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Selection bias in clinical sciences: Difference between revisions

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{{draft task|Probability and statistics}}
 
In epidemiology, retrospective analyses have well-known limitations compared to prospective studies.
Line 36:
* 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 KruscalKruskal 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]].
 
* You should get a statistical result highly favoring the REGULAR group.
Line 48:
 
;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 />
 
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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>
 
Line 330 ⟶ 735:
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
The task description specifies that the Kruskal statistic is to be used (presumably the Kruskal-Wallis H test) though, unlike Julia and Python, languages which are not normally used for statistical purposes are unlikely to have this easily available.
 
Using the Wikipedia description as a guide, I've written a function to calculate and return the H value and left it at that for now.
 
Also, it's not completely clear to me how this test can be applied to lists of boolean values (whether the subject got Covid or not). I've just converted them to numbers (false = 0, true = 1) and proceeded from there.
<syntaxhighlight lang="ecmascript">import "random" for Random
import "./math" for Nums
 
PureFox
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