DATA SET1;
/* This program is stored as comodds.sas */
INPUT F1 S1
F1= TREATMENT FAILURES
/*****************************************
S2= CONTROL SUCCESSES
This program uses PROC IML in SAS to
F2= CONTROL FAILURES;
compute three estimates of a common
CARDS;
odds ratio for a set of 2x2 tables. It
also evaluates seven test statistics to
test homogeneity of odds ratio across
tables.
Some of these tests may produce
unreliable p-values in some situations.
The data file should contain one line for
each 2x2 table with the counts arranged
in the order shown below.
The example
includes data from eighteen 2x2 tables.
Odds ratios are
F2 S2;
LABEL S1= TREATMENT SUCCESSES
1 0 3 5
1 0 2 4
. . . .
. . . .
run;
PROC PRINT DATA= SET1;
PROC IML;
START CC;
(S1)(F2)/(F1)(S2),
the odds of success in the treatment
/* Enter the observed counts
group (group 1) divided by the odds of
success in the other group.
*******************************
USE SET1;
READ ALL INTO
*/
X;
1
K=NROW(X);
2
/*----- COMPUTE MH ESTIMATOR --------*/
K1=K+1;
F1=X[ ,1]; /* Treatment group failures*/
R1=J(K,1);
S1=X[ ,2]; /* Treatment group succeses*/
R2=R1;
F2=X[ ,3]; /* Control group failures */
S2=X[ ,4]; /* Control group successes */
N1=S1+F1;
R1[I4,1]= (S1[I4,1]*F2[I4,1])/N[I4,1];
R2[I4,1]= (S2[I4,1]*F1[I4,1])/N[I4,1];
N2=S2+F2;
END;
N=N1+N2;
MH=SUM(R1)/SUM(R2);
MV=S1+S2;
PRINT,,,"
DO I4=1 TO K;
THE OBSERVED COUNTS", X;
/*---STD. DEVIATION FOR MH ESTIMATOR--*/
/* Terminate the program if either the
L1=J(K,1);
control group or the treatment group
L2=L1;
has all successes in every table or
L11=L1;
all failures in every table */
L22=L1;
L3=L1;
CHECK=SUM(S1)*SUM(S2)*SUM(F1)*SUM(F2);
IF (CHECK=0) THEN DO;
DO I5=1 to k;
PRINT,,,"EITHER ALL SUCCESSES OR ALL
L1[I5,1]=((S1[I5,1]+F2[I5,1])*(S1[I5,1]
FAILURES FOR AT LEAST ONE GROUP";
*F2[I5,1]))/(N[I5,1]##2);
STOP;
L11[I5,1]=(S1[I5,1]*F2[I5,1])/N[I5,1];
END;
3
4
/*--COMPUTE MLE OF COMMON ODDS RATIO--*/
L2[I5,1]=((S1[I5,1]+F2[I5,1])
*(S2[I5,1]*F1[I5,1])+(S2[I5,1]+F1[I5,1])
/* USE MH ESTIMATOR FOR THE STARTING VALUE */
*(S1[I5,1]*F2[I5,1]))/(N[I5,1]##2);
L22[I5,1]= (S2[I5,1]*F1[I5,1])/N[I5,1];
BA=LOG(MH);
BP=.5*(LOG((S1+.5)/(N1-S1+.5))+
L3[I5,1]=((S2[I5,1]+F1[I5,1])*(S2[I5,1]
LOG((S2+.5)/(N2-S2+.5))+LOG(MH));
*F1[I5,1]))/(N[I5,1]##2);
B=BP//BA;
end;
BT=B`;
L7=SUM(L1)/(2*(SUM(L11)##2));
/*
L8=SUM(L2)/(2*SUM(L11)*SUM(L22));
USE THE NEWTON-RAPHSON ALGORITHM
TO GET THE MLE */
L9=SUM(L3)/(2*(SUM(L22)##2));
MAXIT=50;
SLMH=SQRT(L7+L8+L9);
HALVING=16;
SMH=MH*SLMH;
CONVERGE=.0001;
MHL=EXP(LOG(MH)-(1.96)*SLMH);
RUN NEWTON;
MHU=EXP(LOG(MH)+(1.96)*SLMH);
RUN DERIV;
HI=INV(H);
5
6
BP=B[1:K,1];
BA=B[K1,1];
run TEST3;
PI=EXP(BP)/(KO+EXP(BP));
PVAL3=1-PROBCHI(BD,DF);
PRINT '
COR=EXP(B[K1,1]);
Breslow-Day test for
a common odds ratio:' BD PVAL3;
SCOR=COR*SQRT(HI[K1,K1]);
MLEL=exp(log(cor)-(1.96)*scor/cor);
MLEU= exp(log(cor)+(1.96)*scor/cor);
run test4;
run ccorprg;
PVAL4=1-PROBCHI(MBD,DF);
PRINT 'Modified Breslow-Day test for
RUN TEST1;
a common odds ratio:' MBD PVAL4;
DF=K-1;
PVAL1=1-PROBCHI(LR,DF);
RUN TEST6;
PRINT '
PVAL5=1-PROBCHI(CS,DF);
Likelihood ratio test for
a common odds ratio:' LR PVAL1;
PVAL6=1-PROBNORM(T4);
PRINT '
run TEST2;
Conditional score test for
a common odds ratio:' CS PVAL5;
PVAL2=1-PROBCHI(P,DF);
PRINT '
PRINT ' Pearson chi-squared test for
Liang & Self T4 test for
a common odds ratio:' T4 PVAL6;
a common odds ratio:' P PVAL2;
7
8
/*--MODIFIED NEWTON-RAPHSON ALGORITHM-------*/
/* USER MUST SUPPLY INITIAL VALUES FOR
RUN TEST7;
PARAMETERS IN B, AND THE FUN AND DERIV
PVAL7=1-PROBNORM(T5);
PRINT '
FUNCTIONS. FUN EVALUATES THE FUNCTION TO
Liang & Self T5 test for
BE MAXIMIZED.
a common odds ratio:' T5 PVAL7;
SECOND PARTIAL DERIVATIVES. FIRST PARTIAL
PRINT,,,, "ESTIMATES OF THE COMMON ODDS RATIO ";
PRINT,"
MANTEL-HAENZEL ESTIMATE " MH;
PRINT "
STANDARD ERROR FOR MH ESTIMATE " SMH;
PRINT "
DERIV EVALUATES FIRST AND
95% CONFIDENCE INTERVAL " MHL
MHU;
PRINT,"
MAXIMUM LIKELIHOOD ESTIMATE " COR;
PRINT "
STANDARD ERROR FOR MLE " SCOR;
PRINT "
95% CONFIDENCE INTERVAL " MLEL MLEU;
PRINT,"COND. MAXIMUM LIKELIHOOD ESTIMATE " COR;
PRINT "
STANDARD ERROR FOR COND. MLE " SCOR;
PRINT "
95% CONFIDENCE INTERVAL " MLEL MLEU;
DERIVATIVES ARE PUT IN Q. THE NEGETIVE OF
THE MATRIX OF SECOND PARTIAL DERIVATIVES
ARE PUT INTO H */
START NEWTON;
CHECK=1;
DO ITER =1 TO MAXIT WHILE (INT(CHECK/CONVERGE));
RUN FUN;
FOLD=F;
BT=B`;
STEP=ITER-1;
*PRINT,STEP BT F;
FINISH;
BOLD=B;
B2=BOLD;
RUN DERIV;
9
HI=INV(H);
10
/*--USER SUPPLIED FUNCTION EVALUATION--*/
B=BOLD + HI*Q;
RUN FUN;
DO HITER= 1 TO HALVING WHILE(FOLD-F >= 0);
B=B2+2.*((.5)##HITER)*HI*Q;
START FUN;
KO = J(K,1);
BP=B[1:k,1];
BT=B`;
BA=B[k1,1];
*PRINT STEP HITER BT F;
RUN FUN;
G1=LGAMMA(N1+KO)+LGAMMA(N2+KO);
END;
G2=LGAMMA(S1+KO)+LGAMMA(S2+KO)+
LGAMMA(N1-S1+KO)+LGAMMA(N2-S2+KO);
IF(HITER=HALVING) THEN DO;
G5=(S1+S2)`*BP;
PRINT,,,"DID NOT CONVERGE AFTER
G6=(SUM (N2-S2))*BA;
USING ALL HALVING STEPS";
G7=N1`*LOG(KO+EXP(BP));
STOP;
G8=N2`*LOG(EXP(BA)*KO+EXP(BP));
END;
CHECK=((BOLD-B)`*(BOLD-B))/(B`*B);
F=SUM(G1-G2)+G5+G6-G7-G8;
end;
FINISH;
FINISH;
11
12
/*--USER SUPPLIED DERIVATIVE EVALUATION----
H2= EXP(BA)*(N2#EXP(BP))/
FIRST PARTIAL DERIVATIVES ARE RETURNED
(((EXP(BA)*KO)+EXP(BP))##2);
IN Q AND THE NEGETIVE OF THE 2ND PARTIAL
DERIVATIVES ARE RETURNED IN THE MATRIX H.
H3= -EXP(BA)*SUM((N2#EXP(BP))
-------------------------------------------*/
START DERIV;
/(((EXP(BA)*KO)+EXP(BP))##2));
H4= (H2//H3)`;
KO = J(K,1);
H5= H1||H2;
BP= B[1:K,1];
H = H5//H4;
BA= B[K1,1];
H = -H;
Q1=(S1+S2)-(N1#EXP(BP))/(KO+EXP(BP))-
FINISH;
(N2#EXP(BP))/((EXP(BA)*KO)+EXP(BP));
Q2=SUM(N2-S2)-EXP(BA)*
/*@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@
(SUM(N2/((EXP(BA)*KO)+EXP(BP))));
* @ ************************************ @
Q=Q1//Q2;
H1=-((N1#EXP(BP))/((KO+EXP(BP))##2))(EXP(BA)*(N2#EXP(BP))/
((((EXP(BA)*KO)+EXP(BP))##2)));
* @ *
* @
* @ * Program to find out the values
* @
* @ * of the Seven(7) Test Statistics
* @
* @ *
* @
* @ ************************************ @
* @@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@*/
H1=DIAG(H1);
13
14
IF (S2[I,1]>0) THEN
/*****************************************
*
LR=LR+(S2[I,1])*(LOG(BL[I,1])
*
-LOG(S2[I,1]));
*(1) Compute the value of the likelihood *
*
Ratio Test Statistic ( L-R TEST )
*
*
IF (F2[I,1]>0) THEN
*
LR=LR+(F2[I,1])*(LOG(N2[I,1]
******************************************/
-BL[I,1])-LOG(F2[I,1]));
END;
START TEST1;
LR=-2*LR;
BI=N1#PI;
FINISH;
BL=((N2#BI)/(BI+COR*(N1-BI)));
/******************************************
LR=0;
*
*
DO I=1 TO K;
* (2) Compute the value of the
*
IF (S1[I,1]>0) THEN
*
LR=LR+(S1[I,1])*(LOG(BI[I,1])
Pearson Chi-square test statistic
*
-LOG(S1[I,1]));
*
*
*******************************************/
IF (F1[I,1]>0) THEN
START TEST2;
LR=LR+(F1[I,1])*(LOG(N1[I,1]
P=SUM((N1#((S1-BI)##2))/(BI#(N1-BI)))+
-BI[I,1])-LOG(F1[I,1]));
SUM((N2#((S2-BL)##2))/(BL#(N2-BL)));
FINISH;
15
16
/* Z is a solution of the quadratic
equation at the Mantel-Hanszel
estimator */
/**********************************
*
*
U=(S1-Z);
* (3) Compute the value of the
*
W=((KO/Z)+(KO/(N1-Z))+(KO/(MV-Z))
*
*
Breslow-Day test statistic
*
+(KO/(N2-MV+Z)));
*
***********************************/
v=(1/w);
BD= sum((U##2)/V);
START TEST3;
FINISH;
KO=J(K,1);
/*~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~*
Z1= N2-(((1-MH)*KO)#MV)+((MH*KO)#N1);
Z2=
*
SQRT(((N2-(((1-MH)*KO)#MV)+
((MH*KO)#N1))##2)+(((4*(1-MH)*MH)
*
* (4) Modified Breslow and Day statistic
*
*
*
*~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~*/
*KO) #N1)#MV);
START TEST4;
Z3= 2*(1-MH)*KO;
Z=(-Z1+Z2)/Z3;
CT=((SUM(S1-Z))##2)/SUM(v);
MBD=BD-CT;
FINISH;
17
18
DC = TC;
/*~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~*
*
*
* (5) CONDITIONAL SCORE TEST
*
* (6) LIANG AND SELF'S T4 STATISTIC *
*
*
*~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~*/
START TEST6;
EC1=J(K,1);
EC2=EC1;
EC3=EC1;
EC4=EC1;
VC=EC1;
DO I1 =1 TO K;
M=S1[I1,1]+S2[I1,1];
K2=N1[I1,1];
K3=M-N2[I1,1];
IF (K3<0) THEN K3=0;
IF (M<K2) THEN K2=M;
D1=K3*DC;
D2=K3*D1;
D3=K3*D2;
D4=K3*D3;
DO
I2 = K3+1 TO K2;
TC = TC*(N1[I1,1]-I2+1)*(M-I2+1)/
(I2*(N2[I1,1]-M+I2));
TC=TC*CCOR;
DC=DC+TC;
D1=D1+I2*TC;
D2=D2+(I2**2)*TC;
D3=D3+(I2**3)*TC;
D4=D4+(I2**4)*TC;
END;
EC1[I1,1]=D1/DC;
TC=EXP(LGAMMA(N1[I1,1]+1)-LGAMMA(K3+1)
-LGAMMA(N1[I1,1]-K3+1)+
LGAMMA(N2[I1,1]+1)-LGAMMA(M-K3+1)
-LGAMMA(N2[I1,1]-M+K3+1)
+log(CCOR)*K3);
19
EC2[I1,1]=D2/DC;
EC3[I1,1]=D3/DC;
EC4[I1,1]=D4/DC;
VC[I1,1]=EC2[I1,1]-(EC1[I1,1]##2);
END;
20
V1=(CCOR##2)/SUM(VC);
B1=SUM((EC3-3*EC2#EC1+2*(EC1##3))/(CCOR*VC));
START TEST7;
V2=SUM((EC4-4*EC1#EC3+6*(EC1##2)
S11=SUM((Q11##2)-VC);
#EC2-3*(EC1##4))/(VC##2));
I11=SUM(EC4-4*EC3#EC1+6*EC2#(EC1##2)
Q11=(S1-EC1);
-3*(EC1##4)-2*VC#(EC2-(EC1##2))+(VC##2));
CS= SUM((Q11##2)/VC);
I12=SUM(EC3-3*EC2#EC1+2*(EC1##3));
k11=0;
I22=SUM(VC);
do I1=1 TO K;
T5=S11/SQRT(I11-((I12##2)/I22));
if (S1[I1,1]+S2[I1,1] > 0) &
FINISH;
(S1[I1,1]+S2[I1,1]<N[I1,1])
THEN K11=K11+1;
/*-----------------------------------
END;
Subroutine for evaluating the
conditional likelihood
T4=(CS-K11)/SQRT((V2-K11)-(B1##2)*V1);
------------------------------------*/
FINISH;
start condexp;
E=0;
/*###############################
*
*
do I1=1 to k;
*
(7) T5 TEST STATISTIC
*
*
M=S1[I1,1]+S2[I1,1];
*
K2=N1[I1,1];
################################*/
21
K3=M-N2[I1,1];
IF(K3<0) THEN K3=0;
22
/*----------------------------------------
IF( M < K2 ) THEN K2=M;
C1=EXP(LGAMMA(N1[I1,1]+1)LGAMMA(K3+1)-LGAMMA(N1[I1,1]-K3+1));
C2=EXP(LGAMMA(N2[I1,1]+1)-LGAMMA(M-K3+1)
-LGAMMA(N2[I1,1]-M+K3+1));
C3=PHI##K3;
Bisection routine to compute conditional
mle for the common odds ratio( CCOR )
----------------------------------------*/
start ccorprg;
PHI=MHL;
CALL CONDEXP;
E2=C1*C2*C3;
E1=E2*K3;
EL=E;
PHI=MHU;
IF( K2 > K3 ) THEN DO;
DO I2= K3+1 TO K2;
C1=C1*(N1[I1,1]-I2+1)/I2;
C2=C2*(M-I2+1)/(N2[I1,1]-M+I2);
C3=C3*PHI;
E1=E1+(I2*C1*C2*C3);
E2=E2+(C1*C2*C3);
END;
END;
E=E+(E1/E2);
END;
E=E-SUM(S1);
FINISH;
23
CALL CONDEXP;
EU=E;
PHI=MH;
CALL CONDEXP;
EM=E;
PHIU=MHU;
PHIL=MHL;
IF( EL >0 & EM<0) THEN DO;
PHIU=MH;
EU=EM;
END;
24
IF( EM > 0 & EU < 0 ) THEN DO;
PHIL=MH;
EL=EM;
END;
IF( EL < 0 & E > 0) THEN DO;
PHIU=PHI;
EU=E;
END;
IF( EL < 0 & EM > 0 ) THEN DO;
PHIU=MH;
EU=EM;
END;
IF( EL < 0 & E < 0 ) THEN DO;
PHIL=PHI;
EL=E;
END;
IF( EM < 0 & EU > 0 ) THEN DO;
PHIL=MH;
EL=EM;
END;
IF( EL > 0 & E > 0 ) THEN DO;
PHIL=PHI;
EL=E;
END;
/* COMPUTE THE NUMBER OF ITERATIONS
FOR THE BISECTION SEARCH */
IF( EL > 0 & E < 0 ) THEN DO;
PHIU=PHI;
EU=E;
END;
END;
NIT=LOG10((PHIU-PHIL)*1000000)/LOG10(2);
NIT=INT(NIT+1);
IF( NIT > 50 ) THEN NIT=50;
DO J1=1 TO NIT;
PHI=( PHIU+PHIL )/2;
CALL CONDEXP;
CCOR=(PHIL+PHIU)/2;
FINISH;
RUN CC;
25
26
THE OBSERVED COUNTS
LR
Likelihood ratio test for a
X
common odds ratio:
1
0
3
5
1
0
2
4
1
0
1
4
0
1
1
5
1
0
4
1
1
0
4
5
1
0
5
3
1
0
4
4
1
0
3
2
0
1
8
1
1
0
5
1
1
0
8
1
1
0
5
3
1
0
4
1
1
0
4
2
1
0
7
1
0
1
4
2
1
0
5
3
27
16.308133
PVAL1
0.5021057
P
Pearson chi-squared test for a
common odds ratio:
24.769313
PVAL2
0.0999935
BD
Breslow-Day test for a
common odds ratio: 21.421637
PVAL3
0.207996
28
T5
MBD
Liang & Self T5 test for a
Modified Breslow-Day test for a
common odds ratio:
21.324071
common odds ratio:
0.0104599
PVAL7
PVAL4
0.4958272
0.212129
CS
Conditional score test for a
common odds ratio: 22.043525
ESTIMATES OF THE COMMON ODDS RATIO
PVAL5
0.183051
MH
MANTEL-HAENZEL ESTIMATE
0.3001888
STANDARD ERROR FOR MH ESTIMATE
0.2077417
T4
Liang & Self T4 test for a
common odds ratio:
0.4307947
SMH
PVAL6
0.3333088
MHL
95% CONFIDENCE INTERVAL
0.07732
MHU
1.16538
29
30
COR
MAXIMUM LIKELIHOOD ESTIMATE
0.2387576
# This code computes values of the
SCOR
STANDARD ERROR FOR MLE
0.1752867
# Mantel-Haenszel estimator of a
# common odds ratio and evaluates
# the Breslow-Day and Liang-Self T4
# tests for homogeneity of odds ratios
95% CONFIDENCE INTERVAL
MLEL
MLEU
0.05663
1.00667
# It is stored in the file comodds.spl
#------------------------------------------# Evaluation of the conditional log-
COR
CONDITIONAL MLE
0.2387576
SCOR
STANDARD ERROR FOR CONDITIONAL MLE
95% CONFIDENCE INTERVAL
0.1752867
MLEL
MLEU
0.05663
1.00667
31
# likelihood uses the following function
# to calculte the number of ways of
# choosing k items out of n items
#------------------------------------------n.pick.k<-function(n, k) dbinom(k,n,0.5)*2^n
32
#-----------------------------------------# This function evaluates the conditional
# log-likelihood function conditioning on
# the marginal counts and assuming a common
# odds ratio for all 2x2 tables.
#-----------------------------------------cond.loglik<-function(alpha, s1, f1, s,
f.tot, n1, j.start, j.end)
{
denom <- c()
num <- n.pick.k(s, s1)*
n.pick.k(f.tot, f1) * alpha^s1
for(kk in 1:k) {
j <- j.start[kk]:j.end[kk]
denom[kk] <- sum(n.pick.k(s[kk], j) *
n.pick.k(f.tot[kk], n1[kk] - j)
* alpha^j)
}
sum(log(num/denom))
}
33
# Compute the MH estimator
comodds<-function(X,pout=as.logical(c("T")))
{
f1 <- X[, 1]
s1 <- X[, 2]
f2 <- X[, 3]
s2 <- X[, 4]
k <- dim(X)[1]
k1 <- k + 1
n1 <- s1 + f1
n2 <- s2 + f2
n <- n1 + n2
s <- s1 + s2
f.tot <- f1 + f2
34
# Compute the Breslow-Day test
mh <- sum((s1 * f2)/n)/sum((s2 * f1)/n)
# Compute std and a
#--------------------------------------------# MAIN FUNCTION.
# For k 2x2 independent tables,
# (1) Calculate the Mantel-Haenszel estimator
#
of common odds ratio and an approximate
#
95% confidence interval.
# (2) Use the Breslow-Day test to check for
#
a common odds ratio.
# (3) Use Liang-Self T4 test to check for a
#
common odds ratio.
#---------------------------------------------
95% CI for common odds
s1pf2 <- s1 + f2
s2pf1 <- s2 + f1
s1tf2 <- s1 * f2
s2tf1 <- s2 * f1
n.sqr <- n^2
L1 <- (s1pf2 * s1tf2)/n.sqr
L11 <- s1tf2/n
L2 <- (s1pf2 * s2tf1 + s2pf1 * s1tf2)/n.sqr
L22 <- s2tf1/n
L3 <- (s2pf1 * s2tf1)/n.sqr
sum.L11<-sum(L11)
sum.L22<-sum(L22)
L7 <- sum(L1)/(2 * sum.L11^2)
L8 <- sum(L2)/(2 * sum.L11 * sum.L22)
L9 <- sum(L3)/(2 * sum.L22^2)
slmh <- sqrt(L7 + L8 + L9)
smh <-mh*slmh
mhl <- exp(log(mh) - 1.96 * slmh)
mhu <- exp(log(mh) + 1.96 * slmh)
35
z1 <- n2 - (1 - mh) * s + mh * n1
z2 <- sqrt(z1^2 + 4 * (1 - mh) * mh * n1 * s)
z <- (z2 - z1)/(2 * (1 - mh))
w <- 1/z + 1/(n1 - z) + 1/(s - z) +
1/(n2 - s + z)
BD <- sum(w * (s1 - z)^2)
df <- k - 1
pvalue.BD <- 1 - pchisq(BD, df)
# Compute Liang's T4 test;
j.start <- s1 - f2
j.start[j.start < 0] <- 0
j.end <- s
temp<-s > n1
j.end[temp] <- n1[temp]
lower<-exp(log(mh) - 3* slmh)
upper<-exp(log(mh) + 3* slmh)
obj <- optimize(cond.loglik, lower = lower,
upper = upper, max = T, s1 = s1,
f1 = f1, s = s, f.tot = f.tot,
n1 = n1, j.start = j.start,
j.end = j.end)
36
# Conditional mle of the common odds ratio
v.cond <- EC2 - EC1^2
cs <- sum((s1 - EC1)^2/v.cond)
alpha.c <- obj$maximum
k.star <- sum((s > 0) * (f.tot > 0))
EC1 <- c()
V <- alpha.c^2/sum(v.cond)
EC2 <- c()
B <- sum((EC3 - 3 * EC2 * EC1 + 2 * EC1^3)/
EC3 <- c()
v.cond)/alpha.c
EC4 <- c()
var.cs.cond <- sum((EC4 - 4 * EC1 * EC3 + 6 *
for(kk in 1:k) {
EC1^2 * EC2 - 3 * EC1^4)/v.cond^2)
j <- j.start[kk]:j.end[kk]
T4 <- (cs - k.star)/sqrt(var.cs.cond -
temp <- n.pick.k(s[kk], j) *
k.star - B^2 * V)
n.pick.k(f.tot[kk], n1[kk]
pvalue.T4 <- (1 - pnorm(abs(T4)))
- j) * alpha.c^j
den <- sum(temp)
list(mh.estimate = mh, mh.std=smh,
EC1[kk] <- sum(j * temp)/den
conditional.estimate=alpha.c, ci95 = c(mhl, mhu),
EC2[kk] <- sum(j^2 * temp)/den
Breslow.Day.test = c(BD.statistic= BD,
EC3[kk] <- sum(j^3 * temp)/den
df = df, BD.pvalue= pvalue.BD),
EC4[kk] <- sum(j^4 * temp)/den
Liang.Self.T4test = c(T4.statistic = T4,
}
T4.pvalue = pvalue.T4))
37
#Print out the results
38
#--------------------------------------
if(pout) {
cat("***Mantel-Haenszel estimate \n
of the common odds ratio: ",
signif(mh,digits=6), "\n \n")
cat("***Standard error of the \n
Mantael-Haenszel estimator: ",
signif(smh,digits=6), "\n \n")
cat("*** 95% confidence interval for \n
the common odds ratio:\n")
cat("
(", signif(mhl,digits=6), " ",
signif(mhu,digits=6), ")\n \n")
cat("*** Breslow-Day test for a \n
common odds ratio: \n")
cat("test statistic = ", signif(BD,digits=6), "\n",
"
df = ", signif(df,digits=6), "\n",
"p-value = ", signif(pvalue.BD,digits=6), "\n \n")
cat("***Conditional m.l.e. of the \n
common odds ratio: ",
signif(alpha.c,digits=6), "\n \n")
cat("*** Liang-Self T4 test for \n
common odds ratio: \n")
cat("test statistic = ", signif(T4,digits=6), "\n",
"p-value = ", signif(pvalue.T4,digits=6), "\n")
}}
39
#
Enter the data.
#
corresponds to one row in data
Each 2x2 table
#
matrix.
#
failures for treatment 1 and the
#
second column contains the successes
#
for treatment 1.
#
contains failures for treatment 2
#
and the fourth column contains
#
successes for treatment 2.
The first column contains
The third column
#-------------------------------------X<-matrix(c(1, 0, 3, 5,
1, 0, 2, 4,
1, 0, 1, 4,
.
.
.
.
.
.
.
.
.
.
.
.
0, 1, 4, 2,
1, 0, 5, 3), ncol=4, byrow=T)
obj<-comodds(X)
40
***Mantel-Haenszel estimate
of the common odds ratio:
0.300189
***Standard error of the
Mantael-Haenszel estimator:
0.207742
*** 95% confidence interval for
the common odds ratio:
( 0.0773252
1.16538 )
*** Breslow-Day test for a
common odds ratio:
test statistic =
df =
p-value =
21.4216
17
0.207996
***Conditional m.l.e. of the
common odds ratio:
0.284776
*** Liang-Self T4 test for
common odds ratio:
test statistic =
p-value =
0.430778
0.333315
41