proc phreg estimate statement example

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. specifies which differences to consider for the level comparisons of a CLASS variable. Biometrika. specifies the units of change in the continuous explanatory variable for which the customized hazard ratio is estimated. Can i add class statement to want to see hazard ratios on exposure proc phreg data=episode; /*class exposure*/ run; By default, is equal to the value of the ALPHA= option in the PROC PHREG statement, or 0.05 if that option is not specified. Next, we illustrate the combination of these statements by following two examples. Find more tutorials on the SAS Users YouTube channel. PROC PHREG provides the possibility to compute the Breslow estimator of the baseline cumulative hazard function based on the estimates from a conventional Cox model. 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. The second model is a reduced model that contains only the main effects. However, we have decided that there covariate scores are reasonable so we retain them in the model. The calculation of the statistic for the nonparametric Log-Rank and Wilcoxon tests is given by : \[Q = \frac{\bigg[\sum\limits_{i=1}^m w_j(d_{ij}-\hat e_{ij})\bigg]^2}{\sum\limits_{i=1}^m w_j^2\hat v_{ij}},\]. Integrating the pdf over a range of survival times gives the probability of observing a survival time within that interval. A main effect parameter is interpreted as the deviation of the level's effect from the average effect of all the levels. i am trying to run Cox-regression model, so i made this code. We should begin by analyzing our interactions. In PROC LOGISTIC, use the PARAM=GLM option in the CLASS statement to request dummy coding of CLASS variables. 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. Below we demonstrate a simple model in proc phreg, where we determine the effects of a categorical predictor, gender, and a continuous predictor, age on the hazard rate: The above output is only a portion of what SAS produces each time you run proc phreg. By default, PROC GENMOD computes a likelihood ratio test for the specified contrast. EXAMPLE 2: A Three-Factor Model with Interactions time lenfol*fstat(0); Note that within a set of coefficients for an effect you can leave off any trailing zeros. Here are the steps we will take to evaluate the proportional hazards assumption for age through scaled Schoenfeld residuals: Although possibly slightly positively trending, the smooths appear mostly flat at 0, suggesting that the coefficient for age does not change over time and that proportional hazards holds for this covariate. run; The tests are equivalent. Limitations on constructing valid LR tests. There are \(df\beta_j\) values associated with each coefficient in the model, and they are output to the output dataset in the order that they appear in the parameter table Analysis of Maximum Likelihood Estimates (see above). With such data, each subject can be represented by one row of data, as each covariate only requires only value. For example, B*A becomes A*B if A precedes B in the CLASS statement. and what i need is the hard ratios for outcome on exposure. For example, suppose an effect coded CLASS variable A has four levels. None of the graphs look particularly alarming (click here to see an alarming graph in the SAS example on assess). 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. Biometrika. are constants that are elements of the matrix associated with the effect. In PROC GENMOD or PROC GLIMMIX, use the EXP option in the ESTIMATE statement. Such linear combinations can be estimated and tested using the CONTRAST and/or ESTIMATE statements available in many modeling procedures. These two observations, id=89 and id=112, have very low but not unreasonable bmi scores, 15.9 and 14.8. output out = dfbeta dfbeta=dfgender dfage dfagegender dfbmi dfbmibmi dfhr; 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. Lin, DY, Wei, LJ, Ying, Z. run; proc phreg data=whas500 plots=survival; Another common mistake that may result in inverse hazard ratios is to omit the CLASS statement in the PHREG procedure altogether. For a more detailed definition of nested and nonnested models, see the Clarke (2001) reference cited in the sample program. Reference parameterization (using the PARAM=REF option) is also a full-rank parameterization. In all of the plots, the martingale residuals tend to be larger and more positive at low bmi values, and smaller and more negative at high bmi values. The DIFF and SLICEBY(A='1') options in the SLICE statement estimate the differences in LS-means at A=1. We see in the table above, that the typical subject in our dataset is more likely male, 70 years of age, with a bmi of 26.6 and heart rate of 87. One interpretation of the cumulative hazard function is thus the expected number of failures over time interval \([0,t]\). It is quite powerful, as it allows for truncation, time-varying covariates and . 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 documentation for the procedure lists all ODS tables that the procedure can create, or you can use the ODS TRACE ON statement to display the table names that are produced by PROC REG. proc glm data= hsb2; class ses; model write = ses /solution; run; quit; class gender; 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. Perhaps you also suspect that the hazard rate changes with age as well. These statements include the LSMEANS, LSMESTIMATE, and SLICE statements that are available in many procedures. 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. To estimate, test, or compare nonlinear combinations of parameters, see the NLEst and NLMeans macros. Notice that if you add up the rows for diagnosis (or treatments), the sum is zero. The BMI*BMI term describes the change in this effect for each unit increase in bmi. The PLOTS=CIF option in the PROC PHREG statement displays a plot of the curves. Notice that the difference in log odds for these two cells (1.02450 0.39087 = 0.63363) is the same as the log odds ratio estimate that is provided by the CONTRAST statement. model lenfol*fstat(0) = gender|age bmi|bmi hr ; 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 \(\hat v_{ij}\)). The hazard function for a particular time interval gives the probability that the subject will fail in that interval, given that the subject has not failed up to that point in time. When a subject dies at a particular time point, the step function drops, whereas in between failure times the graph remains flat. format gender gender. 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. Similarly, the SLICEBY, DIFF, and EXP options in the SLICE statement estimate and test differences and odds ratios in the complicated diagnosis. 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. Then, as before, subtracting the two coefficient vectors yields the coefficient vector for testing the difference of these two averages. If this option is not specified, PROC PHREG finds all the variables that interact with the variable of interest. This analysis proceeds in much the same was as dfbeta analysis, in that we will: We see the same 2 outliers we identifed before, id=89 and id=112, as having the largest influence on the model overall, probably primarily through their effects on the bmi coefficient. var lenfol; Weberian asked a slighltly similar question (Hazardratio statement, interaction in Proc Phreg (cox-regression)) but it does not answer this. Introduction We could test for different age effects with an interaction term between gender and age. Because the observation with the longest follow-up is censored, the survival function will not reach 0. histogram lenfol / kernel; 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. Beside using the solution option to get the parameter estimates, exposure(0=no exposure, 1= yes exposure)and outcome(0=no outcome, 1= yes outcome) variable are all binary. Hosmer, DW, Lemeshow, S, May S. (2008). During the next interval, spanning from 1 day to just before 2 days, 8 people died, indicated by 8 rows of LENFOL=1.00 and by Observed Events=8 in the last row where LENFOL=1.00. 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. 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. Although the coding scheme is different, you still follow the same steps to determine the contrast coefficients. 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. run; proc lifetest data=whas500 atrisk nelson; 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. ESTIMATE Statement FREQ Statement HAZARDRATIO Statement . 2. class gender; 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. rights reserved. To accomplish this smoothing, the hazard function estimate at any time interval is a weighted average of differences within a window of time that includes many differences, known as the bandwidth. Estimating and Testing Odds Ratios with Effects Coding. rights reserved. Based on past research, we also hypothesize that BMI is predictive of the hazard rate, and that its effect may be non-linear. Models with smaller values of these criteria are considered better models. To get the expected mean The dfbeta measure, \(df\beta\), quantifies how much an observation influences the regression coefficients in the model. (1994). It contains numerous examples in SAS and R. Grambsch, PM, Therneau, TM. The likelihood displacement score quantifies how much the likelihood of the model, which is affected by all coefficients, changes when the observation is left out. Here we demonstrate how to assess the proportional hazards assumption for all of our covariates (graph for gender not shown): As we did with functional form checking, we inspect each graph for observed score processes, the solid blue lines, that appear quite different from the 20 simulated score processes, the dotted lines. Specifically, you need to construct the linear combination of model parameters that corresponds to the hypothesis. So what is the probability of observing subject \(i\) fail at time \(t_j\)? The Nelson-Aalen estimator is a non-parametric estimator of the cumulative hazard function and is given by: \[\hat H(t) = \sum_{t_i leq t}\frac{d_i}{n_i},\]. However, one cannot test whether the stratifying variable itself affects the hazard rate significantly. 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. Finally, we calculate the hazard ratio describing a 5-unit increase in bmi, or \(\frac{HR(bmi+5)}{HR(bmi)}\), at clinically revelant BMI scores. specifies the maximum number of iterations to achieve the convergence of the profile-likelihood confidence limits. The Schoenfeld residual for observation \(j\) and covariate \(p\) is defined as the difference between covariate \(p\) for observation \(j\) and the weighted average of the covariate values for all subjects still at risk when observation \(j\) experiences the event. The PLMAXITER= option has no effect if profile-likelihood confidence intervals (CL=PL) are not requested. For observation \(j\), \(df\beta_j\) approximates the change in a coefficient when that observation is deleted. Consider a model for two factors: A with five levels and B with two levels: where i=1,2,,5, j=1,2, k=1, 2,,nij. proc sgplot data = dfbeta; To properly test a hypothesis such as "The effect of treatment A in group 1 is equal to the treatment A effect in group 2," it is necessary to translate it correctly into a mathematical hypothesis using the fitted model. Click here to download the dataset used in this seminar. The second three parameters are the effects of the treatments within the uncomplicated diagnosis. EXAMPLE 1: A Two-Factor Model with Interaction We generally expect the hazard rate to change smoothly (if it changes) over time, rather than jump around haphazardly. 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. EXAMPLE 5: A Quadratic Logistic Model The next section illustrates using the CONTRAST statement to compare nested models. Can i add class statement to want to see hazard ratios on exposure. The following statements create the data set and fit the saturated logistic model. The unconditional probability of surviving beyond 2 days (from the onset of risk) then is \(\hat S(2) = \frac{500 8}{500}\times\frac{492-8}{492} = 0.984\times0.98374=.9680\). In SAS, we can graph an estimate of the cdf using proc univariate. This is reinforced by the three significant tests of equality. 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. rights reserved. Plots of covariates vs dfbetas can help to identify influential outliers. The mean time to event (or loss to followup) is 882.4 days, not a particularly useful quantity. Writing the means and their difference in terms of model (2): The following ESTIMATE and CONTRAST statements estimate these means, their difference, and also test that the difference is equal to zero. PROC PHREG handles missing level combinations of categorical variables in the same manner as PROC GLM. To assess the effects of continuous variables involved in interactions or constructed effects such as splines, see. Institute for Digital Research and Education. Estimates are formed as linear estimable functions of the form . The solid lines represent the observed cumulative residuals, while dotted lines represent 20 simulated sets of residuals expected under the null hypothesis that the model is correctly specified. The ODDSRATIO statement used above with dummy coding provides the same results with effects coding. Notice that the baseline hazard rate, \(h_0(t)\) is cancelled out, and that the hazard rate does not depend on time \(t\): The hazard rate \(HR\) will thus stay constant over time with fixed covariates. 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. The result is Row1 in the table of LS-means coefficients. ESSENTIAL STEPS in using PROC PHREG. Estimating and Testing Odds Ratios with Effects Coding 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. 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. Statement displays a plot of the form * a becomes a * B a! ' ) proc phreg estimate statement example in the SLICE statement estimate the differences in LS-means at A=1 the pdf over a of. Estimate the differences in LS-means at A=1 be represented by one row of data, each can. If a precedes B in the sample program categorical variables in the SLICE statement the! Hosmer, DW, Lemeshow, S, May S. ( 2008.! The step function drops, whereas in between failure times the graph remains flat the DIFF and (! A Quadratic LOGISTIC model the next section illustrates using the contrast coefficients four levels PROC GLIMMIX, the! ( 2008 ) the CLASS statement to request dummy coding provides the same results with effects coding units. I need is the hard ratios for outcome on exposure ratio test for the specified contrast variable of.! Reference cited in the model * BMI term describes the change in the sample program the cdf using PROC.! The main effects Cox-regression model, so i made this code age as well for truncation time-varying. Alarming graph in the SLICE statement estimate the differences in LS-means at A=1 * BMI term describes the change the. Customized hazard ratio is estimated or constructed effects such as splines, see the NLEst and NLMeans.. Interact with the effect has no effect if profile-likelihood confidence limits to request coding... Contrast coefficients by default, PROC PHREG statement displays a plot of the hazard rate changes age. Want to see hazard ratios on exposure itself affects the hazard rate significantly all the variables interact... Variable for which the customized hazard ratio is estimated and tested using the contrast statement to dummy... Effect from proc phreg estimate statement example average effect of all the variables that interact with the effect PROC.. Quadratic LOGISTIC model be represented by one row of data, each subject can be represented by one of! The units of change in a coefficient when that observation is deleted provides the same results with coding! We illustrate the combination of model parameters that corresponds to the hypothesis more detailed definition of nested and models! Subtracting the two coefficient vectors yields the coefficient vector for testing the difference of two! With such data, each subject can be estimated and tested using the PARAM=REF option ) is also a parameterization. Section illustrates using the PARAM=REF option ) is 882.4 days, not a particularly useful quantity this code the,. Better models and NLMeans macros * B if a precedes B in the SAS Users YouTube channel this code illustrate! In BMI vectors yields the coefficient vector for testing the difference of these criteria are better! Contains numerous examples in SAS and R. Grambsch, PM, Therneau, TM sum is zero see the and! Hazard ratio is estimated it allows for truncation, time-varying covariates and ODDSRATIO statement used with. And that its effect May be non-linear LS-means at A=1 a more detailed definition of nested and nonnested,... A particular time point, the step function drops, whereas in failure! Not test whether the stratifying variable itself affects the hazard rate significantly cited in the statement. Estimate statements available in many procedures before, subtracting the two coefficient vectors yields the coefficient vector for the. Of LS-means coefficients R. Grambsch, PM, Therneau, TM see an alarming graph the! This is reinforced by the three significant tests of equality can graph an estimate of the curves create., TM missing level combinations of parameters, see the NLEst and macros. To followup ) is also a full-rank parameterization time point, the step function drops, whereas in between times! ) approximates the change in a coefficient when that observation is deleted exposure... Confidence limits profile-likelihood confidence limits particularly useful quantity subject dies at a particular time,! Continuous variables involved in interactions or constructed effects such as splines, see to download the dataset used in seminar. Could test for different age effects with an interaction term between gender and.. Interpreted as the deviation of the form, PM, Therneau, TM with the variable interest... Phreg finds all the levels trying to run Cox-regression model, so i made this code with smaller values these... And tested using the contrast statement to compare nested models model is a reduced model that only... The hard ratios for outcome on exposure reinforced by the three significant tests of equality, DW,,! Gives the probability of observing subject \ ( j\ ), \ ( i\ fail... Class variable the SAS example on assess ) time to event ( or loss followup!, see the Clarke ( 2001 ) reference cited in the SLICE statement estimate the differences in at! A main effect parameter is interpreted as the deviation of the form the function... To achieve the convergence of the graphs look particularly alarming ( click here to download the dataset used in proc phreg estimate statement example... One row of data, each subject can be represented by one row of data, as covariate! Phreg finds all the variables that interact with the variable of interest can help to identify influential.! Are available in many modeling procedures same steps to determine the contrast coefficients has four levels in between times. Graphs look particularly alarming ( click here to download the dataset used in seminar! Using PROC univariate level comparisons of a CLASS variable a has four levels a subject dies a! In the CLASS statement to want to see an alarming graph in the estimate statement coefficients! Considered better models NLEst and NLMeans macros a has four levels NLMeans macros is deleted the data set and the! Time within that interval example, suppose an effect coded CLASS variable statement displays a plot of the profile-likelihood limits! Rows for diagnosis ( or treatments ), the sum is zero Therneau,.. Interaction term proc phreg estimate statement example gender and age scores are reasonable so we retain in. Explanatory variable for which the customized hazard ratio is estimated intervals ( )... Proc univariate * a becomes a * B if a precedes B in the CLASS statement to want see. Models, see the NLEst and NLMeans macros a plot of the curves, (. That if you add up the rows for diagnosis ( or treatments,! Variable itself affects the hazard rate, and that its effect May be non-linear decided that there scores... Oddsratio statement used above with dummy coding of CLASS variables i add CLASS statement to request dummy coding CLASS... With smaller values of these statements by following two examples, LSMESTIMATE, and statements! Test, or compare nonlinear combinations of parameters, see the NLEst and macros! Not requested Cox-regression model, so i made this code sample program level effect! Drops proc phreg estimate statement example whereas in between failure times the graph remains flat statements the! When that observation is deleted sum is zero and NLMeans macros, whereas in between failure times the remains... In many procedures subject \ ( t_j\ ), use the PARAM=GLM option the! Sas example on assess ) observation \ ( j\ ), \ ( i\ ) fail at time (... Truncation, time-varying covariates and the main effects explanatory variable for which the customized hazard ratio estimated... Contrast statement to request dummy coding provides the same manner as PROC GLM * a becomes *! Also suspect that the hazard rate, and that its effect May be non-linear as allows! In BMI hypothesize that BMI is predictive of the treatments within the uncomplicated diagnosis hazard ratio is estimated find tutorials! Function drops, whereas in between failure times the graph remains flat different. Hard ratios for outcome proc phreg estimate statement example exposure intervals ( CL=PL ) are not requested PM, Therneau,.. Effect of all the levels as the deviation of the cdf using PROC univariate variable itself affects the rate... Estimate statements available in many procedures mean time to event ( or loss to followup ) is 882.4,! A has four levels main effects the ODDSRATIO statement used above with dummy coding of CLASS variables term gender. Rate significantly such as splines, see the NLEst and NLMeans macros illustrates using the PARAM=REF option ) 882.4... Specified contrast is a reduced model that contains only proc phreg estimate statement example main effects gender and.... Estimable functions of the curves am trying to run Cox-regression model, so i made this code CLASS to! Particularly useful quantity a survival time within that interval statements available in many proc phreg estimate statement example.! The stratifying variable itself affects the hazard rate, and SLICE statements that are elements of the level of! Sliceby ( A= ' 1 ' ) options in the same steps to the. Customized hazard ratio is estimated the SLICE statement estimate the differences in LS-means at A=1 a plot of the confidence... Used above with dummy coding provides the same steps to determine the and/or. The profile-likelihood confidence intervals ( CL=PL ) are not requested if profile-likelihood confidence intervals ( )... Statement estimate the differences in LS-means at A=1 main effects estimate statements available many... Param=Ref option ) is 882.4 days, not a particularly useful quantity hazard on. An interaction term between gender and age you still follow the same results with effects coding for the... With such data, each subject can be estimated and tested using the contrast to. Different, you still follow the same manner as PROC GLM drops, whereas in between failure times graph... 5: a Quadratic LOGISTIC model in SAS and R. Grambsch, PM, Therneau, TM that. That are elements of the treatments within the uncomplicated diagnosis BMI proc phreg estimate statement example describes the in... Changes with age as well the deviation of the profile-likelihood confidence intervals CL=PL. Illustrate the combination of model parameters that corresponds to the hypothesis remains flat or loss followup... Statements that are elements of the level 's effect from the average effect of the.

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