Suppose it is of interest to test the null hypothesis that cell means ABC121 and ABC212 are equal that is, H0: 121 - 212 = 0. In other words, we would expect to find a lot of failure times in a given time interval if 1) the hazard rate is high and 2) there are still a lot of subjects at-risk. In PROC GENMOD or PROC GLIMMIX, use the EXP option in the ESTIMATE statement. 2009 by SAS Institute Inc., Cary, NC, USA. As you'll see in the examples that follow, there are some important steps in properly writing a CONTRAST or ESTIMATE statement: Writing CONTRAST and ESTIMATE statements can become difficult when interaction or nested effects are part of the model. In the CONTRAST statement, the rows of L are separated by commas. fixed. Survival analysis models factors that influence the time to an event. Therneau and colleagues(1990) 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. The first element is the estimate of the intercept, . SAS provides built-in methods for evaluating the functional form of covariates through its assess statement. i am wondering either i add "CLASS" statement ornot. On the right panel, Residuals at Specified Smooths for martingale, are the smoothed residual plots, all of which appear to have no structure. run; model (start, stop)*status(0) = in_hosp ; class gender; In large datasets, very small departures from proportional hazards can be detected. Notice that the interval during which the first 25% of the population is expected to fail, [0,297) is much shorter than the interval during which the second 25% of the population is expected to fail, [297,1671). INTRODUCTION The PROC LIFEREG and the PROC PHREG procedures both can do survival analysis using time-to-event data, . Additionally, another variable counts the number of events occurring in each interval (either 0 or 1 in Cox regression, same as the censoring variable). We can remove the dependence of the hazard rate on time by expressing the hazard rate as a product of \(h_0(t)\), a baseline hazard rate which describes the hazard rates dependence on time alone, and \(r(x,\beta_x)\), which describes the hazard rates dependence on the other \(x\) covariates: In this parameterization, \(h(t)\) will equal \(h_0(t)\) when \(r(x,\beta_x) = 1\). The surface where the smoothing parameter=0.2 appears to be overfit and jagged, and such a shape would be difficult to model. run; proc phreg data = whas500; However, we have decided that there covariate scores are reasonable so we retain them in the model. However, it can happen (and it did in your example) that the CLASS statement uses level '1' of that explanatory variable as the reference level so that the sign of the corresponding parameter estimate changes and the inverse hazard ratio and confidence limits are computed,here: the hazard ratio of "no exposure" vs. Thus, we again feel justified in our choice of modeling a quadratic effect of bmi. The coefficients for the mean estimates of AB11 and AB12 are again determined by writing them in terms of the model. 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). which has three levels. Estimating and Testing Odds Ratios with Effects Coding. These provide some statistical background for survival analysis for the interested reader (and for the author of the seminar!). The problem is greatly simplified using effects coding, which is available in some procedures via the PARAM=EFFECT option in the CLASS statement. This coding scheme is used by default by PROC CATMOD and PROC LOGISTIC and can be specified in these and some other procedures such as PROC GENMOD with the PARAM=EFFECT option in the CLASS statement. First, write the model, being sure to verify its parameters and their order from the procedure's displayed results: Now write each part of the contrast in terms of the effects-coded model (3e). This example shows the use of the CONTRAST and ODDSRATIO statements to compare the response at two levels of a continuous predictor when the model contains a higher-order effect. You can use the same method of writing the AB12 cell mean in terms of the model: You can write the average of cell means in terms of the model: So, the coefficient for the A parameters is 1/2; for B it is 1/3; and for AB it is 1/6. ESSENTIAL STEPS in using PROC PHREG. assess var=(age bmi hr) / resample; For example, if there were three subjects still at risk at time \(t_j\), the probability of observing subject 2 fail at time \(t_j\) would be: \[Pr(subject=2|failure=t_j)=\frac{h(t_j|x_2)}{h(t_j|x_1)+h(t_j|x_2)+h(t_j|x_3)}\]. We write the null hypothesis this way: The following table summarizes the data within the complicated diagnosis: The odds ratio can be computed from the data as: This means that, when the diagnosis is complicated, the odds of being cured by treatment A are 1.8845 times the odds of being cured by treatment C. The following statements display the table above and compute the odds ratio: To estimate and test this same contrast of log odds using model 3c, follow the same process as in Example 1 to obtain the contrast coefficients that are needed in the CONTRAST or ESTIMATE statement. Phreg For Survival Analysis In Sas 9 has been minimal coverage in the available literature to9 guide researchers, practitioners, and students who wish to apply these methods to health-related areas of study. 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. This matches closely with the Kaplan Meier product-limit estimate of survival beyond 3 days of 0.9620. run; proc corr data = whas500 plots(maxpoints=none)=matrix(histogram); However, this is something that cannot be estimated with the ODDSRATIO statement which only compares odds of levels of a specified variable. The basic idea is that martingale residuals can be grouped cumulatively either by follow up time and/or by covariate value. We previously saw that the gender effect was modest, and it appears that for ages 40 and up, which are the ages of patients in our dataset, the hazard rates do not differ by gender. By default, PLMAXITER=25. The following statements show all five ways of computing and testing this contrast. Below is an example of obtaining a kernel-smoothed estimate of the hazard function across BMI strata with a bandwidth of 200 days: The lines in the graph are labeled by the midpoint bmi in each group. Because log odds are being modeled instead of means, we talk about estimating or testing contrasts of log odds rather than means as in PROC MIXED or PROC GLM. From these equations we can also see that we would expect the pdf, \(f(t)\), to be high when \(h(t)\) the hazard rate is high (the beginning, in this study) and when the cumulative hazard \(H(t)\) is low (the beginning, for all studies). The above relationship between the cdf and pdf also implies: In SAS, we can graph an estimate of the cdf using proc univariate. As expected, the results show that there is no significant interaction (p=0.3129) or that the reduced model fits as well as the saturated model. specifies that both the contrast and the exponentiated contrast be estimated. Nonparametric methods provide simple and quick looks at the survival experience, and the Cox proportional hazards regression model remains the dominant analysis method. specifies which differences to consider for the level comparisons of a CLASS variable. We request Cox regression through proc phreg in SAS. Estimates are formed as linear estimable functions of the form . proc phreg data=event; run; proc phreg data = whas500; Estimating and Testing Odds Ratios with Dummy Coding Estimating and Testing a Difference of Means So, this test can be used with models that are fit by many procedures such as GENMOD, LOGISTIC, MIXED, GLIMMIX, PHREG, PROBIT, and others, but there are cases with some of these procedures in which a LR test cannot be constructed: Nonnested models can still be compared using information criteria such as AIC, AICC, and BIC (also called SC). The Analysis of Maximum Likelihood Estimates table confirms the ordering of design variables in model 3d. The partial results shown below suggest that interactions are not needed in the model: The simpler main-effects-only model can be fit by restricting the parameters for the interactions in the above model to zero. One caveat is that this method for determining functional form is less reliable when covariates are correlated. \[f(t) = h(t)exp(-H(t))\]. A simple transformation of the cumulative distribution function produces the survival function, \(S(t)\): The survivor function, \(S(t)\), describes the probability of surviving past time \(t\), or \(Pr(Time > t)\). This note focuses on assessing the effects of categorical (CLASS) variables in models containing interactions. =2. An ESTIMATE statement for the AB11 cell mean can be written as above by rewriting the cell mean in terms of the model yielding the appropriate linear combination of parameter estimates. Table 64.4 summarizes important options in the ESTIMATE statement. Suppose A has two levels and B has three levels and you want to test if the AB12 cell mean is different from the average of all six cell means. In an example from Ries and Smith (1963), the choice of detergent brand (Brand= M or X) is related to three other categorical variables: the softness of the laundry water (Softness= soft, medium, or hard); the temperature of the water (Temperature= high or low); and whether the subject was a previous user of Brand M (Previous= yes or no). Specifically, PROC LOGISTIC is used to fit a logistic model containing effects X and X2. model lenfol*fstat(0) = gender|age bmi|bmi hr in_hosp ; This simpler model is nested in the above model. The hazard function for a particular time interval gives the probability that the subject will fail in that interval, given that the subject has not failed up to that point in time. Specifically, you need to construct the linear combination of model parameters that corresponds to the hypothesis. The EXP option exponentiates each difference providing odds ratio estimates for each pair. Be careful to order the coefficients to match the order of the model parameters in the procedure. Consider the following data from Kalbeisch and Prentice (1980). To correctly specify your contrast, it is crucial to know the ordering of parameters within each effect and the variable levels associated with any parameter. All of the statements mentioned above can be used for this purpose. One can request that SAS estimate the survival function by exponentiating the negative of the Nelson-Aalen estimator, also known as the Breslow estimator, rather than by the Kaplan-Meier estimator through the method=breslow option on the proc lifetest statement. 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. Notice, however, that \(t\) does not appear in the formula for the hazard function, thus implying that in this parameterization, we do not model the hazard rates dependence on time. See the "Parameterization of PROC GLM Models" section in the PROC GLM documentation for some important details on how the design variables are created. Notice that id, the individual subject identifier, has been added to the class statement and is also on the repeated statement (with an unstructured correlation matrix), telling proc genmod to calculate the robust errors. The contrast of the ten LS-means specified in the LSMESTIMATE statement estimates and tests the difference between the AB11 and AB12 LS-means. Looking at the table of Product-Limit Survival Estimates below, for the first interval, from 1 day to just before 2 days, \(n_i\) = 500, \(d_i\) = 8, so \(\hat S(1) = \frac{500 8}{500} = 0.984\). 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