Surviving Survival Analysis – An Applied Introduction

1 ST-1471 Surviving Survival Analysis An Applied IntroductionChristianna S. Williams, abt associates inc , Durham, NCABSTRACTBy incorporating time-to -event information, Survival Analysis can be more powerful than simply examiningwhether or not an endpoint ofinterest occurs, and it has the added benefit of accounting for censoring,thus allowing inclusion of individuals who leave the study early. This tutorial-style presentation will gothrough the basics of Survival Analysis , starting withdefining key variables,examining and comparingsurvival curves using PROC LIFETEST and leading intoa brief Introduction toestimating Cox regressionmodels using PROC PHREG. The evaluation of the proportional hazards assumption and coding of time-dependent covariates will also be explained. The emphasis will be on application, not theory, but pitfallsthe analyst must watch out for will be covered.

2 Examples will be taken from real-world data from healthresearch, and some features newly available in SAS will be speaking, Survival Analysis is a set of statistical methods for examining not only eventoccurrencebut also thetimingof events. These methods were developed for studying death hence the namesurvival Analysis and havebeen used extensively for that purpose; however, theyhave beensuccessfullyapplied to many different kinds of events, across a range of disciplines. Examples includemanufacturing or engineering:how long it takes widgets to fail; meteorology: when will the next hurricanebehit the North Carolina coast; social: what determines how long a marriage will last; financial: the timingof stock market drops the list goes other names are used to refer to this class ofmethods such as eventhistory Analysis , or failure time Analysis or transition Analysis , but many of thebasic techniques are the same as is the underlying idea understanding the pattern of events in time andwhat factors are associated with when those events course, books have been written on this topic a couple are even listed at the end of this paper andI have neither the time, nor the space nor the competence to describe all aspects of Survival Analysis or even all the SAS Survival Analysis , this paper is not intended to explain thestatistical underpinnings of Survival Analysis .

3 Rather, it is my intent to go through the Analysis of one setof data in some detail, covering many of the basic concepts and SAS methods that theprogrammer/analyst needs to know. I want to give you an intuitive sense of how some basic survivalanalysis techniques work, and how to write the SAS code to implement them. Also, the last few releasesof SAS, including , have some great new features for the Survival Analysis procedures I will give youa taste of those too. The specific topics to be covered include: Creating the Survival time and censoring variables the good old DATA step; A fairly detailed treatment ofKaplan-Meier survivalcurves; overall and stratified, as implementedin PROC LIFETEST; and A brief Introduction toCox Proportional hazard models(PROC PHREG), includinga fewcomments onproportionalityand the coding of time-dependent ll also be upfront about some of the topics I am not going to cover.

4 I m not going to give more than apassing mention to the following:parametric Survival Analysis ( PROC LIFEREG), recurrent events,leftor intervalcensoring, Bayesian methods. Many of the more advanced features in PHREG will alsonot be am also not going to talk about ODS graphics with respect to Iencourage you to explore!GETTING STARTEDA schematic depiction of simple Survival data for six subjects is shown in Figure 1. In this figure,allsubjects start their Survival time at the same point the study baseline. Further, we assume that eachperson can have the event only once. Three of the six patients (lines ending in solid circles-- #1,3, and6) have an event , and we can ascertain how long each of them was in the study prior to their event their Survival time .As noted abovethe event may be death, but it can also be any other endpoint ofinterest, where we can measure the date of onset.

5 In the study from which the examplesin this paper willbe drawn, the outcome event of interest is nursing home the Figure, there also 3 subjects (#2, 4 and 5) who do not have an event at least notwhile they are inthe study. Subject #5 is theonly one who completed the entire study without having an event. Incontrast,two of the cases (open circles, #2 and 4) are lost to the study before having an event and beforethe study follow-up ends; they are said to becensored. Actually, #5 is censored also in this context,censoring simply means that at the end of a given individual s follow-up (whether that was early or at theend of the study), he/she had not had the event of things can cause censoring,depending on the study design. It may be that these study participants decided they did not want tocontinue in the study, and so all we know is that at the time they left the study, they had not yet had theevent of interest.

6 If our event of interest isnotdeath, then itmay be that censoring is caused by death again, we know that at the time we stopped following that person ( when she died), she had not hadthe event of as notedabove, peoplewho have not had the event when all follow-up ends forallsubjects, are also censored. We can view this as a special type of censoring, because everyone whohas not had the event or already been censored for some other reason, is censored at this of the appeals of Survival Analysis techniques is thatwe can include data(including information oncovariates or independent variables of interest, such as treatment status)fromsubjects who are censored(either by drop-out, death, or some other competing event) up to the time that they are censored. Forexample, in this hypothetical study, if we were only recording whether or not a person had the event ofinterest during the full study period our dependent variable was a dichotomous yes/no then wemight well have to completely drop cases #2 and 4because we don t know whether or not they had anevent during the full time window of the study.

7 Additionally, of course, Survival Analysis allows us toexamine not just whether an event occurred but how long it took to occur, which can also addconsiderable power to a study, particularly ifthe study is evaluatinga treatment designed to delay (butpossibly not prevent entirely) some undesired BRIEF INTRO TO THEEXAMPLE DATAThe study from which the example data for this paperare drawn was alongitudinal observational study ofthe association between eldermistreatmentand nursing home mistreatment includesphysical or psychological abuse, as well as neglect by a responsible caregiver, and the study alsoevaluated self-neglect , the term for the situation where an older person in the community, is failing toadequately take care of him or research question was whether or notmistreated or self-neglectingolder adultswere more likelyto be admitted to a nursinghome or be admitted to nursinghomes sooner--thanolder adults who were not identified as being mistreated or self-neglecting.

8 EndofstudyStartofstudyTime= drop-out /censored= event123456 Figure 1. Hypothetical Survival data for six patients. See text for further for other factors that might increase risk of nursing home placement. The study populationwas a cohort ofabout2,800 persons 65 and older living in New Haven, connecticut who enrolled in alargestudy of aging in 1982. These persons were interviewed approximately every year for twelve years,from which we obtained data on a large number of risk factors for nursing home placement, such associal support, cognitive status and functional ability ( ability to prepare meals, bath and dressoneself).To obtain information on elder mistreatment, nursing home placement and mortality, weconducted a record linkage tothreeother data sources:(1)Adult Protective Servicesrecords--todetermine if (and when) each person had been the victim of elder mistreatmentor was identified as self-neglecting; (2) the connecticut Long-term Care Registry-- to determine if (and when) each person hadbeen admitted to a nursing home; and(3) death records to determine if and when the person had records covered the time period of the , in this study, we have the timing of the outcome events, the timing of censorship, and indeed ourmain independent variable of interestchanges over time ( time-dependent).

9 Specifically, atbaseline,none of the participants had been reported to protective services those that were so reportedduring the study, thus became exposed at different times, which is a key feature of the , for this paper,the purpose of which is mainly toteach about Survival Analysis using SAS, I haveleft out lots of study details and am not focusing on the findings; for more information about the real study,see(Lachs, Williams et al. 1997; Lachs, Williams et al. 1998; Lachs, Williams et al. 2002)and(Foley,Ostfeld et al. 1992).FIRST STEP CONSTRUCTSURVIVAL TIME AND CENSORING VARIABLESB efore we can do any Survival Analysis , we need to make surethat our data are structured appropriatelyand thatwe have constructed the needed variables for our outcome which are the Survival time variableand thecensoring variable.

10 We need to construct these variables for every case in the data set, whetheror not the person has the event of interestor iscensored. Let s give a conceptual definition of each ofthese, before we dive into SAS code: Survival time for an individual subject,timefrom study start (that is, when we started observingthis person for an event) to when one of three things that if more than one of thesethings happens, we will choose the earliest. Also note that time canbe measured in any units( days, months or even years in some laboratory studies it might be hours or minutes), butfor the methods described in this paper, it needs to be essentially continuous because it is veryimportant that we be able toorderevents precisely, and if time is too crudely measured, there willbe lots of tied Survival times, which can cause has the event of has some other event that makes him/her no longer at risk for the event thiscould be dropping out of the study or having some other event ( death)