proc phreg estimate statement example

You can specify the following options after a slash (/). Estimating and Testing Odds Ratios with Dummy Coding We can estimate the hazard function is SAS as well using proc lifetest: As we have seen before, the hazard appears to be greatest at the beginning of follow-up time and then rapidly declines and finally levels off. Above we described that integrating the pdf over some range yields the probability of observing \(Time\) in that range. model lenfol*fstat(0) = gender|age bmi|bmi hr ; 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. As an example, imagine subject 1 in the table above, who died at 2,178 days, was in a treatment group of interest for the first 100 days after hospital admission. The estimator is calculated, then, by summing the proportion of those at risk who failed in each interval up to time \(t\). 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. In PROC LOGISTIC, odds ratio estimates for variables involved in interactions can be most easily obtained using the ODDSRATIO statement. You can also duplicate the results of the CONTRAST statement with an ESTIMATE statement. model (start, stop)*status(0) = in_hosp ; Now consider a model in three factors, with five, two, and three levels, respectively. Similarly, the SLICEBY, DIFF, and EXP options in the SLICE statement estimate and test differences and odds ratios in the complicated diagnosis. PROC PHREG displays the point estimate, its standard error, a Wald confidence interval, and a Wald chi-square test for each contrast. Within SAS, proc univariate provides easy, quick looks into the distributions of each variable, whereas proc corr can be used to examine bivariate relationships. The contrast table that shows the log odds ratio and odds ratio estimates is exactly as before. For example, B*A becomes A*B if A precedes B in the CLASS statement. 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. The next five elements are the parameter estimates for the levels of A, 1 through 5. The default is the value of the ALPHA= option in the PROC PHREG statement, or 0.05 if that option is not specified. For example, we found that the gender effect seems to disappear after accounting for age, but we may suspect that the effect of age is different for each gender. When testing, write the null hypothesis in the form. This coding scheme is used by default by PROC CATMOD and PROC LOGISTIC and can be specified in these and some other procedures such as PROC GENMOD with the PARAM=EFFECT option in the CLASS statement. controls the convergence criterion for the profile-likelihood confidence limits. PROC PLM was released with SAS 9.22 in 2010. Earlier in the seminar we graphed the Kaplan-Meier survivor function estimates for males and females, and gender appears to adhere to the proportional hazards assumption. Use the Class Level Information table which shows the design variable settings. The CONTRAST statement enables you to specify a matrix, , for testing the hypothesis . 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. Another common mistake that may result in inverse hazard ratios is to omit the CLASS statement in the PHREG procedure altogether. 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. The DIVISOR= option is used to ensure precision and avoid nonestimability. All yl (1994). It is similar to the CONTRAST statement in PROC GLM and PROC CATMOD, depending on the coding schemes used with any categorical variables involved. Checking the Cox model with cumulative sums of martingale-based residuals. 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. We see that beyond beyond 1,671 days, 50% of the population is expected to have failed. Find more tutorials on the SAS Users YouTube channel. The LSMESTIMATE statement can also be used. Also notice that the distribution has been changed to Poisson, but the link function remains log. 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. 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. Indeed, exclusion of these two outliers causes an almost doubling of \(\hat{\beta}_{bmi}\), from -0.23323 to -0.39619. proc univariate data = whas500(where=(fstat=1)); In the output we find three Chi-square based tests of the equality of the survival function over strata, which support our suspicion that survival differs between genders. The value for must be between 0 and 1; the default value is 1E4. The value must be between 0 and 1. When a subject dies at a particular time point, the step function drops, whereas in between failure times the graph remains flat. In the case of categorical covariates, graphs of the Kaplan-Meier estimates of the survival function provide quick and easy checks of proportional hazards. output out = dfbeta dfbeta=dfgender dfage dfagegender dfbmi dfbmibmi dfhr; First, there may be one row of data per subject, with one outcome variable representing the time to event, one variable that codes for whether the event occurred or not (censored), and explanatory variables of interest, each with fixed values across follow up time. For more information, see the "Generation of the Design Matrix" section in the CATMOD documentation. class gender; The Cox model contains no explicit intercept parameter, so it is not valid to specify one in the CONTRAST statement. Thus, by 200 days, a patient has accumulated quite a bit of risk, which accumulates more slowly after this point. The log-rank and Wilcoxon tests in the output table differ in the weights \(w_j\) used. ANOVA, or Analysis Of Variance, is used to compare the averages or means of two or more populations to better understand how they differ. 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. 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. Some procedures allow multiple types of coding. The regression equation is the If ABS is greater than , then is declared nonestimable. The CONTRAST and ESTIMATE statements allow for estimation and testing of any linear combination of model parameters. 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. As time progresses, the Survival function proceeds towards it minimum, while the cumulative hazard function proceeds to its maximum. You can request the CIF curves for a particular set of covariates by using the BASELINE statement. The effect of bmi is significantly lower than 1 at low bmi scores, indicating that higher bmi patients survive better when patients are very underweight, but that this advantage disappears and almost seems to reverse at higher bmi levels. This option is ignored in the estimation of hazard ratios for a continuous variable. 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 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. These statements generate data from the above model: The following statements fit model (2) and display the solution vector and cell means. Computing the Cell Means Using the ESTIMATE Statement, Estimating and Testing a Difference of Means, Comparing One Interaction Mean to the Average of All Interaction Means, Example 1: A Two-Factor Model with Interaction, coefficient vectors that are used in calculating the LS-means, Example 2: A Three-Factor Model with Interactions, Example 3: A Two-Factor Logistic Model with Interaction Using Dummy and Effects Coding, Some procedures allow multiple types of coding. specifies the alpha level of the interval estimates for the hazard ratios. Thus, it appears, that when bmi=0, as bmi increases, the hazard rate decreases, but that this negative slope flattens and becomes more positive as bmi increases. Similarly, because we included a BMI*BMI interaction term in our model, the BMI term is interpreted as the effect of bmi when bmi is 0. 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. 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. Standard nonparametric techniques do not typically estimate the hazard function directly. model lenfol*fstat(0) = gender|age bmi|bmi hr ; For these models, the response is no longer modeled directly. 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 \(\hat S(1) = \frac{500 8}{500} = 0.984\). 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. The next two elements are the parameter estimates for the levels of B, 1 and 2. In the relation above, \(s^\star_{kp}\) is the scaled Schoenfeld residual for covariate \(p\) at time \(k\), \(\beta_p\) is the time-invariant coefficient, and \(\beta_j(t_k)\) is the time-variant coefficient. Dummy Coding 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. To get the expected mean The parameter for ses1 is the difference Diagnostic plots to reveal functional form for covariates in multiplicative intensity models. ESTIMATE Statement FREQ Statement HAZARDRATIO Statement . Finally, you can use the SLICE statement. \[f(t) = h(t)exp(-H(t))\]. The log-rank or Mantel-Haenzel test uses \(w_j = 1\), so differences at all time intervals are weighted equally. In the code below, we show how to obtain a table and graph of the Kaplan-Meier estimator of the survival function from proc lifetest: Above we see the table of Kaplan-Meier estimates of the survival function produced by proc lifetest. Note that these are the fourth and eighth cell means in the Least Squares Means table. For this seminar, it is enough to know that the martingale residual can be interpreted as a measure of excess observed events, or the difference between the observed number of events and the expected number of events under the model: \[martingale~ residual = excess~ observed~ events = observed~ events (expected~ events|model)\]. 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. The survival function estimate of the the unconditional probability of survival beyond time \(t\) (the probability of survival beyond time \(t\) from the onset of risk) is then obtained by multiplying together these conditional probabilities up to time \(t\) together. The second three parameters are the effects of the treatments within the uncomplicated diagnosis. However, no statistical tests comparing criterion values is possible. Above, we discussed that expressing the hazard rates dependence on its covariates as an exponential function conveniently allows the regression coefficients to take on any value while still constraining the hazard rate to be positive. It is quite powerful, as it allows for truncation, time-varying covariates and . scatter x = bmi y=dfbmi / markerchar=id; Below we demonstrate use of the assess statement to the functional form of the covariates. The next section illustrates using the CONTRAST statement to compare nested models. Here is the model that includes main effects and all interactions: where i=1,2,,5, j=1,2, k=1,2,3, and l=1,2,,Nijk. The estimate of survival beyond 3 days based off this Nelson-Aalen estimate of the cumulative hazard would then be \(\hat S(3) = exp(-0.0385) = 0.9623\). This can be easily accomplished in. The ESTIMATE statement provides a mechanism for obtaining custom hypothesis tests. This is exactly the contrast that was constructed earlier. This suggests that perhaps the functional form of bmi should be modified. The HAZARDRATIO statement enables you to request hazard ratios for any variable in the model at customized settings. This option is not applicable to a Bayesian analysis. For each subject, the entirety of follow up time is partitioned into intervals, each defined by a start and stop time. 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. The following statements print the log odds for treatments A and C in the complicated diagnosis. scatter x = age y=dfage / markerchar=id; 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%. With appropriate data modification and weighting as described above, this baseline hazard function is exactly equal to the baseline subdistribution hazard function of a PSH model. 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. The change in coding scheme does not affect how you specify the ODDSRATIO statement. The XBETA= option in the OUTPUT statement requests the linear predictor, x, for each observation. You can use the EFFECTPLOT statement to visualize the model. 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, \(H(t)\). From these equations we can see that the cumulative hazard function \(H(t)\) and the survival function \(S(t)\) have a simple monotonic relationship, such that when the Survival function is at its maximum at the beginning of analysis time, the cumulative hazard function is at its minimum. The first three parameters of the nested effect are the effects of treatments within the complicated diagnosis. See, In most cases, models fit in PROC GLIMMIX using the RANDOM statement do not use a true log likelihood. In PROC GENMOD or PROC GLIMMIX, use the EXP option in the ESTIMATE statement. Copyright SAS Institute, Inc. All Rights Reserved. proc sgplot data = dfbeta; This is the default coding scheme for CLASS variables in most procedures including GLM, MIXED, GLIMMIX, and GENMOD. Technical Support can assist you with syntax and other questions that relate to CONTRAST and ESTIMATE statements. 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. See the Analysis of Maximum Likelihood Estimates table to verify the order of the design variables. Widening the bandwidth smooths the function by averaging more differences together. 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. 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. 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. Then, as before, subtracting the two coefficient vectors yields the coefficient vector for testing the difference of these two averages. Thus, both genders accumulate the risk for death with age, but females accumulate risk more slowly. Other nonparametric tests using other weighting schemes are available through the test= option on the strata statement. Therefore, the estimate of the last level of an effect, A, is a= (1 + 2 + + a1). The null hypothesis, in terms of model 3e, is: We saw above that the first component of the hypothesis, log(OddsOA) = + d + t1 + g1. The LSMESTIMATE statement again makes this easier. Applied Survival Analysis, Second Edition provides a comprehensive and up-to-date introduction to regression modeling for time-to-event With this simple model, we Cox models are typically fitted by maximum likelihood methods, which estimate the regression parameters that maximize the probability of observing the given set of survival times. 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. 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 \(\frac{355-1}{355}=0.9972\). You do not need to include all effects that are included in the MODEL statement. Particular emphasis is given to proc lifetest for nonparametric estimation, and proc phreg for Cox regression and model evaluation. For details about the syntax of the ESTIMATE statement, see the section ESTIMATE Statement of Our goal is to transform the data from its original state: to an expanded state that can accommodate time-varying covariates, like this (notice the new variable in_hosp): Notice the creation of start and stop variables, which denote the beginning and end intervals defined by hospitalization and death (or censoring). ALPHA=number specifies the level of significance for % confidence intervals. 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. The covariance matrix of the parameter estimator is computed as a sandwich estimate. 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). We will use scatterplot smooths to explore the scaled Schoenfeld residuals relationship with time, as we did to check functional forms before. run; proc phreg data = whas500; As the hazard function \(h(t)\) is the derivative of the cumulative hazard function \(H(t)\), we can roughly estimate the rate of change in \(H(t)\) by taking successive differences in \(\hat H(t)\) between adjacent time points, \(\Delta \hat H(t) = \hat H(t_j) \hat H(t_{j-1})\). Based on past research, we also hypothesize that BMI is predictive of the hazard rate, and that its effect may be non-linear. 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. This article emphasizes four features of PROC PLM: You can use the SCORE statement to score the model on new data. 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 \(k\): \[E(s^\star_{kp}) + \hat{\beta}_p \approx \beta_j(t_k)\]. PROC PHREG handles missing level combinations of categorical variables in the same manner as PROC GLM. Stratification allows each stratum to have its own baseline hazard, which solves the problem of nonproportionality. 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. you might need to print it in landscape mode to avoid truncation of the right edge. The first 12 examples use the classical method of maximum likelihood, while the last two examples illustrate the Bayesian methodology. 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. and then i would like to see the trends on age group. The cumulative distribution function (cdf), \(F(t)\), describes the probability of observing \(Time\) less than or equal to some time \(t\), or \(Pr(Time t)\). model lenfol*fstat(0) = gender|age bmi hr; For software releases that are not yet generally available, the Fixed PROC GENMOD can also be used to estimate this odds ratio. So the log odds is: The following PROC LOGISTIC statements fit the effects-coded model and estimate the contrast: The same log odds ratio and odds ratio estimates are obtained as from the dummy-coded model. since it is the comparison group. 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. In each of the graphs above, a covariate is plotted against cumulative martingale residuals. Institute for Digital Research and Education. assess var=(age bmi bmi*bmi hr) / resample; Hello. All Limitations on constructing valid LR tests. A simple transformation of the cumulative distribution function produces the survival function, \(S(t)\): The survivor function, \(S(t)\), describes the probability of surviving past time \(t\), or \(Pr(Time > t)\). There is no limit to the number of CONTRAST statements that you can specify, but they must appear after the MODEL statement. model lenfol*fstat(0) = gender|age bmi|bmi hr; Optionally, the CONTRAST statement enables you to estimate each row, , of and test the hypothesis . Here is the SAS code: Code: proc phreg data=Data; class Drug(ref='0') Disease(ref='0') /param=glm; 1 Answer Sorted by: 3 I'm not into statistics, so I'm just guessing what value you mean - here's an example I think could help you: ods trace on; ods output ParameterEstimates=work.my_estimates_dataset; proc phreg data=sashelp.class; model age = height; run; ods trace off; This is using SAS Output Delivery System component of SAS/Base.

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