An Overview of Survival Analysis using Complex Sample Data

This paper presents practical guidance on conducting survival analysis using data derived from a complex sample survey. Survival curves, Cox models, and discrete-time logistic regression are demonstrated through use of PROC LIFETEST, PROC SGPLOT, PROC SURVEYPHREG and PROC SURVEYLOGISTIC. The analytic techniques presented can be used on any operating system and are intended for an intermediate level audience. INTRODUCTION The primary objective of this paper is to provide guidance for the analyst performing survival analysis using SAS® v9.2 with complex sample data. A short overview of survival analysis including theoretical background on time to event techniques is presented along with an introduction to analysis of complex sample data. These introductory sections are followed by a typical analytic progression of descriptive and inferential survival analyses using appropriate SAS SURVEY procedures. The analysis examples include survival curves using the Kaplan-Meier method and regression models predicting onset of the event of interest using common covariates such as age at interview, race/ethnicity and gender. Cox Proportional Hazards and discrete-time logistic regression models are demonstrated and contrasted. The descriptive examples focus on the use of PROC LIFETEST with ODS graphics to produce survival plots as well as plot generation using PROC SGPLOT with an output data set from the LIFETEST procedure. The modeling examples demonstrate the use of PROC SURVEYPHREG and PROC SURVEYLOGISTIC with selected options such as reference category specification, estimate and class statements, and model link options. Where possible, the analysis examples include use of the survey design variables and weights to correctly account for the complex sample design. OVERVIEW OF SURVIVAL ANALYSIS EVENT HISTORY DATA Event history data is common in many disciplines and at its core, is focused on time. Analysis of event history data or survival analysis is used to refer to a statistical analysis of the time at which the event of interest occurs (Kalbfleisch and Prentice, 2002 and Allison, 1995). Event history data can be categorized into broad categories: 1. longitudinal data, 2. administrative follow-up data, and 3. retrospective event history data. Longitudinal data is prospectively collected on individuals followed over time. One example is the Panel Study for Income Dynamics, an ongoing US panel study focused on income dynamics and related topics (http://psidonline.isr.umich.edu/). Administrative follow-up data comes from a study that collects administrative records and additional survey data for a sample of respondents and then prospectively follows those individuals to a key event such as death by linking to another data source. An example of this type of data might be a medical claims data set that is linked to a mortality data set using respondent Social Security Numbers. The linked files would provide an opportunity to study time to death using a survival analysis approach. An example of this type data is the NHANES III linked mortality file (http://cdc.gov/nchs/data/datalinkage). The third category is retrospective event history data where respondents are asked to recall details about an event of interest which occurred at some point in the past. An example of this type of data is the National Comorbidity SurveyReplication survey (http://www.hcp.med.harvard.edu/ncs/) which contains retrospective data on mental illness and related physical conditions. FEATURES OF SURVIVAL ANALYSIS Survival analysis centers on analysis of time to an event of interest, denoted as (T), given the event occurred, or time to censoring, denoted as (C). If an individual is right censored, the respondent does not experience the event of interest before follow-up ends and it is unknown if the event occurs after censoring. Left censoring means that followup began after the beginning of data collection. See Figure 1 for a graphic presentation of the common types of timelines. Time and censoring are key pieces of information used in statistical analysis of event history data. Statistics and Data Analysis SAS Global Forum 2011