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[1] [4]?
DBe(p))D=(
0Cuandoelindividuonopresentaelevento
1Cuandoelindividuos{presentaelevento
prevalencia=p=Pr(0estado0= 1) =Pr(D= 1) =Pr(presentarelevento)
1p=Pr(0estado0= 0) =Pr(D= 0) =Pr(nopresentarelevento)
0
Prueba0=(
Positivoy= 1sixc
Negativoy= 0six < c
8>>>< >>:V +si(D= 1; y= 1) F +si(D= 0; y= 1) F si(D= 1; y= 0) V si(D= 0; y= 0) ??????? ?? ?????c?? ?? ????? ?? ????? ? ????? ??????? ??? ?????? ??? ???? ?????
S=Pr(y= 1jD= 1) =Pr(y= 1\D= 1)P
r(D= 1) S=V+V ++F ++F V +V ++F=FV
E=Pr(y= 0jD= 0) =Pr(y= 0\D= 0)P
r(D= 0) E=VV +F+
1E= 1VV
+F+=V+F+V +F+VV +F+=F+V +F+ P r(D= 1jy= 1) =
Pr(y= 1jD= 1)Pr(D= 1)P
r(y= 1jD= 1)Pr(D= 1) +Pr(y= 1jD= 0)Pr(D= 0)=
SpSp+ (1E)(1p)
V PP=V+V
++F+ P r(D= 0jy= 0) =
Pr(y= 0jD= 0)Pr(D= 0)P
r(y= 0jD= 0)Pr(D= 0) +Pr(y= 0jD= 1)Pr(D= 1)=
E(1p)(1S)p+E(1p)
V PN=VV
+F
V G=V++VV
++F++V+F
FV P+FFN=Pr(y= 1jD= 1) +Pr(y= 0jD= 1) = 1
FFP+FV N=Pr(y= 1jD= 0) +Pr(y= 0jD= 0) = 1
D= 1FV P=V+V
++FFFN=FV ++F1
D= 0FFP=F+V
+F+FV N=VV +F+1
ROC(c) =(
y=S(c) x= 1E(c) ROC p(c) =( y=FV P(c) x=FFP(c) P
ROC(t) = 1FE(F1
S(1t)) 0t1
t= 1E= 1FS(x0) q=S= 1FE(x0) ???? ???? ???????x0????? ?? ????? ?? ??????
E=P(y= 0jD= 0))E(u) =FS(xu) =FS(u))
)(1E)(u) =FS(u > t) = 1FS(u)
S=P(y= 1jD= 1))S(u) =FE(x > u) = 1FE(u)
(1E;S) = (1FS(u);1FE(u))) t= 1FS(u))u=F1
S(1t))
ROC(t) = 1FE(F1
S(1t))
Z=^prprSD(pr)=^prprp^pr^qr=n
SD(S) =v
uutV +(V++F)F(V++F)(V++F)=sV +F(V++F)3
SD(E) =v
uutV (V+F+)F+(V+F+)(V+F+)=sV
F+(V+F+)3
IC(S) =FV PZ=2sV
+F(V++F)3
IC(E) =FV NZ=2sV
F+(V+F+)3
[42]?????? ??? ????
Fn:R![0;1]
x!^Fn(x) =1n n X i=1" i(x) i(x) =( 1xix
0xi> x
FnE(x) =1n
En EX i=1" i(x)
FnS(x) =1n
Sn SX i=1" i(x) fx1;:::;xnSg??? ??? ???
1^FnS(x);1^FnE(x)
ROCn(t) = 1^FnE(1^FnS(x))
?????F+?V+ [30]? ??? ????? ??? ?????[31]? fE(x) =1n Eh1n EX i=1K 1xxih 1 fS(x) =1m Sh2n SX i=1K 2xxih 2
RKi(x)x= 1
RxKi(x)x= 0
Rx2Ki(x)x >0
????i= 1;2?
FE(x) =1n
En EX i=1x 11h
1K1uxiEh
1 u
FS(x) =1m
Sm SX i=1x 11h
2K2uxiSh
2 u
FE(x) =1n
En EX i=1xxiEh 1
FS(x) =1m
Sm SX i=1xxiSh 2
ROC(t) = 1~FE~F1
S(1t) [7]? [1]? ??????? ? ???[33]? [36] [24]? ^a=^E^S^E b=^S^E
ROC(t) = 1(^a+^b1(1t)) 0t1
[7]? ?? ??????? ???
ROC(t) = 1FE(F1
F w;E(t) =FE(T1(t)) F w;S(t) =FS(T1(t)) ROC w(t) = 1Fw;E(F1 w;S(1t)) = = 1Fw;E(T(F1
S(1t))) =
= 1FE(T1(T(F1
S(1t)))) =
= 1FE(F1
S(1t)) =ROC(t)
ROC(t) = 1FE(F1
S(1t))
ROC(t) = 1FETT1F1
S(1t) =
= 1S+S1(1t)E E ???????S?E? = 1(^a+^b1(1t)) ROC H
0: ^a1= ^a2^^b1=^b2
H
1: ^a16= ^a2_^b16=^b2
2=^a12^V(^b12) +^b212^V(^a12)2^a12^b12cov(^a12;^b12)^
V(^a12)^V(^b12)cov(^a12;^b12)
[43]? ?????^a12= ^a1^a2?^b12=^b1^b2? ???
AC=Pr(y= 1jD= 1)Pr(D= 1) +Pr(y= 0jD= 0)Pr(D= 0))
AC=SPr(D= 1) +EPr(D= 0))
AC=Sprevalencia+E(1prevalencia)
AC=V++VV
Si(F++F)!0)^AC!1
PD=^ACFV NFV PFV N
=Pr(y= 1jD= 1) +Pr(y= 1jD= 0) =S+E1 =FV PFFP
LRP=Pr(y= 1jD= 1)P
r(y= 1jD= 0)
LRN=Pr(y= 0jD= 1)P
r(y= 0jD= 0)
LRN=1SE
LRP=FV PFFP
LRN=FFNFV N
SD([LRP) =sFFN
V ++FV NF
SD(\LRN) =sFV P
F +FFPV
IC(LRP) =FV PFFP
exp(Z1=2SD([LRP))
IC(LRN) =FFNFV N
exp(Z1=2SD([LRP))
Odds(A) =Pr(A)1Pr(A)=Pr(A)P
r(A) Odds presencia=Pr(y= 1jD= 1)P r(y= 0jD= 1) Odds Odds ausencia=Pr(y= 1jD= 0)P r(y= 0jD= 0) Odds ausencia=1EE
Oddsratio=OddspresenciaOdds
ausencia
Oddsratio=SE(1S)(1E)
d
OD=V+VF
F+ xjD= 0N(1;) xjD= 1N(2;) =separaciondispersion=jESj 8>< E=x E S=x S =SD(x) AUC=1 0
ROC(t)t
[9]???? ??????? ??????? [9]????? ??? ?? ???? ??? ?????? ??0;7????? ??? ???? ?????
AUC=TX
t=112 (FFPtFFPt1)(FV Pt+FV Pt1) ?????H0:Pr(x > y) = 1=2? ??? ?? ??????? ???? ?????H0:Pr(xS> xE) = 1=2? [10]? SD(AUC) =sAUC(1AUC) + (nE1)(Q1AUC2) + (nS1)(Q2AUC2)n EnS ???????Q Q
1=Pr(yEi> ySj; yEk> ySj)
i;k= 1;:::;nE j= 1;:::;nSQ Q
2=Pr(ySi> yEj; ySk> yEj)
i;k= 1;:::;nS j= 1;:::;nE AUC=1 0
ROC(t)t
ROC(t) = 1~FE~F1
S(1t) AUC=1 0
ROC(t)t=1
0
1~FE~F1
S(1t) t AUC=1 0
ROC(t)t=1
0 1FEF1
S(1t)t
AUC=1 0
ROC(t)t=1
0
1(^a+^b1(1t))t=
^ap1 +b2 ^E^Sp
2E+2S!
AUC (a;b)=b a
ROC(t)t
AUC(a;b)=b
a
ROC(t)t
AUC(a;b)=b1+b2+BX
t=A12 (FFPtFFPt1)(FV Pt+FV Pt1) ??????? ??1E???? ???? ????? ?? ??????B=min(bj)=jb???j= 1;:::;T?
1= (ia)12
(FV Pi+FV Pi1)b
2= (bj)12
(FV Pj+1+FV Pj)
0[AUC(a;b)ba1
AUC(1)
(a;b)[AUC(2) (a;b) [AUC(1) (a;b)?? ???? ??????? ????? ??? ???????(x=a; x=b)?? ??? ?? ??? [AUC(2) ?? ???? ?????? ?? ?? ???(a= 0; b= 1)? H
0:AUC1=AUC2
H
1:AUC16=AUC2
z=([AUC1[AUC2)SD([AUC1[AUC2)
SD([AUC1[AUC2) =
q^
V([AUC1) +^V([AUC2)2rSD([AUC1)SD([AUC2)
r=cov([AUC1;[AUC2)SD([AUC1)SD([AUC2) H
0:AUC= 0;5
H
1:AUC6= 0;5
z=[AUC0;5SD([AUC) [45]????? ????? ???? ? ????? ??? ?????? ??120? x dist(x) =x2+ (y1)2=x2+ [f(x)1]2
2x+ 2[f(x)1]f0(x) = 0 =)f0(x) =x1f(x)
x=f
0(x) =1E1S=1Pr(Y= 0jD= 0)1Pr(Y= 1jD= 1)=Pr(Y= 1jD= 0)P
r(Y= 0jD= 1)= P r(Y= 1TD= 0)P r(D= 0)Pr(D= 1)P r(Y= 0TD= 1)=pPr(falsospositivos)(1p)Pr(falsosnegativos) C esp=C0+CV+Pr(V+) +CVPr(V) +CF+Pr(F+) +CFPr(F)
8>>>>>><
>>>>>:C
0Costebase
C
V+Costedeverdaderospositivos
C
VCostedeverdaderosnegativos
C
F+Costedefalsospositivos
C
FCostedefalsosnegativos
8>>>< >>:P r(V+) =Pr(Enfermo)Pr(Y= 1jEnfermo) =pS prevalenciasensibilidad P r(V) =Pr(Sano)Pr(Y= 0jSano) = (1p)E(1prevalencia)especificidad P r(F+) =Pr(Sano)Pr(Y= 1jSano) = (1p)(1E) (1prevalencia)(1especificidad) P r(F) =Pr(Enfermo)Pr(Y= 0jEnfermo) =p(1S)prevalencia(1sensibilidad) C esp=C0+CV+pS+CV(1p)E+CF+(1p)(1E)+CFp(1S) =quotesdbs_dbs18.pdfusesText_24
Curvas ROC - Fisterra