The LOGISTIC statement performs power and sample size analyses for the likelihood ratio chisquare test of a single predictor in binary logistic regression, possibly in the presence of one or more covariates that might be correlated with the tested predictor.
Table 77.2 summarizes the options available in the LOGISTIC statement.
Table 77.2: LOGISTIC Statement Options
Option 
Description 

Define analysis 

Specifies the statistical analysis 

Specify analysis information 

Specifies the significance level 

Specifies the distributions of predictor variables 

Specifies the distribution of the predictor variable being tested 

Defines a distribution for a predictor variable 

Specify effects 

Specifies the multiple correlation between the predictor and the covariates 

Specifies the odds ratios for the covariates 

Specifies the regression coefficients for the covariates 

Specifies the default change in the predictor variables 

Specifies the intercept 

Specifies the response probability 

Specifies the odds ratio being tested 

Specifies the regression coefficient for the predictor variable 

Specifies the changes in the predictor variables 

Specify sample size 

Enables fractional input and output for sample sizes 

Specifies the sample size 

Specify power 

Specifies the desired power of the test 

Specify computational method 

Specifies the default number of categories for each predictor variable 

Specifies the number of categories for predictor variables 

Control ordering in output 

Controls the output order of parameters 
Table 77.3 summarizes the valid result parameters in the LOGISTIC statement.
To specify the intercept in the full model, choose one of the following two parameterizations:
intercept (using the INTERCEPT= options)
Prob(Y = 1) when all predictors are equal to their means (using the RESPONSEPROB= option)
To specify the effect associated with the predictor variable being tested, choose one of the following two parameterizations:
odds ratio (using the TESTODDSRATIO= options)
regression coefficient (using the TESTREGCOEFFS= option)
To describe the effects of the covariates in the full model, choose one of the following two parameterizations:
odds ratios (using the COVODDSRATIOS= options)
regression coefficients (using the COVREGCOEFFS= options)
This section summarizes the syntax for the common analyses supported in the LOGISTIC statement.
You can express effects in terms of response probability and odds ratios, as in the following statements:
proc power; logistic vardist("x1a") = normal(0, 2) vardist("x1b") = normal(0, 3) vardist("x2") = poisson(7) vardist("x3a") = ordinal((5 0 5) : (.3 .4 .3)) vardist("x3b") = ordinal((5 0 5) : (.4 .3 .3)) testpredictor = "x1a" "x1b" covariates = "x2"  "x3a" "x3b" responseprob = 0.15 testoddsratio = 1.75 covoddsratios = (2.1 1.4) ntotal = 100 power = .; run;
The VARDIST= options define the distributions of the predictor variables. The TESTPREDICTOR= option specifies two scenarios for the test predictor distribution, Normal(10,2) and Normal(10,3). The COVARIATES= option specifies two covariates, the first with a Poisson(7) distribution. The second covariate has an ordinal distribution on the values –5, 0, and 5 with two scenarios for the associated probabilities: (.3, .4, .3) and (.4, .3, .3). The response probability in the full model with all variables equal to zero is specified by the RESPONSEPROB= option as 0.15. The odds ratio for a unit decrease in the tested predictor is specified by the TESTODDSRATIO= option to be 1.75. Corresponding odds ratios for the two covariates in the full model are specified by the COVODDSRATIOS= option to be 2.1 and 1.4. The POWER= . option requests a solution for the power at a sample size of 100 as specified by the NTOTAL= option.
Default values of the TEST= and ALPHA= options specify a likelihood ratio test of the first predictor with a significance level of 0.05. The default of DEFAULTUNIT= 1 specifies that all odds ratios are defined in terms of unit changes in predictors. The default of DEFAULTNBINS= 10 specifies that each of the three predictor variables is discretized into a distribution with 10 categories in internal calculations.
You can also express effects in terms of regression coefficients, as in the following statements:
proc power; logistic vardist("x1a") = normal(0, 2) vardist("x1b") = normal(0, 3) vardist("x2") = poisson(7) vardist("x3a") = ordinal((5 0 5) : (.3 .4 .3)) vardist("x3b") = ordinal((5 0 5) : (.4 .3 .3)) testpredictor = "x1a" "x1b" covariates = "x2"  "x3a" "x3b" intercept = 6.928162 testregcoeff = 0.5596158 covregcoeffs = (0.7419373 0.3364722) ntotal = 100 power = .; run;
The regression coefficients for the tested predictor (TESTREGCOEFF= 0.5596158) and covariates (COVREGCOEFFS= (0.7419373 0.3364722)) are determined by taking the logarithm of the corresponding odds ratios. The intercept in the full model is specified as –6.928162 by the INTERCEPT= option. This number is calculated according to the formula at the end of Analyses in the LOGISTIC Statement, which expresses the intercept in terms of the response probability, regression coefficients, and predictor means: