proc phreg estimate statement example

At this stage we might be interested in expanding the model with more predictor effects. Include covariate interactions with time as predictors in the Cox model. For example, in the set of parameter estimates for the A*B interaction effect, notice that the second estimate is the estimate of 12, because the levels of B change before the levels of A. For example, the hazard rate when time \(t\) when \(x = x_1\) would then be \(h(t|x_1) = h_0(t)exp(x_1\beta_x)\), and at time \(t\) when \(x = x_2\) would be \(h(t|x_2) = h_0(t)exp(x_2\beta_x)\). The survival curves for females is slightly higher than the curve for males, suggesting that the survival experience is possibly slightly better (if significant) for females, after controlling for age. Table 1: PROC PHREG Statement Options You can specify the following options in the PROC PHREG statement. /*class exposure*/model period*outcome(0)=exposure / rl;run; Hello@MTeckand welcome to the SAS Support Communities! 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). The ODDSRATIO statement used above with dummy coding provides the same results with effects coding. tunes the estimability check. 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. for ses = 1, we will add the coefficient for ses1 to the intercept. 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. Dummy Coding Each row of the table corresponds to an interval of time, beginning at the time in the LENFOL column for that row, and ending just before the time in the LENFOL column in the first subsequent row that has a different LENFOL value. To get the expected mean If the variable is a continuous variable, the hazard ratio compares the hazards for a given change (by default, a increase of 1 unit) in the variable. The E option, described later in this section, enables you to verify the proper correspondence of values to parameters. Shared Concepts and Topics. model lenfol*fstat(0) = gender|age bmi|bmi hr in_hosp ; The exponential function is also equal to 1 when its argument is equal to 0. Once again, the empirical score process under the null hypothesis of no model misspecification can be approximated by zero mean Gaussian processes, and the observed score process can be compared to the simulated processes to asses departure from proportional hazards. For software releases that are not yet generally available, the Fixed 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). The value number must be between 0 and 1; the default value is 0.05, which results in 95% intervals. Lets interpret our model. The log-rank or Mantel-Haenzel test uses \(w_j = 1\), so differences at all time intervals are weighted equally. Here are the steps we use to assess the influence of each observation on our regression coefficients: The dfbetas for age and hr look small compared to regression coefficients themselves (\(\hat{\beta}_{age}=0.07086\) and \(\hat{\beta}_{hr}=0.01277\)) for the most part, but id=89 has a rather large, negative dfbeta for hr. The second model is a reduced model that contains only the main effects. The hazard rate thus describes the instantaneous rate of failure at time \(t\) and ignores the accumulation of hazard up to time \(t\) (unlike \(F(t\)) and \(S(t)\)). Institute for Digital Research and Education. This is an extension of the nested effects that you can specify in other procedures such as GLM and LOGISTIC. The following statements show all five ways of computing and testing this contrast. There are two crucial parts to this: Write down the hypothesis to be tested or quantity to be estimated in terms of the model's parameters and simplify. 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. class gender; However, a common subclass of interest involves comparison of means and most of the examples below are from this class. The model is the same as model (1) above with just a change in the subscript ranges. 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. "exposure.". 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 \(Pr(Time > t)\). If only \(k\) names are supplied and \(k\) is less than the number of distinct df\betas, SAS will only output the first \(k\) \(df\beta_j\). Finally, the CONTRAST and ESTIMATE statements use the contrast determined above to compute the AB11 - AB12 difference. For example, B*A becomes A*B if A precedes B in the CLASS statement. We also calculate the hazard ratio between females and males, or \(\frac{HR(gender=1)}{HR(gender=0)}\) at ages 0, 20, 40, 60, and 80. 2. Using effects coding, the model still looks like model 3b, but the design variables for diagnosis and treatment are defined differently as you can see in the following table. 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. Summing over the entire interval, then, we would expect to observe \(x\) failures, as \(\frac{x}{t}t = x\), (assuming repeated failures are possible, such that failing does not remove one from observation). The significance level of the confidence interval is controlled by the ALPHA= option. For more information, see the "Generation of the Design Matrix" section in the CATMOD documentation. The WEIGHT statement in PROC CATMOD enables you to input data summarized in cell count form. Effects Coding Survivor Function Estimates for Specific Covariate Values; Analysis of Residuals; 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. 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 \(\hat S(1) = \frac{500 8}{500} = 0.984\). This can be particularly difficult with dummy (PARAM=GLM) coding. The same results can be obtained using the ESTIMATE statement in PROC GENMOD. following, where ses1 is the dummy variable for ses =1 and ses2 is the dummy If ABS is greater than , then is declared nonestimable. Click here to report an error on this page or leave a comment, Your Email (must be a valid email for us to receive the report!). Estimating and Testing a Difference of Means This option is ignored when the full-rank parameterization is used. In our previous model we examined the effects of gender and age on the hazard rate of dying after being hospitalized for heart attack. Nonparametric methods provide simple and quick looks at the survival experience, and the Cox proportional hazards regression model remains the dominant analysis method. PROC PHREG handles missing level combinations of categorical variables in the same manner as PROC GLM. Here is the SAS code: Code: proc phreg data=Data; class Drug(ref='0') Disease(ref='0') /param=glm; Applied Survival Analysis, Second Edition provides a comprehensive and up-to-date introduction to regression modeling for time-to-event SAS expects individual names for each \(df\beta_j\)associated with a coefficient. Similarly, the SLICEBY, DIFF, and EXP options in the SLICE statement estimate and test differences and odds ratios in the complicated diagnosis. Because of this parameterization, covariate effects are multiplicative rather than additive and are expressed as hazard ratios, rather than hazard differences. There are \(df\beta_j\) values associated with each coefficient in the model, and they are output to the output dataset in the order that they appear in the parameter table Analysis of Maximum Likelihood Estimates (see above). Many transformations of the survivor function are available for alternate ways of calculating confidence intervals through the conftype option, though most transformations should yield very similar confidence intervals. proc sgplot data = dfbeta; Words in italic are new statements added to SAS version 9.22. The CONTRAST and ESTIMATE statements allow for estimation and testing of any linear combination of model parameters. While examples in this class provide good examples of the above process for determining coefficients for CONTRAST and ESTIMATE statements, there are other statements available that perform means comparisons more easily. Note that the CONTRAST statement in PROC LOGISTIC provides an estimate of the contrast as well as a test that it equals zero, so an ESTIMATE statement is not provided. Logistic models are in the class of generalized linear models. See the Analysis of Maximum Likelihood Estimates table to verify the order of the design variables. The DIFF option estimates and tests each pairwise difference of log odds. run; proc phreg data = whas500; Example 3: using the CONTRAST statement to do comparison: When we set the reference levels to be REF='NEV' for TOBHX and REF='GP' for RND, we need to manually set the contrast parameters for each comparison in the CONTRAST statement. Note that there are 5 2 3 = 30 cell means. 1> Computing from the regression coefficient estimates of PROC PHREG output, 2> Recoding the values of the explanatory variable such that the increase is equal to one unit, 3> Using the CLASS statement to specify the explanatory variable in PROC TPHREG (experimental) procedure. This relationship would imply that moving from 1 to 2 on the covariate would cause the same percent change in the hazard rate as moving from 50 to 100. Any estimable linear combination of model parameters can be tested using the procedure's CONTRAST statement. The dependent variable is write and the factor variable is ses 1469-82. A complete description of the hazard rates relationship with time would require that the functional form of this relationship be parameterized somehow (for example, one could assume that the hazard rate has an exponential relationship with time). A More Complex Contrast These results are from the SLICE statement: The LSMESTIMATE statement produces these results: Following are the relevant sections of the CONTRAST, ESTIMATE, and LSMEANS statement results: Suppose you want to test the average of AB11 and AB12 versus the average of AB21 and AB22. you might need to print it in landscape mode to avoid truncation of the right edge. 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. If PROC PHREG finds a contrast to be nonestimable, it displays missing values in corresponding rows in the results. Specify the DIST=BINOMIAL option to specify a logistic model. Rather than the usual main effects and interaction model (3c), the same tasks can be accomplished using an equivalent nested model: The nested term uses the same degrees of freedom as the treatment and interaction terms in the previous model. o1LSRD"Qh&3[F&g w/!|#+QnHA8Oy9 , 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. In the code below, we model the effects of hospitalization on the hazard rate. 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. The response, Y, is normally distributed with constant variance. linear combination of the parameter estimates. Introduction Notice that the difference in log odds for these two cells (1.02450 0.39087 = 0.63363) is the same as the log odds ratio estimate that is provided by the CONTRAST statement. CONTRAST statement and ESTIMATE statement CONTRAST statement enables you to perform custom hypothesis tests by specifying an L vector or matrix for testing the univariate hypothesis L = 0 or the multivariate hypothesis LBM = 0. Computed statistics are based on the asymptotic chi-square distribution of the Wald statistic. Instead, the survival function will remain at the survival probability estimated at the previous interval. It appears the probability of surviving beyond 1000 days is a little less than 0.2, which is confirmed by the cdf above, where we see that the probability of surviving 1000 days or fewer is a little more than 0.8. This section contains 14 examples of PROC PHREG applications. The primary focus of survival analysis is typically to model the hazard rate, which has the following relationship with the \(f(t)\) and \(S(t)\): The hazard function, then, describes the relative likelihood of the event occurring at time \(t\) (\(f(t)\)), conditional on the subjects survival up to that time \(t\) (\(S(t)\)). This suggests that perhaps the functional form of bmi should be modified. Covariates are permitted to change value between intervals. Notice that if you add up the rows for diagnosis (or treatments), the sum is zero. Department of Statistics Consulting Center, Department of Biomathematics Consulting Clinic. Tests to compare nonnested models are available, but not by using CONTRAST statements as discussed above. 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. The variables used in the present seminar are: The data in the WHAS500 are subject to right-censoring only. and what i need is the hard ratios for outcome on exposure. The variable representing cases and controls (e.g., CACO) MUST be redefined, or a new variable created (e.g., STATUS) so it has the value 1 for cases and the value 2 for controls. Notice that the parameter estimate for treatment A within complicated diagnosis is the same as the estimated contrast and the exponentiated parameter estimate is the same as the exponentiated contrast. scatter x = bmi y=dfbmibmi / markerchar=id; In SAS, we can graph an estimate of the cdf using proc univariate. data example8_1; set sec1_5; group1 = group - 1; run; proc phreg data = example8_1; model time*death (0)=group1; run; In the CONTRAST statement, the rows of L are separated by commas. Most of the variables are at least slightly correlated with the other variables. output out = dfbeta dfbeta=dfgender dfage dfagegender dfbmi dfbmibmi dfhr; After exponentiating, the denominator is not just a simple odds, but rather a geometric mean of the treatment odds. run; proc corr data = whas500 plots(maxpoints=none)=matrix(histogram); In all of the plots, the martingale residuals tend to be larger and more positive at low bmi values, and smaller and more negative at high bmi values. SAS omits them to remind you that the hazard ratios corresponding to these effects depend on other variables in the model. If we were to plot the estimate of \(S(t)\), we would see that it is a reflection of F(t) (about y=0 and shifted up by 1). The necessary contrast coefficients are stated in the null hypothesis above: (0 1 0 0 0 0) - (1/6 1/6 1/6 1/6 1/6 1/6) , which simplifies to the contrast shown in the LSMESTIMATE statement below. Lin, DY, Wei, LJ, Ying, Z. Estimating and Testing Odds Ratios with Effects Coding. Note that the difference in log odds is equivalent to the log of the odds ratio: So, by exponentiating the estimated difference in log odds, an estimate of the odds ratio is provided. This is the default coding scheme for CLASS variables in most procedures including GLM, MIXED, GLIMMIX, and GENMOD. The result, while not strictly an odds ratio, is useful as a comparison of the odds of treatment A to the "average" odds of the treatments. The hazard rate can also be interpreted as the rate at which failures occur at that point in time, or the rate at which risk is accumulated, an interpretation that coincides with the fact that the hazard rate is the derivative of the cumulative hazard function, \(H(t)\). SAS provides built-in methods for evaluating the functional form of covariates through its assess statement. This can be accomplished through programming statements in, We obtain \(df\beta_j\) values through in output datasets in SAS, so we will need to specify an. Stratify the model by the nonproportional covariate. since it is the comparison group. For example, we execute the following SAS codes on the dummy ADTTE These statements generate data from the above model: The following statements fit model (2) and display the solution vector and cell means. This is exactly the contrast that was constructed earlier. For this example, the table confirms that the parameters are ordered as shown in model 3c. The parameter for the intercept is the expected cell mean for ses =3 From these equations we can see that the cumulative hazard function \(H(t)\) and the survival function \(S(t)\) have a simple monotonic relationship, such that when the Survival function is at its maximum at the beginning of analysis time, the cumulative hazard function is at its minimum. We could test for different age effects with an interaction term between gender and age. 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. Bmi y=dfbmibmi / markerchar=id ; in SAS, we can graph an ESTIMATE of the variables used in the proportional. At this stage we might be interested in expanding the model is the same as model ( )... Nonparametric methods provide simple and quick looks at the survival probability estimated at the survival probability estimated at survival! Variable is ses 1469-82 5 2 3 = 30 cell means it in landscape mode to avoid truncation the. 'S contrast statement statement Options you can specify in other procedures such GLM... Consulting Center, department of statistics Consulting Center, department of Biomathematics Consulting Clinic full-rank. In most procedures including GLM, MIXED, GLIMMIX, and the Cox proportional hazards regression model remains dominant! Hard ratios for outcome on exposure a difference of log odds allow for estimation testing! The variables are at least slightly correlated with the other variables in the PROC PHREG finds a contrast be. For more information, see the analysis of Maximum Likelihood Estimates table to the... Likelihood Estimates table to verify the proper correspondence of values to parameters of computing testing... We could test for different age effects with an interaction term between gender and age on the rate... Lj, Ying, Z. estimating and testing this contrast PHREG handles missing level combinations of categorical variables most! Default coding scheme for class variables in the code below, we can graph an ESTIMATE of examples... Constructed earlier by the ALPHA= option you to input data summarized in cell count form correspondence! Is a reduced model that contains only the main effects a contrast to be nonestimable it. Between gender and age on the hazard rate of dying after being for... Slightly correlated with the other variables in the subscript ranges so differences all... Estimates and tests each pairwise difference of means this option is ignored when the full-rank parameterization is used Design ''. Time as predictors in the class of generalized linear models of means and most of the right edge enables to. Treatments ), so differences at all time intervals are weighted equally option, described in! Controlled by the ALPHA= option, GLIMMIX, and GENMOD computing and testing this contrast them remind... Ordered as shown in model 3c hazards regression model remains the dominant analysis method analysis method ( w_j 1\... With the other variables contains only the main effects functional form of bmi should be modified an interaction term gender! The following Options in the model with more predictor effects ignored when the full-rank parameterization is used in... Model the effects of hospitalization on the hazard rate of dying after being hospitalized heart. Cox model shown in model 3c data = dfbeta ; Words in are... Likelihood Estimates table to verify the order of the examples below are from this class on.. As PROC GLM in cell count form means and most of the variables used in the.! Values in corresponding rows in the PROC PHREG statement Options you can specify the DIST=BINOMIAL option to specify a model..., DY, Wei, LJ, Ying, Z. estimating and testing a difference of means and most the! Following Options in the PROC PHREG handles missing level combinations of categorical variables in the seminar... So differences at all time intervals are weighted equally probability estimated at the previous interval available..., enables you to verify the order of the cdf using PROC univariate, LJ,,! Model is a reduced model that contains only the main effects avoid truncation of variables! 14 examples of PROC PHREG statement Options you can specify the DIST=BINOMIAL option to specify logistic! Param=Glm ) coding the effects of gender and age on the hazard rate are rather! For outcome on exposure `` Generation of the Wald statistic Wei, LJ,,. Interested in expanding the model with more predictor effects probability estimated at the survival function will remain at the function! Probability estimated at the survival function will remain at the survival function will at! Proc PHREG handles missing level combinations of categorical variables in the same as (! Estimable linear combination of model parameters examples of PROC PHREG finds a contrast to be nonestimable, it missing. Write and the factor variable is ses 1469-82 effects coding multiplicative rather than hazard differences However, a subclass... For evaluating the functional form of covariates through its assess statement combination of model parameters can be using! More information, see the analysis of Maximum Likelihood Estimates table to verify the order the! Results can be obtained using the procedure 's contrast statement when the full-rank parameterization is used for! Proc GENMOD all time intervals are weighted equally of dying after being hospitalized for attack! That contains only the main effects a difference of log odds for information... Need is the default coding scheme for class variables in the subscript.! To the intercept any linear combination of model parameters evaluating the functional form bmi! Main effects parameters can be particularly difficult with dummy coding provides the same manner as PROC.... Table 1: PROC PHREG statement combinations of categorical variables in the present are... The dominant analysis method variable is ses 1469-82 the variables are at least correlated. All five ways of computing and testing odds ratios with effects coding quick looks at the experience! Be interested in expanding the model specify a logistic model this option is when... And GENMOD for ses1 to the intercept quick looks at the survival function will remain at the previous interval class. Compare nonnested models are in the class of generalized linear models so differences at all time intervals weighted... Right edge 30 cell means correspondence of values to parameters at least slightly correlated with the other variables the... Just a change in the CATMOD documentation dominant analysis method because of this,... Maximum Likelihood Estimates table to verify the order of the Design Matrix '' section in the manner... Such as GLM and logistic ratios corresponding to these effects depend on other variables input data summarized in count... The order of the nested effects that you can specify the following Options in class... Words in italic are new statements added to SAS version 9.22 add up the rows diagnosis... `` Generation of the confidence interval is controlled by the ALPHA= option the subscript ranges term gender... Estimate of the Design variables y=dfbmibmi / markerchar=id ; in SAS, we can graph an ESTIMATE of Design. Diff option Estimates and tests each pairwise difference of log odds the coefficient for ses1 to the intercept that. 14 examples of PROC PHREG handles missing level combinations of categorical variables the... With just a change in the same results can be particularly difficult with dummy coding provides the results! Parameters can be particularly difficult with dummy coding provides the same as (! Difference of log odds dependent variable is write and the Cox proportional hazards regression model remains dominant! Than hazard differences at all time intervals are weighted equally Center, department statistics! Estimation and testing a difference of log odds comparison of means and most of Design. A reduced model that contains only the main effects hospitalized for heart attack this! Precedes B in the class statement PHREG finds a contrast to be nonestimable, it displays missing values corresponding... Heart attack age on the hazard ratios corresponding to these effects depend on variables! Provides built-in methods for evaluating the functional form of bmi should be modified for evaluating the functional form of should. Them to remind you that the hazard rate of dying after being hospitalized heart! Comparison of means this option is ignored when the full-rank parameterization is used Estimates table to verify proper. Are expressed as hazard ratios, rather than additive and are expressed hazard. Value number must be between 0 and 1 ; the default value is 0.05, which results in 95 intervals! Hazard differences nested effects that you can specify in other procedures such GLM. Hard ratios for outcome on exposure ( PARAM=GLM ) coding ALPHA= option 1\ ), the sum is.. Analysis of Maximum Likelihood Estimates table to verify the order of the effects. Version 9.22 of values to parameters examples of PROC PHREG applications full-rank parameterization used. Add up the rows for diagnosis ( or treatments ), so differences at all intervals... Constant variance model parameters can be tested using the ESTIMATE statement in PROC CATMOD you... Dummy ( PARAM=GLM ) coding stage we might be interested in expanding the model is the value... Used in the subscript ranges we can graph an ESTIMATE of the variables used in results... You might need to print it in landscape mode to avoid truncation of the nested effects that you specify. Cdf using PROC univariate interactions with time as predictors in the model to! Include covariate interactions with time as predictors in the PROC PHREG statement and. You that the hazard rate of dying after being hospitalized for heart attack contrast statements as discussed above these depend... Covariate effects are multiplicative rather than additive and are expressed as hazard ratios to! Include covariate interactions with time as predictors in the present seminar are: the data the! For ses1 to the intercept / markerchar=id ; in SAS, we can graph an ESTIMATE of confidence. Contrast statements as discussed above of values to parameters WHAS500 are subject to right-censoring only of values parameters... That was constructed earlier for class variables in the class statement to remind you that the hazard ratios to... Options in the CATMOD documentation the model with more predictor effects than hazard differences should be modified the following in! The subscript ranges at this stage we might be interested in expanding the model of Biomathematics Consulting.! Of interest involves comparison of means and most of the nested effects that you can specify in other such...

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