Cause-Specific Analysis of Competing Risks Using the …

1 Paper SAS2159-2018 Cause-Specific Analysis of Competing Risks Using the PHREG ProcedureChangbin Guo and Ying So, SAS Institute Analysis extends the capabilities of conventional survival Analysis to deal with time-to-event data thathave multiple causes of failure. Two regression modeling approaches can be used: one focuses on the cumulativeincidence function (CIF) from a particular cause, and the other focuses on the Cause-Specific hazard function. Thesetwo quantities, unlike the hazard function and the survival function in conventional survival settings, are not connectedthrough a simple one-to-one relationship. The Fine and Gray model extends the Cox model to analyze the cumulativeincidence function but is often mistakenly assumed to be the only modeling technique available. The cause-specificapproach that simultaneously models all the Cause-Specific hazard functions offers a more natural includes updates to the PHREG procedure to perform the Cause-Specific Analysis of Competing paper describes how Cause-Specific hazard regression works and compares it to the Fine and Gray illustrate how to interpret the models appropriately and how to obtain predicted cumulative Risks arise in studies in which individuals are subject to a number of potential failure events and theoccurrence of one event might impede the occurrence of other events.

2 For example, after a bone marrow transplant, apatient might experience a relapse, or the patient might die while in remission. For relapse, death is a Competing riskbecause the event of relapse can no longer occur after the patient dies. The survival function and the hazard function,two familiar concepts in conventional survival Analysis , become elusive under Competing Risks . To meet the analysisneeds, concepts that pertain to a specific cause of the event have been developed. The Cause-Specific hazard functiongeneralizes the classical concept of the hazard function to the Competing - Risks setting, and it describes the rate offailure from one event type in the presence of others. The cumulative incidence function quantifies the risk of failurefrom a particular event type when there are Competing Analysis extends conventional survival Analysis . For the latter, statistical methods such as theKaplan-Meier estimate, the log-rank test, and the Cox regression are widely used in many applications.

3 Although thelog-rank test and the Cox regression can be adapted with minimal effort to make inferences about the cause-specifichazard function, they do not automatically lead to a correct Analysis of the cumulative incidence function because ofthe presence of Competing Risks . To overcome this hurdle, specialized methods that target the cumulative incidencefunction have been developed (Gray 1988;Fine and Gray 1999).The method ofFine and Gray(1999) extends the Cox regression to model the cumulative incidence function andmarks a milestone in the development of modeling techniques for Competing - Risks data. Despite achieving greatpopularity, the Fine and Gray model has been criticized for its weakness of interpretation. The model covariates,although they can be interpreted as having an effect on the cumulative incidence function, do not directly link to anunderlying event rate in the real world (Andersen and Keiding 2012).

4 On the other hand, proportional hazards modelsfor Cause-Specific hazards are easy to fit and offer a more natural interpretation in terms of rate LIFETEST and PHREG procedures in SAS/STAT software provide a comprehensive set of techniques for theanalysis of Competing - Risks data. The LIFETEST procedure focuses on nonparametric Analysis , and recent updatesinclude specialized features for analyzing the cumulative incidence function. For example, you can compute thenonparametric estimate of the cumulative incidence function and use Gray s (1988) test to investigate group the other hand, the PHREG procedure provides two regression approaches for analyzing Competing - Risks can apply Fine and Gray s method to directly model the cumulative incidence function; alternatively, you can fitCox proportional hazards models to Cause-Specific hazard , Lin, and Johnston(2015) provide a tutorialon how to apply these techniques to study single causes of failure by Using PROC in SAS/STAT , you can use the EVENTCODE(COX)= option in the PHREG procedure to perform thecause-specific Analysis of Competing Risks by fitting the Cause-Specific Cox models to different causes of failure1simultaneously.

5 Moreover, you can make predictions about the cumulative incidence function based on the paper first reviews the basic concepts of Competing - Risks Analysis . It then discusses regression modelingstrategies and uses a real-world data example of bone marrow transplantation to illustrate how to perform Competing - Risks regression by Using Fine and Gray s method as well as the Cause-Specific Cox models. Connections anddifferences between these two methods are discussed. The last section demonstrates how to use the two approachesto predict the cumulative incidence QUANTITIES IN Competing RISKSLetTandCdenote the failure time and censoring time, respectively. For data that haveKcompeting Risks , the pair(X, ) is observed, ;C/and D1;:::;Kis an indicator that has values of 0 for censoring andother values that designate specific failure causes. For analyzing Competing - Risks data, two useful quantities are thecause-specific hazard function and the cumulative incidence function: The Cause-Specific hazard timetis the instantaneous rate of failure due to causekconditionalon survival until timetor later.

6 It is defined t > < T < TC t; DkjT > t/ t; kD1;:::;K The cumulative incidence function, denoted , is the probability of failure due to causekprior to is defined t; Dk/; kD1;:::;KThe cumulative incidence function is also referred to as the subdistribution function, because it is not a trueprobability , thekth cumulative incidence function can be expressed in terms ofallthe Cause-Specific hazardfunctions via the integral as follows, ; kD1;:::; the Cause-Specific cumulative hazard function isthe overall survival function, which is the probability of surviving beyond timet. It is clear not also all the Competing Cause-Specific hazard functions whenK > 1. WhenKD1, the subdistributionfunction degenerates exp. becomes a function of one-to-one relationship does not exist between the Cause-Specific hazard function and the correspondingcumulative incidence function when Competing Risks are present. This feature, as pointed out byAndersen et al.

7 (2012), is the key to understanding the finesse required in Competing - Risks Analysis and to choosing EXAMPLE OF Competing - Risks DATABone marrow transplant is a standard treatment for acute and Moeschberger(2003) present a set ofbone marrow transplant data for 137 patients, divided into three disease groups based on their diagnosis at the timeof transplantation: acute lymphoblastic leukemia (ALL), acute myelocytic leukemia (AML) low-risk, and AML the 137 patients in the study, 38 patients were diagnosed as having ALL, 54 patients were diagnosed ashaving AML low-risk, and 45 patients were diagnosed as having AML high-risk. There are a number of concomitantvariables in the data set; for simplicity, only the waiting time for transplant is included the follow-up period, some patients might experience a relapse of the leukemia, and some patients might diewhile in remission. The comparison of the disease groups focuses on the occurrence of following statements provide the data.

8 The variableGroupdesignates the disease group of a patient, which iseither ALL, AML low-risk, or AML high-risk. The variableTis the disease-free survival time in days, which is either thetime to censoring, the time to relapse, or the time to death while in remission, whichever occurs first. The indicator2variableStatushas three values: 0 for censored observations, 1 for patients who relapse, and 2 for patients who diebefore experiencing a relapse. The concomitant variableWaitTimeis the waiting time for transplant, in days. Becausethis variable has a very large variation, a log transform is applied to stabilize the format;value DiseaseGroup 1='ALL'2='AML-Low Risk'3='AML-High Risk';data bmt;input Group T Status WaitTime @@;logWaittime=log(WaitTime);format Group DiseaseGroup.;datalines;1 2081 0 98 1 1602 0 1720 1 1496 0 127 1 1462 0 1681 1433 0 93 1 1377 0 2187 1 1330 0 1006 1 996 0 13191 226 0 208 1 1199 0 174 1 1111 0 236 1 530 0 1511 1182 0 203 1 1167 0 191 1 418 2 110 1 383 1 8241 276 2 146 1 104 1 85 1 609 1 187 1 172 2 1291 487 2 128 1 662 1 84 1 194 2 329 1 230 1 1471 526 2 943 1 122 2 2616 1 129 1 937 1 74 1 3031 122 1 170 1 86 2 239 1 466 2 508 1 192 1 741 109 1 393 1 55 1 331 1 1 2 196 1 107 2 1781 110 1 361 1 332 2 834 2 2569 0 270 2 2506 0 602 2409 0 120 2 2218 0 60 2 1857 0 90 2 1829 0 2102 1562 0 90 2 1470 0 240 2 1363 0 90 2 1030 0 2102 860 0 180 2 1258 0

9 180 2 2246 0 105 2 1870 0 2252 1799 0 120 2 1709 0 90 2 1674 0 60 2 1568 0 902 1527 0 450 2 1324 0 75 2 957 0 90 2 932 0 602 847 0 75 2 848 0 180 2 1850 0 180 2 1843 0 2702 1535 0 180 2 1447 0 150 2 1384 0 120 2 414 2 1202 2204 2 60 2 1063 2 270 2 481 2 90 2 105 2 1202 641 2 90 2 390 2 120 2 288 2 90 2 421 1 902 79 2 90 2 748 1 60 2 486 1 120 2 48 2 1502 272 1 120 2 1074 2 150 2 381 1 120 2 10 2 2402 53 2 180 2 80 2 150 2 35 2 150 2 248 1 302 704 2 105 2 211 1 90 2 219 1 120 2 606 1 2103 2640 0 750 3 2430 0 24 3 2252 0 120 3 2140 0 2103 2133 0 240 3 1238 0 240 3 1631 0 690 3 2024 0 1053 1345 0 120 3 1136 0 900 3 845 0 210 3 422 1 2103 162 2 300 3 84 1 105 3 100 1 210 3 2 2 753 47 1 90 3 242 1 180 3 456 1 630 3 268 1 1803 318 2 300 3 32 1 90 3 467 1 120 3 47 1 1353 390 1 210 3 183 2 120 3 105 2 150 3 115 1 2703 164 2 285 3 93 1 240 3 120 1 510 3 80 2 7803 677 2 150 3 64 1 180 3 168 2 150 3 74 2 7503 16 2 180 3 157 1 180 3 625 1 150 3 48 1 2103 273 1 240 3 63 2 360 3 76 1 330 3 113 1 2403 363 2 180;To study the occurrence of relapse, you can estimate the cumulative incidence function of each disease , you can use Gray s (1988) test to compare the disease groups.

10 However, if you also want to adjust forsome concomitant variables, such as the effect of the waiting time for transplant, you need to perform a regressionanalysis. The next two sections show how to use the PHREG procedure to fit the standard Cox model , the Cause-Specific Cox models, and the Fine and Gray model to the Competing - Risks COX REGRESSIONS uppose a random sample ofnsubjects is collected. For theith subject,iD1;:::;n, letXi, i, andZibe theobserved time, cause of failure, and covariate vector at timet, respectively. Assume thatKcauses of failure areobservable ( i2f1;:::;Kg); D0indicates a censored Competing - Risks data, it is always possible to fit a standard Cox regression model to the overall hazard disregarding the different event types. This is sometimes referred to as a composite endpointanalysis (Wolbers et al. 2014), and it is still widely used in many applications, especially for studying event-free survivalin clinical cox proportional hazards model 0 the baseline hazard function and the vector represents the covariate regression coefficients are obtained by maximizing the partial likelihoodL.