Ý nghĩa giá trị P trong nghiên cứu y khoa

YKHOA.NET - Nghin cu khoa hc Nguyn Vn Tun 1

LTS. Tr s P trong nghin cu y khoa vn thnh thong c em ra tho lun trn cc tp san y hc quc t, v ngha ca n vn l mt ti cho chng ta khai thc hiu r hn. Bi vit sau y mt ln na bn v ngha ca tr s P nhng khng phi ng trn quan im thng k, m qua ci nhn chn on lm sng. C th cc bn s thy th v v s tng ng gia nghin cu y khoa v chn on lm sng trong bi vit ny. Bi vit c ng trn tp san Thng tin Y hc; do , bn c c th tham kho tp san bit thm chi tit.

ngha ca tr s P trong nghin cu y hc

Nguyn Vn Tun

Trong mt cng trnh nghin cu nh gi hiu qu chng gy xng ca thuc zoledronate, cc nh nghin cu iu tr 1065 bnh nhn bng zoledronate v 1062 bnh nhn khng c iu tr bng zoledronate (placebo), v kt qu c trnh by qua mt on vn quan trng sau y: The rates of any new fracture were 8,6% in the zoledronic acid group and 13,9% in the placebo group, a 35% risk reduction with zoledronic acid (p = 0,001); the respective rates of new vertebral fracture were 1,7% and 3,8% (p = 0,02) [1]. Cu vn trn y gn lin vi tr s p c ngha g?

Khi mt cu hi tng t c em i hi mt nhm bc s chuyn khoa v c kinh nghim trong nghin cu y hc, c n 85% tr li sai [2]. i a s nhng ngi c hi hiu rng mt kt lun (v s khc bit) vi tr s p = 0,05 c ngha l kh nng m kt lun sai l 5%, hay kh nng m kt lun ng l 95% (ly 1 tr cho 0,05). Nhiu ngi khc th hiu rng mt s khc bit vi tr s P cng nh th mc nh hng cng c ngha v tin cy ca kt lun cng cao. Nhng rt tic rng c hai cch hiu ny u sai. iu ng ngc nhin l khng nhng gii lm nghin cu khoa hc hiu sai, m ngay c cc nh nghin cu c kin thc thng k kh nh dch t hc cng hiu sai. Tht ra, mt s nh thng k chuyn nghip cng hiu sai ngha ca tr s P bi v mt s sch gio khoa gii thch hoc l sai, hoc khng r rng!

Trong bi vit ngn ny, ti s gii thch ngha tht ca tr s P, bn qua nhng khim khuyt ca n, v gii thiu mt trng phi suy lun khoa hc c ch cho nghin cu lm sng.

1. Tr s P v trit l phn nghim (falsificationism)

Khi c cc bi bo khoa hc trn cc tp san y hc, chng ta thng hay gp nhng tr s P. Mt s khc bit vi tr s p < 0,05 thng c hiu l s khc bit c ngha thng k (statistically significant); ngc li, khi p > 0,05 chng ta thng hiu rng s khc bit khng c ngha thng k, khng ng k, hay do ngu nhin.


Tuy nhin, cch hiu P [l mt xc sut phi iu kin] nh th rt sai lm. Tr s P l mt xc sut c iu kin. ngha ca tr s P gn lin vi trit l phn nghim (falsificationism) trong khoa hc. Do , trc khi bn v ngha ca tr s P, thit tng chng ta cn phi hiu qua v trit l phn nghim.

Mt gi thuyt c xem l mang tnh khoa hc nu gi thuyt c kh nng phn nghim. Theo Karl Popper [3], nh trit hc khoa hc, c im duy nht c th phn bit gia mt l thuyt khoa hc thc th vi ngy khoa hc (pseudoscience) l thuyt khoa hc lun c c tnh c th b bc b hay kh nng phn nghim (falsified) bng nhng thc nghim n gin. ng gi l kh nng phn nghim (falsifiability) [4]. Php phn nghim l phng cch tin hnh nhng thc nghim khng phi xc minh m ph phn cc l thuyt khoa hc, v c th coi y nh l mt nn tng cho khoa hc thc th. Chng hn nh gi thuyt [n gin] Tt c cc qu u mu en c th b bc b nu chng ta quan st c mt con qu mu . Hay, gi thuyt vi khun V. cholerae gy bnh dch t c th bc b nu c mt bnh nhn dch t khng nhim vi khun V. cholerae.

ng trn phng din khoa hc, c hai m hnh thc t tip cn l thuyt phn nghim: l m hnh kim nh thng k v m hnh kim nh gi thuyt. Rt nhiu sch gio khoa thng k v khoa hc c vit ra, nhng rt tic, nhiu tc gi khng gii thch hay khng phn bit c hai m hnh ny. C tc gi thm ch cn nhm ln khi din dch, v cng chnh l mt trong nhng nguyn nhn dn n tnh trng hiu lm ngha ca tr s P. Trong phn ny, ti s gii thch ngn gn v cung cp ti liu tham kho ca hai m hnh bn c c th hiu qua v nghin cu thm.

1.1 Fisher v m hnh kim nh ngha thng k

Trit l phn nghim rt ph bin v tr thnh mt m hnh gii thch s tin b ca khoa hc. Chu nh hng bi trit l ny, Ronald A. Fisher (1890 1962), mt nh di truyn hc ngi Anh v cng l cha ca nn thng k hc hin i, xut mt phng php nh lng phn nghim mt gi thuyt khoa hc. ng gi phng php ny l Test of Significance [5-6] (ti tm dch l: phng php kim nh ngha thng k). Fisher quan nim rng thng k l mt b phn quan trng ca phng php suy lun theo php qui np (inductive inference), tc l phng php suy lun da vo quan st t cc mu (sample) v khi qut cho mt qun th (population). Phng php kim nh ngha thng k c tin hnh theo 3 bc nh sau:

Bc 1, pht biu mt gi thuyt v hiu (null hypothesis). Gi thuyt v hiu l gi thuyt ngc li vi gi thuyt m nh nghin cu mun kim nh. Chng hn nh nu gi thuyt iu tr bng thuc zoledronate lm gim nguy c t vong (nhm c iu tr bng zoledronate c t l t vong thp hn nhm gi dc),


th gi thuyt v hiu s pht biu l t l t vong bnh nhn c iu tr bng zoledronate bng vi nhm gi dc. Gi gi thuyt v hiu l H0.

Bc 2, thu thp d liu lin quan n gi thuyt. Trong v d trn, s liu s l s trng hp t vong. Gi d liu l D.

Bc 3, c tnh xc sut quan st d liu D nu gi thuyt H0 ng. Ni cch khc v vit theo ngn ng ton, bc ny c tnh P(D | H0). y chnh l tr s P (p-value).

Fisher ngh bo co tr s P mt cch chnh xc. Tc l khng c nhng cch vit nh p < 0,05 hay p > 0,01 m phi l p = 0,043 hay p = 0,002. Fisher cn ngh rng nu tr s p thp hn 0,05 th gi thuyt H0 (v hiu) khng ph hp vi s liu quan st c. i vi Fisher, khng c chuyn bc b gi thuyt hay chng minh gi thuyt m ch c s liu c ph hp, c nht qun vi gi thuyt hay khng m thi. Quan im ny chu nh hng m ca trit l phn nghim ca Popper, v theo trit l ny, chng ta khng th chng minh bt c mt gi thuyt no, m ch c th bc b (disprove) mt gi thuyt bng d liu quan st c.

V d 1. C th minh ha cho cc bc trn bng mt v d nh sau: chng ta c 10 bnh nhn, mi bnh nhn c iu tr bng 2 loi thuc (A v B). Sau khi theo di mt thi gian, c 8 bnh nhn m hiu qu ca thuc A tt hn thuc B. Kt qu ny c ph hp vi gi thuyt thuc A tt hn thuc B?

tr li cu hi v cng l kim nh gi thuyt trn, chng ta pht biu mt gi thuyt v hiu: nu hai loi thuc ny c hiu qu nh nhau, th s c 5 bnh nhn vi kt qu A tt hn B, v 5 bnh nhn vi kt qu B tt hn A. Gi pi l xc sut m kt qu thuc A tt hn thuc B. Gi thuyt v hiu ny cng c ngha l pi = 0,5. Nu gi thuyt v hiu ny ng (tc pi = 0,5), chng ta c th tnh ton xc sut quan st k bnh nhn (k = 0, 1, 2, 3, , 10) vi kt qu A tt hn B theo lut phn phi nh phn nh sau:

( ) ( )( ) ( ) kkkkP == 1010 5,015,05,0| pi

V kt qu c th trnh by trong bng sau y:

Bng 1. Xc sut quan st k bnh nhn (trong s 10 bnh nhn) vi kt qu A>B nu gi thuyt v hiu (pipipipi = 0,5) ng

k = Pr(k | pipipipi=0,5)


0 0,0009765625 1 0,009765625 2 0,04394531 3 0,1171875 4 0,2050781 5 0,2460938 6 0,2050781 7 0,1171875 8 0,04394531 9 0,009765625

10 0,0009765625 P(k 8) 0,054687

C nhin, tng s xc sut k = 0, 1, 2, , 10 phi bng 1. Theo kt qu trn, nu khng c s khc bit v hiu qu ca hai thuc, xc sut m chng ta quan st 8 bnh nhn vi kt qu A>B l khong 4,39%. Din dch tng t, chng ta c tnh rng xc sut vi 9 bnh nhn kt qu A>B l 0,97%, v xc sut tt c 10 bnh nhn vi kt qu A>B l 0,097%. Xc sut m ti thiu 8 bnh nhn vi kt qu A>B l 0,055 hay 5,5%. Vit theo k hiu ton: P(k 8) = 0,0547. y chnh l tr s P.

S dng tiu ch 0,05, chng ta c th ni rng d 80% (8 trn 10) bnh nhn vi kt qu A>B, chng ta vn cha c y bng chng khng nh rng kt qu ny nht qun vi gi thuyt thuc A tt hn B.

1.2 Neyman v Pearson v m hnh Kim nh gi thuyt

Jerzy Neyman (1894 1981) l mt nh ton hc xut sc gc Ba Lan v Egon Pearson (1895 1980) l mt nh thng k hc (con ca gio s Karl Pearson, cha ca l thuyt Chi-square v h s tng quan) cng lc vi Fisher, pht trin mt phng php rt khc vi Fisher, m hai ng gi l Test of Hypothesis (Kim nh gi thuyt) [7]. Neyman v Pearson bc b khi nim suy lun theo qui np; hai ng ngh rng thng k hc l mt phng php hay c ch hng dn chng ta i n mt quyt nh ng v lu v di. Ni cch khc, Neyman v Pearson cho rng phng php ca Fisher v ngha!

Mt cch n gin, m hnh kim nh gi thuyt ca Neyman v Pearson c th thc hin qua cc bc nh sau:


Bc 1, pht biu gi thuyt chnh (H1) v gi thuyt v hiu (H0).

Bc 2, quyt nh mc v c th chp nhn c v c tnh c mu cn thuyt. l xc sut bc b gi thuyt H1 nhng l gi thuyt ng. l xc sut bc b H0 trong khi H0 ng.

Bc 3, thu thp d liu lin quan n gi thuyt.

Bc 4, nu d liu nm trong khong bc b gi thuyt H0, th chp nhn gi thuyt H1; nu khng th chp nhn gi thuyt H0. Ch rng chp nhn mt gi thuyt khng c ngha l chng ta tin vo gi thuyt , m ch c ngha l chng ta hnh ng vi iu kin l gi thuyt ng.

Nguyn l ca m hnh Neyman v Pearson l chng ta da vo d liu chn mt gi thuyt sao cho v lu v di chng ta khng qu sai. Chnh v th m ngy nay chng ta thng chn = 5% v = 10% n 20%.

Fisher bc b hon ton m hnh ca Neyman v Pearson [8]. ng cho rng l mt m hnh v duyn. Fisher nho bng rng cc nh ton hc (m ch Neyman v Pearson) chng hiu g v thc nghim v ra mt m hnh qu phi thc t. Trong nhng nm sau (thp nin 1930s) cng ng thng k hc chng kin mt cuc tranh lun dai dng v i khi nng bng gia Fisher v Neyman-Pearson trn cc tp san thng k hc Anh. Fisher tuy l mt ngi thng minh tuyt vi, mt nh t tng vi nhng suy ngh tru tng, nhng li l mt ngi rt kh tnh v c khi hp hi. S hp hi ca Fisher th hin ch ng s dng chc quyn khoa bng ca mnh gy kh khn cho Neyman n ni ng ny chu khng ni v phi di c sang M v sau ny tr thnh gio s ti trng i hc Berkeley. Sau ny, Neyman c lch s ghi nhn l mt nh thng k hc xut sc c cng cc k to ln cho khoa hc hin i, snh vai cng cc i th trong khoa hc hin i. Nc M qu tht l mi trng cho ng thi th ti nng!

1.2 Mt m hnh hn hp

Tr tru thay, my mi nm sau, hai m hnh ca Fisher v Neyman-Pearson c hun c thnh mt m hnh tng hp m chng ta ng dng ngy nay trong nghin cu y hc. M hnh ny s dng kt qu kim nh thng k ca Fisher i n quyt nh chp nhn hay bc b gi thuyt v hiu H0 hay gi thuyt chnh H1 theo m hnh ca Neyman v Pearson. Tiu biu cho m hnh ny l nghin cu lm sng i chng ngu nhin (randomized controlled clinical trial hay RCT). Theo , mt nghin cu lm sng c tin hnh theo cc bc nh sau:


Bc 1, nh ngha mt gi thuyt v hiu v mt gi thuyt chnh. Th d trong mt nghin cu lm sng, gm hai nhm bnh nhn: mt nhm c iu tr bng thuc A, v mt nhm c iu tr bng placebo, nh nghin cu c th pht biu gi thuyt v hiu rng hiu nghim thuc A tng ng vi placebo.

Bc 2, xc nh xc sut (cn gi l sai s loi I) v (cn gi l sai s loi II), v c tnh c mu da vo hai xc sut ny.

Bc 3, thu thp d liu lin quan n gi thuyt. Gi d liu l D.

Bc 4, s dng phng php kim nh ngha thng k ca Fisher c tnh xc sut P(D | H0). Gi tr s ny l P.

Bc 5, nu P < 0,05, bc b gi thuyt H0. Ch , bc b H0 khng c ngha l chng ta chp nhn gi thuyt H1.

V d 2. C th minh ha cho cc bc trn bng mt v d v nghin cu hiu qu ca thuc zoledronate trong vic phng chng long xng [1]. Vi gi thuyt rng thuc c hiu nghim gim nguy c gy xng, cc nh nghin cu so snh t l gy xng gia hai nhm bnh nhn: nhm 1 c iu tr bng zoledronate v nhm 2 l nhm gi c (nhn calcium v vitamin D). Bt u bng cch xc nh = 0,05 v = 0,80, cc nh nghin cu c tnh s lng bnh nhn cn thit. Sau ba nm thu thp s liu, kt qu c th tm lc trong bng s liu sau y:

Bng 2. Nguy c gy xng bnh nhn c iu tr bng zoledronate v placebo

Ch s Zoledronate Placebo Tr s P S bnh nhn 1065 1062 S gy xng 92 139 T l gy xng 8,6% 13,9 0,001

Bi v tr s P thp hn mc (0,05) m cc nh nghin cu ra t lc u (trc khi thu thp s liu); cho nn, cc nh nghin cu kt lun rng s khc bit v t l gy xng gia hai nhm (8,6% vs 13,9%) c ngha thng k. Tt nhin, tr s P trn khng c ngha l nghin cu chng minh rng thuc zoledronate c hiu qu gim nguy c gy xng. N c ngha l nu tht s thuc zoledronate khng c hiu qu gim nguy c gy xng th xc sut m cc nh nghin cu quan st cc s liu trn (13,9% so vi 8,6%) l 0,001.


2. Vn ca tr s P

C l ni khng ngoa rng tr s P l mt con s ph bin nht trong khoa hc t khong 100 nm qua [9]. Hu ht cc bi bo khoa hc u trnh by tr s P nh hm nng cao tnh khoa hc v tin cy ca bi bo. Tuy nhin, ngay t lc mi ra i, tr s P b ph bnh d di. C ngi cho rng vic ng dng tr s P trong suy lun khoa hc l mt bc li, l mt s thoi ha ca khoa hc, nn ngh khng s dng tr s ny trong nghin cu khoa hc. Nhng d chu nhiu ch trch v ph bnh, ng dng phng php kim nh gi thuyt v tr s P vn cng ngy cng ph bin, n gin v chng ta cha c mt phng php khc tt hn, hay hp l hn, hay n gin hn. Trong phn ny, ti s khng im qua tt c cc ph bnh tr s P (v lm nh th cn mt cun sch), m ch nu mt s vn chng ta cn lu khi din dch tr s P.

2.1 Vn logic

Nh qua minh ha trn, tr s P khng cho chng ta bit g v s kh d ca mt gi thuyt, bi v n l mt xc sut c iu kin. Tr s P cho chng ta bit xc sut ca d liu (data) nu mt gi thuyt l ng. Ci khim khuyt ln nht ca tr s P l n thiu tnh logic. Tht vy, nu chng ta chu kh xem xt li v d trn, c th khi qut tin trnh ca mt nghin cu y hc (da vo tr s P) nh sau:

ra mt gi thuyt chnh v hiu (H0) T gi thuyt v hiu, ra mt gi thuyt chnh (H1) Tin hnh thu thp d liu (D) Phn tch d kin: tnh ton xc sut D xy ra nu H0 l tht. Ni theo ngn

ng ton xc sut, bc ny chnh l bc tnh ton tr s P hay P(D | H0).

V th, con s P c ngha l xc sut ca d liu D xy ra nu (nhn mnh: nu) gi thuyt v hiu H0 l ng. Nh vy, con s P khng trc tip cho chng ta mt nim g v s tht ca gi thuyt chnh H1; n ch gin tip cung cp bng chng chng ta chp nhn gi thuyt chnh v bc b gi thuyt v hiu.

Logic ng sau ca tr s P c th c hiu nh l mt qui trnh chng minh o ngc (proof by contradiction):

Mnh 1: Nu gi thuyt v hiu ng, th s kin ny khng th xy ra; Mnh 2: S kin xy ra; Mnh 3 (kt lun): Gi thuyt v hiu khng th ng.

Nu cch lp lun trn kh hiu, chng ta th xem mt v d c th nh sau:


Nu ng Tun b cao huyt p, th ng khng th c triu chng rng tc (hai hin tng sinh hc ny khng lin quan vi nhau, t ra l theo kin thc y khoa hin nay);

ng Tun b rng tc; Do , ng Tun khng th b cao huyt p.

Tr s P, do , gin tip phn nh xc sut ca mnh 3. V cng chnh l mt khim khuyt quan trng ca tr s P, bi v n c tnh mc kh d ca d liu, ch khng ni cho chng ta bit mc kh d ca mt gi thuyt. iu ny lm cho vic suy lun da vo tr s P rt xa ri vi thc t, xa ri vi khoa hc thc nghim. Trong khoa hc thc nghim, iu m nh nghin cu mun bit l vi d liu m h c c, xc sut ca gi thuyt chnh l bao nhiu, ch h khng mun bit nu gi thuyt o l s tht th xc sut ca d liu l bao nhiu. Ni cch khc v dng k hiu m t trn, nh nghin cu mun bit P(H1 | D), ch khng mun bit P(D | H0) hay P(D | H1).

2.2 ngha thng k khng tng ng vi ngha lm sng

Mt sai lm rt ph bin trong gii y khoa l xem mt khc bit c ngha thng k (statistical significance) tng ng vi ngha lm sng (clinical significance). C th xem tr s P c tnh ton t t s ca tn hiu (signal, mc khc bit gia hai nhm) v nhiu (noise hay dao ng ca mu). Gi T l kim nh thng k, S l tn hiu, v E l nhiu, tng trn c th m t nh sau:

STE

=

Khi s lng c mu tng v nu S bt bin th T s tng, tc c c hi t ngha thng k. iu ny c ngha l chng ta c th gim E ti a bng cch tng s lng c mu, v n cng c ngha l mt khc bit rt nh chng c ngha g trong thc t nhng vn c th c ngha thng k. Ngc li, mt khc bit hay nh hng (effect) ln, nhng nu s lng c mu khng y khng th t c ci chun c ngha thng k (tc p > 0,05).

Bng 3 sau y trnh by 4 nghin cu (tng tng) vi s c mu khc nhau, t 20 n 2.000.000 bnh nhn. Ct Kt qu trnh by s bnh nhn c iu tr dt bnh v s trong ngoc l phn trm. Gi thuyt v hiu l xc sut kt qu 0,5 (tc 50%). Tt c 4 nghin cu u c tr s P = 0,041. Nh c th thy qua bng ny, nghin cu 1 c t l nh hng cao v c ngha lm sng (75%), v ch vi 20 bnh nhn, cc nh nghin cu c th bc b gi thuyt H0. Nhng nghin cu 4, mc nh hng rt thp (ch 50,07%, tc ch cao hn gi thuyt v hiu 0,07%) nhng vn c ngha thng k v s c mu qu ln !


Bng 3. nh hng ca c mu n tr s P

Nghin cu S lng i tng

Kt qu iu tr thnh cng (%)

Tr s P

1 20 15 (75%) 0,041 2 200 114 (57%) 0,041 3 2000 1.046 (52,5%) 0,041 4 2.000.000 1.001.445

(50,07%) 0,041

Trong thc t, c rt nhiu nghin cu m khc bit gia hai nhm rt nh, nhng vn c ngha thng k [10-11]. iu ng quan tm l kt qu c ngha thng k nh th c cc nh nghin cu din dch vi hm c ngha lm sng.

Ngc li, c nhng nghin cu m kt qu c ngha lm sng nhng v khng t ci chun p < 0,05, nn cc nh nghin cu li din dch rng khng c ngha lm sng! Chng hn nh mt nghin cu v hiu qu ca b sung vitamin C v E ph n mang thai [12], cc nh nghin cu kt lun rng Supplementation with vitamin C and E during pregnancy does not reduce the risk of serious outcomes in their infants (B sung vitamin E v E khng lm gim cc triu chng lm sng nghim trng). Nhng khi xt qua s liu thc t th thy tr em m m c b sung vitamin C v E, t l vi triu chng lm sng gim n 21% (p = 0,06). Ch v p = 0,06 m cc nh nghin cu c xu hng din dch sai kt qu, v sai lm ny rt nghim trng!

2.2 Vn kim nh nhiu gi thuyt

Nh ni trn, nghin cu y hc l mt qui trnh kim nh gi thuyt. Trong mt nghin cu, t khi no chng ta kim nh ch mt gi thuyt duy nht, m rt nhiu gi thuyt cng mt lc. Chng hn nh trong mt nghin cu v mi lin h gia vitamin D v nguy c gy c xng i, cc nh nghin cu c th phn tch mi lin h gia vitamin D v mt xng (bone mineral density), gia vitamin D v nguy c gy xng theo tng gii tnh, tng nhm tui, hay phn tch theo cc c tnh lm sng ca bnh nhn, v.v Mi mt phn tch nh th c th xem l mt kim nh gi thuyt. y, chng ta phi i din vi vn nhiu gi thuyt (multiple tests of hypothesis hay cn gi l multiple comparisons).

Vn l nh sau: nu chng ta kim nh mt gi chng ta chp nhn mt sai st 5% (gi d chng ta chp nhn tiu chun p = 0,05 tuyn b c ngha hay khng c ngha thng k). Ni cch khc, s tht l khng thuc c hiu qu sai, nhng kt qu kim nh thng k cho ra kt qu c ngha thng k, v chng ta chp nhn rng s


kin ny c th xy ra vi tn s 5%. Vn t ra l trong bi cnh kim nh nhiu gi thuyt l nh sau: nu trong s n th nghim, chng ta tuyn b k th nghim c ngha thng k (tc l p


cho kt qu tr s P c ngha nguyn thy ca n trong bi cnh th nghim nhiu gi thuyt, cc nh nghin cu ngh s dng thut iu chnh Bonferroni (tn ca mt nh thng k hc ngi tng ngh cch lm ny). Theo ngh ny, trc khi tin hnh nghin cu, nh nghin cu phi xc nh r gi thuyt no l chnh, v gi thuyt no l ph. Ngoi ra, nh nghin cu cn phi ra k hoch s th nghim bao nhiu gi thuyt trc khi phn tch d liu. Chng hn nh nu nh nghin cu c k hoch th nghim 20 so snh v mun gi cho tr s p 0,05, th thay v da vo 0,05 l tiu chun tuyn bsignificant, nh nghin cu phi da vo tiu chun 0,0025 (tc ly 0,05 chia cho 20) tuyn b significant. Ni cch khc, ch khi no mt kt qu c tr s p thp hn 0,0025 (hay ni chung l p/n) th nh nghin cu mi c quyn tuyn b kt qu c ngha thng k.

3. Tr s P v chn on y khoa

C mt mi tng quan gia nghin cu khoa hc v chn on y khoa, m ti thy gii y hc t khi no n gii thch v ngha ca tr s P:

Hai lnh vc u c cng mc ch: i tm ci cha c bit. Trong nghin cu y hc chng ta tm mt mi lin h (hay c tnh / nh gi hiu qu ca mt thut can thip), cn trong chn on chng ta mun bit bnh nhn c bnh hay khng c bnh.

Nghin cu y hc s dng thng k hc lm phng php kim nh, cn chn on y khoa s dng xt nghim lm sng hay sinh ha nh bnh. Do , phng php kim nh thng k tng ng vi phng php xt nghim sinh ha / lm sng.

Trong nghin cu y hc, thuc thc s khng hiu qu, nhng kt qu phn tch thng k cho rng c ngha thng k. Trong chn on y khoa, bnh nhn khng c bnh, nhng kt qu xt nghim l dng tnh.

Tng t, trong nghin cu y hc, thuc thc s c hiu qu, nhng kt qu phn tch thng k cho rng khng c ngha thng k. Trong chn on y khoa, bnh nhn c bnh, nhng kt qu xt nghim l m tnh.

Do , hiu ngha v cch din dch tr s P, chng ta cn bn qua v qun trit ngha ca mt kt qu chn on y khoa. Ti s ly v d chn on ung th lm v d. bit mt ph n b ung th v hay khng, cch chnh xc nht l qua gii phu, hay trong trng hp nhng ngi cht, l qua gio nghim t thi. Nhng gii phu l mt thut mang tnh xm phm cao, v tn km. Do , cc nh khoa hc pht trin nhiu phng php c th chn on ung th m khng cn n gii phu bit bnh


trng ca ca bnh nhn. Trong trng hp ung th v, mt phng php cng ngh cao l chp quang tuyn X, hay cn gi l mammography.

Kt qu ca vic xt nghim bng quang tuyn X c th l dng tnh (positive, s vit tt l +ve), hay m tnh (negative, -ve). Mt kt qu dng tnh c ngha rng bnh nhn c th b ung th v, v mt kt qu m tnh cho bit bnh nhn c th khng b ung th v. (Hai ch c th y rt quan trng, v n ni ln mt s bt nh trong vic chn on ung th v bng quang tuyn X). Do , i chiu kt qu th nghim ca X-quang tuyn vi thc trng ca bnh nhn, chng ta c 4 kh nng:

Chn on ung th v Nghin cu y hc K : bnh nhn tht s ung th H1 : gi thuyt chnh l ng N : bnh nhn khng b ung th H0 : gi thuyt v hiu ng +ve : kt qu xt nghim dng tnh S (P0,05) : khng c ngha thng k Kh nng Kh nng

Bnh nhn qu tht b ung th v, v kt qu xt nghim l dng tnh; trong chn on y khoa, trng hp ny c gi l dng tnh tht hay nhy (danh t chuyn mn ting Anh gi l sensitivity). Pht biu theo ngn ng xc sut, y chnh P(+ve | K).

Gi thuyt H1 ng (chng hn nh thuc c hiu nghim), v kt qu phn tch c ngha thng k. y l trng hp m cc nh nghin cu cp n l power. Ni theo xc sut: P(H1 | S) = power, tng ng vi dng tnh tht.

Bnh nhn qu tht b ung th, nhng kt qu th nghim li m tnh; y l trng hp cn c gi ngn gn l m tnh gi (false negative) hay P(-ve | K).

Gi thuyt H1 ng, nhng kt qu phn tch khng c ngha thng k. y l trng hp m cc nh nghin cu cp n l type II error (sai st loi II). Ni theo xc sut: P(NS | H1), tng ng vi m tnh gi.

Bnh nhn khng b ung th, v kt qu th nghim l m tnh; y l trng hp ca m tnh tht hay c hiu (specificity) hay P(-ve | N)

Gi thuyt H0 ng (tc thuc khng c hiu qu), v kt qu phn tch cng khng c ngha thng k. y l trng hp m cc nh nghin cu cp n l confidence level. Ni theo ngn ng xc sut: P(NS | H0), tng ng vi m tnh tht.


Bnh nhn qu tht khng c ung th, nhng kt qu th nghim l dng tnh; y l trng hp ca dng tnh gi (false positive) hay P(+ve | K).

Gi thuyt H0 ng, nhng kt qu phn tch c ngha thng k. y l trng hp m cc nh nghin cu cp n l type I error (sai st loi I). Ni theo xc sut: P(S | H0), tng ng vi dng tnh gi.

ngha ca nhy, c hiu, dng tnh gi, m tnh gi c th hiu qua cc gii thch sau y:

nhy (hay sensitivity, dng tnh tht) c th din gii nh sau: nu 100 bnh nhn mc bnh u i xt nghim, c bao nhiu ngi c kt qu dng tnh.

c hiu (specificity, m tnh tht) tr li cu hi sau y: nu 100 ngi khng mc bnh u i xt nghim, c bao nhiu ngi c kt qu m tnh.

Do , dng tnh gi (false positive) l s ngi khng mc bnh nhng c kt qu xt nghim dng tnh.

Tng t, m tnh gi (false negative) l s ngi mc bnh nhng c kt qu xt nghim m tnh.

Mt phng php chn on hon ho l phng php c t l dng tnh tht v m tnh tht 100% (tc t l dng tnh gi v m tnh gi l 0%). Nhng trong thc t, khng c phng php th nghim no l hon ho c. Thc vy, bt c mt phng php th nghim y khoa no, k c quang tuyn X, cng u c, khng t th nhiu, t l dng tnh gi v m tnh gi. Hai sai st ny l u mi ca nhiu vn trong vic khm nghim ung th v.

Do , mt kt qu xt nghim dng tnh khng c ngha l bnh nhn mc bnh ung th v. iu ny ng, bi v kt qu xt nghim c phn nh sai thc trng ca bnh. Nn nh rng cc ch s nh nhy, c hiu ch cho chng ta bit chnh xc ca phng php xt nghim, ch khng cho bit kh nng mc bnh. y l mt iu rt quan trng m rt tic rt nhiu bc s khng hay cha nhn thc c.

Tng t, trong nghin cu y hc, mt kt qu c ngha thng k (p


3.1 Cn phn bit P(+ve | K) v P(K | +ve)

Xin nhc li: P(+ve | K) l xc sut c kt qu xt nghim dng tnh nu c nhn tht s mc bnh (hay t l nhng bnh nhn mc bnh ung th c kt qu dng tnh), cn v P(K | +ve) l xc sut mt c nhn mc bnh nu kt qu xt nghim dng tnh (tc l trong s nhng ngi c kt qu dng tnh, bao nhiu ngi tht s mc bnh).

Cn phi phn bit hai ch s trn!

Vn t ra l chng ta cn bit ch s no? Chng ta khng mun bit nu bnh nhn mc bnh, xc sut m bnh nhn c kt qu dng tnh l bao nhiu, tc P(+ve | K), tc l nhy. (Nu bnh nhn mc bnh th chng ta iu tr, ch khng cn hi cu hi ngc v qu kh nh th!)

i vi bc s v bnh nhn, khi nhn c kt qu xt nghim [hy cho l] dng tnh, ngi ta mun bit xc sut m c nhn mc bnh l bao nhiu. Tc l chng ta mun bit P(K | +ve). Trong chn on y khoa, thut ng cho ch s ny l positive predictive value (PPV), hay gi tr tin lng dng tnh.

3.2 c tnh P(K | +ve)

Gi tr tin lng dng tnh ty thuc vo ba thng s: nhy, c hiu ca phng php xt nghim, v tn s mc bnh trong cng ng (cn gi l t l lu hnh prevalence). Theo thng l khoa hc quc t, gi nhy l Se, c hiu l Sp, v t l lu hnh l P. Vi ba thng s ny, chng ta c th c tnh gi tr tin lng dng tnh:

( ) ( ) ( )| 1 1P SeP K ve

P Se P Sp

+ = +

[1]

V d: N bnh nhn ngi M, 50 tui, i xt nghim ung th v v kt qu dng tnh. Bnh nhn mun bit xc sut m b tht s mc bnh l bao nhiu? Y vn cho bit nhy ca phng php X quang (mammography) l 90% (tc Se = 0,90), v c hiu l 95% (hay Sp = 0,95). Y vn cng cho bit trong nhng ngi u tui bnh nhn, c khong 1% (hay P = 0,01). Da vo cng thc trn, chng ta c th c tr li cu hi ca bnh nhn:

( ) ( ) ( )0,01 0,90|

0,01 0,9 1 0,01 1 0,95P K ve + =

+ == 0,15


Ni cch khc, xc sut m bnh nhn tht s mc bnh nu kt qu xt nghim dng tnh l 15%. Ni c th hn, c 100 ph n nh bnh nhn c kt qu xt nghim dng tnh, khong 15 ngi tht s mc bnh ung th v. Tuy nhin, chng ta vn khng bit v ph n nm trong s 15 bnh nhn hay khng!

3.3 c tnh P(H1 | S)

Tng t, trong nghin cu y hc, chng ta cng mun bit nu kt qu kim nh c ngha thng k (S) th xc sut m gi thuyt chnh ng l bao nhiu. Ni cch khc, chng ta mun bit P(H1 | S).

Cng nh trong chn on y khoa, P(H1 | S) ty thuc vo ba thng s: power hay P(S | H1), sai st loi I, v xc sut m gi thuyt H1 ng l bao nhiu hay P(H1). Gi sai st loi I l , chng ta c th c tnh P(H1 | S) nh sau:

( ) ( )( ) ( )1

1|1 1 1

P H powerP H S

P H power P H

=

+ [2]

Trong cng thc trn, hai thng s u (power v sai st loi I) thng c hoch nh trc khi nghin cu c thc hin. Thng thng, power dao ng trong khong 0,80 n 0,90, v sai st loi I thng = 0,01 n 0,05. Nhng P(H1) c l l thng s kh nht trong nghin cu, v trong nhiu trng hp chng ta khng bit xc sut H1 l bao nhiu. Tuy nhin, ty trng hp c th, chng ta c th tip cn P(H1) qua tn s ca mt s kin. Chng hn nh trong nghin cu v mi lin h gia mt gien v bnh, trong s 30.000 gien, xc sut m mt gien c lin h n bnh c th l 1/30.000, hoc cao hn cht t nu c bng chng khoa hc lm c s.

V d: Mt nghin cu v mi lin h gia gien VDR v long xng, cc nh nghin cu c tnh rng h cn 1000 i tng c power 90% v sai st loi I l 1%. Kt qu phn tch thng k cho thy mi lin h c ngha thng k vi tr s P = 0,015. Cu hi t ra l xc sut m gi thuyt v mi lin h gia VDR v long xng l bao nhiu? Chng ta tm thi cho xc sut P(H1) = 1/30000 = 0,0000333. p dng cng thc trn, chng ta c:

( ) [ ]0,0000333 0,91|

0,0000333 0,9 1 0,0000333 0,05P H S =

+ = 0,0006

Ni cch khc, cho d kt qu c ngha thng k, nhng xc sut m VDR tht s c lin quan n long xng ch 0,06% -- mt mi lin h cn qu nhiu bt nh.


Cng thc (1) v (2) va trnh by trn chnh l nh l Bayes (Bayesian theorem) rt ni ting trong xc sut hc [13]. nh l Bayes pht biu rng c th c tnh xc sut mt s kin sau khi c d liu quan st st hay o lng c. Ni mt cch thc t hn, c th xem nh l Bayes l qui trnh cp nht ha kin thc. Trong v d v chn on trn, trc khi xt nghim, chng ta bit rng xc sut m ngi ph n mc bnh l 1% (t l lu hnh). Sau khi kt qu xt nghim dng tnh, xc sut ny tng ln 15% -- hay 15 ln. Tng t, trc khi lm nghin cu, chng ta c th ni rng xc sut gien VDR lin h n long xng l 0,0000333, nhng sau khi c s liu dng tnh, chng ta c th ni xc sut ca mi lin h ny ln 0,0006, tc tng gn 1800 ln, nhng vn cn nhiu bt nh.

4. Yu t Bayes

Mt trong nhng kh khn trong vic c tnh P(H1 | S) theo nh l Bayes nh va trnh by vn l xc nh thng s P(H1), hay cn gi l xc sut tin nh ca mt gi thuyt (prior probability of a hypthesis). y cng chnh l im gy ra nhiu tranh lun m mu sc trit hc trong sut 100 nm qua.

Mt cch khch quan hn nh gi hai gi thuyt l so snh trc tip kh nng ca hai gi thuyt . Thay v c tnh trc tip xc sut mt gi thuyt, chng ta c th c tnh xc sut d liu cho mt gi thuyt. Gi D (vit tt t data) l d liu, H0 l gi thuyt v hiu, v H1 l gi thuyt chnh, chng ta nh ngha:

P(D | H0) l xc sut d liu quan st c nu gi thuyt H0 ng; v

P(D | H1) l xc sut d liu quan st c nu gi thuyt H0 ng.

Yu t Bayes (Bayes Factor BF) [14-15] c nh ngha nh l t s ca hai xc sut trn:

( )( )

| 1| 0

P D HBF

P D H= [3]

Nu chng ta xem d liu D l bng chng, th Yu t Bayes chnh l mt o lng bng chng nghing v gi thuyt no. Nhn qua cng thc trn chng ta c th thy:

Nu BF = 1, bng chng khng nghing v mt gi thuyt no c (hai gi thuyt c xc sut nh nhau);

Nu BF > 1, bng chng nghing v (ym tr) gi thuyt H1 hn l H0;


Ngc li, nu BF < 1, bng chng nghing v (ym tr) gi thuyt H0 hn l H1.

Theo mt qui c chung, cch din dch Yu t Bayes nh sau:

Yu t Bayes (BF) Bng chng nghing v H1 mc BF = 3 n BF = 10 ng k (substantial evidence) BF = 10 n BF = 30 thuyt phc (strong evidence) BF = 30 n BF = 100 rt thuyt phc (very strong evidence) BF > 100 gn nh xc nh

V d: Trong nn dch tiu chy vo cui nm 2007 mt s tnh pha Bc, mt s quan chc y t cho rng mm tm l nguyn nhn, l ngun gc ca nn dch, v h nghi rng mm tm hm cha vi khun gy bnh t (Vibrio cholerae). Vin v sinh dch t trung ng xt nghim 75 mu mm tm c chn ngu nhin t H Ni, Ngh An, v Thanh Ha. Kt qu xt nghim tt c u m tnh (khng c vi khun t). Chng ta c th din gii bng chng ny nh th no?

Gi pi l xc sut mm tm cha vi khun t. Chng ta bit rng theo lut phn phi nh phn (binomial distribution), nu xc sut nhim t l pi, v nu chng ta xt nghim n mu, th xc sut c k mu b nhim l:

( ) ( )| , 1 n kknP k nk

pi pi pi

=

Gi H0 l gi thuyt mm tm khng hm cha vi khun t, do , pi = 0. Vi 75 mu mm tm c xt nghim, chng ta c k = 0 (khng c kt qu dng tnh). Do , xc sut k = 0 di gi thuyt H0 l:

( ) ( ) ( )75 0075| 0 0 | 0,75 0 1 00

P D H P

= =

= 1

Nu H1 l gi thuyt mm tm c vi khun t, chng ta hy cho rng 20% mm tm nhim khun, v do : pi = 0,20. Xc sut d liu (k = 0) di gi thuyt ny l:

( ) ( ) ( )( ) ( ) ( ) 80750752,0 39,52,012,075;2,0|01| === PHDP

Do , Yu t Bayes, theo nh ngha (3) l:


( )( ) ( ) 8

| 1 1| 0 5.39

P D HBF

P D H = = = 18.546.031

Ni cch khc, bng chng (d liu t 75/75 m tnh) nghing v gi thuyt mm tm khng nhim vi khun t n 18,5 triu ln!

Trn y l mt cch tnh tng rt n gin minh ho cho ngha ca Yu t Bayes. Trong thc t, cc nghin cu vi cc phn tch phc tp, cch tnh Yu t Bayes cng rt phc tp. Tuy nhin, chng ta c th c tnh gi tr ti thiu ca Yu t Bayes c th c tnh bng mt cng thc rt n gin, ch l hm s ca tr s p, m Sellke v ng nghip [16-17] pht trin nh sau:

BFmin > 1 / (e p ln(p) ) [4]

Trong e = 2,71828. Chng hn nh mt nghin cu vi tro s p = 0,05, Yu t Bayes ti thiu l: 1 / (-2,71828 x 0,05 x log(0,05)) = 2,45. Theo cch hiu thng thng, khi p 0,95 kt lun, th qua cch tnh ny, chng ta c bng chng (p =0,0009) kt lun rng gi thuyt H1 c xc sut ng ln n 98%.

Hy ly mt v d khc: mi y bo ch kh quan tm v mt nghin cu m trong cc nh nghin cu pht hin rng t l b ung th v trong cc ph n dng thuc aspirin (gim au) cao hn cc ph n khng dng aspirin khong 20% [6]. Kt lun ny ch n thun da vo tr s p = 0,022, tc c ngha. Cc nh nghin cu khng gii thch c hin tng ny, v pht hin cng nm ngoi d on sinh hc ca


h. Ni cch khc, y xc sut gi thuyt H1 rt thp, c th ch 0,01 (tc 1%). V nu P(H1) = 0,01, v gi tr ti thiu BF l 1/[-2,71828 x 0,022 x log(0.022)] = 4,38, xc sut ti a ca P(H1 | S) ch 0,042 hay 4,2%.

Cho d P(H1) = 0,1 i na, xc sut ti a ca P(H1 | S) cng ch 0,33. V xc sut P(H1 | S) thp hn 0,95, chng ta c th pht biu rng gi thuyt v mi lin h gia aspirin v ung th v cha c bng chng thuyt phc, hay bng chng hin c khng nht qun vi gi thuyt . Ni cch khc, cc nh nghin cu c th i n mt kt lun sai v pht hin ca h c th l mt pht hin dng tnh gi!

5. Vi nhn xt v kt lun

Tr s p l mt s c nh hng cc k ln n hot ng khoa hc. Nhiu tp san v nh khoa hc xem mt nghin cu khoa hc vi tr s p cao hn 0,05 l mt kt qu tiu cc (negative result) v bi bo c th b t chi cho cng b. Chnh v th m i vi i a s nh khoa hc, con s P < 0,05 tr thnh mt ci giy thng hnh cng b kt qu nghin cu. Nu kt qu vi P < 0,05, bi bo c c may xut hin trn mt tp san no v tc gi c th s ni ting; nu kt qu P > 0,05, s phn bi bo v cng trnh nghin cu c c may i vo lng qun!

Nhng cn phi nhn mnh mt ln na hiu ngha ca tr s P nh sau: Mc ch ca tr s p l nhm tr li cu hi: nu gi thuyt v hiu H0 ng, th xc sut m d liu chng ta quan st c l bao nhiu? Ni cch khc, chnh l phng php chng minh o ngc. Do , din dch tr s P phi c iu kin. Tr s P khng cung cp cho chng ta mt nh lng g ni n mt gi thuyt.

Trong sut mt th k qua khoa hc thc nghim da vo tr s p ca trng phi thng k [c khi] gi l frequentist (trng phi tn s) suy lun v i n kt cc lun khoa hc. Cch suy lun ny hin vn l cch lm vic chun trong khoa hc. Th nhng ci logic ng sau tr s p c rt nhiu vn , k c s phn trc gic (counter-intuitive) v rt kh hiu, c khi ... phi logic. Theo trng phi tn s, xc sut c nh ngha ch qua th nghim (experiments) m trn l thuyt cc th nghim c th lp i lp li nhiu ln n v tn, trong nhng iu kin ging nhau nhng c lp vi nhau. Ni c lp c ngha l th nghim th hai khng c lin quan g n th nghim th nht hay bt c th nghim no sau . V d nh mt ng xu c qung 1 ln, th cng chnh l mt th nghim, v nu ng xu c qung lin tc 1 triu ln cng c ngha l 1 triu th nghim, v cc th nghim ny c lp vi nhau. Theo cch hiu ny, xc sut c ngha l s ln mt s kin xy ra trong v s th nghim , v tn s ny c din t qua con s t l hay phn trm. Ni cch khc, xc sut l mt tn s tng i (relative frequency).


Ni cho cng, xc sut l mt cm nhn c nhn, l mc tin tng ca mt c nhn v mt s kin hay hin tng no . Ni cch khc, xc sut phn nh kinh nghim c nhn, hay kh nng ca c nhn tch ly v phn tch thng tin t cc ngun ngoi ti. Do , cu pht biu xc sut aspirin gy ra ung th v l 0.33 phn nh mc tin tng ca ngi pht biu i vi mi lin h gia aspirin v ung th v. V l cm nhn c nhn, con s cng c cm nhn khc nhau gia cc c nhn: i vi ng A, 0,33 c th l mc tin tng cn thp; nhng i vi ch B, 0.33 c th l mt kh d cao. V l cm nhn c nhn, con s xc sut khng phi l mt ch s khch quan nh cch hiu ca trng phi tn s. Theo trng phi tn s, xc sut n thng minh hn nam l 0,98 c th c din dch nhiu cch khc nhau: n c th c ngha l trong 100 cp nam n c chn mt cch ngu nhin, c 98 cp m trong ch s IQ ca n cao hn nam; n cng c th c ngha l nu nghin cu c lp li 100 ln, mi ln vi i tng khc nhau, c 98 nghin cu cho thy s trung bnh IQ ca phi n cao hn phi nam. Tt nhin, trong thc t t ai nu khng mun ni l chng ai chu kh lp li nghin cu 100 ln hay 1000 ln; do , cch din dch ca trng phi tn s rt l phi thc t.

Trong suy lun khoa hc, c th ni khng ngoa rng ch c suy lun da vo nh l Bayes l logic nht. Tuy tr s p = P(D | H0) v tr s P(H1 | D) hay P(H1 | S)u l xc sut, nhng tr s p theo trng phi tn s cho chng ta bit nhiu v tnh chnh xc ca nghim ton thng k, hn l v mc kh d ca mt gi thuyt nghin cu. i vi nh nghin cu ch c P(H1 | S) l c ngha, cng nh i vi bnh nhn ch c P(K | +ve) l c ngha. Mun c tnh mc kh d ca mt gi thuyt nghin cu, chng ta cn phi ng dng nh l Bayes v cc phng php lin quan n nh l Bayes. Qua bi vit mang tnh gii thiu ny, tc gi hi vng thuyt phc bn c, nht l cc nh nghin cu thc nghim, nn tm hiu v tip cn cc phng php thng k thuc trng phi Bayes, hin ang rt thnh hnh trong lnh vc y sinh hc, vt l hc, v ngay c tin hc. Hi vng bn c s c dp ng gp vo s pht trin ca cc phng php Bayes trong tng lai v lm cho suy lun khoa hc hon ho hn v logic hn.

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ca ng. T l thuyt phn nghim ca ng m sau ny ngi ta c th phn nh s khc bit gia khoa hc vi ngu khoa hc. ng nhn c rt nhiu gii thng vinh d ca c Hip hi Khoa hc Chnh tr M, Vin Hn lm Anh v.v.. ng c N hong Elisabeth II phong tc hip s nm 1965, v Hun chng Danh d nm 1982. Ngoi tc phm ni ting nu trn ng cng hin cho khoa hc th gii nhiu tc phm v gi v trit l khoa hc.

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[8] Xem thm chi tit v nhng tranh lun lin quan n kim nh ngha thng k v kim nh gi thuyt trong sch The Significance Test Controversy, do DE Morrison v RE Henkel bin tp, Nh xut bn Aldine, Chicago: 1970.

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[12] Rumbold AR, Crowther CA, Haslam RR, Dekker GA, Robinson JS; ACTS Study Group. Vitamins C and E and the risks of preeclampsia and perinatal complications. N Engl J Med 2006;354(17):1796-806.

[13] Thomas Bayes (1702 1761) l mt linh mc sng Anh vo th k 18. Ngoi cng vic ging gio l, ng cn l nh ton hc c hng. Nm 1763 (tc sau khi ng qua i), mt ngi ng nghip ca ng cng b mt cng thc xc sut m ngy nay c bit n l nh l Bayes (Bayesian theorem) do ng vit lc cn sng nh v qu cn thn nn ng khng cho xut bn. nh l ny c mt nh hng cc k to ln trong nghin cu khoa hc v chn on y khoa, nhng cng l mt nh l gy ra nhiu tranh ci gay gt trong khoa hc sut 2 th k qua (m ti s cp n trong mt dp khc). gii thch nh l ny ngn gn, c l chng ta cn phi im qua vi s tht c bn v xc sut c iu kin (conditional probability).

tin theo di l gii, ti s dng k hiu H l gi thuyt v D l d kin nh cp trong phn u ca bi vit. Nh chng ta bit, nu hai hin tng H v D c lp, th xc sut c iu kin pht biu rng:

P(D H) = P(D|H) x P(H) [A1]


Ni cch khc, P(D|H)= P(DH) / P(H), vi iu kin d nhin l P(H) khng phi 0. n y bn c thy P(D|H)chnh l sai st loi I m ti cp. Hay ni c th hn P(D|H)chnh l P(S|H0) sau khi nghin cu d kin c phn tch bng mt kim nh thng k.

Nhng vn l chng ta mun c tnh P(H|D). Mt vi sp xp cng thc [A1] chng ta s i n nh l Bayes:

P(H|D) = P(D|H) x P(H) / P(D) [A2]

ngha ca nh l Bayes trn y l mun c tnh xc sut mt gi thuyt H sau khi quan st d kin D, th chng ta phi bit xc sut ca d kin hay P(D), v quan trng hn ht l xc sut ca gi thuyt, tc P(H).

Mun tm hiu thm v l thuyt v ng dng thng k theo trng phi Bayes (Bayesian Statistics) c th tham kho cc sch mang tnh nhp mn sau y: (1) sch v l thuyt: Peter M. Lee, Bayesian Statistics, 2nd Edition, London: Arnold, 1997; (2) sch v ng dng: Donald A. Berry, Statistics: A Bayesian Perspective, Belmont: Duxbury Press, 1996; (3) hay sch cho cc nh vt l hc: Giulio DAgistini, Bayesian Reasoning in Data Analysis, World Scientific, 2003.

[14] Jeffreys H. The Theory of Probability (3e), Oxford (1961); trang 432.

[15] Goodman SN. Toward evidence-based medical statistics. 2: The Bayes factor. Ann Intern Med 1999;130 (12): 1005-13.

[16] Sellke T, Bayarri MJ, Berger JO. Calibration of p-values for testing precise null hypothesis. The American Statistician 2001.

[17] Berger JO, Sellke T. Testing a point null hypothesis: the irreconcilability of P-values and evidence. Journal of the American Statistical Association 1987; 82:112-20.

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