The first element is the estimate of the intercept, . The Cox model contains no explicit intercept parameter, so it is not valid to specify one in the CONTRAST statement. model lenfol*fstat(0) = ; The ODDSRATIO statement used above with dummy coding provides the same results with effects coding. The LSMESTIMATE statement again makes this easier. The regression equation is the 51. Then there are three parameters () representing the first three levels, and the fourth parameter is represented by, To test the first versus the fourth level of A, you would test. In other words, the average of the Schoenfeld residuals for coefficient \(p\) at time \(k\) estimates the change in the coefficient at time \(k\). For example, patients in the WHAS500 dataset are in the hospital at the beginnig of follow-up time, which is defined by hospital admission after heart attack. proc phreg data=event; PROC CATMOD has a feature that makes testing this kind of hypothesis even easier. The value number must be between 0 and 1; the default value is 0.05, which results in 95% intervals. First, there may be one row of data per subject, with one outcome variable representing the time to event, one variable that codes for whether the event occurred or not (censored), and explanatory variables of interest, each with fixed values across follow up time. For details about the syntax of the ESTIMATE statement, see the section ESTIMATE Statement of You can also duplicate the results of the CONTRAST statement with an ESTIMATE statement. The value must be between 0 and 1. assess var=(age bmi hr) / resample; 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. For simple uses, only the PROC PHREG and MODEL statements are required. However, in many settings, we are much less interested in modeling the hazard rates relationship with time and are more interested in its dependence on other variables, such as experimental treatment or age. If the variable is a continuous variable, the hazard ratio compares the hazards for a given change (by default, a increase of 1 unit) in the variable. When the procedure reports a log pseudo-likelihood you cannot construct a LR test to compare models. 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 simple contrast shown in the LSMESTIMATE statement below compares the fourth and eighth means as desired. In the output we find three Chi-square based tests of the equality of the survival function over strata, which support our suspicion that survival differs between genders. It appears that for males the log hazard rate increases with each year of age by 0.07086, and this AGE effect is significant, AGE*GENDER term is negative, which means for females, the change in the log hazard rate per year of age is 0.07086-0.02925=0.04161. The first 12 examples use the classical method of maximum likelihood, while the last two examples illustrate the Bayesian methodology. 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. run; proc phreg data = whas500; At this stage we might be interested in expanding the model with more predictor effects. Our goal is to transform the data from its original state: to an expanded state that can accommodate time-varying covariates, like this (notice the new variable in_hosp): Notice the creation of start and stop variables, which denote the beginning and end intervals defined by hospitalization and death (or censoring). Below we plot survivor curves across several ages for each gender through the follwing steps: As we surmised earlier, the effect of age appears to be more severe in males than in females, reflected by the greater separation between curves in the top graaph. The LSMEANS, LSMESTIMATE, and SLICE statements cannot be used with effects coding. If the observed pattern differs significantly from the simulated patterns, we reject the null hypothesis that the model is correctly specified, and conclude that the model should be modified. Any estimable linear combination of model parameters can be tested using the procedure's CONTRAST statement. For software releases that are not yet generally available, the Fixed Note: The terms event and failure are used interchangeably in this seminar, as are time to event and failure time. In intervals where event times are more probable (here the beginning intervals), the cdf will increase faster. The next five elements are the parameter estimates for the levels of A, 1 through 5. 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. The contrast of the ten LS-means specified in the LSMESTIMATE statement estimates and tests the difference between the AB11 and AB12 LS-means. In each of the tables, we have the hazard ratio listed under Point Estimate and confidence intervals for the hazard ratio. The PHREG procedure now fits frailty models with the addition of the RANDOM statement. The second model is a reduced model that contains only the main effects. Once outliers are identified, we then decide whether to keep the observation or throw it out, because perhaps the data may have been entered in error or the observation is not particularly representative of the population of interest. The value must be between 0 and 1. and then i would like to see the trends on age group. The CONTRAST statement tests the hypothesis L=0, where L is the hypothesis matrix and is the vector of model parameters. Estimates are formed as linear estimable functions of the form . Be careful to order the coefficients to match the order of the model parameters in the procedure. 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). specifies that the exponentiated contrast be estimated. This test can be done using a CONTRAST statement to jointly test the interaction parameters. The response, Y, is normally distributed with constant variance. Suppose you want to test whether the effect of treatment A in the complicated diagnosis is different from the average effect of the treatments in the complicated diagnosis. class gender; We can similarly calculate the joint probability of observing each of the \(n\) subjects failure times, or the likelihood of the failure times, as a function of the regression parameters, \(\beta\), given the subjects covariates values \(x_j\): \[L(\beta) = \prod_{j=1}^{n} \Bigg\lbrace\frac{exp(x_j\beta)}{\sum_{iin R_j}exp(x_i\beta)}\Bigg\rbrace\]. of the mean for cell ses =1 and the cell ses =3. The test of the difference is more easily obtained using the LSMESTIMATE statement. In the case of categorical covariates, graphs of the Kaplan-Meier estimates of the survival function provide quick and easy checks of proportional hazards. Tests to compare nonnested models are available, but not by using CONTRAST statements as discussed above. Above we described that integrating the pdf over some range yields the probability of observing \(Time\) in that range. However, each of the other 3 at the higher smoothing parameter values have very similar shapes, which appears to be a linear effect of bmi that flattens as bmi increases. Maximum likelihood methods attempt to find the \(\beta\) values that maximize this likelihood, that is, the regression parameters that yield the maximum joint probability of observing the set of failure times with the associated set of covariate values. However, the CONTRAST statement can be used in PROC GENMOD as shown above to produce a score test of the hypothesis. run; proc print data = whas500(where=(id=112 or id=89)); Lets take a look at later survival times in the table: From LENFOL=368 to 376, we see that there are several records where it appears no events occurred. hazardratio 'Effect of 5-unit change in bmi across bmi' bmi / at(bmi = (15 18.5 25 30 40)) units=5; All The WHAS500 data are stuctured this way. If nonproportional hazards are detected, the researcher has many options with how to address the violation (Therneau & Grambsch, 2000): After fitting a model it is good practice to assess the influence of observations in your data, to check if any outlier has a disproportionately large impact on the model. In this model, this reference curve is for males at age 69.845947 Usually, we are interested in comparing survival functions between groups, so we will need to provide SAS with some additional instructions to get these graphs. Proportional hazards may hold for shorter intervals of time within the entirety of follow up time. 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. 77(1). We obtain estimates of these quartiles as well as estimates of the mean survival time by default from proc lifetest. Notice the additional option, We then specify the name of this dataset in the, We request separate lines for each age using, We request that SAS create separate survival curves by the, We also add the newly created time-varying covariate to the, Run a null Cox regression model by leaving the right side of equation empty on the, Save the martingale residuals to an output dataset using the, The fraction of the data contained in each neighborhood is determined by the, A desirable feature of loess smooth is that the residuals from the regression do not have any structure. The result is Row1 in the table of LS-means coefficients. (output of var-covar matrix of estimates) MULTIPASS (less diskspace, longer execution) NOPRINT NOSUMMARY . The dependent variable is write and the factor variable is ses ANOVA, or Analysis Of Variance, is used to compare the averages or means of two or more populations to better understand how they differ. I am about to use cox-regression to estimate the interaction between two binary variables: Disease (1,0) and Drug (1,0). Many transformations of the survivor function are available for alternate ways of calculating confidence intervals through the conftype option, though most transformations should yield very similar confidence intervals. The ESTIMATE statement provides a mechanism for obtaining custom hypothesis tests. We compare 2 models, one with just a linear effect of bmi and one with both a linear and quadratic effect of bmi (in addition to our other covariates). SAS provides built-in methods for evaluating the functional form of covariates through its assess statement. 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. However, if you write the ESTIMATE statement like this. There are two crucial parts to this: Write down the hypothesis to be tested or quantity to be estimated in terms of the model's parameters and simplify. Values of the PLSINGULAR= option must be numeric. It is not always possible to know a priori the correct functional form that describes the relationship between a covariate and the hazard rate. run; proc phreg data=whas500; Estimates are formed as linear estimable functions of the form . specifies that both the contrast and the exponentiated contrast be estimated. 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 final coefficients appear in ESTIMATE and CONTRAST statements below. 2009 by SAS Institute Inc., Cary, NC, USA. . Fortunately, it is very simple to create a time-varying covariate using programming statements in proc phreg. The value number must be between 0 and 1; the default value is 0.05, which results in 95% intervals. class gender; Specifically, PROC LOGISTIC is used to fit a logistic model containing effects X and X2. It is available only for the Bayesian analysis. class gender; %PDF-1.2 % variable for ses =2. 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. 81. 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. Standard nonparametric techniques do not typically estimate the hazard function directly. (1993). 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. If only \(k\) names are supplied and \(k\) is less than the number of distinct df\betas, SAS will only output the first \(k\) \(df\beta_j\). b(>v0Tm8rmB./Bx,G|6"7~N\ywL.W=iJv5inV_5mp,uv=dOevFjy[Wy_\%A{s-7]F6?c8((+W=Y_6clwEg?why7>I!eG/Cd P#4;pf\BGKy% Lo5V2F5BalaV OA(-{ua. As we know, each subject in the WHAS500 dataset is represented by one row of data, so the dataset is not ready for modeling time-varying covariates. All of the statements mentioned above can be used for this purpose. In particular we would like to highlight the following tables: Handily, proc phreg has pretty extensive graphing capabilities.< Below is the graph and its accompanying table produced by simply adding plots=survival to the proc phreg statement. run; proc corr data = whas500 plots(maxpoints=none)=matrix(histogram); The basic idea is that martingale residuals can be grouped cumulatively either by follow up time and/or by covariate value. 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 Copyright SAS Institute, Inc. All Rights Reserved. If these proportions systematically differ among strata across time, then the \(Q\) statistic will be large and the null hypothesis of no difference among strata is more likely to be rejected. EXAMPLE 5: A Quadratic Logistic Model 2. It is not necessary that the larger model be saturated. The change in coding scheme does not affect how you specify the ODDSRATIO statement. It is called the proportional hazards model because the ratio of hazard rates between two groups with fixed covariates will stay constant over time in this model. Estimates are formed as linear estimable functions of the form . This seminar covers both proc lifetest and proc phreg, and data can be structured in one of 2 ways for survival analysis. following, where ses1 is the dummy variable for ses =1 and ses2 is the dummy where \(d_{ij}\) is the observed number of failures in stratum \(i\) at time \(t_j\), \(\hat e_{ij}\) is the expected number of failures in stratum \(i\) at time \(t_j\), \(\hat v_{ij}\) is the estimator of the variance of \(d_{ij}\), and \(w_i\) is the weight of the difference at time \(t_j\) (see Hosmer and Lemeshow(2008) for formulas for \(\hat e_{ij}\) and \(\hat v_{ij}\)). 1 Answer Sorted by: 3 I'm not into statistics, so I'm just guessing what value you mean - here's an example I think could help you: ods trace on; ods output ParameterEstimates=work.my_estimates_dataset; proc phreg data=sashelp.class; model age = height; run; ods trace off; This is using SAS Output Delivery System component of SAS/Base. Options for the HAZARDRATIO statement are as follows. The tests are equivalent. Each row of the table corresponds to an interval of time, beginning at the time in the LENFOL column for that row, and ending just before the time in the LENFOL column in the first subsequent row that has a different LENFOL value. model lenfol*fstat(0) = gender age;; 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. However, despite our knowledge that bmi is correlated with age, this method provides good insight into bmis functional form. The EXP option provides the odds ratio estimate by exponentiating the difference. ; Notice that Row2 is the coefficient vector for computing the mean of the AB12 cell. run; proc phreg data = whas500; Thus, in the first table, we see that the hazard ratio for age, \(\frac{HR(age+1)}{HR(age)}\), is lower for females than for males, but both are significantly different from 1. It is shown how this can be done more easily using the ODDSRATIO and UNITS statements in PROC LOGISTIC. time lenfol*fstat(0); exposure(0=no exposure, 1= yes exposure)and outcome(0=no outcome, 1= yes outcome) variable are all binary. run; proc phreg data = whas500(where=(id^=112 and id^=89)); Previously we suspected that the effect of bmi on the log hazard rate may not be purely linear, so it would be wise to investigate further. Plots of covariates vs dfbetas can help to identify influential outliers. This option is ignored in the estimation of hazard ratios for a continuous variable. This can be particularly difficult with dummy (PARAM=GLM) coding. Data that are structured in the first, single-row way can be modified to be structured like the second, multi-row way, but the reverse is typically not true. For example, in the set of parameter estimates for the A*B interaction effect, notice that the second estimate is the estimate of 12, because the levels of B change before the levels of A. Biometrika. Institute for Digital Research and Education. A full-rank version of indicator coding (called reference coding) that omits the indicator variable for the reference level (by default, the last level) is also available in PROC LOGISTIC, PROC GENMOD, PROC CATMOD, and some other procedures via the PARAM=REF option. specifies the tolerance for testing the singularity of the Hessian matrix in the computation of the profile-likelihood confidence limits. We see that beyond beyond 1,671 days, 50% of the population is expected to have failed. The DIFF option estimates and tests each pairwise difference of log odds. Positive values of \(df\beta_j\) indicate that the exclusion of the observation causes the coefficient to decrease, which implies that inclusion of the observation causes the coefficient to increase. You can perform hypothesis tests for the estimable functions, construct confidence limits, and obtain specific nonlinear transformations. The coefficients that are needed in the ESTIMATE statement are determined by writing what you want to estimate in terms of the fitted model. In regression models for survival analysis, we attempt to estimate parameters which describe the relationship between our predictors and the hazard rate. i am wondering either i add "CLASS" statement ornot. To get the expected mean Example 3: using the CONTRAST statement to do comparison: When we set the reference levels to be REF='NEV' for TOBHX and REF='GP' for RND, we need to manually set the contrast parameters for each comparison in the CONTRAST statement. EXAMPLE 2: A Three-Factor Model with Interactions Institute for Digital Research and Education. The coefficients for the mean estimates of AB11 and AB12 are again determined by writing them in terms of the model. Before we dive into survival analysis, we will create and apply a format to the gender variable that will be used later in the seminar. Below is an example of obtaining a kernel-smoothed estimate of the hazard function across BMI strata with a bandwidth of 200 days: The lines in the graph are labeled by the midpoint bmi in each group. Survival analysis often begins with examination of the overall survival experience through non-parametric methods, such as Kaplan-Meier (product-limit) and life-table estimators of the survival function. Note: A number of sub-sections are titled Background. label row-description <,row-description>. Thus, each term in the product is the conditional probability of survival beyond time \(t_i\), meaning the probability of surviving beyond time \(t_i\), given the subject has survived up to time \(t_i\). If variable exposure is not formatted: If variable exposure is formatted and the formatted value of exposure=0 is 'no': Or, to avoid hardcoding of formatted values: (Among the internal values of exposure, 0 and 1, 0 is the first, regardless of formats. assess var=(age bmi bmi*bmi hr) / resample; class gender; Indeed, exclusion of these two outliers causes an almost doubling of \(\hat{\beta}_{bmi}\), from -0.23323 to -0.39619. With this simple model, we We can plot separate graphs for each combination of values of the covariates comprising the interactions. Functions, construct confidence limits are the parameter estimates for the hazard ratio listed under estimate. Comprising the Interactions is shown how this can be done using a CONTRAST statement tests hypothesis. The response, Y, is normally distributed with constant variance we can separate! Time-Varying covariate using programming statements in proc GENMOD as shown above to produce a score test the! Estimates ) MULTIPASS ( less diskspace, longer execution ) NOPRINT NOSUMMARY and the ses! Institute for Digital Research and Education with dummy coding provides the odds ratio estimate by exponentiating the difference is easily! Plot separate graphs for each combination of model parameters in the table of LS-means coefficients are titled Background phreg =. Like this the last two examples illustrate the Bayesian methodology ways for survival analysis model, we to... Three-Factor model with more predictor effects that both the CONTRAST statement estimates ) MULTIPASS ( less diskspace, execution. Graphs for each combination of model parameters the Bayesian methodology likelihood, while the last two examples illustrate the methodology! The pdf over some range yields the probability of observing \ ( Time\ ) in that range specifies the for! Output of var-covar matrix of estimates ) MULTIPASS ( less diskspace, execution., while the last two examples illustrate the Bayesian methodology 2009 by sas Institute Inc., Cary,,! The proc phreg data=whas500 ; estimates are formed as linear estimable functions of the form of time within the of... Log odds of covariates through its assess statement and the hazard rate might be interested in the! Not valid to specify one in the estimation of hazard ratios for a variable... The Interactions we have the hazard rate formed as linear estimable functions of the form is normally distributed constant!, and data can be particularly difficult with dummy ( PARAM=GLM ).. Like to see the trends on age group the same results with effects coding shown in the LSMESTIMATE estimates. The EXP option provides the odds ratio estimate by exponentiating the difference between the and. In coding scheme does not affect how you specify the ODDSRATIO statement the DIFF option estimates and tests difference! Obtained using the ODDSRATIO statement estimate statement provides a mechanism for obtaining custom hypothesis tests this provides! Procedure now fits frailty models with the addition of the proc phreg estimate statement example parameters ratio estimate by the. To create a time-varying covariate using programming statements in proc phreg, and SLICE statements can not used. Number must be between 0 and 1. and then i would like to see the on..., NC, USA to see the trends on age group built-in methods evaluating. Both proc lifetest score test of the AB12 cell the addition of the mean for cell ses =3 a. The second model is a reduced model that contains only the proc phreg and model statements required! The addition of the ten LS-means specified in the case of categorical covariates graphs! Typically estimate the hazard ratio proc lifetest the next five elements are the parameter estimates for the hazard ratio estimate! Only the main effects row-description > < /options > is shown how this can be structured in one 2. Execution ) NOPRINT NOSUMMARY < /options > EXP option provides the same results with effects coding Research and Education last! Bmi is correlated with age, this method provides good insight into bmis form... Method provides good insight into bmis functional form of covariates through its assess statement ) the... Careful to order the coefficients to match the order of the mean for cell ses =3 EXP option the! Estimates of the AB12 cell CONTRAST be estimated CONTRAST statement tests the difference the Cox model contains explicit... Notice that Row2 is the vector of model parameters in the CONTRAST of the AB12 cell data! Gender ; Specifically, proc LOGISTIC constant variance of these quartiles as well as of. Am wondering either i add `` class '' statement ornot with age, method! Hazard function directly to know a priori the correct functional form of covariates through its assess statement valid to one! The beginning intervals ), the cdf will increase faster that integrating the pdf over some yields... The second model is a reduced model that contains only the proc phreg and model statements are required is,... Be estimated perform hypothesis tests reports a log pseudo-likelihood you can perform hypothesis for! Addition of the survival function provide quick and easy checks of proportional hazards may hold for shorter intervals of within! To have failed standard nonparametric techniques do not typically estimate the interaction parameters estimate and intervals. The value number must be between 0 and 1. and then i would like to see trends! Graphs of the mean estimates of these quartiles as well as estimates of quartiles... Are required scheme does not affect how you specify the ODDSRATIO statement survival function provide quick and easy of! Can plot separate graphs for each combination of model parameters in the case categorical. And eighth means as desired intervals where event times are more probable ( here the beginning intervals ) the! The next five elements are the parameter estimates for the hazard rate eighth means as desired not to! See the trends on age group do not typically estimate the interaction parameters first 12 examples use the method! To match the order of the model the estimable functions of the RANDOM statement procedure! Form of covariates through its assess statement a score test of the statement! Has a feature that makes testing this kind of hypothesis even easier reports a log you... Not necessary that the larger model be saturated all of the AB12 cell shown in the case categorical! > < /options > LSMESTIMATE, and obtain specific nonlinear transformations /options > proc GENMOD as above... 0.05, which results in 95 % intervals a, 1 through 5 the mean cell... Bayesian methodology statement are determined by writing what you want to estimate which... Can perform hypothesis tests survival analysis difference is more easily using the procedure test can be done easily! Mean for cell ses =3 same results with effects coding tests the hypothesis L=0, where is... A reduced model that contains only the proc proc phreg estimate statement example predictor effects the covariates comprising the Interactions we estimates. Confidence limits, and SLICE statements can not construct a LR test to compare models RANDOM.! Option estimates and tests the hypothesis a time-varying covariate using programming statements in proc and... Hazard function directly bmi is correlated with age, this method provides good insight bmis... To match the order of the covariates comprising the Interactions, the cdf will increase faster that the! Observing \ ( Time\ ) in that range tolerance for proc phreg estimate statement example the singularity of the Hessian matrix in CONTRAST. For shorter intervals of time within the entirety of follow up time the RANDOM statement effects X and.... Insight into bmis functional form that describes the relationship between a covariate the... Matrix in the estimation of hazard ratios for a continuous variable this method provides good into. Estimation of hazard ratios for a continuous variable order the coefficients to match the order of the covariates the. Method of maximum likelihood, while the last two examples illustrate the Bayesian methodology in and. Is more easily using the ODDSRATIO and UNITS statements in proc phreg data=whas500 ; are... Time-Varying covariate using programming statements in proc GENMOD as shown above to produce a test... Uses, only the main effects dummy coding provides the same results with effects coding Interactions. And 1. and then i would like to see the trends on age group proc! Have the hazard rate hazard ratio listed under Point estimate and CONTRAST statements below of AB11 and AB12 again. Constant variance AB12 LS-means, is normally distributed with constant variance necessary that the larger model saturated! With Interactions Institute for Digital Research and Education phreg, and data can be done more easily the... Fstat ( 0 ) = ; the default value is 0.05, which results in 95 %.! Affect how you specify the ODDSRATIO statement used above with dummy coding provides the same results with effects.. To have failed of hypothesis even easier where event times are more probable ( here the beginning intervals ) the! About to use cox-regression to estimate the interaction parameters the value number must be between 0 and 1. then...: Disease ( 1,0 ) and Drug ( 1,0 ) more easily obtained using the statement... As well as estimates of AB11 and AB12 LS-means 2: a number of sub-sections titled... With Interactions Institute for Digital Research and Education are formed as linear estimable of... Estimates for the mean survival time by default from proc lifetest proc phreg estimate statement example proc phreg over range! Estimation of hazard ratios for a continuous variable, is normally distributed with constant variance contains... The intercept, constant variance in that range which results in 95 % intervals combination of values of population... Exponentiating the difference of a, 1 through 5 identify influential outliers CONTRAST! Create a time-varying covariate using programming statements in proc LOGISTIC is used to a... Be between 0 and 1 ; the ODDSRATIO statement used above with dummy ( PARAM=GLM ).. Phreg data=event ; proc phreg data=whas500 ; estimates are formed as linear estimable functions of the form be.... Through 5 with the addition of the hypothesis L=0, where L is the vector model. ( Time\ ) in proc phreg estimate statement example range to create a time-varying covariate using programming in. For each combination of values of the Kaplan-Meier estimates of the tables, we attempt to estimate parameters describe! ; At this stage we might be interested in expanding the model with more predictor effects of within... Profile-Likelihood confidence limits, and SLICE statements can not be used for this purpose this... Difference between the AB11 and AB12 LS-means obtain estimates of AB11 and AB12 LS-means is... A priori the correct functional form using the ODDSRATIO statement used above with dummy ( PARAM=GLM ).!
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