The ICPHREG Procedure

MODEL Statement

MODEL (t1, t2)= effects </ options>;

The MODEL statement identifies the variables to be used as the failure-time variables and the explanatory effects, including covariates, main effects, interactions, nested effects. For more information, see the section Specification of Effects in Chapter 45: The GLM Procedure.

The MODEL syntax specifies two variables, t1 and t2, that contain values of the endpoints of the censoring interval. Only nonnegative values are accepted. If the two values are the same (and not missing), it is assumed that there is no censoring and the actual response value is observed. If the lower value is missing, then the upper value is used as a left-censored value. If the upper value is missing, then the lower value is used as a right-censored value. If both values are present and the lower value is less than the upper value, it is assumed that the values specify a censoring interval. If the lower value is greater than the upper value or both values are missing, then the observation is not used in the analysis.

The following table summarizes the ways of specifying censoring.

Lower Value	Upper Value	Comparison	Interpretation
Not missing	Not missing	Equal	No censoring
Not missing	Not missing	Lower < upper	Censoring interval
Missing	Not missing		Upper used as left-
			censoring value
Not missing	Missing		Lower used as right-
			censoring value
Not missing	Not missing	Lower > upper	Observation not used
Missing	Missing		Observation not used

Table 51.5 summarizes the options that you can specify in the MODEL statement.

Table 51.5: MODEL Statement Options

Option	Description
Model Specification Options
ALPHA=	Specifies the confidence level
BASE=	Specifies the functional form for the baseline function
NOPOLISH	Suppresses polishing of parameter estimates of the hazard function
OFFSET=	Specifies an offset variable to be added to the linear predictor
HAZSCALE=	Requests parameterization of the hazard function in the original scale or in log scale
Output Options
CORRB	Displays the estimated correlation matrix
COVB	Displays the estimated covariance matrix

ALPHA=value

specifies the level for the confidence intervals for parameters. The value must be between 0 and 1. By default, ALPHA=0.05.

CORRB

displays the estimated correlation matrix of the parameter estimates.

COVB

displays the estimated covariance matrix of the parameter estimates.

BASE=baseline-type BASEHAZ=baseline-type B=baseline-type

specifies a functional form for the baseline function. You can specify one of the following baseline-types:

PCH (<NINTERVAL=number>, <INTERVALS=(numeric-list)>) PIECEWISE (<NINTERVAL=number>, <INTERVALS=(numeric-list)>) PIECEWISEEXPONENTIAL (<NINTERVAL=number>, <INTERVALS=(numeric-list)>) PCBH (<NINTERVAL=number>, <INTERVALS=(numeric-list)>)

partitions the time scale into disjoint intervals and assumes the baseline hazard function is piecewise constant within intervals. The parameters are the piecewise constant values of the baseline hazard functions and are named Haz1, Haz2, $\ldots$ , and so on. If HAZARDSCALE=LOGHAZ is specified, the names are LogHaz1, LogHaz2, $\ldots$ , and so on.

You can specify one of the following two options to control how to partition the time axis into intervals of constant baseline hazards:

NINTERVAL=number N=number: specifies the number of intervals that have a constant hazard rate in each interval. PROC ICPHREG partitions the time axis into the number of intervals so that each interval contains an approximately equal number of unique boundary values and imputed middle points.
INTERVALS=(numeric-list) INTERVAL=(numeric-list): specifies a list of numbers that partition the time axis into disjoint intervals that have constant hazard rate in each interval. For example, INTERVALS=(100, 150, 200, 250, 300) specifies a model that has a constant hazard in the intervals [0,100), [100,150), [150,200), [200,250), [250,300), and [300, $\infty$ ).

If you specify neither NINTERVAL= nor INTERVAL= , NINTERVAL=5 by default.

SPLINES (<DF=number>) CUBICSPLINES (<DF=number>)

models the baseline cumulative hazard function by cubic splines (Royston and Parmar, 2002). The parameters are the spline coefficients and are named Coef1, Coef2, $\ldots$ , and so on.

You can specify the degrees of freedom in the DF=number option, where number must be an integer. The number of knots equals number plus one. The actual positions of the knots are determined from an imputed data set as follows. First, PROC ICPHREG imputes a middle point for each observation in the input data set that is not right-censored. Then, it sorts these imputed times and the input boundary values in increasing order and selects only unique values. PROC ICPHREG places the terminal knots at the minimum and maximum of this sequence and chooses the interval knots by using the same method it uses to choose the break points for the piecewise constant model. For more information, see the section Choosing Break Points.

By default, DF=2.

If you do not specify the BASEHAZ= option, the ICPHREG procedure fits a piecewise constant model as if NINTERVAL=5.

NOPOLISH

suppresses polishing of parameter estimates of the baseline function. Occasionally, the parameter estimates of the baseline function can reach the default optimization lower bounds. This might indicate that the model is overparameterized. By default, the ICPHREG procedure "polishes" the hazard estimates by fixing these parameters at the lower bound value and refitting the model.

The lower bound values are set 0 if the baseline parameters are on the original scale (HAZSCALE=HAZARD). The values are set to –10.0 if they are on the log scale (HAZSCALE=LOGHAZ).

This option does not apply to the cubic spline model because its baseline parameters are unbounded.

OFFSET=variable

specifies a variable in the input data set to be used as an offset variable. This variable cannot be a CLASS variable, the response variable, or any of the explanatory variables.

HAZSCALE=hazard-type

specifies a transformation to be applied to the baseline parameters for fitting the piecewise constant model. You can choose either of the following two options:

LOGHAZ LOG LOGHAZARD: uses the log transformed baseline parameters.
HAZARD HAZ: does not transform the baseline parameters. A lower bound of 0 is used for fitting the models.

This option does not apply to the cubic spline model.