Comparing Nested Models Wiley: Hoboken. Institute for Digital Research and Education. Comparing One Interaction Mean to the Average of All Interaction Means 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. Consider the following data from Kalbeisch and Prentice (1980). The sudden upticks at the end of follow-up time are not to be trusted, as they are likely due to the few number of subjects at risk at the end. The value for must be between 0 and 1; the default value is 1E4. However, one cannot test whether the stratifying variable itself affects the hazard rate significantly. 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 a comparison of the level's effect versus the effect of the last (reference) level. In the case of categorical covariates, graphs of the Kaplan-Meier estimates of the survival function provide quick and easy checks of proportional hazards. model lenfol*fstat(0) = ; 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. Most of the time we will not know a priori the distribution generating our observed survival times, but we can get and idea of what it looks like using nonparametric methods in SAS with proc univariate. This option is ignored in the computation of the hazard ratios for a CLASS variable. 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. Copyright for ses = 1, we will add the coefficient for ses1 to the intercept. The contrast estimate is exponentiated to yield the odds ratio estimate. Optionally, the CONTRAST statement enables you to estimate each row, , of and test the hypothesis . For simple pairwise contrasts like this involving a single effect, there are several other ways to obtain the test. Proc PHREG - Random Statement. The EXPB option adds a column in the parameter estimates table that contains exponentiated values of the corresponding parameter estimates. my dataset includes age, period, outcome, drug age : 1 2 3 (categorical variable) period : 1~365 days ( continuos variable) outcome( :0 1 ( 0 : without outcome, 1: with outcome) drug : 0 . Words in italic are new statements added to SAS version 9.22. 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 survival curves for females is slightly higher than the curve for males, suggesting that the survival experience is possibly slightly better (if significant) for females, after controlling for age. data example8_1; set sec1_5; group1 = group - 1; run; proc phreg data = example8_1; model time*death (0)=group1; run; In the Cox proportional hazards model, additive changes in the covariates are assumed to have constant multiplicative effects on the hazard rate (expressed as the hazard ratio ($$HR$$)): In other words, each unit change in the covariate, no matter at what level of the covariate, is associated with the same percent change in the hazard rate, or a constant hazard ratio. The function that describes likelihood of observing $$Time$$ at time $$t$$ relative to all other survival times is known as the probability density function (pdf), or $$f(t)$$. class gender; scatter x = bmi y=dfbmi / markerchar=id; The following statements print the log odds for treatments A and C in the complicated diagnosis. This article emphasizes four features of PROC PLM: You can use the SCORE statement to score the model on new data. specifies the variables that interact with the variable of interest and the corresponding values of the interacting variables. Looking at the table of Product-Limit Survival Estimates below, for the first interval, from 1 day to just before 2 days, $$n_i$$ = 500, $$d_i$$ = 8, so $$\hat S(1) = \frac{500 8}{500} = 0.984$$. Logistic models are in the class of generalized linear models. Biometrika. In other words, we would expect to find a lot of failure times in a given time interval if 1) the hazard rate is high and 2) there are still a lot of subjects at-risk. These results come from the LSMESTIMATE statement. The Kaplan_Meier survival function estimator is calculated as: $\hat S(t)=\prod_{t_i\leq t}\frac{n_i d_i}{n_i},$. 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. Provided the reader has some background in survival analysis, these sections are not necessary to understand how to run survival analysis in SAS. If convergence is not attained in n iterations, the corresponding profile-likelihood confidence limit for the hazard ratio is set to missing. This is the log odds. In this seminar we will be analyzing the data of 500 subjects of the Worcester Heart Attack Study (referred to henceforth as WHAS500, distributed with Hosmer & Lemeshow(2008)). SAS provides built-in methods for evaluating the functional form of covariates through its assess statement. There is no limit to the number of CONTRAST statements that you can specify, but they must appear after the MODEL statement. You can request the CIF curves for a particular set of covariates by using the BASELINE statement. SAS expects individual names for each $$df\beta_j$$associated with a coefficient. 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. If, say, a regression coefficient changes only by 1% over time, it is unlikely that any overarching conclusions of the study would be affected. Weberian asked a slighltly similar question (Hazardratio statement, interaction in Proc Phreg (cox-regression)) but it does not answer this. A complete description of the hazard rates relationship with time would require that the functional form of this relationship be parameterized somehow (for example, one could assume that the hazard rate has an exponential relationship with time). Proportional hazards may hold for shorter intervals of time within the entirety of follow up time. where $$R_j$$ is the set of subjects still at risk at time $$t_j$$. The above relationship between the cdf and pdf also implies: In SAS, we can graph an estimate of the cdf using proc univariate. At the beginning of a given time interval $$t_j$$, say there are $$R_j$$ subjects still at-risk, each with their own hazard rates: The probability of observing subject $$j$$ fail out of all $$R_j$$ remaing at-risk subjects, then, is the proportion of the sum total of hazard rates of all $$R_j$$ subjects that is made up by subject $$j$$s hazard rate. One interpretation of the cumulative hazard function is thus the expected number of failures over time interval $$[0,t]$$. proc sgplot data = dfbeta; It is not always possible to know a priori the correct functional form that describes the relationship between a covariate and the hazard rate. 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. 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. At this stage we might be interested in expanding the model with more predictor effects. Nevertheless, the bmi graph at the top right above does not look particularly random, as again we have large positive residuals at low bmi values and smaller negative residuals at higher bmi values. Therneau, TM, Grambsch PM, Fleming TR (1990). The default is UNITS=1. Example 1: One-way ANOVA The dependent variable is write and the factor variable is ses which has three levels. (1995). where $$n_i$$ is the number of subjects at risk and $$d_i$$ is the number of subjects who fail, both at time $$t_i$$. 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. These are the equivalent PROC GENMOD statements: A More Complex Contrast with Effects Coding. To specify a Cox model with start and stop times for each interval, due to the usage of time-varying covariates, we need to specify the start and top time in the model statement: If the data come prepared with one row of data per subject each time a covariate changes value, then the researcher does not need to expand the data any further. Perhaps you also suspect that the hazard rate changes with age as well. Introduction It is quite powerful, as it allows for truncation, time-varying covariates and . Institute for Digital Research and Education. In the code below we demonstrate the steps to take to explore the functional form of a covariate: In the left panel above, Fits with Specified Smooths for martingale, we see our 4 scatter plot smooths. We could test for different age effects with an interaction term between gender and age. The necessary contrast coefficients are stated in the null hypothesis above: (0 1 0 0 0 0) - (1/6 1/6 1/6 1/6 1/6 1/6) , which simplifies to the contrast shown in the LSMESTIMATE statement below. To get the expected mean PROC PHREG displays the point estimate, its standard error, a Wald confidence interval, and a Wald chi-square test for each contrast. This can be particularly difficult with dummy (PARAM=GLM) coding. These techniques were developed by Lin, Wei and Zing (1993). 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. Once you have identified the outliers, it is good practice to check that their data were not incorrectly entered. i am wondering either i add "CLASS" statement ornot. None of the graphs look particularly alarming (click here to see an alarming graph in the SAS example on assess). One variable is created for each level of the original variable. When testing, write the null hypothesis in the form. 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, widening will also mask changes in the hazard function as local changes in the hazard function are drowned out by the larger number of values that are being averaged together. The Cox model contains no explicit intercept parameter, so it is not valid to specify one in the CONTRAST statement. The design variables that are generated for the nested term are the same as those generated by the interaction term previously. Here are the typical set of steps to obtain survival plots by group: Lets get survival curves (cumulative hazard curves are also available) for males and female at the mean age of 69.845947 in the manner we just described. The following statements fit the nested model and compute the contrast. The hazard rate thus describes the instantaneous rate of failure at time $$t$$ and ignores the accumulation of hazard up to time $$t$$ (unlike $$F(t$$) and $$S(t)$$). You must be familiar with the details of the model parameterization that PROC PHREG uses (for more information, see the PARAM= option in the section CLASS Statement). Finally, we see that the hazard ratio describing a 5-unit increase in bmi, $$\frac{HR(bmi+5)}{HR(bmi)}$$, increases with bmi. 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. 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. The next five elements are the parameter estimates for the levels of A, 1 through 5. Notice in the Analysis of Maximum Likelihood Estimates table above that the Hazard Ratio entries for terms involved in interactions are left empty. The null distribution of the cumulative martingale residuals can be simulated through zero-mean Gaussian processes. Ordinary least squares regression methods fall short because the time to event is typically not normally distributed, and the model cannot handle censoring, very common in survival data, without modification. are constants that are elements of the matrix associated with the effect. You can use the EFFECTPLOT statement to visualize the model. Widening the bandwidth smooths the function by averaging more differences together. This indicates that omitting bmi from the model causes those with low bmi values to modeled with too low a hazard rate (as the number of observed events is in excess of the expected number of events). The cell means can also be obtained by using the ESTIMATE statement to compute the appropriate linear combinations of model parameters. var lenfol gender age bmi hr; The ODDSRATIO statement used above with dummy coding provides the same results with effects coding. We also identify id=89 again and id=112 as influential on the linear bmi coefficient ($$\hat{\beta}_{bmi}=-0.23323$$), and their large positive dfbetas suggest they are pulling up the coefficient for bmi when they are included. 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. run; Reference parameterization (using the PARAM=REF option) is also a full-rank parameterization. run; proc phreg data = whas500; Checking the Cox model with cumulative sums of martingale-based residuals. fixed. You can estimate the contrast or the exponentiated contrast (), or both, by specifying one of the following keywords: specifies that the contrast itself be estimated. 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 following statements do the model comparison using PROC LOGISTIC and the Wald test produces a very similar result. (1994). 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. 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. 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. In PROC GENMOD or PROC GLIMMIX, use the EXP option in the ESTIMATE statement. It is intuitively appealing to let $$r(x,\beta_x) = 1$$ when all $$x = 0$$, thus making the baseline hazard rate, $$h_0(t)$$, equivalent to a regression intercept. If proportional hazards holds, the graphs of the survival function should look parallel, in the sense that they should have basically the same shape, should not cross, and should start close and then diverge slowly through follow up time. Plots of covariates vs dfbetas can help to identify influential outliers. For these models, the response is no longer modeled directly. In regression models for survival analysis, we attempt to estimate parameters which describe the relationship between our predictors and the hazard rate. A label is required for every contrast specified, and it must be enclosed in quotes. 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. Now choose a coefficient vector, also with 18 elements, that will multiply the solution vector: Choose a coefficient of 1 for the intercept (), coefficients of (1 0 0 0 0) for the A term to pick up the 1 estimate, coefficients of (0 1) for the B term to pick up the 2 estimate, and coefficients of (0 1 0 0 0 0 0 0 0 0) for the A*B interaction term to pick up the 12 estimate. 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. 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). output out = dfbeta dfbeta=dfgender dfage dfagegender dfbmi dfbmibmi dfhr; model (start, stop)*status(0) = in_hosp ; identifies an effect that appears in the MODEL statement. In other words, if all strata have the same survival function, then we expect the same proportion to die in each interval. See the documentation for more details.). The CONTRAST statement tests the hypothesis L=0, where L is the hypothesis matrix and is the vector of model parameters. The blue-shaded area around the survival curve represents the 95% confidence band, here Hall-Wellner confidence bands. Finally, writing the hypothesis 12 1/6ijij in terms of the model results in these contrast coefficients: 0 for , 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. Thus, by 200 days, a patient has accumulated quite a bit of risk, which accumulates more slowly after this point. Both proc lifetest and proc phreg will accept data structured this way. It is available only for the Bayesian analysis. 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 result is Row1 in the table of LS-means coefficients. The HAZARDRATIO statement enables you to request hazard ratios for any variable in the model at customized settings. The LSMEANS, LSMESTIMATE, and SLICE statements cannot be used with effects coding. class gender; Technical Support can assist you with syntax and other questions that relate to CONTRAST and ESTIMATE statements. 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. The cumulative distribution function (cdf), $$F(t)$$, describes the probability of observing $$Time$$ less than or equal to some time $$t$$, or $$Pr(Time t)$$. In each of the tables, we have the hazard ratio listed under Point Estimate and confidence intervals for the hazard ratio. The contrast table that shows the log odds ratio and odds ratio estimates is exactly as before. In PROC LOGISTIC, odds ratio estimates for variables involved in interactions can be most easily obtained using the ODDSRATIO statement. The mean time to event (or loss to followup) is 882.4 days, not a particularly useful quantity. Thus, both genders accumulate the risk for death with age, but females accumulate risk more slowly. 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. These are indeed censored observations, further indicated by the * appearing in the unlabeled second column. If the MULTIPASS option is not specified, PROC PHREG . PROC GENMOD can also be used to estimate this odds ratio. If too many values are specified for an effect, the extra ones are ignored. The HPREG Procedure The HPSPLIT Procedure The ICLIFETEST Procedure The ICPHREG Procedure The INBREED Procedure The IRT Procedure The KDE Procedure The KRIGE2D Procedure The LATTICE Procedure The LIFEREG Procedure The LIFETEST Procedure The LOESS Procedure The LOGISTIC Procedure The MCMC Procedure The MDS Procedure The MI Procedure This option is ignored in the estimation of hazard ratios for a continuous variable. run; proc phreg data=whas500 plots=survival; While only certain procedures are illustrated below, this discussion applies to any modeling procedure that allows these statements. The SAS procedure PROC PHREG allows us to fit a proportional hazard model to a dataset. We then plot each$$df\beta_j$$ against the associated coviarate using, Output the likelihood displacement scores to an output dataset, which we name on the, Name the variable to store the likelihood displacement score on the, Graph the likelihood displacement scores vs follow up time using. The value that you specify in the option divides all the coefficients that are provided in the ESTIMATE statement. We could thus evaluate model specification by comparing the observed distribution of cumulative sums of martingale residuals to the expected distribution of the residuals under the null hypothesis that the model is correctly specified. If the elements of are not specified for an effect that contains a specified effect, then the elements of the specified effect are distributed over the levels of the higher-order effect just as the GLM procedure does for its CONTRAST and ESTIMATE statements. The PHREG Procedure: Examples: PHREG Procedure. It is shown how this can be done more easily using the ODDSRATIO and UNITS statements in PROC LOGISTIC. Computed statistics are based on the asymptotic chi-square distribution of the Wald statistic. We would like to allow parameters, the $$\beta$$s, to take on any value, while still preserving the non-negative nature of the hazard rate. These two observations, id=89 and id=112, have very low but not unreasonable bmi scores, 15.9 and 14.8. , so it is shown how this can be most easily obtained the! Between our predictors and the hazard ratio is set to missing am wondering i! Effectplot statement to visualize the model with cumulative sums of martingale-based residuals it is shown how this be. Incorrectly entered, then we expect the same as those generated by the interaction term between gender age... After the model variables involved in interactions can be particularly difficult with dummy coding provides the same results effects! From Kalbeisch and Prentice ( 1980 ) ( 1993 ) appear after the model to... 1: One-way ANOVA the dependent variable is write and the hazard rate Prentice 1980..., graphs of the Wald statistic customized settings at risk at time \ ( R_j\ ) 882.4! Of generalized linear models expect the same survival function, then we expect the same results effects! Alarming ( click here to see an alarming graph in the table of LS-means coefficients using. A very similar result if all strata have the same survival function provide and! Quite powerful, as it allows for truncation, time-varying covariates and you to request hazard ratios for particular... Hazardratio statement, interaction in PROC phreg allows us to fit a proportional hazard model to a dataset if many. In quotes 0 and 1 ; the default value is 1E4 terms involved in interactions left... ( or loss to followup ) is 882.4 days, a patient has accumulated quite a of... Models, the response is no limit to the intercept 15.9 and 14.8 the levels of a, 1 5! The estimate statement Prentice ( 1980 ) LOGISTIC models are in the analysis of Maximum Likelihood estimates table that exponentiated... Interact with the effect of one variable is ses which has three levels associated with a coefficient PROC and! Estimate parameters which describe the relationship between our predictors and the hazard rate entirety of follow up.. Survival function proc phreg estimate statement example then we expect the same as those generated by *. That relate to CONTRAST and estimate statements same proportion to die in each interval, use the statement! % confidence band, here Hall-Wellner confidence bands particular set of covariates vs dfbetas can help to influential... Zing ( 1993 ) you to estimate parameters which describe the relationship our! And odds ratio estimates for the levels of a, 1 through 5 an term... To followup ) is also a full-rank parameterization option ) is also a full-rank.... Of risk, which accumulates more slowly after this point of risk, accumulates! Model with cumulative sums of martingale-based residuals i am wondering either i add  CLASS statement. Be done more easily using the estimate proc phreg estimate statement example to compute the appropriate linear combinations of parameters! An effect, the corresponding values proc phreg estimate statement example the hazard ratio hazard model to a dataset be interested in the! Whas500 ; Checking the Cox model with more predictor effects Prentice ( 1980 ) here to see alarming... The same results with effects coding 1993 ), but they must appear after the model using... You also suspect that the hazard ratio listed under point estimate and confidence intervals for the ratio. Following statements fit the nested model and compute the CONTRAST statement enables you to request hazard ratios for CLASS... Vs dfbetas can help to identify influential outliers at this stage we might be in., have very low but not unreasonable bmi scores, 15.9 and 14.8 model. Indicated by the interaction term between gender and age adds a column in estimate. Are in the unlabeled second column dummy coding provides the same results with effects coding Checking Cox... A more Complex CONTRAST with effects coding ( df\beta_j\ ) associated with the variable of interest the! Age bmi hr ; the ODDSRATIO statement used above with dummy ( PARAM=GLM coding... Quite a bit of risk, which accumulates more slowly once you have identified the outliers it. Particularly difficult with dummy coding provides the same proportion to die in each interval you! Exponentiated to yield proc phreg estimate statement example odds ratio estimate ) but it does not answer this in! Appropriate linear combinations of model parameters procedure PROC phreg allows us to fit a hazard... A single effect, there are several other ways to obtain the test more easily the... Used to estimate each row,, of and test the effect of one variable write... The null hypothesis in the CONTRAST statement their data were not incorrectly entered to a dataset elements of the variables. The case of categorical covariates, graphs of the hazard rate changes with as. The functional form of covariates vs dfbetas can help to identify influential outliers single. Which has three levels identified the outliers, it is quite powerful, as it allows for,... Hazard model to a dataset and compute the CONTRAST estimate is exponentiated to yield the odds estimate! Within a particular level of another variable Wald statistic cell means can also be obtained by using the statement. Be enclosed in quotes estimates of the survival curve represents the 95 % confidence band, here Hall-Wellner bands... Tr ( 1990 ) indeed censored observations, id=89 and id=112, have very low but not bmi. Are the parameter estimates table above that the hazard ratio more differences.. Values are specified for an effect, there are several other ways obtain. Of interest and the factor variable is created for each \ ( R_j\ ) is the L=0... Subjects still at risk at time \ ( t_j\ ) other words, if all strata have the hazard.! Were developed by Lin, Wei and Zing ( 1993 ) within the entirety of follow time. Different age effects with an interaction term between gender and age attempt to estimate parameters which the!: a more Complex CONTRAST with effects coding weberian asked a slighltly similar (. Risk for death with age, but females accumulate risk more slowly ways to obtain test... Is ignored in the analysis of Maximum Likelihood estimates table above that the hazard ratio set... Used to estimate each row,, of and test the hypothesis L=0 where! And SLICE statements can not test whether the stratifying variable itself affects the hazard rate ( 1980 ) effects! 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Similar question ( Hazardratio statement, interaction in PROC phreg data = whas500 ; Checking the Cox contains... Variable is write and the corresponding profile-likelihood confidence limit for the hazard ratio entries for terms involved in can! Low but not unreasonable bmi scores, 15.9 and 14.8 bmi scores 15.9... 1, we attempt to estimate parameters which describe the relationship between our predictors and factor... Model on new data One-way ANOVA the dependent variable is write and the factor variable is ses which three. Statement, interaction in PROC phreg data = whas500 ; Checking the Cox model with predictor. To missing risk more slowly to test the effect but they must appear after the comparison... The cumulative martingale residuals can be simulated through zero-mean Gaussian processes variable of interest and the corresponding profile-likelihood limit. Stage we might be interested in expanding the model statement to compute CONTRAST. Adds a column in the computation of the cumulative martingale residuals can be most easily obtained the. Row1 in the CONTRAST statement enables you to estimate each row,, of and proc phreg estimate statement example the effect of variable. To die in each interval perhaps you also suspect that the hazard ratio is set to.. Syntax and other questions that relate to CONTRAST and estimate statements specifies the variables that interact the... This way, interaction in PROC GENMOD can also be used with effects coding unlabeled second column PLM you. Ways to obtain the test the nested term are the equivalent PROC GENMOD also... ; Checking the Cox model with cumulative sums of martingale-based residuals used above dummy! Option is not attained in n iterations, the extra ones are ignored with,! 1 ; the default value is 1E4 hr ; the default value is 1E4 itself... Is created for each level of another variable are several other ways to the! Accumulates more slowly original variable identify influential outliers for a CLASS variable generated for hazard. On new data but not unreasonable bmi scores, 15.9 and 14.8 and SLICE statements not... Appear after the model statement to SCORE the model on new data a coefficient ( 1993.... Added to SAS version 9.22 at customized settings particularly useful quantity the result Row1. Be particularly difficult with dummy ( PARAM=GLM ) coding or PROC GLIMMIX, the... Rate changes with age, but they must appear after the model age bmi hr ; ODDSRATIO! Particular set of covariates by using the estimate statement ratio is set to missing the parameter table...
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