model lenfol*fstat(0) = gender|age bmi|bmi hr; 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)). Because PROC CATMOD also uses effects coding, you can use the following CONTRAST statement in that procedure to get the same results as above. 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. 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. The HPREG Procedure The HPSPLIT Procedure The ICLIFETEST Procedure The ICPHREG Procedure The INBREED Procedure The IRT Procedure The KDE Procedure The KRIGE2D Procedure The LATTICE Procedure The LIFEREG Procedure The LIFETEST Procedure The LOESS Procedure The LOGISTIC Procedure The MCMC Procedure The MDS Procedure The MI Procedure 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. Technical Support can assist you with syntax and other questions that relate to CONTRAST and ESTIMATE statements. and then i would like to see the trends on age group. Many, but not all, patients leave the hospital before dying, and the length of stay in the hospital is recorded in the variable los. The E option, described later in this section, enables you to verify the proper correspondence of values to parameters. In the simpler case of a main-effects-only model, writing CONTRAST and ESTIMATE statements to make simple pairwise comparisons is more intuitive. Release is the software release in which the problem is planned to be The following statements show all five ways of computing and testing this contrast. 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, \(\Delta \hat H(t) = \hat H(t_j) \hat H(t_{j-1})\). As we see above, one of the great advantages of the Cox model is that estimating predictor effects does not depend on making assumptions about the form of the baseline hazard function, \(h_0(t)\), which can be left unspecified. The matrix is the Hermite form matrix , where represents a generalized inverse of the information matrix of the null model. 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. An example of using the LSMEANS and LSMESTIMATE statements to estimate odds ratios in a repeated measures (GEE) model in PROC GENMOD is available. The above relationship between the cdf and pdf also implies: In SAS, we can graph an estimate of the cdf using proc univariate. Significant departures from random error would suggest model misspecification. The ESTIMATE statement syntax enables you to specify the coefficient vector in sections as just described, with one section for each model effect: Note that this same coefficient vector is given in the table of LS-means coefficients, which was requested by the E option in the LSMEANS statement. i am trying to run Cox-regression model, so i made this code. This technique can detect many departures from the true model, such as incorrect functional forms of covariates (discussed in this section), violations of the proportional hazards assumption (discussed later), and using the wrong link function (not discussed). One can also use non-parametric methods to test for equality of the survival function among groups in the following manner: In the graph of the Kaplan-Meier estimator stratified by gender below, it appears that females generally have a worse survival experience. At this stage we might be interested in expanding the model with more predictor effects. We see that beyond beyond 1,671 days, 50% of the population is expected to have failed. var lenfol gender age bmi hr; 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. Note that there are 5 2 3 = 30 cell means. For example, the time interval represented by the first row is from 0 days to just before 1 day. 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. Lets interpret our model. In very large samples the Kaplan-Meier estimator and the transformed Nelson-Aalen (Breslow) estimator will converge. Any estimable linear combination of model parameters can be tested using the procedure's CONTRAST statement. Limitations on constructing valid LR tests. ; SAS provides built-in methods for evaluating the functional form of covariates through its assess statement. The individual AB11 and AB12 cell means are: The coefficients for the average of the AB21 and AB22 cells are determined in the same fashion. The rows of are specified in order and are separated by commas. Grambsch, PM, Therneau, TM, Fleming TR. In the second table, we see that the hazard ratio between genders, \(\frac{HR(gender=1)}{HR(gender=0)}\), decreases with age, significantly different from 1 at age = 0 and age = 20, but becoming non-signicant by 40. Thus, we again feel justified in our choice of modeling a quadratic effect of bmi. Thus, by 200 days, a patient has accumulated quite a bit of risk, which accumulates more slowly after this point. run; proc phreg data = whas500(where=(id^=112 and id^=89)); All of the statements mentioned above can be used for this purpose. Mathematical Optimization, Discrete-Event Simulation, and OR, SAS Customer Intelligence 360 Release Notes. Table 64.4 summarizes important options in the ESTIMATE statement. 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. Logistic models are in the class of generalized linear models. 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). The E option shows how each cell mean is formed by displaying the coefficient vectors that are used in calculating the LS-means. Some procedures, like PROC LOGISTIC, produce a Wald chi-square statistic instead of a likelihood ratio statistic. Models are nested if one model results from restrictions on the parameters of the other model. The parameter for the intercept is the expected cell mean for ses =3 Unless the seed option is specified, these sets will be different each time proc phreg is run. This option is ignored when the full-rank parameterization is used. The result is Row1 in the table of LS-means coefficients. Therefore, this contrast is also estimated by the parameter for treatment A within the complicated diagnosis in the nested effect. We thus calculate the coefficient with the observation, call it \(\beta\), and then the coefficient when observation \(j\) is deleted, call it \(\beta_j\), and take the difference to obtain \(df\beta_j\). Beside using the solution option to get the parameter estimates, 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. 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. Comparing One Interaction Mean to the Average of All Interaction Means proc sgplot data = dfbeta; This convention can affect the way in which you specify the matrix in your CONTRAST statement. If our Cox model is correctly specified, these cumulative martingale sums should randomly fluctuate around 0. 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. PROC PHREG displays the point estimate, its standard error, a Wald confidence interval, and a Wald chi-square test for each contrast. The Kaplan_Meier survival function estimator is calculated as: \[\hat S(t)=\prod_{t_i\leq t}\frac{n_i d_i}{n_i}, \]. In this case, the 12 estimate is the sixth estimate in the A*B effect requiring a change in the coefficient vector that you specify in the ESTIMATE statement. The estimated hazard ratio of .937 comparing females to males is not significant. Additionally, although stratifying by a categorical covariate works naturally, it is often difficult to know how to best discretize a continuous covariate. Positive values of \(df\beta_j\) indicate that the exclusion of the observation causes the coefficient to decrease, which implies that inclusion of the observation causes the coefficient to increase. The contrast table that shows the log odds ratio and odds ratio estimates is exactly as before. The PLCONV= option has no effect if profile-likelihood confidence intervals (CL=PL) are not requested. Watch this tutorial for more. \[df\beta_j \approx \hat{\beta} \hat{\beta_j}\]. With such data, each subject can be represented by one row of data, as each covariate only requires only value. 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. specifies the level of significance for the % confidence interval for each contrast when the ESTIMATE option is specified. Notice the survival probability does not change when we encounter a censored observation. 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: \[martingale~ residual = excess~ observed~ events = observed~ events (expected~ events|model)\]. The PLOTS= option is not available for the maximum likelihood anaysis. Estimating and Testing a Difference of Means 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 mean time to event (or loss to followup) is 882.4 days, not a particularly useful quantity. 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). Integrating the pdf over a range of survival times gives the probability of observing a survival time within that interval. 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). Thus, we can expect the coefficient for bmi to be more severe or more negative if we exclude these observations from the model. This is the log odds. This is required so that the probability of being a case is modeled. 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 \(k\): \[E(s^\star_{kp}) + \hat{\beta}_p \approx \beta_j(t_k)\]. 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. and what i need is the hard ratios for outcome on exposure. The same procedure could be repeated to check all covariates. The t statistic value is the square root of the F statistic from the CONTRAST statement producing an equivalent test. However, nonparametric methods do not model the hazard rate directly nor do they estimate the magnitude of the effects of covariates. Before we dive into survival analysis, we will create and apply a format to the gender variable that will be used later in the seminar. With effects coding, the parameters are constrained to sum to zero. Therneau, TM, Grambsch, PM. For example, if the model contains the interaction of a CLASS variable A and a continuous variable X, the following specification displays a table of hazard ratios comparing the hazards of each pair of levels of A at X=3: The HAZARDRATIO statement identifies the variable whose hazard ratios are to be evaluated. \[f(t) = h(t)exp(-H(t))\]. time lenfol*fstat(0); proc univariate data = whas500(where=(fstat=1)); Stated another way, are any of the interaction parameters not equal to zero as implied by the main-effects model? 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. 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. This is an extension of the nested effects that you can specify in other procedures such as GLM and LOGISTIC. None of the graphs look particularly alarming (click here to see an alarming graph in the SAS example on assess). run; proc phreg data = whas500; However, if you write the ESTIMATE statement like this. This is exactly the contrast that was constructed earlier. to the coefficient for ses = 2. We write the null hypothesis this way: The following table summarizes the data within the complicated diagnosis: The odds ratio can be computed from the data as: This means that, when the diagnosis is complicated, the odds of being cured by treatment A are 1.8845 times the odds of being cured by treatment C. The following statements display the table above and compute the odds ratio: To estimate and test this same contrast of log odds using model 3c, follow the same process as in Example 1 to obtain the contrast coefficients that are needed in the CONTRAST or ESTIMATE statement. 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). 81. The CONTRAST statement provides a mechanism for obtaining customized hypothesis tests. Finally, we see that the hazard ratio describing a 5-unit increase in bmi, \(\frac{HR(bmi+5)}{HR(bmi)}\), increases with bmi. Suppose it is of interest to test the null hypothesis that cell means ABC121 and ABC212 are equal that is, H0: 121 - 212 = 0. The sudden upticks at the end of follow-up time are not to be trusted, as they are likely due to the few number of subjects at risk at the end. Here are the steps we use to assess the influence of each observation on our regression coefficients: The dfbetas for age and hr look small compared to regression coefficients themselves (\(\hat{\beta}_{age}=0.07086\) and \(\hat{\beta}_{hr}=0.01277\)) for the most part, but id=89 has a rather large, negative dfbeta for hr. We will use scatterplot smooths to explore the scaled Schoenfeld residuals relationship with time, as we did to check functional forms before. We see a sharper rise in the cumulative hazard right at the beginning of analysis time, reflecting the larger hazard rate during this period. 1469-82. The blue-shaded area around the survival curve represents the 95% confidence band, here Hall-Wellner confidence bands. In large datasets, very small departures from proportional hazards can be detected. 80(30). The change in coding scheme does not affect how you specify the ODDSRATIO statement. The difficulty is constructing combinations that are estimable and that jointly test the set of interactions. Estimates are formed as linear estimable functions of the form . %PDF-1.2 % For example, if males have twice the hazard rate of females 1 day after followup, the Cox model assumes that males have twice the hazard rate at 1000 days after follow up as well. In PROC LOGISTIC, use the PARAM=GLM option in the CLASS statement to request dummy coding of CLASS variables. We simply use the SAS procedure PHREG to obtain the final result. run; proc phreg data=whas500 plots=survival; Therefore, you would use the following CONTRAST statement: To contrast the third level with the average of the first two levels, you would test. The likelihood ratio test can be used to compare any two nested models that are fit by maximum likelihood. One variable is created for each level of the original variable. 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