SAS/STAT 9.2 User's Guide: The PHREG Procedure (Book …

1 SAS/STAT s GuideThe PHREG Procedure (Book excerpt )SAS DocumentationThis document is an individual chapter fromSAS/STAT User s correct bibliographic citation for the complete manual is as follows: SAS Institute Inc. s guide . Cary, NC: SAS Institute 2008, SAS Institute Inc., Cary, NC, USAAll rights reserved. Produced in the United States of a Web download or e- book : Your use of this publication shall be governed by the terms established by the vendorat the time you acquire this Government Restricted Rights Notice: Use, duplication, or disclosure of this software and related documentationby the government is subject to the Agreement with SAS Institute and the restrictions set forth in FAR ,Commercial Computer Software-Restricted Rights (June 1987).

2 SAS Institute Inc., SAS Campus Drive, Cary, North Carolina electronic book , March 20082nd electronic book , February 2009 SAS Publishing provides a complete selection of books and electronic products to help customers use SAS software toits fullest potential. For more information about our e-books, e-learning products, CDs, and hard-copy books, visit theSAS Publishing Web site call and all other SAS Institute Inc. product or service names are registered trademarks or trademarks of SAS InstituteInc. in the USA and other countries. indicates USA brand and product names are registered trademarks or trademarks of their respective PHREG ProcedureContentsOverview: PHREG Procedure ..4517 Getting Started: PHREG Procedure ..4520 Classical Method of Maximum Likelihood.

3 4521 Bayesian Analysis.. 4525 Syntax: PHREG Procedure ..4529 PROC PHREG Statement.. 4530 ASSESS Statement.. 4534 BASELINE Statement.. 4535 BAYES Statement.. 4539BY Statement.. 4550 CLASS Statement.. 4551 CONTRAST Statement.. 4553 FREQ Statement.. 4555 HAZARDRATIO Statement.. 4556ID Statement.. 4558 MODEL Statement.. 4558 OUTPUT Statement.. 4567 Programming Statements.. 4569 STRATA Statement.. 4571 TEST Statement.. 4571 WEIGHT Statement.. 4572 Details: PHREG Procedure ..4573 Failure Time Distribution.. 4573 CLASS Variable Parameterization.. 4574 Clarification of the Time and CLASS Variables Usage.. 4576 Partial Likelihood Function for the Cox Model.. 4581 Counting Process Style of Input.. 4582 Left Truncation of Failure Times.

4 4583 The Multiplicative Hazards Model.. 4584 Hazard Ratios.. 4584 Specifics for Classical Analysis.. 4587 Proportional Rates/Means Models for Recurrent Events.. 4587 Newton-Raphson Method.. 4589 Firth s Modification for Maximum Likelihood Estimation.. 45894516 FChapter 64: The PHREG ProcedureRobust Sandwich Variance Estimate.. 4591 Testing the Global Null Hypothesis.. 4591 Confidence Limits for a Hazard Ratio.. 4592 Testing Linear Hypotheses about Regression Coefficients.. 4594 Analysis of Multivariate Failure Time Data.. 4595 Model Fit Statistics.. 4604 Residuals.. 4605 Diagnostics Based on Weighted Residuals.. 4607 Influence of Observations on Overall Fit of the Model.. 4608 Survivor Function Estimation for the Cox Model.

5 4609 Effect Selection Methods.. 4611 Assessment of the Proportional Hazards Model.. 4612 Specifics for Bayesian Analysis.. 4614 Piecewise Constant Baseline Hazard Model.. 4615 Priors for Model Parameters.. 4617 Posterior Distribution.. 4619 Sampling from the Posterior Distribution.. 4620 Starting Values of the Markov Chains.. 4621 Fit Statistics.. 4622 Posterior Distribution for Quantities of Interest.. 4622 Computational Resources.. 4624 Input and Output Data Sets.. 4624 OUTEST= Output Data Set.. 4624 INEST= Input Data Set.. 4625 OUT= Output Data Set in the OUTPUT Statement.. 4625 OUT= Output Data Set in the BASELINE Statement.. 4626 OUTPOST= Output Data Set in the BAYES Statement.. 4626 Displayed Output.

6 4626 Maximum Likelihood Analysis Displayed Output.. 4626 Bayesian Analysis Displayed Output.. 4631 ODS Table Names.. 4634 ODS Graphics.. 4637 Examples: PHREG Procedure ..4638 Example : Stepwise Regression.. 4638 Example : Best Subset Selection.. 4646 Example : Modeling with Categorical Predictors.. 4648 Example : Firth s Correction for Monotone Likelihood.. 4656 Example : Conditional Logistic Regression for m:n Matching.. 4658 Example : Model Using Time-Dependent Explanatory Variables.. 4662 Example : Time-Dependent Repeated Measurements of a Covariate.. 4669 Example : Survivor Function Estimates for Specific Covariate Values. 4677 Example : Analysis of Residuals.. 4679 Example : Analysis of Recurrent Events Data.

7 4681 Example : Analysis of Clustered Data.. 4691 Overview: PHREG ProcedureF4517 Example : Model Assessment Using Cumulative Sums of MartingaleResiduals.. 4694 Example : Bayesian Analysis of the Cox Model.. 4706 Example : Bayesian Analysis of Piecewise Exponential Model.. 4717 References..4721 Overview: PHREG ProcedureThe analysis of survival data requires special techniques because the data are almost always in-complete, and familiar parametric assumptions might be unjustifiable. Investigators follow subjectsuntil they reach a prespecified endpoint (for example, death). However, subjects sometimes with-draw from a study, or the study is completed before the endpoint is reached. In these cases, thesurvival times (also known as failure times) arecensored; subjects survived to a certain time be-yond which their status is unknown.

8 The uncensored survival times are sometimes referred to aseventtimes. Methods of survival analysis must account for both censored and uncensored types of models have been used for survival data. Two of the more popular types of modelsare the accelerated failure time model (Kalbfleisch and Prentice1980) and the Cox proportionalhazards model (Cox1972). Each has its own assumptions about the underlying distribution of thesurvival times. Two closely related functions often used to describe the distribution of survivaltimes are the survivor function and the hazard function (see the section Failure Time Distribution on page 4573 for definitions). The accelerated failure time model assumes a parametric form forthe effects of the explanatory variables and usually assumes a parametric form for the underlyingsurvivor function.

9 Cox s proportional hazards model also assumes a parametric form for the effectsof the explanatory variables, but it allows an unspecified form for the underlying survivor PHREG Procedure performs regression analysis of survival data based on the Cox proportionalhazards model. Cox s semiparametric model is widely used in the analysis of survival data toexplain the effect of explanatory variables on hazard survival time of each member of a population is assumed to follow its own hazard function, , expressed as .tIZi/D /where an arbitrary and unspecified baseline hazard function,Ziis the vector of explanatoryvariables for theith individual, and is the vector of unknown regression parameters associatedwith the explanatory variables.

10 The vector is assumed to be the same for all individuals. Thesurvivor function can be expressed Rt0 the baseline survivor function. To estimate ,Cox(1972,1975) introduced the partial likelihood function, which eliminates the unknown baselinehazard accounts for censored survival 64: The PHREG ProcedureThe partial likelihood of Cox also allows time-dependent explanatory variables. An explana-tory variable is time-dependent if its value for any given individual can change over time. Time-dependent variables have many useful applications in survival analysis. You can use a time-dependent variable to model the effect of subjects changing treatment groups. Or you can includetime-dependent variables such as blood pressure or blood chemistry measures that vary with timeduring the course of a study.