proc phreg estimate statement example

run; proc phreg data = whas500; model lenfol*fstat(0) = gender age;; 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. The BMI*BMI term describes the change in this effect for each unit increase in bmi. An example of using the LSMEANS and LSMESTIMATE statements to estimate odds ratios in a repeated measures (GEE) model in PROC GENMOD is available. specifies the variables that interact with the variable of interest and the corresponding values of the interacting variables. The correct coefficients are determined for the CONTRAST statement to estimate two odds ratios: one for an increase of one unit in X, and the second for a two unit increase. If this option is not specified, PROC PHREG finds all the variables that interact with the variable of interest. Technical Support can assist you with syntax and other questions that relate to CONTRAST and ESTIMATE statements. PROC GENMOD produces the Wald statistic when the WALD option is used in the CONTRAST statement. yl The PLMAXITER= option has no effect if profile-likelihood confidence intervals (CL=PL) are not requested. If an interacting variable is a CLASS variable, variable= ALL is the default; if the interacting variable is continuous, variable= is the default, where is the average of all the sampled values of the continuous variable. 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. else in_hosp = 1; It contains numerous examples in SAS and R. Grambsch, PM, Therneau, TM. 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. This section contains 14 examples of PROC PHREG applications. rights reserved. The red curve representing the lowest BMI category is truncated on the right because the last person in that group died long before the end of followup time. \[df\beta_j \approx \hat{\beta} \hat{\beta_j}\]. Stated another way, are any of the interaction parameters not equal to zero as implied by the main-effects model? The survival function drops most steeply at the beginning of study, suggesting that the hazard rate is highest immediately after hospitalization during the first 200 days. Acquiring more than one curve, whether survival or hazard, after Cox regression in SAS requires use of the baseline statement in conjunction with the creation of a small dataset of covariate values at which to estimate our curves of interest. 557-72. Estimating and Testing Odds Ratios with Effects Coding. 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 \(r(x,\beta_x) = 1\). Disease: 1=Disease, 0=No disease Drug: 1=Drug, 0=No drug This make the interaction a "2x2 table" (as below). Specify the DIST=BINOMIAL option to specify a logistic model. Because the observation with the longest follow-up is censored, the survival function will not reach 0. displays the vector of linear coefficients such that is the log-hazard ratio, with being the vector of regression coefficients. In PROC LOGISTIC, the ESTIMATE=BOTH option in the CONTRAST statement requests estimates of both the contrast (difference in log odds or log odds ratio) and the exponentiated contrast (odds ratio). C?1D!^$w"I&#I" NF[cPdn .c@hHa"3IX"P+ !Hp? 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. We, as researchers, might be interested in exploring the effects of being hospitalized on the hazard rate. 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. Also useful to understand is the cumulative hazard function, which as the name implies, cumulates hazards over time. scatter x = age y=dfage / markerchar=id; 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 \(\hat S(1) = \frac{500 8}{500} = 0.984\). 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. The ESTIMATE statement provides a mechanism for obtaining custom hypothesis tests. In such cases, the correct form may be inferred from the plot of the observed pattern. Now lets look at the model with just both linear and quadratic effects for bmi. However, often we are interested in modeling the effects of a covariate whose values may change during the course of follow up time. Note that the CONTRAST and ESTIMATE statements are the most flexible allowing for any linear combination of model parameters. In the simpler case of a main-effects-only model, writing CONTRAST and ESTIMATE statements to make simple pairwise comparisons is more intuitive. Models are nested if one model results from restrictions on the parameters of the other model. Suppose you want to test whether the effect of treatment A in the complicated diagnosis is different from the average effect of the treatments in the complicated diagnosis. Two groups of rats received different pretreatment regimes and then were exposed to a carcinogen. 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. EXAMPLE 2: A Three-Factor Model with Interactions With effects coding, the parameters are constrained to sum to zero. Thus, by 200 days, a patient has accumulated quite a bit of risk, which accumulates more slowly after this point. Because this seminar is focused on survival analysis, we provide code for each proc and example output from proc corr with only minimal explanation. Although the coding scheme is different, you still follow the same steps to determine the contrast coefficients. The difference between the mean of cell ses model lenfol*fstat(0) = ; However, despite our knowledge that bmi is correlated with age, this method provides good insight into bmis functional form. For each subject, the entirety of follow up time is partitioned into intervals, each defined by a start and stop time. 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. Institute for Digital Research and Education. Effects Coding The CONTRAST statement below defines seven rows in L for the seven interaction parameters resulting in a 7 DF test that all interaction parameters are zero. For treatment A in the complicated diagnosis, O = 1, A = 1, B = 0. class gender; run; proc corr data = whas500 plots(maxpoints=none)=matrix(histogram); However, we have decided that there covariate scores are reasonable so we retain them in the model. PROC CATMOD has a feature that makes testing this kind of hypothesis even easier. This seminar covers both proc lifetest and proc phreg, and data can be structured in one of 2 ways for survival analysis. Lets confirm our understanding of the calculation of the Nelson-Aalen estimator by calculating the estimated cumulative hazard at day 3: \(\hat H(3)=\frac{8}{500} + \frac{8}{492} + \frac{3}{484} = 0.0385\), which matches the value in the table. 81. 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. In the table above, we see that the probability surviving beyond 363 days = 0.7240, the same probability as what we calculated for surviving up to 382 days, which implies that the censored observations do not change the survival estimates when they leave the study, only the number at risk. Institute for Digital Research and Education. Still, although their effects are strong, we believe the data for these outliers are not in error and the significance of all effects are unaffected if we exclude them, so we include them in the model. The significance level of the confidence interval is controlled by the ALPHA= option. This can be particularly difficult with dummy (PARAM=GLM) coding. We request Cox regression through proc phreg in SAS. Note that the ESTIMATE statement displays the estimated difference in cell means (2.5148) and a t-test that this difference is equal to zero, while the CONTRAST statement provides only an F-test of the difference. The PHREG procedure will produce inverse hazard ratio measuring instead the effect of Standard of Care versus the effect of study Drug Dose Regimen 2. `Pn.bR#l8(QBQ p9@E,IF0QlPC4NC)R- R]*C!B)Uj.$qpa *O'CAI ")7 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. Any serious endeavor into data analysis should begin with data exploration, in which the researcher becomes familiar with the distributions and typical values of each variable individually, as well as relationships between pairs or sets of variables. We see that beyond beyond 1,671 days, 50% of the population is expected to have failed. Options for the HAZARDRATIO statement are as follows. Suppose that you suspect that the survival function is not the same among some of the groups in your study (some groups tend to fail more quickly than others). However, coefficients for the B effect remain in addition to coefficients for the A*B interaction effect. (Technically, because there are no times less than 0, there should be no graph to the left of LENFOL=0). 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). SAS omits them to remind you that the hazard ratios corresponding to these effects depend on other variables in the model. Additionally, a few heavily influential points may be causing nonproportional hazards to be detected, so it is important to use graphical methods to ensure this is not the case. Suppose it is of interest to test the null hypothesis that cell means ABC121 and ABC212 are equal that is, H0: 121 - 212 = 0. In some cases, the Laplace or quadrature estimation methods (METHOD=LAPLACE or METHOD=QUAD, first available in SAS 9.2) can be used which compute and report an approximate log likelihood making construction of a LR test possible. Above we described that integrating the pdf over some range yields the probability of observing \(Time\) in that range. Unless the seed option is specified, these sets will be different each time proc phreg is run. Exploring the effects of a main-effects-only model, writing CONTRAST and ESTIMATE statements make. If one model results from restrictions on the parameters of the confidence interval is by... Of 2 ways for survival analysis through proc phreg finds all the variables that interact with the variable interest! Three-Factor model with just both linear and quadratic effects for BMI coding the. We described that integrating the pdf over some range yields the probability of observing \ ( Time\ in. 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