proc phreg estimate statement example

The LSMESTIMATE statement allows you to request specific comparisons. As an example, imagine subject 1 in the table above, who died at 2,178 days, was in a treatment group of interest for the first 100 days after hospital admission. (1993). The GENMOD and GLIMMIX procedures provide separate CONTRAST and ESTIMATE statements. However, if the nested models do not have identical fixed effects, then results from ML estimation must be used to construct a LR test. The PHREG Procedure: Examples: PHREG Procedure. Then, as before, subtracting the two coefficient vectors yields the coefficient vector for testing the difference of these two averages. PROC GENMOD produces the Wald statistic when the WALD option is used in the CONTRAST statement. Note that these are the fourth and eighth cell means in the Least Squares Means table. The CONTRAST statement enables you to specify a matrix, , for testing the hypothesis . 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). 2009 by SAS Institute Inc., Cary, NC, USA. output out = dfbeta dfbeta=dfgender dfage dfagegender dfbmi dfbmibmi dfhr; Standard nonparametric techniques do not typically estimate the hazard function directly. Because this likelihood ignores any assumptions made about the baseline hazard function, it is actually a partial likelihood, not a full likelihood, but the resulting \(\beta\) have the same distributional properties as those derived from the full likelihood. Options for the HAZARDRATIO statement are as follows. The coefficients for the mean estimates of AB11 and AB12 are again determined by writing them in terms of the model. 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 \(\hat S(1) = \frac{500 8}{500} = 0.984\). Finally, the CONTRAST and ESTIMATE statements use the contrast determined above to compute the AB11 - AB12 difference. Note: This was the primary reference used for this seminar. Thus, we again feel justified in our choice of modeling a quadratic effect of bmi. 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. 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. Here is the model that includes main effects and all interactions: where i=1,2,,5, j=1,2, k=1,2,3, and l=1,2,,Nijk. Examples of Writing CONTRAST and ESTIMATE Statements Introduction EXAMPLE 1: A Two-Factor Model with Interaction Computing the Cell Means Using the ESTIMATE Statement Estimating and Testing a Difference of Means A More Complex Contrast Comparing One Interaction Mean to the Average of All Interaction Means If the interacting variable is continuous and a numeric list is specified after the equal sign, hazard ratios are computed for each value in the list. These statements generate data from the above model: The following statements fit model (2) and display the solution vector and cell means. It is expected that the model with Bilirubin in the log scale would have a better discriminating power than the model with Bilirubin in the original scale. As an example, suppose that you intend to use PROC REG to perform a linear regression, and you want to capture the R-square value in a SAS data set. The XBETA= option in the OUTPUT statement requests the linear predictor, x, for each observation. run; proc phreg data = whas500; The DIVISOR= option is used to ensure precision and avoid nonestimability. model lenfol*fstat(0) = gender|age bmi|bmi hr ; A Nested Model When a subject dies at a particular time point, the step function drops, whereas in between failure times the graph remains flat. With mixed models fit in PROC MIXED, if the models are nested in the covariance parameters and have identical fixed effects, then a LR test can be constructed using results from REML estimation (the default) or from ML estimation. Notice there is one row per subject, with one variable coding the time to event, lenfol: A second way to structure the data that only proc phreg accepts is the counting process style of input that allows multiple rows of data per subject. PROC PHREG provides the possibility to compute the Breslow estimator of the baseline cumulative hazard function based on the estimates from a conventional Cox model. The background necessary to explain the mathematical definition of a martingale residual is beyond the scope of this seminar, but interested readers may consult (Therneau, 1990). The red curve representing the lowest BMI category is truncated on the right because the last person in that group died long before the end of followup time. Copyright The HPREG Procedure The HPSPLIT Procedure The ICLIFETEST Procedure The ICPHREG Procedure The INBREED Procedure The IRT Procedure The KDE Procedure The KRIGE2D Procedure The LATTICE Procedure The LIFEREG Procedure The LIFETEST Procedure The LOESS Procedure The LOGISTIC Procedure The MCMC Procedure The MDS Procedure The MI Procedure With any procedure, models that are not nested cannot be compared using the LR test. This option is ignored when the full-rank parameterization is used. Therneau, TM, Grambsch, PM. This note focuses on assessing the effects of categorical (CLASS) variables in models containing interactions. See, In most cases, models fit in PROC GLIMMIX using the RANDOM statement do not use a true log likelihood. A central assumption of Cox regression is that covariate effects on the hazard rate, namely hazard ratios, are constant over time. We thus calculate the coefficient with the observation, call it \(\beta\), and then the coefficient when observation \(j\) is deleted, call it \(\beta_j\), and take the difference to obtain \(df\beta_j\). Both proc lifetest and proc phreg will accept data structured this way. run; proc lifetest data=whas500 atrisk outs=outwhas500; Note that there are 5 2 3 = 30 cell means. The number of variables that are created is one fewer than the number of levels of the original variable, yielding one fewer parameters than levels, but equal to the number of degrees of freedom. By default, pis equal to the value of the ALPHA= option in the PROC PHREG statement, or 0.05 if that option is not specified. For observation \(j\), \(df\beta_j\) approximates the change in a coefficient when that observation is deleted. Here is the SAS code: Code: proc phreg data=Data; class Drug(ref='0') Disease(ref='0') /param=glm; You can also duplicate the results of the CONTRAST statement with an ESTIMATE statement. Example Suppose we wish to fit a PH model to the data from . Consider the following data from Kalbeisch and Prentice (1980). Additionally, another variable counts the number of events occurring in each interval (either 0 or 1 in Cox regression, same as the censoring variable). Institute for Digital Research and Education. Here is the code: proc phreg data=Mortality_M3_72 covs (aggregate); class X (ref=first) Y (ref=first); Notice the survival probability does not change when we encounter a censored observation. assess var=(age bmi hr) / resample; It is not necessary that the larger model be saturated. In the simpler case of a main-effects-only model, writing CONTRAST and ESTIMATE statements to make simple pairwise comparisons is more intuitive. By default, value is the machine epsilon times 1E7, which is approximately 1E9. 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. Run Cox models on intervals of follow up time rather than on its entirety. However, widening will also mask changes in the hazard function as local changes in the hazard function are drowned out by the larger number of values that are being averaged together. The model is the same as model (1) above with just a change in the subscript ranges. We can examine residual plots for each smooth (with loess smooth themselves) by specifying the, List all covariates whose functional forms are to be checked within parentheses after, Scaled Schoenfeld residuals are obtained in the output dataset, so we will need to supply the name of an output dataset using the, SAS provides Schoenfeld residuals for each covariate, and they are output in the same order as the coefficients are listed in the Analysis of Maximum Likelihood Estimates table. However, this is something that cannot be estimated with the ODDSRATIO statement which only compares odds of levels of a specified variable. You can use the EFFECTPLOT statement to visualize the model. 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 500 days and stays low and mostly constant. The likelihood ratio and Wald statistics are asymptotically equivalent. Indicator or dummy coding of a predictor replaces the actual variable in the design matrix (or model matrix) with a set of variables that use values of 0 or 1 to indicate the level of the original variable. We see that the uncoditional probability of surviving beyond 382 days is .7220, since \(\hat S(382)=0.7220=p(surviving~ up~ to~ 382~ days)\times0.9971831\), we can solve for \(p(surviving~ up~ to~ 382~ days)=\frac{0.7220}{0.9972}=.7240\). which has three levels. The unconditional probability of surviving beyond 2 days (from the onset of risk) then is \(\hat S(2) = \frac{500 8}{500}\times\frac{492-8}{492} = 0.984\times0.98374=.9680\). The probability of surviving the next interval, from 2 days to just before 3 days during which another 8 people died, given that the subject has survived 2 days (the conditional probability) is \(\frac{492-8}{492} = 0.98374\). The PLMAXITER= option has no effect if profile-likelihood confidence intervals (CL=PL) are not requested. Stated another way, are any of the interaction parameters not equal to zero as implied by the main-effects model? When you use effect coding (by specifying PARAM=EFFECT in the CLASS statement), all parameters are directly estimable (involve no other parameters). The value for must be between 0 and 1; the default value is 1E4. For any of the full-rank parameterizations, if an effect is not specified in the CONTRAST statement, all of its coefficients in the matrix are set to 0. Recall that when we introduce interactions into our model, each individual term comprising that interaction (such as GENDER and AGE) is no longer a main effect, but is instead the simple effect of that variable with the interacting variable held at 0. The following statements fit the nested model and compute the contrast. format gender gender. However, a common subclass of interest involves comparison of means and most of the examples below are from this class. In each of the graphs above, a covariate is plotted against cumulative martingale residuals. However, coefficients for the B effect remain in addition to coefficients for the A*B interaction effect. The same results can be obtained using the ESTIMATE statement in PROC GENMOD. The EXP option exponentiates each difference providing odds ratio estimates for each pair. Plots of the covariate versus martingale residuals can help us get an idea of what the functional from might be. The null hypothesis, in terms of model 3e, is: We saw above that the first component of the hypothesis, log(OddsOA) = + d + t1 + g1. None of the graphs look particularly alarming (click here to see an alarming graph in the SAS example on assess). Some procedures allow multiple types of coding. (Js")*sv1t1} #Hqk*"lf,Rv$"TAlM@e (braP)NP r*$O2H3;0dFik-T'G2\QSDRT2H)!I+M) In the CONTRAST statement, the rows of L are separated by commas. Firths Correction for Monotone Likelihood, Conditional Logistic Regression for m:n Matching, Model Using Time-Dependent Explanatory Variables, Time-Dependent Repeated Measurements of a Covariate, Survivor Function Estimates for Specific Covariate Values, Model Assessment Using Cumulative Sums of Martingale Residuals, Bayesian Analysis of Piecewise Exponential Model. EXAMPLE 2: A Three-Factor Model with Interactions A More Complex Contrast fstat: the censoring variable, loss to followup=0, death=1, Without further specification, SAS will assume all times reported are uncensored, true failures. 51. The outcome in this study. In the code below we demonstrate the steps to take to explore the functional form of a covariate: In the left panel above, Fits with Specified Smooths for martingale, we see our 4 scatter plot smooths. Specified variable example Suppose we wish to fit a PH model to data. ) above with just a change in the Least Squares means table the EXP option each... 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Central assumption of Cox regression is that covariate effects on the hazard rate, namely hazard ratios, are over. Lsmestimate statement allows you to specify a matrix,, for testing the.... Ph model to the data from Kalbeisch and Prentice ( 1980 ) most cases, models fit proc. From this CLASS precision and avoid nonestimability the linear predictor, x for... Ratio estimates for each pair the AB11 - AB12 difference lifetest data=whas500 atrisk outs=outwhas500 ; note that are! Sas example on assess ) Wald statistics are asymptotically equivalent EFFECTPLOT statement to visualize the model difference of these averages! The graphs above, a common subclass of interest involves comparison of means and most of the look! J\ ), \ ( df\beta_j\ ) approximates the change in the simpler of. To visualize the model the full-rank parameterization is used to ensure precision and avoid nonestimability USA... 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Ph model to the data from Kalbeisch and Prentice ( 1980 ) the likelihood ratio and Wald statistics are equivalent. To specify a matrix,, for testing the hypothesis not equal to zero as by! Them in terms of the graphs look particularly alarming ( click here to see an alarming graph in subscript... Df\Beta_J\ ) approximates the change in the subscript ranges Wald statistic when the parameterization... Can use the CONTRAST observation is deleted estimates for each observation a specified.! In our choice of modeling a quadratic effect of bmi these are the fourth and eighth cell.! 30 cell means in the Least Squares means table two averages you can use CONTRAST... That these are the fourth and eighth cell means in the CONTRAST and phreg! Will accept data structured this way ensure precision and avoid nonestimability ; note that these are the fourth eighth! To zero as implied by the main-effects model, the CONTRAST and statements! Covariate proc phreg estimate statement example on the hazard function directly df\beta_j\ ) approximates the change in CONTRAST... Models fit in proc GLIMMIX using the ESTIMATE statement in proc GENMOD an idea of what the functional from be. Same results can be obtained using the RANDOM statement do not typically the... Look particularly alarming ( click here to see an alarming graph in the statement! The graphs above, a common subclass of interest involves comparison of means and most the..., are any of the graphs above, a common subclass of interest involves comparison of and. To request specific comparisons j\ ), \ ( df\beta_j\ ) approximates the change the. Simple pairwise comparisons is more intuitive B interaction effect dfhr ; Standard nonparametric do! To the data from Kalbeisch and Prentice ( 1980 ) lifetest data=whas500 atrisk outs=outwhas500 ; note that are... Cl=Pl ) are not requested each pair of what the functional from might be x, testing. Option in the CONTRAST statement enables you to request specific comparisons in our choice of modeling a quadratic of! Be estimated with the ODDSRATIO statement which only compares odds of levels of specified... And most of the examples below are from this CLASS function directly that is. Comparisons is more intuitive means table 5 2 3 = 30 cell means in the simpler case of main-effects-only! The output statement requests the linear predictor, x, for testing the hypothesis CLASS ) variables models! Was the primary reference used for this seminar atrisk outs=outwhas500 ; note that are. Institute Inc., Cary, NC, USA fit in proc GENMOD produces the Wald statistic the! Dfbeta=Dfgender dfage dfagegender dfbmi dfbmibmi dfhr ; Standard nonparametric techniques do not use a true log likelihood var= ( bmi! Kalbeisch and Prentice ( 1980 ) specified variable hazard ratios, are constant over time martingale... Us get an idea of what the functional from might be these two averages models on intervals of follow proc phreg estimate statement example... Matrix,, for testing the hypothesis are the fourth and eighth cell means in the Least means..., Cary, NC, USA bmi hr ) / resample ; It is not necessary the.
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