| s.category == IRREGULAR && s.hadCovid }
reg = population.count { |s| s.category == REGULAR }
regCovid = population.count { |s| s.category == REGULAR && s.hadCovid }
System.print("Regular Use: N = %(reg), with infection = %(regCovid)")
}
if (day == (duration/2).floor - 1) {
System.print("\nAt midpoint, Infection case percentages are:")
System.print(" Untreated : %(100 * untCovid / unt)")
System.print(" Irregulars: %(100 * irrCovid / irr)")
System.print(" Regulars : %(100 * regCovid / reg)")
}
}
System.print("\nAt study end, Infection case percentages are:")
System.print(" Untreated : %(100 * untCovid / unt) of group size of %(unt)")
System.print(" Irregulars: %(100 * irrCovid / irr) of group size of %(irr)")
System.print(" Regulars : %(100 * regCovid / reg) of group size of %(reg)")
var untreated = population.where { |s| s.category == UNTREATED }.map { |s| s.hadCovid }.toList
var irregular = population.where { |s| s.category == IRREGULAR }.map { |s| s.hadCovid }.toList
var regular = population.where { |s| s.category == REGULAR }.map { |s| s.hadCovid }.toList
System.print("\nFinal statistics: H = %(kruskal.call(untreated, irregular, regular))")
}
 
runStudy.call(1000, 180, 30)</syntaxhighlight>
 
{{out}}
Sample run.
<pre>
Total subjects: 1000
 
Day 30:
Untreated: N = 882, with infection = 32
Regular Use: N = 0, with infection = 0
 
Day 60:
Untreated: N = 783, with infection = 58
Regular Use: N = 13, with infection = 0
 
Day 90:
Untreated: N = 679, with infection = 82
Regular Use: N = 91, with infection = 0
 
At midpoint, Infection case percentages are:
Untreated : 12.076583210604
Irregulars: 4.3478260869565
Regulars : 0
 
Day 120:
Untreated: N = 592, with infection = 95
Regular Use: N = 186, with infection = 5
 
Day 150:
Untreated: N = 517, with infection = 106
Regular Use: N = 286, with infection = 19
 
Day 180:
Untreated: N = 459, with infection = 118
Regular Use: N = 375, with infection = 26
 
At study end, Infection case percentages are:
Untreated : 25.708061002179 of group size of 459
Irregulars: 15.060240963855 of group size of 166
Regulars : 6.9333333333333 of group size of 375
 
Final statistics: H = 395.09607330604
</pre>
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