# proc lifetest plots

The covariate effect of $$x$$, then is the ratio between these two hazard rates, or a hazard ratio(HR): $HR = \frac{h(t|x_2)}{h(t|x_1)} = \frac{h_0(t)exp(x_2\beta_x)}{h_0(t)exp(x_1\beta_x)}$. In such a case, PROC LIFETEST creates a plot of the cumulative incidence function (CIF) estimates. The estimate of survival beyond 3 days based off this Nelson-Aalen estimate of the cumulative hazard would then be $$\hat S(3) = exp(-0.0385) = 0.9623$$. One way to fix this would with the usage of annotation. Perform search. If the observed pattern differs significantly from the simulated patterns, we reject the null hypothesis that the model is correctly specified, and conclude that the model should be modified. run; proc corr data = whas500 plots(maxpoints=none)=matrix(histogram); Finally, we see that the hazard ratio describing a 5-unit increase in bmi, $$\frac{HR(bmi+5)}{HR(bmi)}$$, increases with bmi. Most of the variables are at least slightly correlated with the other variables. Note: A number of sub-sections are titled Background. However, one cannot test whether the stratifying variable itself affects the hazard rate significantly. The censoring information above the X axis is moved outside the graph. Chapter 22, Any serious endeavor into data analysis should begin with data exploration, in which the researcher becomes familiar with the distributions and typical values of each variable individually, as well as relationships between pairs or sets of variables.     refline 0 / axis=x; However, some customization can be achieved without any annotation by using some additional statements and options. The Subjects at Risk table is shown closer to the survival curves using the LOCATION=INSIDE option. It is not at all necessary that the hazard function stay constant for the above interpretation of the cumulative hazard function to hold, but for illustrative purposes it is easier to calculate the expected number of failures since integration is not needed. During the next interval, spanning from 1 day to just before 2 days, 8 people died, indicated by 8 rows of “LENFOL”=1.00 and by “Observed Events”=8 in the last row where “LENFOL”=1.00. run; The Kaplan_Meier survival function estimator is calculated as: $\hat S(t)=\prod_{t_i\leq t}\frac{n_i – d_i}{n_i},$. Thanks for your suggestion.     xaxistable atrisk / x=tatrisk class=stratum colorgroup=stratum valueattrs=(weight=bold); Additionally, a few heavily influential points may be causing nonproportional hazards to be detected, so it is important to use graphical methods to ensure this is not the case. The survival function is undefined past this final interval at 2358 days. Particular emphasis is given to proc lifetest for nonparametric estimation, and proc phreg for Cox regression and model evaluation. If no options are requested, PROC LIFETEST computes and displays the product-limit estimate of the survivor function; and if an ods graphics on statement is specified, a plot of the estimated survivor function is also displayed. scatter x = hr y=dfhr / markerchar=id; run; proc phreg data = whas500; class gender; These are indeed censored observations, further indicated by the “*” appearing in the unlabeled second column. PROC LIFETEST data=test1dts outsurv=_surv alphaqt=0.05 ties=EFRON plot=(s); time pfstm*pfscen(1); strata treatment; Run; See Figure 1.Sample Kaplan-Meier Curve (Note – Adding the option plot=(s) with create a simple Kaplan-Meier Curve.) SGPLOT code for Survival Graph:  SG_Survival_Plot. Provided the reader has some background in survival analysis, these sections are not necessary to understand how to run survival analysis in SAS. Customizing Survival Plots in In such cases, the correct form may be inferred from the plot of the observed pattern. While a user may get different mileage from the results, this exercise will show you how you can use such statements and options creatively to get different results. The same procedure could be repeated to check all covariates. Trending. We generally expect the hazard rate to change smoothly (if it changes) over time, rather than jump around haphazardly. To do so: It appears that being in the hospital increases the hazard rate, but this is probably due to the fact that all patients were in the hospital immediately after heart attack, when they presumbly are most vulnerable. Data that are structured in the first, single-row way can be modified to be structured like the second, multi-row way, but the reverse is typically not true. We could test for different age effects with an interaction term between gender and age. 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). where $$d_i$$ is the number who failed out of $$n_i$$ at risk in interval $$t_i$$. It appears that for males the log hazard rate increases with each year of age by 0.07086, and this AGE effect is significant, AGE*GENDER term is negative, which means for females, the change in the log hazard rate per year of age is 0.07086-0.02925=0.04161.     keylegend 's' / linelength=20; model lenfol*fstat(0) = gender age;; run; ; See the section Modifying the Layout and Adding a New Inset Table in Here we use proc lifetest to graph $$S(t)$$. Unless the seed option is specified, these sets will be different each time proc phreg is run. run; proc lifetest data=whas500 atrisk outs=outwhas500; Let’s interpret our model. Enabling ODS Graphics and the Default Kaplan-Meier Plot Tree level 6. However, nonparametric methods do not model the hazard rate directly nor do they estimate the magnitude of the effects of covariates. Re: How to change X axis in CIF plot (either in proc lifetest or proc phreg)? Posted 07-19-2018 04:55 PM (2127 views) | In reply to Reeza Thanks - I was playing with your old code before I knew what I was doing and I think I changed it already so I do not have the original template. Plots of the covariate versus martingale residuals can help us get an idea of what the functional from might be. The changed syntax is highlighted in the code. ODS Graphics Template Modification. 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: The step function form of the survival function is apparent in the graph of the Kaplan-Meier estimate. Thus far in this seminar we have only dealt with covariates with values fixed across follow up time. We can similarly calculate the joint probability of observing each of the $$n$$ subject’s failure times, or the likelihood of the failure times, as a function of the regression parameters, $$\beta$$, given the subject’s covariates values $$x_j$$: $L(\beta) = \prod_{j=1}^{n} \Bigg\lbrace\frac{exp(x_j\beta)}{\sum_{iin R_j}exp(x_i\beta)}\Bigg\rbrace$. I want to remove the frame of the survival curve in the topright corner. Notice in the Analysis of Maximum Likelihood Estimates table above that the Hazard Ratio entries for terms involved in interactions are left empty. These two observations, id=89 and id=112, have very low but not unreasonable bmi scores, 15.9 and 14.8. For example, if $$\beta_x$$ is 0.5, each unit increase in $$x$$ will cause a ~65% increase in the hazard rate, whether X is increasing from 0 to 1 or from 99 to 100, as $$HR = exp(0.5(1)) = 1.6487$$. Once outliers are identified, we then decide whether to keep the observation or throw it out, because perhaps the data may have been entered in error or the observation is not particularly representative of the population of interest. On the right panel, “Residuals at Specified Smooths for martingale”, are the smoothed residual plots, all of which appear to have no structure. In the code below, we show how to obtain a table and graph of the Kaplan-Meier estimator of the survival function from proc lifetest: Above we see the table of Kaplan-Meier estimates of the survival function produced by proc lifetest. proc loess data = residuals plots=ResidualsBySmooth(smooth); Because of this parameterization, covariate effects are multiplicative rather than additive and are expressed as hazard ratios, rather than hazard differences. Currently loaded videos are … if lenfol > los then in_hosp = 0; where $$R_j$$ is the set of subjects still at risk at time $$t_j$$. run; proc phreg data=whas500 plots=survival; The corresponding tests are known as the log-rank test and the Wilcoxon test, respectively. title2 h=0.8 'With Number of Subjects at Risk'; Without this offset, long values in the table may get clipped. The template that PROC LIFETEST is using is the Graph template that you see when you run ODS TRACE. 1469-82. See the section Displaying Survival Summary Statistics in The WHAS500 data are stuctured this way. Note: The terms event and failure are used interchangeably in this seminar, as are time to event and failure time. In the code below, we model the effects of hospitalization on the hazard rate. This confidence band is calculated for the entire survival function, and at any given interval must be wider than the pointwise confidence interval (the confidence interval around a single interval) to ensure that 95% of all pointwise confidence intervals are contained within this band. However, we have decided that there covariate scores are reasonable so we retain them in the model. This analysis proceeds in much the same was as dfbeta analysis, in that we will: We see the same 2 outliers we identifed before, id=89 and id=112, as having the largest influence on the model overall, probably primarily through their effects on the bmi coefficient. If ODS Graphics is enabled, PROC LIFETEST also displays a plot of the estimated survivor function. Hosmer, DW, Lemeshow, S, May S. (2008). Only as many residuals are output as names are supplied on the, We should check for non-linear relationships with time, so we include a, As before with checking functional forms, we list all the variables for which we would like to assess the proportional hazards assumption after the.     scatter x=time y=censored / markerattrs=(symbol=plus) name='c'; In this model, this reference curve is for males at age 69.845947 Usually, we are interested in comparing survival functions between groups, so we will need to provide SAS with some additional instructions to get these graphs.