The ICPHREG Procedure

HAZARDRATIO Statement

HAZARDRATIO <'label'> variable </ options>;

The HAZARDRATIO statement enables you to request hazard ratios for any variable in the model at customized settings. For example, if the model contains the interaction of a CLASS variable A and a continuous variable X, the following specification displays a table of hazard ratios that compares the hazards of each pair of levels of A at X = 3:

    hazardratio A / at (X=3);

The HAZARDRATIO statement identifies the variable whose hazard ratios are to be evaluated. If the variable is a continuous variable, the hazard ratio compares the hazards for a particular change (by default, an increase of 1 unit) in the variable. For a CLASS variable, a hazard ratio compares the hazards of two levels of the variable. You can specify more than one HAZARDRATIO statement, and you can provide an optional label (specified as a quoted string) to identify the output.

Table 51.4 summarizes the options that you can specify in the HAZARDRATIO statement.

Table 51.4: HAZARDRATIO Statement Options

Option	Description
ALPHA=	Specifies the alpha level
AT	Specifies the variables that interact with the variable of interest
DIFF=	Specifies which differences to consider
E	Displays the log-hazard ratio
UNITS=	Specifies the units of change for a continuous variable of interest

You can specify the following options after a slash (/).

ALPHA=number

specifies the level of confidence intervals for the hazard ratios. The number must be between 0 and 1. The default is the value of the ALPHA= option in the PROC ICPHREG statement, or 0.05 if that option is not specified.

AT (variable=ALL | REF | list <…variable=ALL | REF | list> )

specifies the variables that interact with the variable of interest and the corresponding values of the interacting variables. If the interacting variable is continuous and you specify a numeric list after the equal sign, hazard ratios are computed for each value in the list. If the interacting variable is a CLASS variable, you can specify, after the equal sign, a list of quoted strings that correspond to various levels of the CLASS variable, or you can specify the keyword ALL or REF. Hazard ratios are computed at each value of the list if you specify a list, at each level of the interacting variable if you specify ALL, or at the reference level of the interacting variable if you specify REF.

If you do not specify the AT option, PROC ICPHREG finds all the variables that interact with the variable of interest. If an interacting variable is a CLASS variable, variable=ALL is the default; if the interacting variable is continuous, variable=m is the default, where m is the average of all the sampled values of the continuous variable.

Suppose the model contains two interactions: an interaction A*B of CLASS variables A and B, and another interaction A*X of A with a continuous variable X. If 3.5 is the average of the sampled values of X, the following two HAZARDRATIO statements are equivalent:

hazardratio A;
hazardratio A / at (B=ALL X=3.5);

DIFF=diff-request

specifies which differences to consider for the level comparisons of a CLASS variable. This option is ignored in the estimation of hazard ratios for a continuous variable. You can specify the following diff-requests:

DISTINCT DISTINCTPAIRS ALL: requests all comparisons of only the distinct combinations of pairs.
PAIRWISE PERM PERMUTATIONS: requests all possible pairwise comparisons of levels.
REF REFERENCE: requests comparisons between the reference level and all other levels of the CLASS variable.

For example, let A be a CLASS variable that has three levels (A1, A2, and A3), and suppose A3 is specified as the reference level. The following table shows the hazard ratios that are displayed for the three alternatives of the DIFF= option:

DIFF=option	A1 vs A2	A2 vs A1	A1 vs A3	A3 vs A1	A2 vs A3	A3 vs A2
	Hazard Ratios Displayed
DISTINCT	$\surd$		$\surd$		$\surd$
PAIRWISE	$\surd$	$\surd$	$\surd$	$\surd$	$\surd$	$\surd$
REF			$\surd$		$\surd$

By default, DIFF=DISTINCT.

E

displays the vector $\mb{h}$ of linear coefficients such that $\mb{h}’\bbeta$ is the log-hazard ratio, where $\bbeta$ is the vector of regression coefficients.

UNITS=value

specifies the units of change in the continuous explanatory variable for which the customized hazard ratio is estimated. By default, UNITS=1. This option is ignored in the computation of the hazard ratios for a CLASS variable.