This simpler model is nested in the above model. The statement is: ESTIMATE ‘(1) T=Yes, V=Baseline, with interaction’ INTERCEPT T 1 V -1 -1 -1 T*V -1 -1 -1; The ‘T*V -1 -1 -1’ are correspondent to the values of T_V4, T_V3 and T_V2 in the equation. 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 following statements show all five ways of computing and testing this contrast. 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. Harrell’s Concordance Statistic. Paul Allison’s well-known Survival Analysis Using the SAS System, for instance, gives examples of the use of such programming statements (pp. See the Analysis of Maximum Likelihood Estimates table to verify the order of the design variables. The following statements create the data set and fit the saturated logistic model. The Moreover, we are going to explore procedures used in Mixed modeling in SAS/STAT. Based on the theory behind Cox proportional hazard model, I need the 95% CI. Again, trailing zero coefficients can be omitted. PHREG can also make it. An ESTIMATE statement for the AB11 cell mean can be written as above by rewriting the cell mean in terms of the model yielding the appropriate linear combination of parameter estimates. 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.             Estimating and Testing Odds Ratios with Dummy Coding EXAMPLE 4: Comparing Models The CONTRAST statement tests the hypothesis Lβ=0, where L is the hypothesis matrix and β is the vector of model parameters. Printing this document: Because some of the tables in this document are wide, SAS Code from All of These Examples. For example, in the previous graph the probability curves for the Drug A and Drug B patients are close to each other. However, the CONTRAST statement can be used in PROC GENMOD as shown above to produce a score test of the hypothesis. • The statement MODELEFFECTS lists the effects to be analyzed. PHREG - ODS Output dataset ParameterEstimates - Parameter only has length of 20? The statements below generate observations from such a model: The following statements fit the main effects and interaction model. It is important to know how variable levels change within the set of parameter estimates for an effect. With effects coding, the parameters are constrained to sum to zero. The DIFF and SLICEBY(A='1') options in the SLICE statement estimate the differences in LS-means at A=1. For treatment A in the complicated diagnosis, O = 1, A = 1, B = 0. It is shown how this can be done more easily using the ODDSRATIO and UNITS statements in PROC LOGISTIC. The DIFF option in the LSMEANS statement provides all pairwise comparisons of the ten LS-means. The DIFF option estimates and tests each pairwise difference of log odds. 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 Exponentiating this value (exp[.63363] = 1.8845) yields the exponentiated contrast value (the odds ratio estimate) from the CONTRAST statement. 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 . 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. The GENMOD and GLIMMIX procedures provide separate CONTRAST and ESTIMATE statements. 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). diagnosis. This is an extension of the nested effects that you can specify in other procedures such as GLM and LOGISTIC. For example, in the set of parameter estimates for the A*B interaction effect, notice that the second estimate is the estimate of αβ12, because the levels of B change before the levels of A. One variable is created for each level of the original variable. We will use a data set called hsb2.sas7bdat to demonstrate. The “GLM” stands for General Linear Model. 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 αβ21. Y is vector of dependent variable values while X is the matrix of independent coeffcients, I is the identity matrix and σ… EXAMPLE 3: A Two-Factor Logistic Model with Interaction Using Dummy and Effects Coding For this example, the table confirms that the parameters are ordered as shown in model 3c. The values of Days are considered censored if the value of Status is 0; otherwise, they are considered event times. Notice that if you add up the rows for diagnosis (or treatments), the sum is zero. PROC CATMOD has a feature that makes testing this kind of hypothesis even easier. Therefore, this contrast is also estimated by the parameter for treatment A within the complicated diagnosis in the nested effect. The first element is the estimate of the intercept, μ. 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). 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. However, this is something that cannot be estimated with the ODDSRATIO statement which only compares odds of levels of a specified variable. Limitations on constructing valid LR tests. The simple contrast shown in the LSMESTIMATE statement below compares the fourth and eighth means as desired. The CONTRAST statement can also be used to compare competing nested models. This is exactly the contrast that was constructed earlier. These statements generate data from the above model: The following statements fit model (2) and display the solution vector and cell means. This is the log odds. 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. The parameter for the intercept is the expected cell mean for ses =3 Note that within a set of coefficients for an effect you can leave off any trailing zeros. For a more detailed definition of nested and nonnested models, see the Clarke (2001) reference cited in the sample program. The likelihood ratio and Wald statistics are asymptotically equivalent.             Estimating and Testing Odds Ratios with Effects Coding In our following figure, y is dependent variable while x1, x2, x3 … are independent variables. 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. In the CONTRAST statement, the rows of L are separated by commas. The next two elements are the parameter estimates for the levels of B, β1 and β2. Means for the AB11 and AB12 cells (highlighted in the above table) are computed below using the ESTIMATE statement. Models are nested if one model results from restrictions on the parameters of the other model. So the log odds are: For treatment C in the complicated diagnosis, O = 1, A = –1, B = –1. The CONTRAST and ESTIMATE statements allow for estimation and testing of any linear combination of model parameters. we can also use the option "e" following the estimate Technical Support can assist you with syntax and other questions that relate to CONTRAST and ESTIMATE statements. The default is the value of the ALPHA= option in the PROC PHREG statement, or 0.05 if that option is not specified. 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. Examples Stepwise Regression ... Table 66.4 summarizes important options in the ESTIMATE statement. The second three parameters are the effects of the treatments within the uncomplicated diagnosis. To get the expected mean You can specify a contrast of the LS-means themselves, rather than the model parameters, by using the LSMESTIMATE statement. Now choose a coefficient vector, also with 18 elements, that will multiply the solution vector: Choose a coefficient of 1 for the intercept (μ), coefficients of (1 0 0 0 0) for the A term to pick up the α1 estimate, coefficients of (0 1) for the B term to pick up the β2 estimate, and coefficients of (0 1 0 0 0 0 0 0 0 0) for the A*B interaction term to pick up the αβ12 estimate. The coefficients for the mean estimates of AB11 and AB12 are again determined by writing them in terms of the model. In the simpler case of a main-effects-only model, writing CONTRAST and ESTIMATE statements to make simple pairwise comparisons is more intuitive. Use the resulting coefficients in a CONTRAST statement to test that the difference in means is zero. You can fit many kinds of logistic models in many procedures including LOGISTIC, GENMOD, GLIMMIX, PROBIT, CATMOD, and others. 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. 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). 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. You can also duplicate the results of the CONTRAST statement with an ESTIMATE statement. However, coefficients for the B effect remain in addition to coefficients for the A*B interaction effect. EXAMPLE 5: A Quadratic Logistic Model 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. Such linear combinations can be estimated and tested using the CONTRAST and/or ESTIMATE statements available in many modeling procedures. 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. The Analysis of Maximum Likelihood Estimates table confirms the ordering of design variables in model 3d. 138-154) but does not discuss counting process format at all. The contrast estimate is exponentiated to yield the odds ratio estimate. Left panel: Survival estimates from PROC PHREG, using a BY statement to get curves for different levels of a strata variable; right panel: survival estimates from PROC PHREG using the covariates = option in the BASELINE statement. However, if the nested models do not have identical fixed effects, then results from ML estimation must be used to construct a LR test. For this reason, it is known as a full-rank parameterization. This is the null hypothesis to test: Writing this contrast in terms of model parameters: Note that the coefficients for the INTERCEPT and A effects cancel out, removing those effects from the final coefficient vector. In PROC GENMOD or PROC GLIMMIX, use the EXP option in the ESTIMATE statement. Use the Class Level Information table which shows the design variable settings. The same results can be obtained using the ESTIMATE statement in PROC GENMOD. Consider a sample of survival data. To avoid this problem, use the DIVISOR= option. 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. Specifically, PROC LOGISTIC is used to fit a logistic model containing effects X and X2. The LSMESTIMATE statement can also be used. Note that the CONTRAST and ESTIMATE statements are the most flexible allowing for any linear combination of model parameters. The ILINK option in the LSMEANS statement provides estimates of the probabilities of cure for each combination of treatment and diagnosis. The (Proportional Hazards Regression) PHREG semi-parametric procedure performs a regression analysis of survival data based on the Cox proportional hazards model. 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. Sample DataSample Data ... 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