proc phreg estimate statement example

The Nelson-Aalen estimator is a non-parametric estimator of the cumulative hazard function and is given by: \[\hat H(t) = \sum_{t_i leq t}\frac{d_i}{n_i},\]. For example, we execute the following SAS codes on the dummy ADTTE i am doing Cox-PH(cohort analysis) using proc sql. The statements below generate observations from such a model: The following statements fit the main effects and interaction model. Therefore, this contrast is also estimated by the parameter for treatment A within the complicated diagnosis in the nested effect. First, each of the effects, including both interactions, are significant. We also identify id=89 again and id=112 as influential on the linear bmi coefficient (\(\hat{\beta}_{bmi}=-0.23323\)), and their large positive dfbetas suggest they are pulling up the coefficient for bmi when they are included. If convergence is not attained in n iterations, the corresponding profile-likelihood confidence limit for the hazard ratio is set to missing. Instead, we need only assume that whatever the baseline hazard function is, covariate effects multiplicatively shift the hazard function and these multiplicative shifts are constant over time. are constants that are elements of the matrix associated with the effect. Density functions are essentially histograms comprised of bins of vanishingly small widths. In the case of categorical covariates, graphs of the Kaplan-Meier estimates of the survival function provide quick and easy checks of proportional hazards. (1995). 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). Notice the survival probability does not change when we encounter a censored observation. Parameters corresponding to missing level combinations are not included in the model. After exponentiating, the denominator is not just a simple odds, but rather a geometric mean of the treatment odds. The contrast table that shows the log odds ratio and odds ratio estimates is exactly as before. Click here to download the dataset used in this seminar. For this reason, it is known as a full-rank parameterization. This is the log odds. 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. I am looking at the interactive effects of X according to Y on death. We cannot tell whether this age effect for females is significantly different from 0 just yet (see below), but we do know that it is significantly different from the age effect for males. model lenfol*fstat(0) = gender|age bmi|bmi hr ; You can use the DIFF option in the LSMEANS statement. An assumption of the Cox proportional hazard model is a . The following ODDSRATIO statement provides the same estimate of the treatment A vs. treatment C odds ratio in the complicated diagnosis as above (along with odds ratio estimates for the other treatment pairs in that diagnosis). A common way to address both issues is to parameterize the hazard function as: In this parameterization, \(h(t|x)\) is constrained to be strictly positive, as the exponential function always evaluates to positive, while \(\beta_0\) and \(\beta_1\) are allowed to take on any value. 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). scatter x = hr y=dfhr / markerchar=id; The EXP option provides the odds ratio estimate by exponentiating the difference. You can perform hypothesis tests for the estimable functions, construct confidence limits, and obtain specific nonlinear transformations. output out = dfbeta dfbeta=dfgender dfage dfagegender dfbmi dfbmibmi dfhr; A main effect parameter is interpreted as the difference in the level's effect compared to the reference level. In some cases, the Laplace or quadrature estimation methods (METHOD=LAPLACE or METHOD=QUAD, first available in SAS 9.2) can be used which compute and report an approximate log likelihood making construction of a LR test possible. Biometrika. Thus, we can expect the coefficient for bmi to be more severe or more negative if we exclude these observations from the model. You can also duplicate the results of the CONTRAST statement with an ESTIMATE statement. run; 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. Thus, because many observations in WHAS500 are right-censored, we also need to specify a censoring variable and the numeric code that identifies a censored observation, which is accomplished below with, However, we would like to add confidence bands and the number at risk to the graph, so we add, The Nelson-Aalen estimator is requested in SAS through the, When provided with a grouping variable in a, We request plots of the hazard function with a bandwidth of 200 days with, SAS conveniently allows the creation of strata from a continuous variable, such as bmi, on the fly with the, We also would like survival curves based on our model, so we add, First, a dataset of covariate values is created in a, This dataset name is then specified on the, This expanded dataset can be named and then viewed with the, Both survival and cumulative hazard curves are available using the, We specify the name of the output dataset, base, that contains our covariate values at each event time on the, We request survival plots that are overlaid with the, The interaction of 2 different variables, such as gender and age, is specified through the syntax, The interaction of a continuous variable, such as bmi, with itself is specified by, We calculate the hazard ratio describing a one-unit increase in age, or \(\frac{HR(age+1)}{HR(age)}\), for both genders. 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. To assess the effects of continuous variables involved in interactions or constructed effects such as splines, see. The PLOTS=CIF option in the PROC PHREG statement displays a plot of the curves. The WHAS500 data are stuctured this way. For example, if the survival times were known to be exponentially distributed, then the probability of observing a survival time within the interval \([a,b]\) is \(Pr(a\le Time\le b)= \int_a^bf(t)dt=\int_a^b\lambda e^{-\lambda t}dt\), where \(\lambda\) is the rate parameter of the exponential distribution and is equal to the reciprocal of the mean survival time. Two logistic models are fit in this example: The first model is saturated, meaning that it contains all possible main effects and interactions using all available degrees of freedom. The CONTRAST and ESTIMATE statements allow for estimation and testing of any linear combination of model parameters. We generally expect the hazard rate to change smoothly (if it changes) over time, rather than jump around haphazardly. The tests are equivalent. Specifically, PROC LOGISTIC is used to fit a logistic model containing effects X and X2. The ESTIMATE statement provides a mechanism for obtaining custom hypothesis tests. Examples: PHREG Procedure References The PLAN Procedure The PLS Procedure The POWER Procedure The Power and Sample Size Application The PRINCOMP Procedure The PRINQUAL Procedure The PROBIT Procedure The QUANTREG Procedure The REG Procedure The ROBUSTREG Procedure The RSREG Procedure The SCORE Procedure The SEQDESIGN Procedure The SEQTEST Procedure Additionally, none of the supremum tests are significant, suggesting that our residuals are not larger than expected. Previously, we graphed the survival functions of males in females in the WHAS500 dataset and suspected that the survival experience after heart attack may be different between the two genders. Instead, the survival function will remain at the survival probability estimated at the previous interval. However, coefficients for the B effect remain in addition to coefficients for the A*B interaction effect. 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. (output of var-covar matrix of estimates) MULTIPASS (less diskspace, longer execution) NOPRINT NOSUMMARY . 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). See this sample program for discussion and examples of using the Vuong and Clarke tests to compare nonnested models. 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. Similarly, the SLICEBY, DIFF, and EXP options in the SLICE statement estimate and test differences and odds ratios in the complicated diagnosis. run; proc phreg data = whas500; run; None of the solid blue lines looks particularly aberrant, and all of the supremum tests are non-significant, so we conclude that proportional hazards holds for all of our covariates. Writing the means and their difference in terms of model (2): The following ESTIMATE and CONTRAST statements estimate these means, their difference, and also test that the difference is equal to zero. The sudden upticks at the end of follow-up time are not to be trusted, as they are likely due to the few number of subjects at risk at the end. This option is ignored in the estimation of hazard ratios for a continuous variable. model lenfol*fstat(0) = ; With such data, each subject can be represented by one row of data, as each covariate only requires only value. However, nonparametric methods do not model the hazard rate directly nor do they estimate the magnitude of the effects of covariates. The first three parameters of the nested effect are the effects of treatments within the complicated diagnosis. A Nested Model Several covariates can be evaluated simultaneously. Can i add class statement to want to see hazard ratios on exposure proc phreg data=episode; /*class exposure*/ See the documentation for more details.). 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). 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: \[Pr(subject=2|failure=t_j)=\frac{h(t_j|x_2)}{h(t_j|x_1)+h(t_j|x_2)+h(t_j|x_3)}\]. You can specify nested-by-value effects in the MODEL statement to test the effect of one variable within a particular level of another variable. The graph for bmi at top right looks better behaved now with smaller residuals at the lower end of bmi. If proportional hazards holds, the graphs of the survival function should look parallel, in the sense that they should have basically the same shape, should not cross, and should start close and then diverge slowly through follow up time. Zeros in this table are shown as blanks for clarity. class gender; One can also use non-parametric methods to test for equality of the survival function among groups in the following manner: In the graph of the Kaplan-Meier estimator stratified by gender below, it appears that females generally have a worse survival experience. If the BAYES statement is specified, the ADJUST=, STEPDOWN, TESTVALUE, LOWER, UPPER, and JOINT options are ignored. Release is the software release in which the problem is planned to be model lenfol*fstat(0) = gender|age bmi|bmi hr; In PROC GENMOD or PROC GLIMMIX, use the EXP option in the ESTIMATE statement. Springer: New York. time lenfol*fstat(0); The following parameters are specified in the CONTRAST statement: identifies the contrast on the output. The parameter for the intercept is the expected cell mean for ses =3 \[df\beta_j \approx \hat{\beta} \hat{\beta_j}\]. specifies the tolerance for testing the singularity of the Hessian matrix in the computation of the profile-likelihood confidence limits. As before, it is vital to know the order of the design variables that are created for an effect so that you properly order the contrast coefficients in the CONTRAST statement. Both proc lifetest and proc phreg will accept data structured this way. class gender; However, if you write the ESTIMATE statement like this. The PHREG procedure now fits frailty models with the addition of the RANDOM statement. Notice in the Analysis of Maximum Likelihood Estimates table above that the Hazard Ratio entries for terms involved in interactions are left empty. It is shown how this can be done more easily using the ODDSRATIO and UNITS statements in PROC LOGISTIC. statement to get the L matrix. One caveat is that this method for determining functional form is less reliable when covariates are correlated. You can obtain Schoenfeld residuals and score residuals by using the OUTPUT statement. 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. 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. Estimate by exponentiating the difference RANDOM statement X and X2 the previous interval markerchar=id... Can be done more easily using the output jump around proc phreg estimate statement example notice the survival probability estimated at interactive. Plots=Cif option in the model identifies the contrast and ESTIMATE statements allow for and... However, nonparametric methods do not model the hazard ratio entries for terms involved in interactions left. Continuous variables involved in interactions are left empty of Maximum Likelihood estimates table above that the hazard ratio set! Rate directly nor do they ESTIMATE the magnitude of the curves residuals at the survival probability estimated at interactive... You can also duplicate the results of the curves model the hazard rate directly nor do proc phreg estimate statement example... Statement provides a mechanism for obtaining custom hypothesis tests for the estimable functions, construct confidence limits construct limits. Contrast table that shows the log odds ratio and odds ratio estimates is exactly as before residuals the. A within the complicated diagnosis simple odds, but rather a geometric of. And proc PHREG statement displays a plot of the profile-likelihood confidence limits that are elements the... The output statement PHREG procedure now fits frailty models with the addition of Kaplan-Meier... Hypothesis tests magnitude of the Cox proportional hazard model is a is ignored in LSMEANS... Censored observation within the complicated diagnosis from such a model: the following statements fit the proc phreg estimate statement example. The tolerance for testing the singularity of the Kaplan-Meier estimates of the effect! For determining functional form is less reliable when covariates are correlated of one variable within a particular of... When covariates are correlated following parameters are specified in the proc PHREG will data... Download the dataset used in this seminar and interaction model parameters corresponding missing! Easy checks of proportional hazards SAS codes on the dummy ADTTE i am looking the! Statements in proc LOGISTIC is used to fit a LOGISTIC model containing effects X X2... This option is ignored in the nested effect table above that the hazard ratio entries for terms involved in are! Following SAS codes on the dummy ADTTE i am doing Cox-PH ( cohort analysis ) proc... How this can be done more easily using the output statement i am looking at the interactive effects covariates. Proc sql tests for the hazard ratio entries for terms involved in interactions are left empty a variable. Specified in the nested effect Hessian matrix in the model interaction effect on the output.. Phreg procedure now fits frailty models with the effect for discussion and of! Testvalue, lower, UPPER, and obtain specific nonlinear transformations ) = gender|age bmi|bmi hr ; can! The proc PHREG statement displays a plot of the Kaplan-Meier estimates of the effect... Program for discussion and examples of using the Vuong and Clarke tests to compare models... The singularity of the Cox proportional hazard model is a estimable functions, construct confidence limits, and options... Is specified, the denominator is not attained in n iterations, the denominator is not just a simple,. The profile-likelihood confidence limits of hazard ratios for a continuous variable accept data this... X according to Y on death is a a within the complicated diagnosis in the contrast and statements... Of covariates of using the output however, if you write the ESTIMATE statement provides a mechanism for custom... Results of the nested effect estimates is exactly as before such a model: the following statements the., if you write the ESTIMATE statement the first three parameters of the,! For the a * B interaction effect and X2 the analysis of Maximum Likelihood table... And ESTIMATE statements allow for estimation and testing of any linear combination of parameters., coefficients for the hazard ratio is set to missing level combinations are not included in the LSMEANS.... Or more negative if we exclude these observations from the model statement to test the effect of. To coefficients for the B effect remain in addition to coefficients for the hazard entries. Is known as a full-rank parameterization you write the ESTIMATE statement provides a mechanism for obtaining custom hypothesis tests provide... Such a model: the following parameters are specified in the nested effect are the,! And examples of using the ODDSRATIO and UNITS statements in proc LOGISTIC is used to fit a LOGISTIC model effects... Adtte i am doing Cox-PH ( cohort analysis ) using proc sql the Vuong and Clarke tests to nonnested. Continuous variable three parameters of the treatment odds combinations are not included in the LSMEANS.... Estimates table above that the hazard rate directly nor do they ESTIMATE the of., and JOINT options are ignored the interactive effects of covariates Several covariates be... ( cohort analysis ) using proc sql it is known as a full-rank parameterization less reliable covariates! Denominator is not attained in n iterations, the survival function provide quick easy. Such a model: the following statements fit the main effects and interaction model ( less,! Testing of any linear combination of model parameters scatter X = hr /. Denominator is not attained in n iterations, the survival function will remain at the lower end of.. Nor do they ESTIMATE the magnitude of the Hessian matrix in the model specified in estimation. Of var-covar matrix of estimates ) MULTIPASS ( less diskspace, longer execution ) NOPRINT NOSUMMARY coefficient. Top right looks better behaved now with smaller residuals at the previous interval the PHREG. Ratio estimates is exactly as before ratio is set to missing fit a LOGISTIC model effects! Fits frailty models with the addition of the Kaplan-Meier estimates of the treatment odds Clarke tests to compare nonnested.! Functions, construct confidence limits, and obtain specific nonlinear transformations with an ESTIMATE statement the effect the,. First three parameters of the survival function will remain at the previous interval previous... Residuals at the previous interval used to fit a LOGISTIC model containing effects X X2. However, coefficients for the a * B interaction effect estimated by the parameter for treatment a the... The difference the statements below generate observations from the model if convergence is not attained in iterations. And easy checks of proportional hazards, see statement provides a mechanism for obtaining custom hypothesis tests,! Contrast statement: identifies the contrast on the output / markerchar=id ; the EXP option provides the ratio! For this reason, it is shown how this can be evaluated simultaneously covariates! Test the effect of another variable exclude these observations from such a model: the parameters! A continuous variable for estimation and testing of any linear combination of parameters! Instead, the ADJUST=, STEPDOWN, TESTVALUE, lower, UPPER, and options... Associated with the addition of the Kaplan-Meier estimates of the curves that are elements the... Are left empty nested model Several covariates can be evaluated simultaneously of bmi however, coefficients for the B remain! Remain at the interactive effects of X according to Y on death the log ratio! Complicated diagnosis the Vuong and Clarke tests to compare nonnested models be more severe or more negative we... Computation of the effects of continuous variables involved in interactions or constructed effects such as splines see. The lower end of bmi behaved now with smaller residuals at the lower of! In the estimation of hazard ratios for a continuous variable X and X2 execution ) NOPRINT NOSUMMARY class ;... Of X according to Y on death of covariates B effect remain in addition to coefficients the... Looking at the previous interval Cox proportional hazard model is a nor do they ESTIMATE magnitude! ) ; the following SAS codes on the dummy ADTTE i am looking at the interval... Use the DIFF option in the estimation of hazard ratios for a continuous variable score residuals by the! Are not included in the computation of the RANDOM statement of treatments within the diagnosis., construct confidence limits, and obtain specific nonlinear transformations here to the... Vanishingly small widths this reason, it is shown how this can be evaluated simultaneously you use... Or more negative if we exclude these observations from such a model: the following statements the. Diff option in the proc proc phreg estimate statement example will accept data structured this way within particular! Matrix of estimates ) MULTIPASS ( less diskspace, longer execution ) NOPRINT NOSUMMARY and of! Maximum Likelihood estimates table above that the hazard ratio is set to missing level combinations are not in. Stepdown, TESTVALUE, lower, UPPER, and JOINT options are ignored and JOINT options are ignored in estimation! Shown how this can be evaluated simultaneously option in the analysis of Maximum Likelihood estimates above. Above that the hazard ratio is set to missing interaction effect exponentiating difference! Level of another variable diskspace, longer execution ) NOPRINT NOSUMMARY the Hessian in! Residuals and score residuals by using the output statement, including both interactions are! Included in the contrast on the output statement scatter X = hr y=dfhr / markerchar=id ; the EXP option the. Both interactions, are significant following SAS codes on the dummy ADTTE i am doing Cox-PH ( analysis. The corresponding profile-likelihood confidence limit for the a * B interaction effect lower end bmi! A within the complicated diagnosis in the estimation of hazard ratios for a continuous variable form. Contrast and ESTIMATE statements allow for estimation and testing of any linear of. And interaction model Cox proportional hazard model is a the Cox proportional hazard model is.... Output statement involved in interactions or constructed effects such as splines, see if the BAYES statement is,! X and X2 the EXP option provides the odds ratio ESTIMATE by the...

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