Comparisonofallocationproceduresinclinicaltrialsin
smallpopulationgroupswithrespecttoaccidentaland
selectionbias
D.Schindler1,D.Uschner 2,M.Tamm,N.Heussen,R.ͲD.Hilgers
Department ofMedicalStatistics,RWTHAachenUniversity,Pauwelsstraße30,52074Aachen,Germany
1,2presentingauthors:[email protected],[email protected]
Introduction
SimulationStudy
଺
‘”•–ƒ–‹•–‹…ƒŽŽ›’”‘˜‹‰–Š‡‡ˆˆ‡…–‹˜‡‡••‘ˆƒ‡†‹…ƒŽ‹–‡”˜‡–‹‘ǡ–Š‡”ƒ†‘‹•‡†
‘”–Š‡•‹—Žƒ–‹‘•–—†›™‡‰‡‡”ƒ–‡†
…‘–”‘ŽŽ‡†…Ž‹‹…ƒŽ–”‹ƒŽ‹•…‘•‹†‡”‡†–Š‡Dz‰‘Ž†•–ƒ†ƒ”†dzǤŠ‡ƒ‹‘ˆ–Š‹•‹˜‡•–‹‰ƒ–‹‘‹•–‘
‡ƒ…Š
…‘’ƒ”‡‡•–ƒ„Ž‹•Š‡†”ƒ†‘‹•ƒ–‹‘’”‘…‡†—”‡•™‹–Š”‡•’‡…––‘•‡Ž‡…–‹‘ƒ†ƒ……‹†‡–ƒŽ
‡ƒ…Š‰‡‡”ƒ–‡†•‡“—‡…‡™‡•‹—Žƒ–‡†ƒ”‡•’‘•‡˜‡…–‘”ƒ……‘”†‹‰–‘–Š‡‘†‡ŽǤŠ‡™‡
„‹ƒ•Ǥƒ––‡”‹•‹˜‡•–‹‰ƒ–‡†‹ˆ‘”‘ˆƒŽ‹‡ƒ”–‹‡–”‡†Ǥ‡…‘•‹†‡”–Š‡•‹–—ƒ–‹‘‘ˆ‘’‡
…‘†—…–‡†–—†‡–ǯ•–Ǧ–‡•–™‹–Š‘—–ƒ†Œ—•–‹‰ˆ‘”„‹ƒ•Ǥ‹ƒŽŽ›ǡ™‡…ƒŽ…—Žƒ–‡†–Š‡’”‘’‘”–‹‘
ȋ‹Ǥ‡Ǥ—ƒ•‡†Ȍ–™‘Ǧƒ”‡†…Ž‹‹…ƒŽ–”‹ƒŽ•™‹–Š’ƒ”ƒŽŽ‡Ž‰”‘—’†‡•‹‰Ǥ‡’”‡•‡–•‹š
‘ˆ–‹‡•–Šƒ–
”ƒ†‘‹•ƒ–‹‘’”‘…‡†—”‡•ƒ†‰‹˜‡ƒ•–ƒ–‹•–‹…ƒŽ‘†‡Žˆ‘”•‡Ž‡…–‹‘„‹ƒ•ƒ†–‹‡–”‡†ǤŠ‡
”ƒ†‘‹•ƒ–‹‘’”‘…‡†—”‡•ƒ”‡…‘’ƒ”‡†…‘…‡”‹‰–Š‡‹”•—•…‡’–‹„‹Ž‹–›–‘„‘–Š„‹ƒ•‡•Ǥ‡
…‘†—…–ƒ•‹—Žƒ–‹‘•–—†›™‹–ŠƒƒƒŽ›•‹•—ƒ†Œ—•–‡†ˆ‘”–Š‹•„‹ƒ•Ǥ‡ˆ‘…—•‘•ƒŽŽ
Ǥ
…Ž‹‹…ƒŽ–”‹ƒŽ•™‹–Š–‘–ƒŽ•ƒ’Ž‡•‹œ‡
ଶ
ா
ǡ
Nሺെͳǡͳሻ
ܻ௡ ‫ ׽‬ቐ NሺͲǡͳሻ
Nሺͳǡͳሻ
CR, EBC(p)
Difference in group size
ǡ
଴
Method
஼
™ƒ•”‡Œ‡…–‡†–‘–Š‡–‘–ƒŽ—„‡”‘ˆ”‡’‡–‹–‹‘•
ƒ†
଺
ǡ•‡––‹‰
Ǥ ‡…ƒŽŽ–Š‹•’”‘’‘”–‹‘(empirical)typeǦIǦerrorrateǤ
SelectionBias
RandomisationProcedures
5
•‡“—‡…‡•ˆ‘”‡ƒ…Š”ƒ†‘‹•ƒ–‹‘’”‘…‡†—”‡ǡ
ƒ†„‘–Š•‡––‹‰••‡Ž‡…–‹‘„‹ƒ•ƒ†–‹‡–”‡†Ǥ‘”
ܰா ሺ݊ െ ͳሻ ൐ ܰ஼ ሺ݊ െ ͳሻ
ܰா ሺ݊ െ ͳሻ ൌ ܰ஼ ሺ݊ െ ͳሻ
ܰா ሺ݊ െ ͳሻ ൏ ܰ஼ ሺ݊ െ ͳሻ
Property
‘’Ž‡–‡
ƒ‹” …‘‹ˆŽ‹’
ƒ†‘‹•ƒ–‹‘ȋȌ
0
−5
0
2
4
6
ˆ”‘ǯ•‹ƒ•‡†‘‹
ȋȋ’ȌȌ
‹ƒ•‡†…‘‹ˆŽ‹’‹‘”†‡”–‘
’”‘†—…‡ „ƒŽƒ…‡™‹–Š
Method
Property
‹‰–‹…‡•‹‰
ȋȋȌȌ
ƒ‹” …‘‹ˆŽ‹’™‹–Šƒ
†‡–‡”‹‹•–‹…ƒŽŽ‘…ƒ–‹‘
™Š‡‹„ƒŽƒ…‡„‘—†ƒ”›
ͳ ‹•Š‹–
ƒš‹ƒŽ ”‘…‡†—”‡
ȋȋȌȌ
“—ƒŽŽ› ’”‘„ƒ„Ž‡
•‡“—‡…‡•™‹–Š„‘—†ƒ”›
ͳ ˆ‘”–Š‡‹„ƒŽƒ…‡ƒ†
ˆ‹ƒŽ„ƒŽƒ…‡
8
Patient n
BSD(2), MP(2)
Difference in group size
5
0
−5
Deterministic Allocation
0
2
4
6
8
„•‡”˜‡–Šƒ––—†‡–ǯ•–Ǧ–‡•–”‡Œ‡…–• ଴ ா
‘ˆ…ƒ•‡•‹ˆ™‡—•‡ǡ‘”Ǥ‘”
஼ ‹
ƒŽŽ‘–Š‡”†‡•‹‰•ǡ–Š‡–›’‡ǦǦ‡””‘””ƒ–‡‰”‘™•™‹–Š Ǥƒ†ƒ”‡Ž‡••Ž‹„‡”ƒŽ–‘•‡Ž‡…–‹‘
ǡ –—†‡–ǯ•–Ǧ–‡•–”‡Œ‡…–• ଴ ‹
‘ˆ…ƒ•‡•Ǥ
„‹ƒ•–ŠƒǤ•‹‰ˆ‘”
LinearTimeTrend
Patient n
PBR(4)
ܻ௡ ̱N ʹ ‫ڄ‬
Method
‡”—–‡†Ž‘…
ƒ†‘‹•ƒ–‹‘
ȋȋ„ȌȌ
Difference in group size
5
0
Allocation Probabilities
0.5
0
Property
“—ƒŽŽ› ’”‘„ƒ„Ž‡
•‡“—‡…‡•™‹–Šˆ‘”…‡†
„ƒŽƒ…‡ƒˆ–‡”—Ž–‹’Ž‡•‘ˆ
ƒŽŽ‘…ƒ–‹‘•
“—ƒŽ’”‘„ƒ„Ž‡•‡“—‡…‡•
™‹–Šˆ‹ƒŽ„ƒŽƒ…‡
ƒ†‘ŽŽ‘…ƒ–‹‘
—Ž‡ȋȌ
−5
<0.5
>0.5
2
4
6
8
Patient n
ͳαƒš‹—‘Ž‡”ƒ–‡†„ƒŽƒ…‡†—”‹‰–Š‡–”‹ƒŽ
Model
ே
‡–
ȋ”‡•’Ǥ
௡
„‡–Š‡˜‡…–‘”‘ˆ–”‡ƒ–‡–ƒ••‹‰‡–•™‹–Š–‘–ƒŽ•ƒ’Ž‡•‹œ‡ Ǥ‡–
ா
௡
௜ୀଵ
ா
ƒ†ǡ”‡•’‡…–‹˜‡Ž›ǡ
௜
Ǥ—’’‘•‡–Š‡”‡‹•‘†‹ˆˆ‡”‡…‡‹–”‡ƒ–‡–‡ˆˆ‡…–•‘ˆ–Š‡–™‘‰”‘—’•Ǥ
‹–Š‘—–Ž‘••‘ˆ‰‡‡”ƒŽ‹–›ǡ™‡ƒ••—‡
ா
‡–
௡
‡‘„•‡”˜‡–Šƒ––—†‡–ǯ•–Ǧ–‡•–ƒ––ƒ‹•ƒ‡’‹”‹…ƒŽ–›’‡ǦǦ‡””‘””ƒ–‡‘ˆͷΨ‹ˆ™‡—•‡‘”
ǤŽŽ‘–Š‡”†‡•‹‰•”‡ƒ…–‘”‡…‘•‡”˜ƒ–‹˜‡Ž›–Š‡‰”‡ƒ–‡” ‹•Ǥƒ†„‡Šƒ˜‡˜‡”›
•‹‹Žƒ”Ž›ƒ†‰‡‡”ƒŽŽ›Ž‡••…‘•‡”˜ƒ–‹˜‡Ž›–Šƒƒ†Ǥ
Ȍ‹ˆ’ƒ–‹‡– ‹•ƒ••‹‰‡†–‘–”‡ƒ–‡– ȋ”‡•’Ǥ ȌǤ‘”–Š‡—„‡”‘ˆ’ƒ–‹‡–•
ƒ••‹‰‡†–‘ ƒˆ–‡” ƒŽŽ‘…ƒ–‹‘•ǡ™‡™”‹–‡
஼
݊െͳ
ǡ ͳ
ܰ
஼
Ȍƒ†Šƒ˜‡–Š‡•ƒ‡˜ƒ”‹ƒ…‡
ଶ
௠
௡
Ǥ
†‡”–Š‡ƒ••—’–‹‘•–Šƒ––Š‡‹˜‡•–‹‰ƒ–‘”ˆƒ˜‘—”• ǡ‘™•–Š‡’ƒ•–ƒ••‹‰‡–•ƒ†–Šƒ–
–Š‡…Š‘•‡”ƒ†‘‹•ƒ–‹‘’”‘…‡†—”‡ˆ‘”…‡•„ƒŽƒ…‡ ȋ‹Ǥ‡Ǥ
ா
஼
Ȍǡ ‹–‹•‘’’‘”–—‡
ˆ‘”–Š‡‹˜‡•–‹‰ƒ–‘”–‘•‡Ž‡…––Š‡‡š–’ƒ–‹‡–ƒ……‘”†‹‰–‘Š‹•‡š’‡…–‡†”‡•’‘•‡ǣ
N െߟǡ ߪ ଶ
୬ ‫ ׽‬ቐ N Ͳǡ ߪ ଶ
N ߟǡ ߪ ଶ
ܰா ݊ െ ͳ ൐ ܰ஼ ݊ െ ͳ
ܰா ݊ െ ͳ ൌ ܰ஼ ݊ െ ͳ Ǥ
ܰா ݊ െ ͳ ൏ ܰ஼ ݊ െ ͳ
ˆ–Š‡’ƒ–‹‡–”‡•’‘•‡•ƒ”‡‹ˆŽ—‡…‡†„›ƒŽ‹‡ƒ”–‹‡–”‡†™‡ƒ••—‡–Šƒ––Š‡›ƒ”‡•Š‹ˆ–‡†
ƒ……‘”†‹‰–‘–Š‡‹†‡š‘ˆ‹…Ž—•‹‘ȋ™‹–Š
ǣ
݊ െ ͳ ଶ
ܻ௡ ̱N ߴ ‫ڄ‬
ǡߪ Ǥ
ܰ
‘”
ǡ•‡Ž‡…–‹‘„‹ƒ•ƒ†Ž‹‡ƒ”–‹‡–”‡†…ƒ•–”‘‰Ž›‹ˆŽ—‡…‡–Š‡–‡•–†‡…‹•‹‘‘ˆƒ
—ƒ†Œ—•–‡†–Ǧ–‡•–ǤŠ‡”ƒ†‘‹•ƒ–‹‘‡–Š‘†–Šƒ–‹•—•‡†ˆ‘”ƒ–”‹ƒŽ•Š‘—Ž†–Š—•„‡…Š‘•‡
†‡‘–‡–Š‡‘”ƒŽŽ›†‹•–”‹„—–‡†response ‘ˆ–Š‡ Ǧ–Š’ƒ–‹‡–Ǥ‡ƒ••—‡–Šƒ–
ƒ”‡•–‘…Šƒ•–‹…ƒŽŽ›‹†‡’‡†‡–ȋˆ‘”
Discussion
…ƒ”‡ˆ—ŽŽ›ƒ……‘”†‹‰–‘–Š‡–›’‡‘ˆ„‹ƒ•–Šƒ–‹•‡š’‡…–‡†ǤŠ‡‡˜ƒŽ—ƒ–‹‘‘ˆ•‡Ž‡…–‹‘„‹ƒ•ƒ†
–‹‡–”‡†•‡‡•–‘”‡˜‡ƒŽ–Šƒ–†‘‡•ǯ–”‡ƒ…– –‘–Š‡‹˜‡•–‹‰ƒ–‡†–›’‡•‘ˆ„‹ƒ•ǤŠ‹•‹•‘Ž›
–”—‡‘ƒ˜‡”ƒ‰‡Ǥ•ƒŽŽ…Ž‹‹…ƒŽ–”‹ƒŽ•–Š‡ƒ•›’–‘–‹…ƒŽŽ›‰‘‘†’”‘’‡”–‹‡•‘ˆ†‘ǯ–Š‘Ž†Ǥ
‡•—‰‰‡•––Š‡—•‡‘ˆ‹ˆˆ‹ƒŽ„ƒŽƒ…‡‹•”‡“—‹”‡†ǡƒ†–Š‡—•‡‘ˆ‘–Š‡”™‹•‡Ǥ
References
Žƒ…™‡ŽŽǡǤǡƒ†‘†‰‡•ǤǤȋͳͻͷ͹ȌǤƒŽ•‘ˆƒ–ŠǤ–ƒ–‹•–ǤǡʹͺǡͶͶͻǦͶ͸ͲǤ
ˆ”‘ǡǤȋͳͻ͹ͳȌǤ‹‘‡–”‹ƒǡͷͺǡͶͲ͵ǦͶͳ͹Ǥ
‡‡•ǡǤǤȋʹͲͳ͵ȌǤTheeffectofandadjustmentforselectionbiasinrandomizedclinicaltrialsǤ‘…–‘”ƒŽ–Š‡•‹•ǡƒ…Š‡Ǥ
‡‡•ǡǤǤǡ”ƒ‡”Ǥǡ‹Ž‰‡”•ǡǤǦǤƒ†‡—••‡ǤȋʹͲͳͳȌǤ–ƒ–‹•–Ǥ‡†Ǥǡ͵Ͳǡʹͷ͹͵ǦʹͷͺͳǤ
”‘•…ŠƒǡǤȋͳͻͻͶȌǤ–ƒ–‹•–‹…ƒ‹‹…ƒǡͶǡʹͳͻǦʹ͵ͳǤ
‘•‡„‡”‰‡”ǡǤǤǡƒ†ƒ…Š‹ǡǤǤȋʹͲͲʹȌǤRandomizationinClinicalTrials. ‡™‘”ǣ‹Ž‡›Ǥ
‘ƒ”‡•ǡǤǤǡƒ†—ǡǤǤǤȋͳͻͺ͵ȌǤ ‘—Ǥ–ƒ–‹•–ǤǦŠ‡‘”Ǥ‡–ŠǤǡͳʹǡʹͲͳ͹ǦʹͲ͵ͶǤ
ƒǡǤǡ”ƒ‡”ǡǤǡ‡‡•ǡǤǤǡƒ†‡—••‡ǡǤȋʹͲͳʹȌǤ‡–ŠǤˆǤ‡†Ǥǡͷͳǡͳ͵ͺǦͳͶ͵Ǥ
ƒǡǤǡƒ†‹Ž‰‡”•ǡǤǦǤȋʹͲͳͶȌǤȋƒ……‡’–‡†ˆ‘”’—„Ž‹…ƒ–‹‘‹‡–ŠǤˆǤ‡†ǤȌ
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