proc phreg estimate statement example
The design variables that are generated for the nested term are the same as those generated by the interaction term previously. As in Example 1, you can also use the LSMEANS, LSMESTIMATE, and SLICE statements in PROC LOGISTIC, PROC GENMOD, and PROC GLIMMIX when dummy coding (PARAM=GLM) is used. Means for the AB11 and AB12 cells (highlighted in the above table) are computed below using the ESTIMATE statement. Finally, the CONTRAST and ESTIMATE statements use the contrast determined above to compute the AB11 - AB12 difference. The contrast table that shows the log odds ratio and odds ratio estimates is exactly as before. For example, in the previous graph the probability curves for the Drug A and Drug B patients are close to each other. 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 problem is greatly simplified using effects coding, which is available in some procedures via the PARAM=EFFECT option in the CLASS statement. As you'll see in the examples that follow, there are some important steps in properly writing a CONTRAST or ESTIMATE statement: Writing CONTRAST and ESTIMATE statements can become difficult when interaction or nested effects are part of the model. 1 Recommendation. Models are nested if one model results from restrictions on the parameters of the other model. 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 CONTRAST statement tests the hypothesis LÎ²=0, where L is the hypothesis matrix and Î² is the vector of model parameters. The DIVISOR= option is used to ensure precision and avoid nonestimability. The EXP option exponentiates each difference providing odds ratio estimates for each pair. In PROC GENMOD or PROC GLIMMIX, use the EXP option in the ESTIMATE statement. Finally, writing the hypothesis Î¼12 â 1/6 Î£ijÎ¼ij in terms of the model results in these contrast coefficients: 0 for Î¼, 1/2 and â1/2 for A, â1/3, 2/3, and â1/3 for B, and â1/6, 5/6, â1/6, â1/6, â1/6, and â1/6 for AB. This is the second reason; it is relatively easy to incorporate time-dependent covariates. Step 2 follows the same thoughts. For simple analyses, only the PROC LIFETEST and TIME statements are required. See the "Parameterization of PROC GLM Models" section in the PROC GLM documentation for some important details on how the design variables are created. Notice that 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. 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. This is the default coding scheme for CLASS variables in most procedures including GLM, MIXED, GLIMMIX, and GENMOD. for ses = 1, we will add the coefficient for ses1 to the intercept. All of the statements mentioned above can be used for this purpose. Consider a model for two factors: A with five levels and B with two levels: where i=1,2,...,5, j=1,2, k=1, 2,...,nij . Note that these are the fourth and eighth cell means in the Least Squares Means table. There are two PROC PHREG sections to the program. You use model 3e to expand the average treatment effect: So the hypothesis, written in terms of the model parameters, is simply: The following CONTRAST statement used in PROC LOGISTIC estimates and tests this hypothesis, and produces the following output tables: In PROC GENMOD, use this equivalent ESTIMATE statement: The exponentiated contrast estimate, 0.83, is not really an odds ratio. Now choose a coefficient vector, also with 18 elements, that will multiply the solution vector: Choose a coefficient of 1 for the intercept (Î¼), coefficients of (1 0 0 0 0) for the A term to pick up the Î±1 estimate, coefficients of (0 1) for the B term to pick up the Î²2 estimate, and coefficients of (0 1 0 0 0 0 0 0 0 0) for the A*B interaction term to pick up the Î±Î²12 estimate. 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 MODEL statement must appear after the CLASS statement if CLASS statement is used. Therefore, the estimate of the last level of an effect, A, is Î±a= â(Î±1 + Î±2 + ... + Î±aâ1). This is exactly the contrast that was constructed earlier. proc phreg data=Myeloma noprint; model Time*VStatus(0)=LogBUN HGB; baseline out=Pred3 survival=S lower=S_lower upper=S_upper; run; Institute for Digital Research and Education. Logistic models are in the class of generalized linear models. The ODDSRATIO statement used above with dummy coding provides the same results with effects coding. we can also use the option "e" following the estimate PROC GENMOD can also be used to estimate this odds ratio. We estimate two sets of hazard ratios for age, one for the interval up to 2 years following diagnosis and one set for the interval 2 years or more subsequent to diagnosis. Because PROC CATMOD also uses effects coding, you can use the following CONTRAST statement in that procedure to get the same results as above. Write down the model that you are using the procedure to fit. The E option shows how each cell mean is formed by displaying the coefficient vectors that are used in calculating the LS-means. Example Program 1 Estimating and Testing Odds Ratios with Effects Coding Use the Class Level Information table which shows the design variable settings. See this sample program for discussion and examples of using the Vuong and Clarke tests to compare nonnested models. The following examples concentrate on using the steps above in this situation. To estimate, test, or compare nonlinear combinations of parameters, see the NLEst and NLMeans macros. Consider the following medical example in which patients with one of two diagnoses (complicated or uncomplicated) are treated with one of three treatments (A, B, or C) and the result (cured or not cured) is observed. Technical Support can assist you with syntax and other questions that relate to CONTRAST and ESTIMATE statements. The PROC PHREG statement is simply a call and specifies the data set. Using dummy coding, the right-hand side of the logistic model looks like it does when modeling a normally distributed response as in Example 1: where i=1,2,...,5, j=1,2, k=1, 2,...,Nij . With this simple model, we An estimate statement corresponds to an L-matrix, which corresponds to a EXAMPLE 3: A Two-Factor Logistic Model with Interaction Using Dummy and Effects Coding The next two elements are the parameter estimates for the levels of B, Î²1 and Î²2. With any procedure, models that are not nested cannot be compared using the LR test. To properly test a hypothesis such as "The effect of treatment A in group 1 is equal to the treatment A effect in group 2," it is necessary to translate it correctly into a mathematical hypothesis using the fitted model. This simpler model is nested in the above model. Any estimable linear combination of model parameters can be tested using the procedure's CONTRAST statement. 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. Consider a sample of survival data. 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. 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 first element is the estimate of the intercept, Î¼. The LSMEANS, LSMESTIMATE, and SLICE statements cannot be used with effects coding. 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. Notice that the difference in log odds for these two cells (1.02450 â 0.39087 = 0.63363) is the same as the log odds ratio estimate that is provided by the CONTRAST statement. 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. A main effect parameter is interpreted as the difference in the level's effect compared to the reference level. One variable is created for each level of the original variable. variable for ses =2. These statements fit the restricted, main effects model: This partial output summarizes the main-effects model: The question is whether there is a significant difference between these two models. However, if you write the ESTIMATE statement like this. We write the null hypothesis this way: The following table summarizes the data within the complicated diagnosis: The odds ratio can be computed from the data as: This means that, when the diagnosis is complicated, the odds of being cured by treatment A are 1.8845 times the odds of being cured by treatment C. The following statements display the table above and compute the odds ratio: To estimate and test this same contrast of log odds using model 3c, follow the same process as in Example 1 to obtain the contrast coefficients that are needed in the CONTRAST or ESTIMATE statement. The likelihood ratio test can be used to compare any two nested models that are fit by maximum likelihood. You write the contrast of log odds in terms of the nested model (3d): Notice that this simple contrast is exactly the same contrast that is estimated for a main effect parameter â a comparison of the level's effect versus the effect of the last (reference) level. 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 first three parameters of the nested effect are the effects of treatments within the complicated diagnosis. The LSMEANS statement computes the cell means for the 10 A*B cells in this example. Estimating and Testing a Difference of Means But the nested term makes it more obvious that you are contrasting levels of treatment within each level of diagnosis. Basing the test on the REML results is generally preferred. 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. Instead, you model a function of the response distribution's mean. 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. The CONTRAST, ESTIMATE, LSMEANS, RANDOM The PROC MIXED and MODEL statements are required. See, In most cases, models fit in PROC GLIMMIX using the RANDOM statement do not use a true log likelihood. Introduction Proportional hazards regression with PHREG The SAS procedure PROC PHREG allows us to fit a proportional hazard model to a dataset. The LSMESTIMATE statement can also be used. 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. Computing the Cell Means Using the ESTIMATE Statement USING THE NATIVE PHREG PROCEDURE . 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 individual AB11 and AB12 cell means are: The coefficients for the average of the AB21 and AB22 cells are determined in the same fashion. After exponentiating, the denominator is not just a simple odds, but rather a geometric mean of the treatment odds. fixed. These statistics are provided in most procedures using maximum likelihood estimation. • The statement MODELEFFECTS lists the effects to be analyzed. 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 . 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. Y is vector of dependent variable values while X is the matrix of independent coeffcients, I is the identity matrix and σ… Note that some functions, like ratios, are nonlinear combinations and cannot generally be obtained with these statements. Proc PHREG - Random Statement The PHREG procedure now fits frailty models with the addition of the RANDOM statement. 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. Estimating and Testing Odds Ratios with Dummy Coding ... You can specify a value in the TAU= option in the PROC PHREG statement. In our following figure, y is dependent variable while x1, x2, x3 … are independent variables. Tom The difficulty is constructing combinations that are estimable and that jointly test the set of interactions. The next section illustrates using the CONTRAST statement to compare nested models. The ODDSRATIO statement in PROC LOGISTIC and the similar HAZARDRATIO statement in PROC PHREG are also available. The regression equation is the In logistic models, the response distribution is binomial and the log odds (or logit of the binomial mean, p) is the response function that you model: For more information about logistic models, see these references. Examples Stepwise Regression ... Table 66.4 summarizes important options in the ESTIMATE statement. The DIFF and SLICEBY(A='1') options in the SLICE statement estimate the differences in LS-means at A=1. 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. The null hypothesis, in terms of model 3e, is: We saw above that the first component of the hypothesis, log(OddsOA) = Î¼ + d + t1 + g1. The (Proportional Hazards Regression) PHREG semi-parametric procedure performs a regression analysis of survival data based on the Cox proportional hazards model. The EXPB option adds a column in the parameter estimates table that contains exponentiated values of the corresponding parameter estimates. The Here we use proc lifetest to graph S ( t). Reference parameterization (using the PARAM=REF option) is also a full-rank parameterization. Specifically, PROC LOGISTIC is used to fit a logistic model containing effects X and X2. And that is the statement for step 1)! When the procedure reports a log pseudo-likelihood you cannot construct a LR test to compare models. Suppose A has two levels and B has three levels and you want to test if the AB12 cell mean is different from the average of all six cell means. In the simpler case of a main-effects-only model, writing CONTRAST and ESTIMATE statements to make simple pairwise comparisons is more intuitive. For simple pairwise contrasts like this involving a single effect, there are several other ways to obtain the test. of the mean for cell ses =1 and the cell ses =3. All produce equivalent results. These statements generate data from the above model: The following statements fit model (2) and display the solution vector and cell means. The DIFF option estimates and tests each pairwise difference of log odds. =2. The result is Row1 in the table of LS-means coefficients. The ESTIMATE statement syntax enables you to specify the coefficient vector in sections as just described, with one section for each model effect: Note that this same coefficient vector is given in the table of LS-means coefficients, which was requested by the E option in the LSMEANS statement. • The statement TEST can test the hypothesis about linear combinations of parameters. 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 … Release is the software release in which the problem is planned to be The following statements fit the nested model and compute the contrast. To assess the effects of continuous variables involved in interactions or constructed effects such as splines, see. To assess the effects of continuous variables involved in interactions or constructed effects such as splines, see this note. When testing, write the null hypothesis in the form. 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. However, the process of constructing CONTRAST statements is the same: write the hypothesis of interest in terms of the fitted model to determine the coefficients for the statement. The last 10 elements are the parameter estimates for the 10 levels of the A*B interaction, Î±Î²11 through Î±Î²52. The CONTRAST and ESTIMATE statements allow for estimation and testing of any linear combination of model parameters. For left truncated lifetime data, a stratified Cox proportional hazards model without covariates can be fit using the PHREG procedure and the BASELINE statement can be used to generate the product limit survival estimates. The Analysis of Maximum Likelihood Estimates table confirms the ordering of design variables in model 3d. linear combination of the parameter estimates. 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). Beside using the solution option to get the parameter estimates, Had B preceded A in the CLASS statement, the levels of A would have changed before the levels of B, resulting in the second estimate being for Î±Î²21. PHREG - ODS Output dataset ParameterEstimates - Parameter only has length of 20? The value that you specify in the option divides all the coefficients that are provided in the ESTIMATE statement. The following statements do the model comparison using PROC LOGISTIC and the Wald test produces a very similar result. Partial Likelihood The partial likelihood function for one covariate is: where t i is the ith death time, x i is the associated covariate, and R i is the risk set at time t i, i.e., the set of subjects is still alive and uncensored just prior to time t i. The next five elements are the parameter estimates for the levels of A, Î±1 through Î±5. Stated another way, are any of the interaction parameters not equal to zero as implied by the main-effects model? The parameter for ses1 is the difference Contrasts like this comparison that estimates the difference of these criteria are considered event times not. A call and specifies the data set called hsb2.sas7bdat to demonstrate, is normally distributed with constant variance that. Adding the intercept, Î¼ for ses = 2 by adding the intercept is the second model is pairwise... 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