# The POWER Procedure

### COXREG Statement

Subsections:

• COXREG <options>;

The COXREG statement performs power and sample size analyses for the score test of a single scalar predictor in Cox proportional hazards regression for survival data, possibly in the presence of one or more covariates that might be correlated with the tested predictor.

#### Summary of Options

Table 89.2 summarizes the options available in the COXREG statement.

Table 89.2: COXREG Statement Options

Option

Description

Define analysis

Specifies the statistical analysis

Specify analysis information

Specifies the significance level

Specifies the number of sides and the direction of the statistical test

Specify effects

Specifies the value from the regression of the predictor of interest on the remaining predictors

Specifies the hazard ratio

Specify variability

Specifies the standard deviation of the predictor variable being tested

Specify sample size

Specifies the probability that an uncensored event occurs

Specifies the expected total number of events

Enables fractional input and output for sample sizes

Specifies the sample size

Specify power

Specifies the desired power of the test

Control ordering in output

Controls the output order of parameters

Table 89.3 summarizes the valid result parameters for different analyses in the COXREG statement.

Table 89.3: Summary of Result Parameters in the COXREG Statement

Analyses

Solve For

Syntax

TEST= SCORE

Power

Sample size

#### Dictionary of Options

ALPHA=number-list

specifies the level of significance of the statistical test. The default is 0.05, which corresponds to the usual 0.05 100% = 5% level of significance. For information about specifying the number-list, see the section Specifying Value Lists in Analysis Statements.

EVENTPROB=number-list

specifies the probability that an uncensored event occurs. You must specify this option when you use the NTOTAL= option, and it is ignored when you use the EVENTSTOTAL= option. If you are computing power, the input sample size is multiplied by the event probability to determine the number of events. If you are computing sample size, the internally computed number of events is divided by the event probability to compute the sample size. For information about specifying the number-list, see the section Specifying Value Lists in Analysis Statements.

EVENTSTOTAL=number-list
EVENTTOTAL=number-list
EETOTAL=number-list

specifies the expected number of uncensored events, or requests a solution for this parameter by specifying a missing value (EVENTSTOTAL= .). The NFRACTIONAL option is automatically enabled when you use the EVENTSTOTAL= option. You must use either the EVENTSTOTAL= option or the NTOTAL= option, and you cannot use both. For information about specifying the number-list, see the section Specifying Value Lists in Analysis Statements.

HAZARDRATIO=number-list
HR=number-list

specifies the hazard ratio for a one-unit increase in the predictor of interest , holding any other predictors constant. The hazard ratio is equal to , where is the regression coefficient of . For information about specifying the number-list, see the section Specifying Value Lists in Analysis Statements.

NFRACTIONAL
NFRAC

enables fractional input and output for sample sizes. This option is automatically enabled when you use the EVENTSTOTAL= option. For information about the ramifications of the presence (and absence) of the NFRACTIONAL option, see the section Sample Size Adjustment Options.

NTOTAL=number-list

specifies the sample size or requests a solution for the sample size by specifying a missing value (NTOTAL= .). You must use either the NTOTAL= option or the EVENTSTOTAL= option, and you cannot use both. The number of events is used internally in calculations, and the sample size is the ratio of the number of events (E VENTSTOTAL) and the event probability EVENTPROB . For information about specifying the number-list, see the section Specifying Value Lists in Analysis Statements.

OUTPUTORDER=INTERNAL | REVERSE | SYNTAX

controls how the input and default analysis parameters are ordered in the output. OUTPUT­ORDER= INTERNAL (the default) arranges the parameters in the output according to the following order of their corresponding options:

The OUTPUTORDER= SYNTAX option arranges the parameters in the output in the same order in which their corresponding options are specified in the COXREG statement. The OUTPUTORDER= REVERSE option arranges the parameters in the output in the reverse of the order in which their corresponding options are specified in the COXREG statement.

POWER=number-list

specifies the desired power of the test or requests a solution for the power by specifying a missing value (POWER= .). The power is expressed as a probability, a number between 0 and 1, rather than as a percentage. For information about specifying the number-list, see the section Specifying Value Lists in Analysis Statements.

RSQUARE=number-list

specifies the value from the regression of the predictor of interest on the remaining predictors. The sample size is either multiplied (if you are computing power) or divided (if you are computing sample size) by a factor of . For information about specifying the number-list, see the section Specifying Value Lists in Analysis Statements.

SIDES=keyword-list

specifies the number of sides (or tails) and the direction of the statistical test or confidence interval. For information about specifying the keyword-list, see the section Specifying Value Lists in Analysis Statements. You can specify the following keywords:

1

specifies a one-sided test, with the alternative hypothesis in the same direction as the effect.

2

specifies a two-sided test.

U

specifies an upper one-sided test, with the alternative hypothesis indicating a positive correlation between the tested predictor and survival—that is, a hazard ratio less than 1.

L

specifies a lower one-sided test, with the alternative hypothesis indicating a negative correlation between the tested predictor and survival—that is, a hazard ratio greater than 1.

By default, SIDES=2.

STDDEV=number-list
STD=number-list

specifies the standard deviation of the predictor of interest. For information about specifying the number-list, see the section Specifying Value Lists in Analysis Statements.

TEST=SCORE

specifies the score test in Cox proportional hazards regression. This is the default test option.

#### Restrictions on Option Combinations

To specify the sample size, choose one of the following parameterizations:

• sample size (by using the NTOTAL= option) and event probability (by using the EVENTPROB= option)

• number of events (by using the EVENTSTOTAL= option)

#### Option Groups for Common Analyses

This section summarizes the syntax for the common analyses that are supported in the TWOSAMPLESURVIVAL statement.

##### Score Test for Cox Proportional Hazards Regression

You can use the NTOTAL= and EVENTPROB= options, as in the following statements. Default values for the SIDES= , ALPHA= , and TEST= options specify a two-sided score test with a significance level of 0.05.

proc power;
coxreg
hazardratio = 1.4
rsquare = 0.15
stddev = 1.2
ntotal = 80
eventprob = 0.8
power = .
;
run;


You can also use the EVENTSTOTAL= option, as in the following statements:

proc power;
coxreg
hazardratio = 1.6
rsquare = 0.2
stddev = 1.1
power = 0.9
eventstotal = .
;
run;