******************************************************* * * * Combining Binary Data * * * * EFFECTVENESS OF CISAPRIDE ON THE * * TREATMENT OF NONULCER DYSPEPSIA * * * * Exact likelihood method via PROC NLMIXED * * * * Logit model and bivariate model * *******************************************************; /* Combining binary data treat = dummy variable (1 = cisapride, 0 = placebo) succ = no. of successes in the treatment group n = sample size in the treatment group */ DATA cisapride; INPUT study treat succ n @@; DATALINES; 1 1 15 16 1 0 9 16 2 1 12 16 2 0 1 16 3 1 29 34 3 0 18 34 4 1 42 56 4 0 31 56 5 1 14 22 5 0 6 22 6 1 44 54 6 0 17 55 7 1 14 17 7 0 7 15 8 1 29 58 8 0 23 58 9 1 10 14 9 0 3 15 10 1 17 26 10 0 6 27 11 1 38 44 11 0 12 45 12 1 19 29 12 0 22 30 13 1 21 38 13 0 19 38 ; /* Logit-normal model */ ODS SELECT ParameterEstimates AdditionalEstimates; * DF=10000 yields Wald-type confidence intervals; PROC NLMIXED DATA=cisapride DF=10000; PARMS beta0=1 beta1=1 tau=1; /* initial values */ BOUNDS tau >=0; /* tau must be nonnegative */ eta = beta0 + beta1*treat + u; expeta = exp(eta); p = expeta / (1 + expeta); MODEL succ ~ BINOMIAL(n,p); RANDOM u ~ NORMAL(0,tau) SUBJECT=study; ESTIMATE "OR" exp(beta1); TITLE "Logit-normal model"; TITLE3 "Cisapride studies"; RUN; /* Bivariate model */ ODS SELECT ParameterEstimates AdditionalEstimates; PROC NLMIXED DATA=cisapride DF=10000; PARMS beta0=1 beta1=1 tau0=1 tau1=1 cov01=1; /* initial values */ BOUNDS tau0 >=0, tau1 >= 0; /* tau0 and tau1 must be nonnegative */ IF (treat=0) THEN eta = beta0 + u0; ELSE eta = beta1 + u1; expeta = exp(eta); p = expeta / (1 + expeta); MODEL succ ~ BINOMIAL(n,p); RANDOM u0 u1 ~ NORMAL([0,0],[tau0,cov01,tau1]) SUBJECT=study; ESTIMATE "LOGOR" beta1-beta0; ESTIMATE "OR" exp(beta1-beta0); TITLE "Bivariate model"; TITLE3 "Cisapride studies"; RUN;