SAS PROC LIFETEST KAPLAN MEIER PLOT
Below we demonstrate a simple model in proc phreg , where we determine the effects of a categorical predictor, gender, and a continuous predictor, age on the hazard rate:. We could test for different age effects with an interaction term between gender and age. It is important to note that the survival probabilities listed in the Survival column are unconditional , and are to be interpreted as the probability of surviving from the beginning of follow up time up to the number days in the LENFOL column. We, as researchers, might be interested in exploring the effects of being hospitalized on the hazard rate. Plots of the covariate versus martingale residuals can help us get an idea of what the functional from might be. It appears the probability of surviving beyond days is a little less than 0. Nevertheless, the bmi graph at the top right above does not look particularly random, as again we have large positive residuals at low bmi values and smaller negative residuals at higher bmi values.
From the plot we can see that the hazard function indeed appears higher at the beginning of follow-up time and then decreases until it levels off at around days and stays low and mostly constant. Suppose that you suspect that the survival function is not the same among some of the groups in your study some groups tend to fail more quickly than others. One can also use non-parametric methods to test for equality of the survival function among groups in the following manner:. Introduction Survival analysis models factors that influence the time to an event. The solid lines represent the observed cumulative residuals, while dotted lines represent 20 simulated sets of residuals expected under the null hypothesis that the model is correctly specified. The estimated hazard ratio of. The terms event and failure are used interchangeably in this seminar, as are time to event and failure time. It is possible that the relationship with time is not linear, so we should check other functional forms of time, such as log time and rank time.
In the output we find three Chi-square based tests of the equality of the survival function over strata, which support our suspicion that survival differs between genders. In such cases, the correct form may be inferred from the plot of the observed pattern. Using the assess statement to check functional form is very simple:. SAS omits them lifetset remind you that the hazard ratios corresponding to these effects depend on other variables in the model. None of the graphs look particularly alarming click here to see an alarming graph in the SAS kapoan on assess.
Survival Estimate Plot with PROC LIFETEST :: SAS/STAT(R) User’s Guide
Below, we show how to use the hazardratio statement to request that SAS estimate 3 hazard ratios at specific levels of our covariates. Plots of the covariate versus martingale residuals can help us get an idea of what the functional from might be.
Notice the creation of start and stop variables, which denote the beginning and end intervals defined by hospitalization and death or censoring. Therneau and colleagues show that the smooth of a scatter plot of the martingale residuals from a null model no covariates at all versus each covariate individually will often approximate the correct functional form of a covariate. First, there may be one row of data per subject, with one outcome variable representing the time to event, one variable that codes prod whether the event occurred or not censoredand explanatory variables of interest, each with fixed values across follow up time.
The survival function is undefined past this final interval at days. Density functions are essentially histograms comprised of bins of vanishingly small widths. In the code below, we show how to obtain a table and graph of the Kaplan-Meier estimator of the survival function from proc meie.
We will model a time-varying covariate later in the seminar. Constant multiplicative changes in the hazard rate may instead be associated with constant multiplicative, rather than additive, changes in the covariate, and might meidr this relationship:. For example, patients in the WHAS dataset are in the hospital at the beginnig of follow-up time, which is defined by hospital admission after heart attack.
In regression models for survival analysis, we attempt to estimate parameters which describe the relationship between our predictors and the hazard rate. Standard nonparametric techniques do not typically estimate the hazard function directly. To specify a Cox model with start and stop times for each interval, due to the usage of time-varying covariates, we need to specify the start and top time in the model statement:.
The above relationship between the cdf and pdf also implies:. In a nutshell, these statistics sum the weighted differences between the observed number of failures and the expected number of failures for each stratum at each timepoint, assuming the same survival function of each stratum.
Here, we would like to introdue two types of interaction:. This was the primary reference used for this seminar. As time progresses, the Survival function proceeds towards it minimum, while the cumulative hazard function proceeds to its maximum.
In pot words, if all strata have the same survival function, then we expect the same proportion to die in each interval. Graphs of the Kaplan-Meier estimate of the survival function allow us to see how the survival function changes over time and are fortunately very easy to generate in SAS:. Below is an example of obtaining a kernel-smoothed estimate of the hazard function across BMI strata with a bandwidth of days:.
Important distributions in survival analysis Understanding the mechanics behind survival analysis is aided by facility with the distributions used, which can be derived from the probability density function and cumulative density functions of survival times. Many, but not all, patients leave the hospital before dying, and the length of stay in the hospital is recorded in the variable los.
Here are the steps we will take to evaluate the proportional hazards assumption for age through scaled Schoenfeld residuals:.
Statistical Graphics Using ODS
It appears that being in the hospital increases the hazard rate, but this szs probably due to the fact that all patients were in the hospital immediately after heart attack, when they presumbly are most vulnerable.
We see that the uncoditional probability of surviving beyond days is.
Below we demonstrate use of the assess statement to the functional form of the covariates. However, it is quite possible that the hazard rate and the covariates do not have such a loglinear relationship.
Thus, both genders accumulate the risk for death with age, but females accumulate risk more slowly. These statement essentially look like data step statements, and function in the same way.
Alternatively, the data can be expanded in a data step, but this can be tedious and prone to errors although instructive, on the other hand. Significant departures from random error would suggest model misspecification.
Introduction to Survival Analysis in SAS
For such studies, a semi-parametric model, in which we estimate regression parameters as covariate effects but ignore leave unspecified the dependence on lifrtest, is appropriate.
As we have seen before, the hazard appears to be greatest at the beginning of follow-up time and then rapidly declines and finally levels off. Click here to download the dataset used in this seminar.
Above we see the table of Kaplan-Meier estimates of the survival function produced by proc lifetest. We, as researchers, might be interested in exploring the effects of being hospitalized kapaln the hazard rate. Survival analysis models factors that influence the time to an event. One can also use non-parametric methods to test for equality of the survival function among groups in the following manner:.
Additionally, another variable counts the number of events occurring in each interval either 0 or 1 in Cox regression, same as the censoring variable.
In the graph above we see the ilfetest between pdfs and histograms. The outcome prof this study. Most of the variables are at least slightly correlated with the other variables.
With such data, each subject can be represented by one row of data, as each covariate only mwier only value. In the case of categorical covariates, graphs of the Kaplan-Meier estimates of the survival function provide quick and easy checks of proportional hazards.
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