proc phreg estimate statement example

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 \(\frac{355-1}{355}=0.9972\). As a consequence, you can test or estimate only homogeneous linear combinations (those with zero-intercept coefficients, such as contrasts that represent group differences) for the GLM parameterization. Effects Coding Phreg For Survival Analysis In Sas 9 has been minimal coverage in the available literature to9 guide researchers, practitioners, and students who wish to apply these methods to health-related areas of study. But an equivalent representation of the model is: where Ai and Bj are sets of design variables that are defined as follows using dummy coding: For the medical example above, model 3b for the odds of being cured are: Estimating and Testing Odds Ratios with Dummy Coding. If 3.5 is the average of the sampled values of X, the following two HAZARDRATIO statements are equivalent: specifies whether to create the Wald or profile-likelihood confidence limits, or both for the classical analyis. Here we use proc lifetest to graph \(S(t)\). This example shows the use of the CONTRAST and ODDSRATIO statements to compare the response at two levels of a continuous predictor when the model contains a higher-order effect. = 1 and cell ses = 2 will be the difference of b_1 and b_2. If this option is not specified, PROC PHREG finds all the variables that interact with the variable of interest. 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. run; proc phreg data = whas500; None of the graphs look particularly alarming (click here to see an alarming graph in the SAS example on assess). You can perform hypothesis tests for the estimable functions, construct confidence limits, and obtain specific nonlinear transformations. For example, suppose an effect coded CLASS variable A has four levels. The first 12 examples use the classical method of maximum likelihood, while the last two examples illustrate the Bayesian methodology. In an example from Ries and Smith (1963), the choice of detergent brand (Brand= M or X) is related to three other categorical variables: the softness of the laundry water (Softness= soft, medium, or hard); the temperature of the water (Temperature= high or low); and whether the subject was a previous user of Brand M (Previous= yes or no). Hosmer, DW, Lemeshow, S, May S. (2008). The LSMESTIMATE statement allows you to request specific comparisons. Firths Correction for Monotone Likelihood, Conditional Logistic Regression for m:n Matching, Model Using Time-Dependent Explanatory Variables, Time-Dependent Repeated Measurements of a Covariate, Survivor Function Estimates for Specific Covariate Values, Model Assessment Using Cumulative Sums of Martingale Residuals, Bayesian Analysis of Piecewise Exponential Model. Here we see the estimated pdf of survival times in the whas500 set, from which all censored observations were removed to aid presentation and explanation. Auto-suggest helps you quickly narrow down your search results by suggesting possible matches as you type. It is not at all necessary that the hazard function stay constant for the above interpretation of the cumulative hazard function to hold, but for illustrative purposes it is easier to calculate the expected number of failures since integration is not needed. In PROC LOGISTIC, odds ratio estimates for variables involved in interactions can be most easily obtained using the ODDSRATIO statement. 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. As an example, suppose that you intend to use PROC REG to perform a linear regression, and you want to capture the R-square value in a SAS data set. The second model is a reduced model that contains only the main effects. In a nutshell, these statistics sum the weighted differences between the observed number of failures and the expected number of failures for each stratum at each timepoint, assuming the same survival function of each stratum. 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 (1993). Censored observations are represented by vertical ticks on the graph. Effects or Deviation from mean coding of a predictor replaces the actual variable in the design matrix (or model matrix) with a set of variables that use values of 1, 0, or 1 to indicate the level of the original variable. The difficulty is constructing combinations that are estimable and that jointly test the set of interactions. Table 64.4 summarizes important options in the ESTIMATE statement. A main effect parameter is interpreted as the deviation of the level's effect from the average effect of all the levels. run; proc phreg data = whas500; 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. Finally, we strongly suspect that heart rate is predictive of survival, so we include this effect in the model as well. We can remove the dependence of the hazard rate on time by expressing the hazard rate as a product of \(h_0(t)\), a baseline hazard rate which describes the hazard rates dependence on time alone, and \(r(x,\beta_x)\), which describes the hazard rates dependence on the other \(x\) covariates: In this parameterization, \(h(t)\) will equal \(h_0(t)\) when \(r(x,\beta_x) = 1\). Unless the seed option is specified, these sets will be different each time proc phreg is run. After fitting both models and constructing a data set with variables containing predicted values from both models, the %VUONG macro with the TEST=LR parameter provides the likelihood ratio test. In other words, if all strata have the same survival function, then we expect the same proportion to die in each interval. This note focuses on assessing the effects of categorical (CLASS) variables in models containing interactions. These techniques were developed by Lin, Wei and Zing (1993). run; proc phreg data = whas500; specifies the alpha level of the interval estimates for the hazard ratios. | SAS FAQ We will use a data set called hsb2.sas7bdat to demonstrate. output out = dfbeta dfbeta=dfgender dfage dfagegender dfbmi dfbmibmi dfhr; An estimate statement corresponds to an L-matrix, which corresponds to a The hazard rate can also be interpreted as the rate at which failures occur at that point in time, or the rate at which risk is accumulated, an interpretation that coincides with the fact that the hazard rate is the derivative of the cumulative hazard function, \(H(t)\). If the MULTIPASS option is not specified, PROC PHREG . The LSMEANS, LSMESTIMATE, and SLICE statements cannot be used with effects coding. Violations of the proportional hazard assumption may cause bias in the estimated coefficients as well as incorrect inference regarding significance of effects. Based on past research, we also hypothesize that BMI is predictive of the hazard rate, and that its effect may be non-linear. However, nonparametric methods do not model the hazard rate directly nor do they estimate the magnitude of the effects of covariates. 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. Disease: 1=Disease, 0=No disease Drug: 1=Drug, 0=No drug This make the interaction a "2x2 table" (as below). The PLMAXITER= option has no effect if profile-likelihood confidence intervals (CL=PL) are not requested. assess var=(age bmi bmi*bmi hr) / resample; 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. Additionally, another variable counts the number of events occurring in each interval (either 0 or 1 in Cox regression, same as the censoring variable). Now consider a model in three factors, with five, two, and three levels, respectively. Therneau and colleagues(1990) show that the smooth of a scatter plot of the martingale residuals from a null model (no covariates at all) versus each covariate individually will often approximate the correct functional form of a covariate. 77(1). Therefore, the estimate of the last level of an effect, A, is a= (1 + 2 + + a1). The contrast of the ten LS-means specified in the LSMESTIMATE statement estimates and tests the difference between the AB11 and AB12 LS-means. 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. (1995). 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. For this example, the table confirms that the parameters are ordered as shown in model 3c. Any estimable linear combination of model parameters can be tested using the procedure's CONTRAST statement. Can i add class statement to want to see hazard ratios on exposure. 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. Note that the difference in log odds is equivalent to the log of the odds ratio: So, by exponentiating the estimated difference in log odds, an estimate of the odds ratio is provided. \[F(t) = 1 exp(-H(t))\] The mean time to event (or loss to followup) is 882.4 days, not a particularly useful quantity. The BMI*BMI term describes the change in this effect for each unit increase in bmi. This can be done by multiplying the vector of parameter estimates (the solution vector) by a vector of coefficients such that their product is this sum. model lenfol*fstat(0) = gender|age bmi hr; Institute for Digital Research and Education. For simple uses, only the PROC PHREG and MODEL statements are required. i am doing Cox-PH(cohort analysis) using proc sql. 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. See the documentation for more details.). Computed statistics are based on the asymptotic chi-square distribution of the Wald statistic. We request Cox regression through proc phreg in SAS. These are the equivalent PROC GENMOD statements: A More Complex Contrast with Effects Coding. model lenfol*fstat(0) = ; o1LSRD"Qh&3[F&g w/!|#+QnHA8Oy9 , Table 86.1: PROC PHREG Statement Options You can specify the following options in the PROC PHREG statement. The SLICE and LSMEANS statements cannot be used for this more complex contrast. It contains numerous examples in SAS and R. Grambsch, PM, Therneau, TM. 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. The solution vector in PROC MIXED is requested with the SOLUTION option in the MODEL statement and appears as the Estimate column in the Solution for Fixed Effects table: For this model, the solution vector of parameter estimates contains 18 elements. 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 Now lets look at the model with just both linear and quadratic effects for bmi. However, no statistical tests comparing criterion values is possible. 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. We can see this reflected in the survival function estimate for LENFOL=382. When a subject dies at a particular time point, the step function drops, whereas in between failure times the graph remains flat. Such linear combinations can be estimated and tested using the CONTRAST and/or ESTIMATE statements available in many modeling procedures. The following statements create the data set and fit the saturated logistic model. The following examples concentrate on using the steps above in this situation. The model is the same as model (1) above with just a change in the subscript ranges. 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. Be careful to order the coefficients to match the order of the model parameters in the procedure. Run Cox models on intervals of follow up time rather than on its entirety. 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. 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). All of these variables vary quite a bit in these data. ALPHA= p specifies the level of significance pfor the % confidence interval for each contrast when the ESTIMATE option is specified. 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. It is important to know how variable levels change within the set of parameter estimates for an effect. run; The PLSINGULAR= option has no effect if profile-likelihood confidence intervals (CL=PL) are not requested. Below we demonstrate use of the assess statement to the functional form of the covariates. 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)). Notice the. The parameter for ses1 is the difference You use model 3e to expand the average treatment effect: So the hypothesis, written in terms of the model parameters, is simply: The following CONTRAST statement used in PROC LOGISTIC estimates and tests this hypothesis, and produces the following output tables: In PROC GENMOD, use this equivalent ESTIMATE statement: The exponentiated contrast estimate, 0.83, is not really an odds ratio. We simply use the SAS procedure PHREG to obtain the final result. First, write the model, being sure to verify its parameters and their order from the procedure's displayed results: Now write each part of the contrast in terms of the effects-coded model (3e). As in Example 1, you can also use the LSMEANS, LSMESTIMATE, and SLICE statements in PROC LOGISTIC, PROC GENMOD, and PROC GLIMMIX when dummy coding (PARAM=GLM) is used. This is an extension of the nested effects that you can specify in other procedures such as GLM and LOGISTIC. 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. Graphs are particularly useful for interpreting interactions. 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. model lenfol*fstat(0) = gender|age bmi|bmi hr ; In the simpler case of a main-effects-only model, writing CONTRAST and ESTIMATE statements to make simple pairwise comparisons is more intuitive. Options for the HAZARDRATIO statement are as follows. to the coefficient for ses = 2. The last 10 elements are the parameter estimates for the 10 levels of the A*B interaction, 11 through 52. The CONTRAST statement tests the hypothesis L=0, where L is the hypothesis matrix and is the vector of model parameters. 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). These two observations, id=89 and id=112, have very low but not unreasonable bmi scores, 15.9 and 14.8. Because of the positive skew often seen with followup-times, medians are often a better indicator of an average survival time. This section contains 14 examples of PROC PHREG applications. The next five elements are the parameter estimates for the levels of A, 1 through 5. This indicates that our choice of modeling a linear and quadratic effect of bmi was a reasonable one. None of the solid blue lines looks particularly aberrant, and all of the supremum tests are non-significant, so we conclude that proportional hazards holds for all of our covariates. The simple contrast shown in the LSMESTIMATE statement below compares the fourth and eighth means as desired. exposure(0=no exposure, 1= yes exposure) and outcome(0=no outcome, 1= yes outcome) variable are all binary. A label is required for every contrast specified, and it must be enclosed in quotes. Two groups of rats received different pretreatment regimes and then were exposed to a carcinogen. In large datasets, very small departures from proportional hazards can be detected. 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. specifies the maximum number of iterations to achieve the convergence of the profile-likelihood confidence limits. class gender; A More Complex Contrast When the procedure reports a log pseudo-likelihood you cannot construct a LR test to compare models. time lenfol*fstat(0); Copyright class gender; The PLOTS= option is not available for the maximum likelihood anaysis. In the following output, the first parameter of the treatment(diagnosis='complicated') effect tests the effect of treatment A versus the average treatment effect in the complicated diagnosis. This test can be done using a CONTRAST statement to jointly test the interaction parameters. 2009 by SAS Institute Inc., Cary, NC, USA. The PLCONV= option has no effect if profile-likelihood confidence intervals (CL=PL) are not requested. 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. Recall that when we introduce interactions into our model, each individual term comprising that interaction (such as GENDER and AGE) is no longer a main effect, but is instead the simple effect of that variable with the interacting variable held at 0. Whereas with non-parametric methods we are typically studying the survival function, with regression methods we examine the hazard function, \(h(t)\). format gender gender. When testing, write the null hypothesis in the form. 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. 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. 1> Computing from the regression coefficient estimates of PROC PHREG output, 2> Recoding the values of the explanatory variable such that the increase is equal to one unit, 3> Using the CLASS statement to specify the explanatory variable in PROC TPHREG (experimental) procedure. scatter x = bmi y=dfbmibmi / markerchar=id; The hazard function is also generally higher for the two lowest BMI categories. In PROC GENMOD or PROC GLIMMIX, use the EXP option in the ESTIMATE statement. Indeed, exclusion of these two outliers causes an almost doubling of \(\hat{\beta}_{bmi}\), from -0.23323 to -0.39619. The degrees of freedom are the number of linearly independent constraints implied by the CONTRAST statementthat is, the rank of . The variable representing cases and controls (e.g., CACO) MUST be redefined, or a new variable created (e.g., STATUS) so it has the value 1 for cases and the value 2 for controls. i am wondering either i add "CLASS" statement ornot. 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). ALPHA=number specifies the level of significance for % confidence intervals. Density functions are essentially histograms comprised of bins of vanishingly small widths. Release is the software release in which the problem is planned to be format gender gender. The interpretation of this estimate is that we expect 0.0385 failures (per person) by the end of 3 days. run; 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. run; proc phreg data = whas500; This note focuses on assessing the effects of categorical (CLASS) variables in models containing interactions. Watch this tutorial for more. The primary focus of survival analysis is typically to model the hazard rate, which has the following relationship with the \(f(t)\) and \(S(t)\): The hazard function, then, describes the relative likelihood of the event occurring at time \(t\) (\(f(t)\)), conditional on the subjects survival up to that time \(t\) (\(S(t)\)). Thus, if the average is 0 across time, then that suggests the coefficient \(p\) does not vary over time and that the proportional hazards assumption holds for covariate \(p\). 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. 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. For example, B*A becomes A*B if A precedes B in the CLASS statement. =2. One can request that SAS estimate the survival function by exponentiating the negative of the Nelson-Aalen estimator, also known as the Breslow estimator, rather than by the Kaplan-Meier estimator through the method=breslow option on the proc lifetest statement. However, despite our knowledge that bmi is correlated with age, this method provides good insight into bmis functional form. Subjects that are censored after a given time point contribute to the survival function until they drop out of the study, but are not counted as a failure. The log odds for treatment A in the complicated diagnosis are: The log odds for treatment C in the complicated diagnosis are: Subtracting these gives the difference in log odds, or equivalently, the log odds ratio: The following statements use PROC LOGISTIC to fit model 3c and estimate the contrast.

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