MODEL Statement 
The MODEL statement identifies the variables to be used as the failure time variables, the optional censoring variable, and the explanatory effects, including covariates, main effects, interactions, nested effects; see the section Specification of Effects of Chapter 41, The GLM Procedure, for more information. A note of caution: specifying the effect T*A in the MODEL statement, where T is the time variable and A is a CLASS variable, does not make the effect timedependent. See the section Time and CLASS Variables Usage for more information.
Two forms of MODEL syntax can be specified; the first form allows one time variable, and the second form allows two time variables for the counting process style of input (see the section Counting Process Style of Input for more information).
In the first MODEL statement, the name of the failure time variable precedes the equal sign. This name can optionally be followed by an asterisk, the name of the censoring variable, and a list of censoring values (separated by blanks or commas if there is more than one) enclosed in parentheses. If the censoring variable takes on one of these values, the corresponding failure time is considered to be censored. Following the equal sign are the explanatory effects (sometimes called independent variables or covariates) for the model.
Instead of a single failuretime variable, the second MODEL statement identifies a pair of failuretime variables. Their names are enclosed in parentheses, and they signify the endpoints of a semiclosed interval during which the subject is at risk. If the censoring variable takes on one of the censoring values, the time is considered to be censored.
The censoring variable must be numeric and the failuretime variables must contain nonnegative values. Any observation with a negative failure time is excluded from the analysis, as is any observation with a missing value for any of the variables listed in the MODEL statement. Failuretime variables with a SAS date format are not recommended because the dates might be translated into negative numbers and consequently the corresponding observation would be discarded.
Table 66.7 summarizes the options available in the MODEL statement, which can be specified after a slash (/). Four convergence criteria are allowed for the maximum likelihood optimization: ABSFCONV=, FCONV=, GCONV=, and XCONV=. If you specify more than one convergence criterion, the optimization is terminated as soon as one of the criteria is satisfied. If none of the criteria is specified, the default is GCONV=1E–8.
Option 
Description 

Model Specification Options 

Suppresses model fitting 

Specifies offset variable 

Specifies effect selection method 

Effect Selection Options 

Controls the number of models displayed for SCORE selection 

Requests detailed results at each step 

Specifies whether and how hierarchy is maintained and whether a single effect or multiple effects are allowed to enter or leave the model per step 

Specifies number of effects included in every model 

Specifies maximum number of steps for STEPWISE selection 

Adds or deletes effects in sequential order 

Specifies significance level for entering effects 

Specifies significance level for removing effects 

Specifies number of variables in first model 

Specifies number of variables in final model 

Adds or deletes variables by residual chisquare criterion 

Maximum Likelihood Optimization Options 

Specifies absolute function convergence criterion 

Specifies relative function convergence criterion 

Specifies Firth’s penalized likelihood method 

Specifies relative gradient convergence criterion 

Specifies relative parameter convergence criterion 

Specifies maximum number of iterations 

Specifies the initial ridging value 

Specifies the technique to improve the log likelihood function when its value is worse than that of the previous step 

Specifies tolerance for testing singularity 

Confidence Interval Options 

Specifies for the confidence intervals 

Specifies profilelikelihood convergence criterion 

Computes confidence intervals for hazard ratios 

Display Options 

Displays correlation matrix 

Displays covariance matrix 

Displays iteration history 

suppresses "Class Level Information" table 

Displays Type 1 analysis 

Displays Type 3 analysis 

Miscellaneous Options 

Specifies the delayed entry time variable 

Specifies the method of handling ties in failure times 
sets the significance level used for the confidence limits for the hazard ratios. The quantity value must be between 0 and 1. The default is the value of the ALPHA= option in the PROC PHREG statement, or 0.05 if that option is not specified. This option has no effect unless the RISKLIMITS option is specified.
specifies the absolute function convergence criterion. Termination requires a small change in the objective function (log partial likelihood function) in subsequent iterations,
where is the value of the objective function at iteration .
is used exclusively with the SCORE model selection method. The BEST=n option specifies that n models with the highestscore chisquare statistics are to be displayed for each model size. If the option is omitted and there are no more than 10 explanatory variables, then all possible models are listed for each model size. If the option is omitted and there are more than 10 explanatory variables, then the number of models selected for each model size is, at most, equal to the number of explanatory variables listed in the MODEL statement.
See Example 66.2 for an illustration of the SCORE selection method and the BEST= option.
displays the estimated correlation matrix of the parameter estimates.
displays the estimated covariance matrix of the parameter estimates.
produces a detailed display at each step of the modelbuilding process. It produces an "Analysis of Variables Not in the Model" table before displaying the variable selected for entry for FORWARD or STEPWISE selection. For each model fitted, it produces the "Analysis of Maximum Likelihood Estimates" table.
See Example 66.1 for a discussion of these tables.
specifies the name of the variable that represents the lefttruncation time. This option has no effect when the counting process style of input is specified. See the section LeftTruncation of Failure Times for more information.
specifies the relative function convergence criterion. Termination requires a small relative change in the objective function (log partial likelihood function) in subsequent iterations,
where is the value of the objective function at iteration .
performs Firth’s penalized maximum likelihood estimation to reduce bias in the parameter estimates (Heinze and Schemper; 2001; Firth; 1993). This method is useful when the likelihood is monotone—that is, the likelihood converges to finite value while at least one estimate diverges to infinity.
specifies the relative gradient convergence criterion. Termination requires that the normalized prediction function reduction is small,
where is the log partial likelihood, is the gradient vector (first partial derivatives of the log partial likelihood), and is the negative Hessian matrix (second partial derivatives of the log partial likelihood), all at iteration .
specifies whether and how the model hierarchy requirement is applied and whether a single effect or multiple effects are allowed to enter or leave the model in one step. You can specify that only CLASS variable effects, or both CLASS and continuous variable effects, be subject to the hierarchy requirement. The HIERARCHY= option is ignored unless you also specify the FORWARD, BACKWARD, or STEPWISE selection method.
Model hierarchy refers to the requirement that, for any term to be in the model, all effects contained in the term must be present in the model. For example, in order for the interaction A*B to enter the model, the main effects A and B must be in the model. Likewise, neither effect A nor B can leave the model while the interaction A*B is in the model.
indicates that the model hierarchy is not maintained. Any single effect can enter or leave the model at any given step of the selection process.
indicates that only one effect can enter or leave the model at one time, subject to the model hierarchy requirement. For example, suppose that you specify the main effects A and B and the interaction of A*B in the model. In the first step of the selection process, either A or B can enter the model. In the second step, the other main effect can enter the model. The interaction effect can enter the model only when both main effects have already been entered. Also, before A or B can be removed from the model, the A*B interaction must first be removed. All effects (CLASS and continuous variables) are subject to the hierarchy requirement.
is the same as HIERARCHY=SINGLE except that only CLASS effects are subject to the hierarchy requirement.
indicates that more than one effect can enter or leave the model at one time, subject to the model hierarchy requirement. In a forward selection step, a single main effect can enter the model, or an interaction can enter the model together with all the effects that are contained in the interaction. In a backward elimination step, an interaction itself, or the interaction together with all the effects that the interaction contains, can be removed. All effects (CLASS and continuous variable) are subject to the hierarchy requirement.
is the same as HIERARCHY=MULTIPLE except that only CLASS effects are subject to the hierarchy requirement.
The default value is HIERARCHY=SINGLE, which means that model hierarchy is to be maintained for all effects (that is, both CLASS and continuous variable effects) and that only a single effect can enter or leave the model at each step.
includes the first n effects in the MODEL statement in every model. By default, INCLUDE=0. The INCLUDE= option has no effect when SELECTION=NONE.
displays the iteration history, including the last evaluation of the gradient vector.
specifies the maximum number of iterations allowed. The default value for n is 25. If convergence is not attained in n iterations, the displayed output and all data sets created by PROC PHREG contain results that are based on the last maximum likelihood iteration.
specifies the maximum number of times the explanatory variables can move in and out of the model before the STEPWISE modelbuilding process ends. The default value for n is twice the number of explanatory variables in the MODEL statement. The option has no effect for other model selection methods.
suppresses the "Class Level Information" table, which shows how the design matrix columns for the CLASS variables are coded.
performs the global score test, which tests the joint significance of all the explanatory variables in the MODEL statement. No parameters are estimated. If the NOFIT option is specified along with other MODEL statement options, NOFIT takes precedence, and all other options are ignored except the TIES= option.
specifies the name of an offset variable, which is an explanatory variable with a regression coefficient fixed as one. This option can be used to incorporate risk weights for the likelihood function.
controls the convergence criterion for confidence intervals based on the profilelikelihood function. The quantity value must be a positive number, with a default value of 1E4. The PLCONV= option has no effect if profilelikelihood based confidence intervals are not requested.
specifies that the diagonal elements of the negative (expected) Hessian be inflated by adding the ridge value.
specifies that the diagonal elements be inflated by the factor equal to 1 plus the ridge value.
specifies the crude linesearch method of taking half a step be used instead of ridging.
specifies the initial ridge value. The maximum ridge value is 2000 times the maximum of 1 and the initial ridge value. The initial ridge value is raised to 1E–4 if it is less than 1E–4. By default, RIDGEINIT=1E–4. This option has no effect for RIDGING=ABSOLUTE.
requests profilelikelihood confidence limits.
requests confidence limits based on the Wald tests.
request both profilelikelihood and Wald confidence limits.
fits the complete model specified in the MODEL statement. This is the default value.
requests best subset selection. It identifies a specified number of models with the highestscore chisquare statistic for all possible model sizes ranging from one explanatory variable to the total number of explanatory variables listed in the MODEL statement. This option is not allowed if an explanatory effect in the MODEL statement contains a CLASS variable.
For more information, see the section Effect Selection Methods.
forces variables to be added to the model in the order specified in the MODEL statement or to be eliminated from the model in the reverse order of that specified in the MODEL statement.
specifies the singularity criterion for determining linear dependencies in the set of explanatory variables. The default value is 1E–12.
specifies the significance level (a value between 0 and 1) for entering an explanatory variable into the model in the FORWARD or STEPWISE method. For all variables not in the model, the one with the smallest pvalue is entered if the pvalue is less than or equal to the specified significance level. The default value is 0.05.
specifies the significance level (a value between 0 and 1) for removing an explanatory variable from the model in the BACKWARD or STEPWISE method. For all variables in the model, the one with the largest pvalue is removed if the pvalue exceeds the specified significance level. The default value is 0.05.
begins the FORWARD, BACKWARD, or STEPWISE selection process with the first n effects listed in the MODEL statement. The value of n ranges from 0 to , where is the total number of effects in the MODEL statement. The default value of n is for the BACKWARD method and 0 for the FORWARD and STEPWISE methods. Note that START=n specifies only that the first n effects appear in the first model, while INCLUDE=n requires that the first n effects be included in every model. For the SCORE method, START=n specifies that the smallest models contain n effects, where n ranges from 1 to ; the default value is 1. The START= option has no effect when SELECTION=NONE.
specifies the maximum (FORWARD method) or minimum (BACKWARD method) number of effects to be included in the final model. The effect selection process is stopped when n effects are found. The value of n ranges from 0 to , where is the total number of effects in the MODEL statement. The default value of is for the FORWARD method and 0 for the BACKWARD method. For the SCORE method, STOP=n specifies that the smallest models contain n effects, where ranges from 1 to ; the default value of n is . The STOP= option has no effect when SELECTION=NONE or STEPWISE.
specifies that the addition and deletion of variables be based on the result of the likelihood score test for testing the joint significance of variables not in the model. This score chisquare statistic is referred to as the residual chisquare. In the FORWARD method, the STOPRES option enters the explanatory variables into the model one at a time until the residual chisquare becomes insignificant (that is, until the pvalue of the residual chisquare exceeds the SLENTRY= value). In the BACKWARD method, the STOPRES option removes variables from the model one at a time until the residual chisquare becomes significant (that is, until the pvalue of the residual chisquare becomes less than the SLSTAY= value). The STOPRES option has no effect for the STEPWISE method.
requests that a Type 1 (sequential) analysis of likelihood ratio test be performed. This consists of sequentially fitting models, beginning with the null model and continuing up to the model specified in the MODEL statement. The likelihood ratio statistic for each successive pair of models is computed and displayed in a table.
requests the likelihood ratio tests, the score tests, and the Wald tests. Specifying TYPE3(ALL) is equivalent to specifying TYPE3=(LR SCORE WALD).
suppresses the Type 3 analysis. Even if the TYPE3 option is not specified, PROC PHREG displays the Wald test results for each model effect if a CLASS variable is involved in a MODEL effect. The NONE option can be used to suppress such display.
requests the likelihood ratio tests. This request is not honored if the COVS option is also specified.
requests the score tests. This request is not honored if the COVS option is also specified.
requests the Wald tests.
uses the approximate likelihood of Breslow (1974). This is the default value.
replaces the proportional hazards model by the discrete logistic model
uses the approximate likelihood of Efron (1977).
computes the exact conditional probability under the proportional hazards assumption that all tied event times occur before censored times of the same value or before larger values. This is equivalent to summing all terms of the marginal likelihood for that are consistent with the observed data (Kalbfleisch and Prentice; 1980; DeLong, Guirguis, and So; 1994).
specifies the relative parameter convergence criterion. Termination requires a small relative parameter change in subsequent iterations,
where
where is the estimate of the th parameter at iteration .