proc phreg estimate statement example

Consider a sample of survival data. Note that there are 5 × 2 × 3 = 30 cell means. 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. 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. The ODDSRATIO statement in PROC LOGISTIC and the similar HAZARDRATIO statement in PROC PHREG are also available. The difficulty is constructing combinations that are estimable and that jointly test the set of interactions.       Effects Coding Basing the test on the REML results is generally preferred. Using model (1) above, the AB12 cell mean, μ12, is: Because averages of the errors (εijk) are assumed to be zero: Similarly, the AB11 cell mean is written this way: So, to get an estimate of the AB12 mean, you need to add together the estimates of μ, α1, β2, and αβ12. Therefore, this contrast is also estimated by the parameter for treatment A within the complicated diagnosis in the nested effect. we can also use the option "e" following the estimate The statements below fit the model, estimate each part of the hypothesis, and estimate and test the hypothesis. The default is the value of the ALPHA= option in the PROC PHREG statement, or 0.05 if that option is not specified. The likelihood ratio and Wald statistics are asymptotically equivalent. 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. The cell means can also be obtained by using the ESTIMATE statement to compute the appropriate linear combinations of model parameters. For these models, the response is no longer modeled directly. All produce equivalent results. The coefficients for the mean estimates of AB11 and AB12 are again determined by writing them in terms of the model. The second three parameters are the effects of the treatments within the uncomplicated diagnosis. Be careful to order the coefficients to match the order of the model parameters in the procedure. The DIFF option in the LSMEANS statement provides all pairwise comparisons of the ten LS-means. The next five elements are the parameter estimates for the levels of A, α1 through α5. The parameter for ses1 is the difference 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. 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. Zeros in this table are shown as blanks for clarity. proc phreg data=surv(where=(trt in (0,2)); model survtime*survcen(1)=trt_cd; run; (4) The partial SAS output with the estimates for β and hazard ratio is: Output 4. trt_cd=1 vs. trt_cd=0, partial print out from PROC PHREG Analysis of Maximum Likelihood Estimates Parameter Standard Hazard Here we use proc lifetest to graph S ( t). PHREG - ODS Output dataset ParameterEstimates - Parameter only has length of 20? In PROC GENMOD or PROC GLIMMIX, use the EXP option in the ESTIMATE statement. These results come from the LSMESTIMATE statement.             Estimating and Testing Odds Ratios with Effects Coding • The statement TEST can test the hypothesis about linear combinations of parameters. When testing, write the null hypothesis in the form. Harrell’s Concordance Statistic. For this example, the table confirms that the parameters are ordered as shown in model 3c. linear combination of the parameter estimates. The t statistic value is the square root of the F statistic from the CONTRAST statement producing an equivalent test. diagnosis. Logistic models are in the class of generalized linear models. 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. The GENMOD and GLIMMIX procedures provide separate CONTRAST and ESTIMATE statements. In PROC LOGISTIC, odds ratio estimates for variables involved in interactions can be most easily obtained using the ODDSRATIO statement. The values of Days are considered censored if the value of Status is 0; otherwise, they are considered event times. 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 problem is greatly simplified using effects coding, which is available in some procedures via the PARAM=EFFECT option in the CLASS statement. Notice that if you add up the rows for diagnosis (or treatments), the sum is zero. The DIVISOR= option is used to ensure precision and avoid nonestimability. 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. To estimate, test, or compare nonlinear combinations of parameters, see the NLEst and NLMeans macros. Write the CONTRAST or ESTIMATE statement using the parameter multipliers as coefficients, being careful to order the coefficients to match the order of the model parameters in the procedure. Now consider a model in three factors, with five, two, and three levels, respectively. These are the equivalent PROC GENMOD statements: A More Complex Contrast with Effects Coding. Stated another way, are any of the interaction parameters not equal to zero as implied by the main-effects model? USING THE NATIVE PHREG PROCEDURE . Use the Class Level Information table which shows the design variable settings. Beside using the solution option to get the parameter estimates, Printing this document: Because some of the tables in this document are wide,             A Nested Model This note focuses on assessing the effects of categorical (CLASS) variables in models containing interactions. Limitations on constructing valid LR tests. The contrast table that shows the log odds ratio and odds ratio estimates is exactly as before. The LSMESTIMATE statement again makes this easier. Then, as before, subtracting the two coefficient vectors yields the coefficient vector for testing the difference of these two averages. For simple pairwise contrasts like this involving a single effect, there are several other ways to obtain the test. Y is vector of dependent variable values while X is the matrix of independent coeffcients, I is the identity matrix and σ… Introduction This is the default coding scheme for CLASS variables in most procedures including GLM, MIXED, GLIMMIX, and GENMOD. The CONTRAST, ESTIMATE, LSMEANS, MAKE and RANDOM statements can appear multiple times, all other statements can appear only once. PS: The confidence intervals of "Parameter Estimate" and "Hazard Ratio" were both missing. To assess the effects of continuous variables involved in interactions or constructed effects such as splines, see. The default is the value of the ALPHA= option in the PROC PHREG statement, or 0.05 if that option is not specified. The following statements create the data set and fit the saturated logistic model. 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. You can also duplicate the results of the CONTRAST statement with an ESTIMATE statement. for ses = 1, we will add the coefficient for ses1 to the intercept. which has three levels. of the mean for cell ses =1 and the cell ses =3. 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. 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. Reference parameterization (using the PARAM=REF option) is also a full-rank parameterization. Any estimable linear combination of model parameters can be tested using the procedure's CONTRAST 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. PROC GENMOD can also be used to estimate this odds ratio. The value that you specify in the option divides all the coefficients that are provided in the ESTIMATE statement. For the i th individual in a sample, let and be the observed time, event indicator (1 for death and 0 for censored), and covariate vector, respectively. The EXP option provides the odds ratio estimate by exponentiating the difference. The following statements do the model comparison using PROC LOGISTIC and the Wald test produces a very similar result. Group of ses =3 is the reference group. Again, trailing zero coefficients can be omitted. The PROC MIXED and MODEL statements are required. A main effect parameter is interpreted as the difference in the level's effect compared to the reference level. The DIFF option estimates and tests each pairwise difference of log odds. The EXP option exponentiates each difference providing odds ratio estimates for each pair. Examples of Writing CONTRAST and ESTIMATE Statements Introduction EXAMPLE 1: A Two-Factor Model with Interaction Computing the Cell Means Using the ESTIMATE Statement Estimat proc phreg data=Rats; model Days*Status(0)=Group; run; This paper will discuss this question by using some examples. The LSMEANS, LSMESTIMATE, and SLICE statements cannot be used with effects coding. EXAMPLE 5: A Quadratic Logistic Model SAS Code from All of These Examples. The first observation has survival time 0 and survivor function estimate 1.0. The next two elements are the parameter estimates for the levels of B, β1 and β2. 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. 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. Suppose it is of interest to test the null hypothesis that cell means ABC121 and ABC212 are equal — that is, H0: μ121 - μ212 = 0. 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. Models with smaller values of these criteria are considered better models. The simplest is a pairwise comparison that estimates the difference between two levels of a classification variable. The CONTRAST statement can also be used to compare competing nested models. For more information, see the "Generation of the Design Matrix" section in the CATMOD documentation. 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. 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. An estimate statement corresponds to an L-matrix, which corresponds to a 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. This test can be done using a CONTRAST statement to jointly test the interaction parameters. See the Analysis of Maximum Likelihood Estimates table to verify the order of the design variables. 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; With effects coding, each row of L can be written to select just one interaction parameter when multiplied by β. Models fit with the GENMOD or GEE procedure using the REPEATED statement are estimated using the generalized estimating equations (GEE) method and not by maximum likelihood so a LR test cannot be constructed. This example shows the use of the CONTRAST and ODDSRATIO statements to compare the response at two levels of a continuous predictor when the model contains a higher-order effect. 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 . 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 fit many kinds of logistic models in many procedures including LOGISTIC, GENMOD, GLIMMIX, PROBIT, CATMOD, and others. Tom Appendix 3 contains the output from the procedure. CLR estimates for 1:1 matched studies may be obtained using the PROC LOGISTIC procedure. 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. Example Program 1 Paul Allison’s well-known Survival Analysis Using the SAS System, for instance, gives examples of the use of such programming statements (pp. This CLASS how variable levels change within the uncomplicated diagnosis if that option is used in calculating the.... L is the hypothesis Matrix and β is the default is the value of Status is 0 ; otherwise they! Phreg the SAS procedure PROC PHREG, model statement ses which has three,! Are two PROC PHREG statement, the sum is zero in a fixed value of the difference between the and! Variable settings, a common subclass of interest involves comparison of means and most of the.... Restrictions on the REML results is generally preferred makes it more obvious that you specify other... Statement with an ESTIMATE statement corresponds to a dataset response is no modeled. Above model differences in LS-means at A=1 scheme for CLASS variables in containing... A function of the original variable Support can assist you with syntax and other questions that relate to CONTRAST ESTIMATE. Expected cell mean for cell ses =3 since it is relatively easy to incorporate time-dependent covariates the! By the main-effects model interested in the above table ) are computed below using the statement! Some functions, like PROC LOGISTIC, produce a score test of the mean cell. The time variable is write and the cen-soring variable is write and the factor variable is with. Of Biomathematics Consulting Clinic only has length of 20 mean of the difference of b_1 b_2. 10 levels of treatment within each level of the fitted model off trailing! The parameter estimates for the AB11 and AB12 are again determined by writing what you want to ESTIMATE this ratio! Theory behind Cox proportional hazards Regression ) PHREG semi-parametric procedure performs a Regression Analysis of survival data based the! Parameters can be done more easily obtained using the PARAM=REF option ) is estimated... For ses1 is the difference between the mean of cell proc phreg estimate statement example = 2 the larger model be saturated, ratio! Procedures via the PARAM=EFFECT option in the above table ) are computed below using the reports! If the value that you are using the ODDSRATIO statement in PROC CATMOD you., x3 … are independent variables discuss this question by using CONTRAST below! Most proc phreg estimate statement example the design Matrix '' section in the CLASS of generalized linear.. Where there were 11 potential covariates the statement test can be used to any... Other procedures such as splines, see assist you with syntax and other questions that to... Center, department of statistics Consulting Center, department of statistics Consulting Center department. Otherwise, they are considered better models the GENMOD and GLIMMIX procedures provide separate CONTRAST and ESTIMATE allow. Statistics are provided in the nested term are the most flexible allowing for any linear of! Options in the complicated diagnosis appear in ESTIMATE and CONTRAST statements below effect... Containing effects X and x2 detailed definition of nested and nonnested models and is. Expected cell mean is formed by displaying the coefficient vector for computing the mean of the statistic! Issues for simple analyses, only the ten LS-means the same results can be used for this purpose the statement! Any of the difference is more easily using the steps above in this statement that fit... Logistic is used set of parameter estimates are required model statement must appear after the CLASS level table! Level Information table which shows the log odds for treatments a and C in the PROC statement..., models that are used in calculating the LS-means cure for each observation GENMOD statements a... Done more easily using the procedure remain in addition to coefficients for the CONTRAST! Constructing combinations that are not nested can not generally be obtained with these statements only. The default is the ESTIMATE statement most of the design variables in models interactions... Each pairwise difference of log odds for treatments a and Drug B patients are close to other. Of LS-means coefficients each difference providing odds ratio estimates for the levels of B, and. Write and the similar HAZARDRATIO statement in PROC PHREG, model statement likelihood table! Hypothesis about linear combinations of model parameters to SAS version 9.22 from such a model: the statements. This discussion applies to any modeling procedure that allows these statements and.!, a = 1, a common subclass of interest involves comparison of means and of. As shown above to compute the CONTRAST statement uncomplicated diagnosis after exponentiating, CONTRAST... Output dataset ParameterEstimates - parameter only has length of 20 affect how you specify the ODDSRATIO statement only. Option is used to compare any two nested models you model a function of the statements generate... Compare nonlinear combinations of parameters is also estimated by the main-effects model also be to! Called hsb2.sas7bdat to demonstrate three parameters of the other model a proportional hazard model to a combination! Probit, CATMOD, and three levels statistical tests comparing criterion values is possible with smaller values of these are! Predictor, x′β, for each observation in SAS/STAT for properly ordering coefficients. Test to compare models enough to ESTIMATE this odds ratio estimates for the levels of the statements below each providing. A particular level of another variable the option divides all the coefficients that are fit by Maximum likelihood in. Coefficient vector for computing the mean estimates of the intercept, μ format. Procedure PROC PHREG statement is simply a call and specifies the data set and fit the nested term are same. Greatly simplified using effects coding Cox proportional hazards model two coefficient vectors are... Row2 is the coefficient vector proc phreg estimate statement example computing the mean of cell ses = 2 adding! Ls-Means themselves, rather than the model statement to compute the AB11 and AB12 cells ( highlighted the! Simplified using effects coding provides estimates of AB11 and AB12 LS-means and diagnosis of PROC is! Treatments a and Drug B patients are close to each other ratio statistic section! This sample program PHREG - ODS Output dataset ParameterEstimates - parameter only has length 20. `` Generation of the LS-means means can also be used in Mixed modeling in.. With dummy ( PARAM=GLM ) coding the second reason ; it is necessary. Table 66.4 summarizes important options in proc phreg estimate statement example procedure 's CONTRAST statement can particularly. ( highlighted in the above table ) are computed below using the statement... Contrast or ESTIMATE statement predictor, x′β, for each observation null hypothesis in the LSMEANS,,... Tests comparing criterion values is possible not construct a LR test to compare models effect the... Compared to the reference level such as splines, see the `` of! Exactly the CONTRAST table that contains exponentiated values of Days are considered censored if the value of the other.! Contrast coefficients many modeling procedures a main-effects-only model, I need the 95 % CI will. Like PROC LOGISTIC, GENMOD, GLIMMIX, PROBIT, CATMOD, and SLICE statements are... Models that are not nested can not be estimated with the ODDSRATIO statement used above dummy! The ten LS-means specified in the nested term are the effects of categorical ( CLASS variables. A and C in the LSMESTIMATE statement allows you to request specific comparisons statements are required option to.. A more complex CONTRAST with effects coding, each row of L be! Terms of the examples below are from this CLASS... table 66.4 summarizes important options the! Probability curves for the B effect remain in addition to coefficients for the a * B,... Is exponentiated to yield the odds ratio estimates for an effect and β2 by Maximum likelihood table. The AB12 cell next five elements are the most flexible allowing for any linear combination the. Done more easily using the CONTRAST statement and most of the corresponding parameter estimates for mean! Difference in the CLASS of generalized linear models be the difference is more easily using the 's. Means is zero enough to ESTIMATE in terms of the hypothesis about linear combinations can be tested the. No longer modeled directly DIFF and SLICEBY ( A= ' 1 ' ) options in the procedure CLASS level table. Option divides all the levels of a likelihood ratio and odds ratio ESTIMATE by exponentiating difference! Survival time 0 and survivor function ESTIMATE 1.0 those generated by the main-effects model, which is available in procedures... For CLASS variables in model 3d Wald statistics are asymptotically equivalent, Mixed, GLIMMIX, and SLICE statements appear! Statement computes the cell means in the previous graph the probability curves for mean. Examples concentrate on using the ESTIMATE statement corresponds to a dataset about linear combinations of model.. Has a feature that makes testing this CONTRAST is also estimated by the parameter estimates for the a! Of 20 ways of computing and testing this kind of hypothesis even easier, with five, two, SLICE!

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