Tom The (Proportional Hazards Regression) PHREG semi-parametric procedure performs a regression analysis of survival data based on the Cox proportional hazards model. Specifically, you need to construct the linear combination of model parameters that corresponds to the hypothesis. The most commonly used test for comparing nested models is the likelihood ratio test, but other tests (such as Wald and score tests) can also be used. By default, PROC GENMOD computes a likelihood ratio test for the specified contrast. As shown in Example 1, tests of simple effects within an interaction can be done using any of several statements other than the CONTRAST and ESTIMATE statements. Note that some functions, like ratios, are nonlinear combinations and cannot generally be obtained with these statements. Specifically, PROC LOGISTIC is used to fit a logistic model containing effects X and X2. See the example titled "Comparing nested models with a likelihood ratio test" which illustrates using the %VUONG macro to produce the same test as obtained above from the CONTRAST statement in PROC GENMOD. The CONTRAST statement can also be used to compare competing nested models. However, to obtain CLR estimates for 1:m and n:m matched studies using SAS, the PROC PHREG procedure must be used. Because PROC CATMOD also uses effects coding, you can use the following CONTRAST statement in that procedure to get the same results as above. Note that the CONTRAST and ESTIMATE statements are the most flexible allowing for any linear combination of model parameters. An estimate statement corresponds to an L-matrix, which corresponds to a The PROC PHREG statement is simply a call and specifies the data set. The first element is the estimate of the intercept, μ. In PROC LOGISTIC, odds ratio estimates for variables involved in interactions can be most easily obtained using the ODDSRATIO statement. The last 10 elements are the parameter estimates for the 10 levels of the A*B interaction, αβ11 through αβ52. 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. The log odds for treatment A in the complicated diagnosis are: The log odds for treatment C in the complicated diagnosis are: Subtracting these gives the difference in log odds, or equivalently, the log odds ratio: The following statements use PROC LOGISTIC to fit model 3c and estimate the contrast. Sample DataSample Data ... Summary Survival Estimates Using Proc Lifetest • Proc Lifetest options; – Time statement – Strata statementStrata statement – Test statement (use phreg) – Btt tBy statement – Freq statement – IDID statement. • Most software packages, will provide estimates of S(t) based on the fitted proportional hazards model for any specified values of explanatory variables (e.g., the BASELINE statement in PROC PHREG… The model is the same as model (1) above with just a change in the subscript ranges. See, In most cases, models fit in PROC GLIMMIX using the RANDOM statement do not use a true log likelihood. ALPHA= number specifies the alpha level of the interval estimates for the hazard ratios. The Examples of this simpler situation can be found in the example titled "Randomized Complete Blocks with Means Comparisons and Contrasts" in the PROC GLM documentation and in this note which uses PROC GENMOD. The LSMEANS statement computes the cell means for the 10 A*B cells in this example. Models are nested if one model results from restrictions on the parameters of the other model. Although the coding scheme is different, you still follow the same steps to determine the contrast coefficients. Estimating and Testing Odds Ratios with Effects Coding. Notice that Row2 is the coefficient vector for computing the mean of the AB12 cell. The test of the difference is more easily obtained using the LSMESTIMATE statement. For this example, the table confirms that the parameters are ordered as shown in model 3c. The ILINK option in the LSMEANS statement provides estimates of the probabilities of cure for each combination of treatment and diagnosis. The change in coding scheme does not affect how you specify the ODDSRATIO statement. The statements below fit the model, estimate each part of the hypothesis, and estimate and test the hypothesis. The CONTRAST statement below defines seven rows in L for the seven interaction parameters resulting in a 7 DF test that all interaction parameters are zero. 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. 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. The GENMOD and GLIMMIX procedures provide separate CONTRAST and ESTIMATE statements. Step 2 follows the same thoughts. CLTYPE= method specifies the transformation used to compute the confidence limits for , the survivor function for a subject with a fixed covariate vector at event time t . statement to get the L matrix. The following statements print out the observations in the data set Pred1for the realization LogBUN=1.00 and HGB=10.0: proc print data=Pred1(where=(logBUN=1 and HGB=10));run; As shown in Output 89.8.2, 32 observations represent the survivor function for the realization LogBUN=1.00 and HGB=10.0. The problem is greatly simplified using effects coding, which is available in some procedures via the PARAM=EFFECT option in the CLASS statement. The contrast table that shows the log odds ratio and odds ratio estimates is exactly as before. This can be particularly difficult with dummy (PARAM=GLM) coding. In PROC LOGISTIC, use the PARAM=GLM option in the CLASS statement to request dummy coding of CLASS variables. It provides the chance to modulate dynamic design, leading to a more robust and accurate outcome. Therefore, the estimate of the last level of an effect, A, is αa= –(α1 + α2 + ... + αa–1). In these SAS Mixed Model, we will focus on 6 different types of procedures: PROC MIXED, PROC NLMIXED, PROC PHREG, PROC GLIMMIX, PROC VARCOMP, and ROC HPMIXED with examples & syntax. PROC CATMOD has a feature that makes testing this kind of hypothesis even easier. 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. In addition to using the CONTRAST statement, a likelihood ratio test can be constructed using the likelihood values obtained by fitting each of the two models. A main effect parameter is interpreted as the deviation of the level's effect from the average effect of all the levels. Proportional hazards regression with PHREG The SAS procedure PROC PHREG allows us to fit a proportional hazard model to a dataset. If you are interested only in the survivor function estimates for the sample means of the explanatory variables, you can omit the COVARIATES= option in the BASELINE statement. The LSMESTIMATE statement can also be used. Consider a sample of survival data. For treatment A in the complicated diagnosis, O = 1, A = 1, B = 0. estimate (PHREG) "Example 49.3: Conditional Logistic Regression for m:n Matching" estimate (PHREG) "Hazards Ratio Estimates and Confidence Limits" PHREG procedure HC= option PROC FASTCLUS statement HEIGHT= option PLOT statement (BOXPLOT) PROC TREE statement HEIGHT statement TREE procedure HELMERT keyword REPEATED statement (ANOVA) HELMERT option following, where ses1 is the dummy variable for ses =1 and ses2 is the dummy In PROC LOGISTIC, the ESTIMATE=BOTH option in the CONTRAST statement requests estimates of both the contrast (difference in log odds or log odds ratio) and the exponentiated contrast (odds ratio). The LSMEANS, LSMESTIMATE, and SLICE statements cannot be used with effects coding. The DIFF option estimates and tests each pairwise difference of log odds. You can also duplicate the results of the CONTRAST statement with an ESTIMATE statement. use eventcode option in proc phreg, model statement. in the PROC PHREG model statement numeric. Note that there are 5 × 2 × 3 = 30 cell means. Words in italic are new statements added to SAS version 9.22. Computing the Cell Means Using the ESTIMATE Statement, Estimating and Testing a Difference of Means, Comparing One Interaction Mean to the Average of All Interaction Means, Example 1: A Two-Factor Model with Interaction, coefficient vectors that are used in calculating the LS-means, Example 2: A Three-Factor Model with Interactions, Example 3: A Two-Factor Logistic Model with Interaction Using Dummy and Effects Coding, Some procedures allow multiple types of coding. The basic code for such PHREG procedure is shown below: proc phreg data = final; strata sex; Again, trailing zero coefficients can be omitted. 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 . The following statements fit the model and compute the AB11 and AB12 cell means by using the LSMEANS statement and equivalent ESTIMATE statements: Suppose you want to test that the AB11 and AB12 cell means are equal. Since treatment A and treatment C are the first and third in the LSMEANS list, the contrast in the LSMESTIMATE statement estimates and tests their difference. as the use of programming statements in the PROC PHREG step itself, for example, to define time-varying covariates. Note that the ESTIMATE statement displays the estimated difference in cell means (–2.5148) and a t-test that this difference is equal to zero, while the CONTRAST statement provides only an F-test of the difference. 138-154) but does not discuss counting process format at all. proc glm data= hsb2; class ses; model write = ses /solution; estimate 'ses 1' intercept 1 ses 1 0 0 /e; /*cell mean for ses = 1*/ estimate 'ses 2' intercept 1 ses 0 1 0; /*cell mean for ses = 2*/ estimate 'ses 3' intercept 1 ses 0 0 1; /*cell mean for ses = 3*/ estimate 'ses 1 … The individual AB11 and AB12 cell means are: The coefficients for the average of the AB21 and AB22 cells are determined in the same fashion. 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. 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. Reference parameterization (using the PARAM=REF option) is also a full-rank parameterization. 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. The DIFF and SLICEBY(A='1') options in the SLICE statement estimate the differences in LS-means at A=1. Beside using the solution option to get the parameter estimates, you might need to print it in landscape mode to avoid truncation of the right edge. The t statistic value is the square root of the F statistic from the CONTRAST statement producing an equivalent test. Examples Stepwise Regression ... Table 66.4 summarizes important options in the ESTIMATE statement. The design variables that are generated for the nested term are the same as those generated by the interaction term previously. In this case, the αβ12 estimate is the sixth estimate in the A*B effect requiring a change in the coefficient vector that you specify in the ESTIMATE statement.       Comparing Nested Models While only certain procedures are illustrated below, this discussion applies to any modeling procedure that allows these statements. However, this is something that cannot be estimated with the ODDSRATIO statement which only compares odds of levels of a specified variable. 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. The basic statistical assumption underlying the least squares approach to general linear modeling is that the observed values of each dependent variable can be written as the sum of two parts: a fixed component and a random noise or error component. It is important to know how variable levels change within the set of parameter estimates for an effect. In the CONTRAST statement, the rows of L are separated by commas. There are two PROC PHREG sections to the program. Release is the software release in which the problem is planned to be For simple pairwise contrasts like this involving a single effect, there are several other ways to obtain the test. variable for ses =2. At last, we also learn SAS mixe… Group of ses =3 is the reference group. 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. 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. The next five elements are the parameter estimates for the levels of A, α1 through α5. It is quite powerful, as it allows for truncation, time-varying covariates and provides us with a few model selection algorithms and model diagnostics. 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). Proc PHREG - Random Statement The PHREG procedure now fits frailty models with the addition of the RANDOM statement. Notice that if you add up the rows for diagnosis (or treatments), the sum is zero. The values of Days are considered censored if the value of Status is 0; otherwise, they are considered event times. Example Program 1 Use the resulting coefficients in a CONTRAST statement to test that the difference in means is zero. In the MODEL statement, the response variable, Days, is crossed with the censoring variable, Status, with the value that indicates censoring enclosed in parentheses (0). ASSESS statement in SAS includes Plot of randomly generated residual processes to allow for graphic assessment of the observed residuals in terms of what is “too large” Formal hypothesis test based on simulation Checking the functional form proc phreg data=in.short_course ; model intxsurv*dead(0)=yeartx/rl; The LSMESTIMATE statement again makes this easier. Use the Class Level Information table which shows the design variable settings. In the medical example, you can use nested-by-value effects to decompose treatment*diagnosis interaction as follows: The model effects, treatment(diagnosis='complicated') and treatment(diagnosis='uncomplicated'), are nested-by-value effects that test the effects of treatments within each of the diagnoses. The flISt uses an expanded data set where there were 11 potential covariates. 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. PS: The confidence intervals of "Parameter Estimate" and "Hazard Ratio" were both missing. This is the default coding scheme for CLASS variables in most procedures including GLM, MIXED, GLIMMIX, and GENMOD. we can also use the option "e" following the estimate A main effect parameter is interpreted as the difference in the level's effect compared to the reference level. In the simpler case of a main-effects-only model, writing CONTRAST and ESTIMATE statements to make simple pairwise comparisons is more intuitive. The second model is a reduced model that contains only the main effects. The contrast of the ten LS-means specified in the LSMESTIMATE statement estimates and tests the difference between the AB11 and AB12 LS-means. Some procedures allow multiple types of coding. The PROC MIXED and MODEL statements are required. The response, Y, is normally distributed with constant variance. 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. In PROC GENMOD or PROC GLIMMIX, use the EXP option in the ESTIMATE statement. The Analysis of Maximum Likelihood Estimates table confirms the ordering of design variables in model 3d. This test can be done using a CONTRAST statement to jointly test the interaction parameters. The following examples concentrate on using the steps above in this situation. 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 DIFF option in the LSMEANS statement provides all pairwise comparisons of the ten LS-means. So the log odds is: The following PROC LOGISTIC statements fit the effects-coded model and estimate the contrast: The same log odds ratio and odds ratio estimates are obtained as from the dummy-coded model. The code is available in melanoma_phreg.sas. The parameter for ses1 is the difference While the main purpose of this note is to illustrate how to write proper CONTRAST and ESTIMATE statements, these additional statements are also presented when they can provide equivalent analyses. The default is the value of the ALPHA= option in the PROC PHREG statement, or 0.05 if that option is not specified. It is shown how this can be done more easily using the ODDSRATIO and UNITS statements in PROC LOGISTIC. The simple contrast shown in the LSMESTIMATE statement below compares the fourth and eighth means as desired. General model syntax proc phreg data =dataset nosummary; model status*censor(0)= variable(s) of interest /ties=discrete [or breslow] risklimits; The solution vector in PROC MIXED is requested with the SOLUTION option in the MODEL statement and appears as the Estimate column in the Solution for Fixed Effects table: For this model, the solution vector of parameter estimates contains 18 elements. Though assisting with the translation of a stated hypothesis into the needed linear combination is beyond the scope of the services that are provided by Technical Support at SAS, we hope that the following discussion and examples will help you. The simplest is a pairwise comparison that estimates the difference between two levels of a classification variable. Institute for Digital Research and Education. To get the expected mean It is not necessary that the larger model be saturated. ... You can specify a value in the TAU= option in the PROC PHREG statement. All of the statements mentioned above can be used for this purpose. CLR estimates for 1:1 matched studies may be obtained using the PROC LOGISTIC procedure. An example of using the LSMEANS and LSMESTIMATE statements to estimate odds ratios in a repeated measures (GEE) model in PROC GENMOD is available. The following statements show all five ways of computing and testing this contrast. See the Analysis of Maximum Likelihood Estimates table to verify the order of the design variables. Appendix 3 contains the output from the procedure. For more information, see the "Generation of the Design Matrix" section in the CATMOD documentation. To avoid this problem, use the DIVISOR= option. PHREG - ODS Output dataset ParameterEstimates - Parameter only has length of 20? See the "Parameterization of PROC GLM Models" section in the PROC GLM documentation for some important details on how the design variables are created. Instead, you model a function of the response distribution's mean. EXAMPLE 4: Comparing Models The coefficients that are needed in the ESTIMATE statement are determined by writing what you want to estimate in terms of the fitted model. Finally, writing the hypothesis μ12 – 1/6 Î£ijμij in terms of the model results in these contrast coefficients: 0 for μ, 1/2 and –1/2 for A, –1/3, 2/3, and –1/3 for B, and –1/6, 5/6, –1/6, –1/6, –1/6, and –1/6 for AB. The tests are equivalent. The final coefficients appear in ESTIMATE and CONTRAST statements below. The result is Row1 in the table of LS-means coefficients. These results come from the LSMESTIMATE statement. So the log odds are: For treatment C in the complicated diagnosis, O = 1, A = –1, B = –1. In our previous article we have seen Longitudinal Data Analysis Procedures, today we will discuss what is SAS mixed model. Logistic models are in the class of generalized linear models. Here we use proc lifetest to graph S ( t).       Dummy Coding The following statements do the model comparison using PROC LOGISTIC and the Wald test produces a very similar result. then the procedure provides no results, either displaying Non-est in the table of results or issuing this message in the log: The estimate is declared nonestimable simply because the coefficients 1/3 and 1/6 are not represented precisely enough. These statements include the LSMEANS, LSMESTIMATE, and SLICE statements that are available in many procedures. The SLICE and LSMEANS statements cannot be used for this more complex contrast. You can specify a contrast of the LS-means themselves, rather than the model parameters, by using the LSMESTIMATE statement. The likelihood ratio and Wald statistics are asymptotically equivalent. linear combination of the parameter estimates. The ODDSRATIO statement in PROC LOGISTIC and the similar HAZARDRATIO statement in PROC PHREG are also available. Be careful to order the coefficients to match the order of the model parameters in the procedure. For the medical example, suppose we are interested in the odds ratio for treatment A versus treatment C in the complicated diagnosis. By default, the PROC PHREG procedure results in a fixed value of hazard ratio, like in the screenshot below. With any procedure, models that are not nested cannot be compared using the LR test. The ODDSRATIO statement used above with dummy coding provides the same results with effects coding. Statement tests the hypothesis, and three levels, respectively F statistic from the average effect of the... Model, we have three parameters, the sum is zero reduced model that you specify the statement! Are required assessing the effects of categorical ( CLASS ) variables in most procedures including LOGISTIC, use EXP! A common subclass of interest involves comparison of means and most of the design Matrix '' section the... 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Score test of the corresponding parameter estimates for variables involved in interactions or constructed effects such splines! For testing the difference between two levels of treatment within each level of another variable parameters equal! Vectors yields the coefficient vector for testing the difference steps above in table. To incorporate time-dependent covariates technical Support can assist you with syntax and questions... Contains proc phreg estimate statement example the ten LS-means, it is important to know how variable levels change the! For CLASS variables Regression ) PHREG semi-parametric procedure performs a Regression Analysis of survival data based the... Jointly test the hypothesis, and SLICE statements that are provided in the divides...
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