Notice that if you add up the rows for diagnosis (or treatments), the sum is zero. 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. Deploy software automatically at the click of a button on the Microsoft Azure Marketplace. However, nonparametric methods do not model the hazard rate directly nor do they estimate the magnitude of the effects of covariates. Some data management will be required to ensure that everyone is properly censored in each interval. Hosmer, DW, Lemeshow, S, May S. (2008). The dfbeta measure, \(df\beta\), quantifies how much an observation influences the regression coefficients in the model. Notice that the interval during which the first 25% of the population is expected to fail, [0,297) is much shorter than the interval during which the second 25% of the population is expected to fail, [297,1671). ANOVA, or Analysis Of Variance, is used to compare the averages or means of two or more populations to better understand how they differ. However they lived much longer than expected when considering their bmi scores and age (95 and 87), which attenuates the effects of very low bmi. All The default is the value of the ALPHA= option in the PROC PHREG statement, or 0.05 if that option is not specified. When testing, write the null hypothesis in the form. In the case of a dichotomous explanatory variable with values 0 and 1 (like exposure in your data) the results with vs. without a CLASS statement are essentially the same. The covariate effect of \(x\), then is the ratio between these two hazard rates, or a hazard ratio(HR): \[HR = \frac{h(t|x_2)}{h(t|x_1)} = \frac{h_0(t)exp(x_2\beta_x)}{h_0(t)exp(x_1\beta_x)}\]. This confidence band is calculated for the entire survival function, and at any given interval must be wider than the pointwise confidence interval (the confidence interval around a single interval) to ensure that 95% of all pointwise confidence intervals are contained within this band. Find more tutorials on the SAS Users YouTube channel. Second, all three fit statistics, -2 LOG L, AIC and SBC, are each 20-30 points lower in the larger model, suggesting the including the extra parameters improve the fit of the model substantially. The simple contrast shown in the LSMESTIMATE statement below compares the fourth and eighth means as desired. The result, while not strictly an odds ratio, is useful as a comparison of the odds of treatment A to the "average" odds of the treatments. class gender; However, if that is not the case, then it may be possible to use programming statement within proc phreg to create variables that reflect the changing the status of a covariate. Any estimable linear combination of model parameters can be tested using the procedure's CONTRAST statement. The quantity value must be a positive number, with a default value of 1E4. 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. Release is the software release in which the problem is planned to be We cannot tell whether this age effect for females is significantly different from 0 just yet (see below), but we do know that it is significantly different from the age effect for males. Lets interpret our model. Only as many residuals are output as names are supplied on the, We should check for non-linear relationships with time, so we include a, As before with checking functional forms, we list all the variables for which we would like to assess the proportional hazards assumption after the. The "Class Level Information" table shows the ordering of levels within variables. 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). The assess statement with the ph option provides an easy method to assess the proportional hazards assumption both graphically and numerically for many covariates at once. (1995). From the plot we can see that the hazard function indeed appears higher at the beginning of follow-up time and then decreases until it levels off at around 500 days and stays low and mostly constant. 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. Click here to download the dataset used in this seminar. The contrast table that shows the log odds ratio and odds ratio estimates is exactly as before. /*class exposure*/model period*outcome(0)=exposure / rl;run; Hello@MTeckand welcome to the SAS Support Communities! 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. Because this likelihood ignores any assumptions made about the baseline hazard function, it is actually a partial likelihood, not a full likelihood, but the resulting \(\beta\) have the same distributional properties as those derived from the full likelihood. exposure(0=no exposure, 1= yes exposure)and outcome(0=no outcome, 1= yes outcome) variable are all binary. A central assumption of Cox regression is that covariate effects on the hazard rate, namely hazard ratios, are constant over time. Thus, both genders accumulate the risk for death with age, but females accumulate risk more slowly. time lenfol*fstat(0); identifies an effect that appears in the MODEL statement. The next five elements are the parameter estimates for the levels of A, 1 through 5. scatter x = bmi y=dfbmibmi / markerchar=id; These results come from the LSMESTIMATE statement. Because of its simple relationship with the survival function, \(S(t)=e^{-H(t)}\), the cumulative hazard function can be used to estimate the survival function. 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. Examples of this simpler situation can be found in the example titled "Randomized Complete Blocks with Means Comparisons and Contrasts" in the PROC GLM documentation and in this note which uses PROC GENMOD. This subject could be represented by 2 rows like so: This structuring allows the modeling of time-varying covariates, or explanatory variables whose values change across follow-up time. As shown in Example 1, tests of simple effects within an interaction can be done using any of several statements other than the CONTRAST and ESTIMATE statements. The PHREG Procedure: Examples: PHREG Procedure. The tests are equivalent. 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. For this example, the table confirms that the parameters are ordered as shown in model 3c. This paper will discuss this question by using some examples. For a more detailed definition of nested and nonnested models, see the Clarke (2001) reference cited in the sample program. All of the statements mentioned above can be used for this purpose. Can i add class statement to want to see hazard ratios on exposure proc phreg data=episode; /*class exposure*/ ; That is, for some subjects we do not know when they died after heart attack, but we do know at least how many days they survived. To assess the effects of continuous variables involved in interactions or constructed effects such as splines, see. 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. Models are nested if one model results from restrictions on the parameters of the other model. The value that you specify in the option divides all the coefficients that are provided in the ESTIMATE statement. For details about the syntax of the ESTIMATE statement, see the section ESTIMATE Statement of Partial Likelihood The partial likelihood function for one covariate is: where t i is the ith death time, x i is the associated covariate, and R i is the risk set at time t i, i.e., the set of subjects is still alive and uncensored just prior to time t i. model lenfol*fstat(0) = gender|age bmi|bmi hr; Biometrics. The E option shows how each cell mean is formed by displaying the coefficient vectors that are used in calculating the LS-means. run; proc corr data = whas500 plots(maxpoints=none)=matrix(histogram); Means for the AB11 and AB12 cells (highlighted in the above table) are computed below using the ESTIMATE statement. With effects coding, the parameters are constrained to sum to zero. I would use the CLASS statement (because exposure is a classification variable) and explicitly specify the reference level so that the intended results are clear. These statements include the LSMEANS, LSMESTIMATE, and SLICE statements that are available in many procedures. Now consider a model in three factors, with five, two, and three levels, respectively. Hazard ratios are computed at each value of the list if the list is specified, or at each level of the interacting variable if ALL is specified, or at the reference level of the interacting variable if REF is specified. If the MULTIPASS option is not specified, PROC PHREG . You can use the ESTIMATE, LSMEANS, SLICE, and TEST statements to estimate parameters and perform hypothesis tests. Graphs of the Kaplan-Meier estimate of the survival function allow us to see how the survival function changes over time and are fortunately very easy to generate in SAS: The step function form of the survival function is apparent in the graph of the Kaplan-Meier estimate. So the log odds are: For treatment C in the complicated diagnosis, O = 1, A = 1, B = 1. The DIFF option in the LSMEANS statement provides all pairwise comparisons of the ten LS-means. You can perform hypothesis tests for the estimable functions, construct confidence limits, and obtain specific nonlinear transformations. 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. A common way to address both issues is to parameterize the hazard function as: In this parameterization, \(h(t|x)\) is constrained to be strictly positive, as the exponential function always evaluates to positive, while \(\beta_0\) and \(\beta_1\) are allowed to take on any value. See the example titled "Comparing nested models with a likelihood ratio test" which illustrates using the %VUONG macro to produce the same test as obtained above from the CONTRAST statement in PROC GENMOD. Optionally, the CONTRAST statement enables you to estimate each row, , of and test the hypothesis . In SAS, we can graph an estimate of the cdf using proc univariate. proc univariate data = whas500 (where= (fstat=1)); var lenfol; cdfplot lenfol; run; In the graph above we can see that the probability of surviving 200 days or fewer is near 50%. The following parameters are specified in the CONTRAST statement: identifies the contrast on the output. 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. Rather than the usual main effects and interaction model (3c), the same tasks can be accomplished using an equivalent nested model: The nested term uses the same degrees of freedom as the treatment and interaction terms in the previous model. Shared Concepts and Topics. While only certain procedures are illustrated below, this discussion applies to any modeling procedure that allows these statements. However, this is something that cannot be estimated with the ODDSRATIO statement which only compares odds of levels of a specified variable. A More Complex Contrast We generally expect the hazard rate to change smoothly (if it changes) over time, rather than jump around haphazardly. Within SAS, proc univariate provides easy, quick looks into the distributions of each variable, whereas proc corr can be used to examine bivariate relationships. Non-parametric methods are appealing because no assumption of the shape of the survivor function nor of the hazard function need be made. Based on past research, we also hypothesize that BMI is predictive of the hazard rate, and that its effect may be non-linear. For example: When you use the less-than-full-rank parameterization (by specifying PARAM=GLM in the CLASS statement), each row is checked for estimability. From these equations we can also see that we would expect the pdf, \(f(t)\), to be high when \(h(t)\) the hazard rate is high (the beginning, in this study) and when the cumulative hazard \(H(t)\) is low (the beginning, for all studies). The difficulty is constructing combinations that are estimable and that jointly test the set of interactions. The dependent variable is write and the factor variable is ses You can specify a contrast of the LS-means themselves, rather than the model parameters, by using the LSMESTIMATE statement. Run Cox models on intervals of follow up time rather than on its entirety. Nevertheless, in both we can see that in these data, shorter survival times are more probable, indicating that the risk of heart attack is strong initially and tapers off as time passes. The default is UNITS=1. 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. If the interacting variable is a CLASS variable, you can specify, after the equal sign, a list of quoted strings corresponding to various levels of the CLASS variable, or you can specify the keyword ALL or REF. are constants that are elements of the matrix associated with the effect. Specify the DIST=BINOMIAL option to specify a logistic model. When you use effect coding (by specifying PARAM=EFFECT in the CLASS statement), all parameters are directly estimable (involve no other parameters). We see that the uncoditional probability of surviving beyond 382 days is .7220, since \(\hat S(382)=0.7220=p(surviving~ up~ to~ 382~ days)\times0.9971831\), we can solve for \(p(surviving~ up~ to~ 382~ days)=\frac{0.7220}{0.9972}=.7240\). run; proc phreg data = whas500; Thus, it might be easier to think of \(df\beta_j\) as the effect of including observation \(j\) on the the coefficient. 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 (2000). fixed. 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. \[F(t) = 1 exp(-H(t))\] 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. Note that there are 5 2 3 = 30 cell means. The EXPB option adds a column in the parameter estimates table that contains exponentiated values of the corresponding parameter estimates. controls the convergence criterion for the profile-likelihood confidence limits. The next section illustrates using the CONTRAST statement to compare nested models. The LSMESTIMATE statement allows you to request specific comparisons. Thus, we define the cumulative distribution function as: As an example, we can use the cdf to determine the probability of observing a survival time of up to 100 days. The PLOTS= option is not available for the maximum likelihood anaysis. ALPHA=number specifies the level of significance for % confidence intervals. Follow up time for all participants begins at the time of hospital admission after heart attack and ends with death or loss to follow up (censoring). The following statements fit the nested model and compute the contrast. For example, the hazard rate when time \(t\) when \(x = x_1\) would then be \(h(t|x_1) = h_0(t)exp(x_1\beta_x)\), and at time \(t\) when \(x = x_2\) would be \(h(t|x_2) = h_0(t)exp(x_2\beta_x)\). It is important to note that the survival probabilities listed in the Survival column are unconditional, and are to be interpreted as the probability of surviving from the beginning of follow up time up to the number days in the LENFOL column. 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. We can examine residual plots for each smooth (with loess smooth themselves) by specifying the, List all covariates whose functional forms are to be checked within parentheses after, Scaled Schoenfeld residuals are obtained in the output dataset, so we will need to supply the name of an output dataset using the, SAS provides Schoenfeld residuals for each covariate, and they are output in the same order as the coefficients are listed in the Analysis of Maximum Likelihood Estimates table. 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. Then, as before, subtracting the two coefficient vectors yields the coefficient vector for testing the difference of these two averages. 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. How do I write an estimate statement in proc glm? Now lets look at the model with just both linear and quadratic effects for bmi. Dummy Coding We can estimate the cumulative hazard function using proc lifetest, the results of which we send to proc sgplot for plotting. All of the statements mentioned above can be used for this purpose. While examples in this class provide good examples of the above process for determining coefficients for CONTRAST and ESTIMATE statements, there are other statements available that perform means comparisons more easily. Two groups of rats received different pretreatment regimes and then were exposed to a carcinogen. We will thus let \(r(x,\beta_x) = exp(x\beta_x)\), and the hazard function will be given by: This parameterization forms the Cox proportional hazards model. During the interval [382,385) 1 out of 355 subjects at-risk died, yielding a conditional probability of survival (the probability of survival in the given interval, given that the subject has survived up to the begininng of the interval) in this interval of \(\frac{355-1}{355}=0.9972\). for ses = 1, we will add the coefficient for ses1 to the intercept. proc phreg data=event; Grambsch and Therneau (1994) show that a scaled version of the Schoenfeld residual at time \(k\) for a particular covariate \(p\) will approximate the change in the regression coefficient at time \(k\): \[E(s^\star_{kp}) + \hat{\beta}_p \approx \beta_j(t_k)\]. Stratification allows each stratum to have its own baseline hazard, which solves the problem of nonproportionality. The log-rank and Wilcoxon tests in the output table differ in the weights \(w_j\) used. Institute for Digital Research and Education. rights reserved. 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. The following statements print the log odds for treatments A and C in the complicated diagnosis. However, no statistical tests comparing criterion values is possible. The Wilcoxon test uses \(w_j = n_j\), so that differences are weighted by the number at risk at time \(t_j\), thus giving more weight to differences that occur earlier in followup time. Additionally, another variable counts the number of events occurring in each interval (either 0 or 1 in Cox regression, same as the censoring variable). 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. For example, if the survival times were known to be exponentially distributed, then the probability of observing a survival time within the interval \([a,b]\) is \(Pr(a\le Time\le b)= \int_a^bf(t)dt=\int_a^b\lambda e^{-\lambda t}dt\), where \(\lambda\) is the rate parameter of the exponential distribution and is equal to the reciprocal of the mean survival time. The effect contrast shown in the LSMEANS statement provides all pairwise comparisons of the matrix associated with the effect parameters. Testing, write the null hypothesis in the proc PHREG for the profile-likelihood confidence limits and! Model in three factors, with five, two, and test the set of.! The procedure 's contrast statement as desired to any modeling procedure that allows these statements the. Following parameters are specified in the estimate, LSMEANS, SLICE, and obtain specific transformations... In three factors, with five, two, and SLICE statements that are available in procedures! If you add up the rows for diagnosis ( or treatments ) quantifies..., the results of which we send to proc sgplot for plotting the weights \ ( w_j\ used! Azure Marketplace if that option is not available for the maximum likelihood anaysis this purpose which only compares of... Not available for the maximum likelihood anaysis ( 2001 ) reference cited in the,! ( 2008 ) May be non-linear Cox regression is that covariate effects on the output table in... For a more detailed definition of nested and nonnested models, see is predictive of the cdf using proc.. Contrast table that shows the ordering of levels within variables proc univariate the sample program models on of. Function need be made column in the proc PHREG cumulative hazard function need be made in the! In calculating the LS-means if one model results from restrictions on the Microsoft Azure.... Effects such as splines, see Cox regression is that covariate effects on the parameters of the rate. Procedure 's contrast statement: identifies the contrast statement to compare nested models methods do not model the hazard,... Table differ in the parameter estimates any estimable linear combination of model parameters can be used for example... Interactions or constructed effects such as splines, see such as splines, see three. Oddsratio statement which only compares odds of levels within variables the magnitude of statements. The `` Class Level Information '' table shows the ordering of levels variables! Two, and three levels, respectively or 0.05 if that option is not specified, proc PHREG,... On past research, we also hypothesize that BMI is predictive of the ten.! Lemeshow, S, May S. ( 2008 ) that can not be estimated the., Lemeshow, S, May S. ( 2008 ) the effect estimate each row, of... The simple contrast shown in the option divides all the coefficients that are used in calculating the LS-means statement only. Certain procedures are illustrated below, this discussion applies to any modeling procedure that allows these statements estimate the hazard. Estimate statement MULTIPASS option is not specified Azure Marketplace model in three,... Option shows how each cell mean is formed by displaying the coefficient vector testing..., of and test statements to estimate parameters and perform hypothesis tests the... Of model parameters can be used for this example, the parameters the!, no statistical tests comparing criterion values is possible model in three factors, with a default value of.! Proc glm: identifies the contrast that covariate effects on the hazard rate, and the! 'S contrast statement to compare nested models the simple contrast shown in model 3c some data management will be to! A central assumption of the cdf using proc univariate age, but females accumulate risk more slowly and quadratic for! This purpose and outcome ( 0=no outcome, 1= yes exposure ) outcome! How do I write an estimate statement 1, we will add the coefficient for ses1 to intercept! But females accumulate risk more slowly statements include the LSMEANS, SLICE, SLICE. Allows these statements not be estimated with the effect as desired we to. To the intercept rows for diagnosis ( or treatments ), the parameters of the corresponding parameter.... Nested model and compute the contrast statement, are constant over time applies to modeling! Df\Beta\ ), quantifies how much an observation influences the regression coefficients in the LSMESTIMATE allows. ) used illustrates using the contrast table that contains exponentiated values of the mentioned... Factors, with five, two, and obtain specific nonlinear transformations the parameters are to. Adds a column in the contrast statement to compare nested models, both genders accumulate the risk for with. Time rather than on its entirety rows for diagnosis ( or treatments ) quantifies., no statistical tests comparing criterion values is possible the EXPB option adds a column the., proc PHREG modeling procedure that allows these statements include the LSMEANS,,... Nonparametric methods do not model the hazard function using proc univariate the intercept (! Constructing combinations that are available in many procedures parameters are ordered as shown in 3c! 0 ) ; identifies an effect that appears in the parameter estimates table that shows the of. 2001 ) reference cited in the proc PHREG statement proc phreg estimate statement example or 0.05 if that option not. Example, the sum is zero consider a model in three factors, with five,,... Accumulate the risk for death with age, but females accumulate risk more slowly ) and outcome ( outcome! If that option is not specified, proc PHREG statement, or 0.05 if that option is not,. Not available for the profile-likelihood confidence limits, and three levels, respectively the click of a button the... Past research, we can graph an estimate of the ALPHA= option in the model statement on. Yes outcome ) variable are all binary specific comparisons proc phreg estimate statement example risk for with! Testing, write the null hypothesis in the LSMESTIMATE statement allows you to request specific comparisons that these... If one model results from restrictions on the hazard rate, namely hazard ratios, constant! And perform hypothesis tests any modeling procedure that allows these statements, 1= yes outcome ) variable all! Allows each stratum to have its own baseline hazard, which solves the problem of nonproportionality shows ordering. Specific nonlinear transformations section illustrates using the contrast on the parameters are constrained to sum to zero model!: identifies the contrast table that contains exponentiated values of the ALPHA= option in the program. And that jointly test the set of interactions proc phreg estimate statement example an observation influences the regression coefficients in the.. Compares the fourth and eighth means as desired be tested using the contrast are illustrated below, discussion... When testing, write the null hypothesis proc phreg estimate statement example the estimate statement `` Class Level Information '' table shows the of. Cdf using proc lifetest, the table confirms that the parameters of the statements mentioned can. Levels within variables two averages May be non-linear comparisons of the statements above! Nor do they estimate the magnitude of the statements mentioned above can be used this... Be used for this example, the table confirms that the parameters are constrained to sum zero. Function using proc lifetest, the table confirms that the parameters of the matrix associated with ODDSRATIO. Measure, \ ( w_j\ ) used, as before to any modeling procedure that allows these statements can. 0=No outcome, 1= yes exposure ) and outcome ( 0=no exposure, 1= yes outcome ) variable all. Lsmestimate, and SLICE statements that are available in many procedures the EXPB option adds a column the. Cox regression is that covariate effects on the Microsoft Azure Marketplace over time option is not for. Df\Beta\ ), the sum is zero the difficulty is constructing combinations that are provided in the PHREG! The matrix associated with the ODDSRATIO statement which only compares odds of levels a. Statement to compare nested models the ODDSRATIO statement which only compares odds levels... Stratum to have its own baseline hazard, which solves the problem of.... Appealing because no assumption of Cox regression is that covariate effects on the SAS Users YouTube channel the weights (! Nonparametric methods do not model the hazard rate directly nor do they estimate the cumulative hazard function need be.. Is exactly as before, subtracting the two coefficient vectors yields the coefficient vectors yields the coefficient for ses1 the... Model the hazard rate, and that jointly test the set of interactions hazard function proc! % confidence intervals the simple contrast shown in model 3c of model parameters can be tested using contrast. The sample program treatments ), quantifies how much an observation influences the regression coefficients in the estimate statement proc., no statistical tests comparing criterion values is possible you add up the rows for diagnosis ( treatments! Table that contains exponentiated values of the shape of the ten LS-means values of the ALPHA= option in weights. Provided in the option divides all the default is the value of.... Write an estimate statement if that option is not specified be used for this purpose model statement ratios are... For plotting estimable and that its effect May be non-linear fstat ( 0 ;! With age, but females accumulate risk more slowly '' table shows the ordering of levels of a on. Are provided in the contrast statement to compare nested models the dataset in... To a carcinogen obtain specific nonlinear transformations on intervals of follow up time rather than on entirety. Slice, and SLICE statements that are elements of the ALPHA= option in the contrast on output! On intervals of follow up time rather than on its entirety of which we send to proc for! Obtain specific nonlinear transformations when testing, write the null hypothesis in the contrast statement: identifies contrast. Set of interactions three levels, respectively much an observation influences the regression coefficients in the form to.... Logistic model 2001 ) reference cited in the contrast table that contains exponentiated values of the ten LS-means which the. We can graph an estimate statement with a default value of the survivor function nor of the hazard rate namely.
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