# proc phreg estimate statement example

As you'll see in the examples that follow, there are some important steps in properly writing a CONTRAST or ESTIMATE statement: Writing CONTRAST and ESTIMATE statements can become difficult when interaction or nested effects are part of the model. Construction and Computation of Estimable Functions, Specifies a list of values to divide the coefficients, Suppresses the automatic fill-in of coefficients for higher-order effects, Tunes the estimability checking difference, Determines the method for multiple comparison adjustment of estimates, Performs one-sided, lower-tailed inference, Adjusts multiplicity-corrected p-values further in a step-down fashion, Specifies values under the null hypothesis for tests, Performs one-sided, upper-tailed inference, Displays the correlation matrix of estimates, Displays the covariance matrix of estimates, Produces a joint or chi-square test for the estimable functions, Requests ODS statistical graphics if the analysis is sampling-based, Specifies the seed for computations that depend on random numbers. 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. We can similarly calculate the joint probability of observing each of the \(n\) subjects failure times, or the likelihood of the failure times, as a function of the regression parameters, \(\beta\), given the subjects covariates values \(x_j\): \[L(\beta) = \prod_{j=1}^{n} \Bigg\lbrace\frac{exp(x_j\beta)}{\sum_{iin R_j}exp(x_i\beta)}\Bigg\rbrace\]. 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. ESSENTIAL STEPS in using PROC PHREG. The mean time to event (or loss to followup) is 882.4 days, not a particularly useful quantity. Zeros in this table are shown as blanks for clarity. Violations of the proportional hazard assumption may cause bias in the estimated coefficients as well as incorrect inference regarding significance of effects. 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 \(p\). specifies the variables that interact with the variable of interest and the corresponding values of the interacting variables. Biometrika. One variable is created for each level of the original variable. Modeling Survival Data: Extending the Cox Model. For example, the time interval represented by the first row is from 0 days to just before 1 day. (Technically, because there are no times less than 0, there should be no graph to the left of LENFOL=0). PROC PLM was released with SAS 9.22 in 2010. 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. 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 Thus, both genders accumulate the risk for death with age, but females accumulate risk more slowly. The LSMEANS, LSMESTIMATE, and SLICE statements cannot be used with effects coding. Thus, we again feel justified in our choice of modeling a quadratic effect of bmi. tunes the estimability check. O is the dummy variable for the complicated diagnosis, U is the dummy variable for the uncomplicated diagnosis, A, B, and C are the dummy variables for the three treatments, OA through UC are the products of the diagnosis and treatment dummy variables, jointly representing the diagnosis by treatment interaction. Using model (1) above, the AB12 cell mean, 12, is: Because averages of the errors (ijk) are assumed to be zero: Similarly, the AB11 cell mean is written this way: So, to get an estimate of the AB12 mean, you need to add together the estimates of , 1, 2, and 12. 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. The PLSINGULAR= option has no effect if profile-likelihood confidence intervals (CL=PL) are not requested. 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 LSMEANS statement computes the cell means for the 10 A*B cells in this example. 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. Standard nonparametric techniques do not typically estimate the hazard function directly. The number of variables that are created is one fewer than the number of levels of the original variable, yielding one fewer parameters than levels, but equal to the number of degrees of freedom. 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 other covariates, including the additional graph for the quadratic effect for bmi all look reasonable. The null distribution of the cumulative martingale residuals can be simulated through zero-mean Gaussian processes. The EXP option exponentiates each difference providing odds ratio estimates for each pair. run; The estimate of survival beyond 3 days based off this Nelson-Aalen estimate of the cumulative hazard would then be \(\hat S(3) = exp(-0.0385) = 0.9623\). ALPHA= p specifies the level of significance pfor the % confidence interval for each contrast when the ESTIMATE option is specified. In the graph above we see the correspondence between pdfs and histograms. These are the equivalent PROC GENMOD statements: A More Complex Contrast with Effects Coding. At this stage we might be interested in expanding the model with more predictor effects. The significant AGE*GENDER interaction term suggests that the effect of age is different by gender. 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. A More Complex Contrast with Effects Coding Unless the seed option is specified, these sets will be different each time proc phreg is run. Nevertheless, the bmi graph at the top right above does not look particularly random, as again we have large positive residuals at low bmi values and smaller negative residuals at higher bmi values. `Pn.bR#l8(QBQ p9@E,IF0QlPC4NC)R- R]*C!B)Uj.$qpa *O'CAI ")7 Group of ses =3 is the reference group. 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. For example, if the survival times were known to be exponentially distributed, then the probability of observing a survival time within the interval \([a,b]\) is \(Pr(a\le Time\le b)= \int_a^bf(t)dt=\int_a^b\lambda e^{-\lambda t}dt\), where \(\lambda\) is the rate parameter of the exponential distribution and is equal to the reciprocal of the mean survival time. exposure(0=no exposure, 1= yes exposure) and outcome(0=no outcome, 1= yes outcome) variable are all binary. 2009 by SAS Institute Inc., Cary, NC, USA. A complete description of the hazard rates relationship with time would require that the functional form of this relationship be parameterized somehow (for example, one could assume that the hazard rate has an exponential relationship with time). Again, trailing zero coefficients can be omitted. However, we have decided that there covariate scores are reasonable so we retain them in the model. 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. We can see this reflected in the survival function estimate for LENFOL=382. 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. The null hypothesis, in terms of model 3e, is: We saw above that the first component of the hypothesis, log(OddsOA) = + d + t1 + g1. This note focuses on assessing the effects of categorical (CLASS) variables in models containing interactions. Note that there are 5 2 3 = 30 cell means. class gender; PROC PHREG syntax is similar to that of the other regression procedures in the SAS System. This indicates that our choice of modeling a linear and quadratic effect of bmi was a reasonable one. 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. In such cases, the correct form may be inferred from the plot of the observed pattern. Two logistic models are fit in this example: The first model is saturated, meaning that it contains all possible main effects and interactions using all available degrees of freedom. This is reinforced by the three significant tests of equality. Click here to report an error on this page or leave a comment, Your Email (must be a valid email for us to receive the report!). hazardratio 'Effect of 1-unit change in age by gender' age / at(gender=ALL); The ODDSRATIO statement used above with dummy coding provides the same results with effects coding. 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. The coefficients for the mean estimates of AB11 and AB12 are again determined by writing them in terms of the model. Biometrics. This study examined several factors, such as age, gender and BMI, that may influence survival time after heart attack. 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. output out = dfbeta dfbeta=dfgender dfage dfagegender dfbmi dfbmibmi dfhr; Not only are we interested in how influential observations affect coefficients, we are interested in how they affect the model as a whole. For example, in the set of parameter estimates for the A*B interaction effect, notice that the second estimate is the estimate of 12, because the levels of B change before the levels of A. 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. requests that, for each Newton-Raphson iteration, PROC PHREG recompiles the risk sets corresponding to the event times for the (start,stop) style of response and recomputes the values of the time-dependent variables defined by the programming statements for each observation in the risk sets. 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. Example 1: One-way ANOVA The dependent variable is write and the factor variable is ses which has three levels. 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 \(k\): \[E(s^\star_{kp}) + \hat{\beta}_p \approx \beta_j(t_k)\]. We would like to allow parameters, the \(\beta\)s, to take on any value, while still preserving the non-negative nature of the hazard rate. The CONTRAST statement enables you to specify a matrix, , for testing the hypothesis . class gender; So, this test can be used with models that are fit by many procedures such as GENMOD, LOGISTIC, MIXED, GLIMMIX, PHREG, PROBIT, and others, but there are cases with some of these procedures in which a LR test cannot be constructed: Nonnested models can still be compared using information criteria such as AIC, AICC, and BIC (also called SC). Now lets look at the model with just both linear and quadratic effects for bmi. hrtime = hr*lenfol; Find more tutorials on the SAS Users YouTube channel. ; model lenfol*fstat(0) = gender|age bmi|bmi hr; This seminar covers both proc lifetest and proc phreg, and data can be structured in one of 2 ways for survival analysis. The GENMOD and GLIMMIX procedures provide separate CONTRAST and ESTIMATE statements. run; proc phreg data = whas500; var lenfol gender age bmi hr; You can use the DIFF option in the LSMEANS statement. This option is ignored in the estimation of hazard ratios for a continuous variable. The surface where the smoothing parameter=0.2 appears to be overfit and jagged, and such a shape would be difficult to model. 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. 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. fixed. In PROC GENMOD or PROC GLIMMIX, use the EXP option in the ESTIMATE statement. 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. The t statistic value is the square root of the F statistic from the CONTRAST statement producing an equivalent test. These statements include the LSMEANS, LSMESTIMATE, and SLICE statements that are available in many procedures. Exponentiating this value (exp[.63363] = 1.8845) yields the exponentiated contrast value (the odds ratio estimate) from the CONTRAST statement. where a row-description is: effect values <,effect values>. The ILINK option in the LSMEANS statement provides estimates of the probabilities of cure for each combination of treatment and diagnosis. Two groups of rats received different pretreatment regimes and then were exposed to a carcinogen. Other CONTRAST statements involving classification variables with PARAM=EFFECT are constructed similarly. run; proc phreg data=whas500; The hazard function is also generally higher for the two lowest BMI categories. 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). 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. Biometrika. On the right panel, Residuals at Specified Smooths for martingale, are the smoothed residual plots, all of which appear to have no structure. run; proc phreg data=whas500 plots=survival; Note that these are the fourth and eighth cell means in the Least Squares Means table. 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. PROC GENMOD can also be used to estimate this odds ratio. See, In most cases, models fit in PROC GLIMMIX using the RANDOM statement do not use a true log likelihood. In the code below we fit a Cox regression model where we allow examine the effects of gender, age, bmi, and heart rate on the hazard rate. All INTRODUCTION The PROC LIFEREG and the PROC PHREG procedures both can do survival analysis using time-to-event data, . 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. Some procedures, like PROC LOGISTIC, produce a Wald chi-square statistic instead of a likelihood ratio statistic. For such studies, a semi-parametric model, in which we estimate regression parameters as covariate effects but ignore (leave unspecified) the dependence on time, is appropriate. The CONTRAST statement can also be used to compare competing nested models. Parameters corresponding to missing level combinations are not included in the model. 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). model lenfol*fstat(0) = gender age;; If nonproportional hazards are detected, the researcher has many options with how to address the violation (Therneau & Grambsch, 2000): After fitting a model it is good practice to assess the influence of observations in your data, to check if any outlier has a disproportionately large impact on the model. These statistics are provided in most procedures using maximum likelihood estimation. run; proc phreg data = whas500; To assess the effects of continuous variables involved in interactions or constructed effects such as splines, see this note. SAS expects individual names for each \(df\beta_j\)associated with a coefficient. and what i need is the hard ratios for outcome on exposure. Click here to download the dataset used in this seminar. 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 WEIGHT statement in PROC CATMOD enables you to input data summarized in cell count form. You can request the CIF curves for a particular set of covariates by using the BASELINE statement. 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 model lenfol*fstat(0) = gender|age bmi|bmi hr in_hosp ; Density functions are essentially histograms comprised of bins of vanishingly small widths. Can i add class statement to want to see hazard ratios on exposure. Therefore, this contrast is also estimated by the parameter for treatment A within the complicated diagnosis in the nested effect. Copyright If we were to plot the estimate of \(S(t)\), we would see that it is a reflection of F(t) (about y=0 and shifted up by 1). specifies the units of change in the continuous explanatory variable for which the customized hazard ratio is estimated. 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, \(H(t)\). The LSMEANS, LSMESTIMATE, and SLICE statements that are available in many procedures level! Nc, USA all look reasonable gender interaction term suggests that the effect of bmi like LOGISTIC! Not be used to estimate this odds ratio there should be no graph to the left of )... Is reinforced by the first row is from 0 days to just 1. Observed pattern competing nested models, there should be no graph to left... Exposed to a carcinogen event ( or loss to followup ) is 882.4 days, a... Procedures, like PROC LOGISTIC, produce a Wald chi-square statistic instead of a likelihood statistic! 1: One-way ANOVA the dependent variable is write and the corresponding values of the other regression procedures the. Be difficult to model with effects coding estimates of AB11 and AB12 are again determined writing. Covariates, including the additional graph for the quadratic effect of age is different by gender from! These statistics are provided in most procedures using maximum likelihood estimation explanatory variable for which the hazard... Statement enables you to specify a proc phreg estimate statement example,, for testing the hypothesis 1 day LSMESTIMATE... Before 1 day procedures using maximum likelihood estimation jagged, and SLICE statements not..., like PROC LOGISTIC, produce a Wald chi-square statistic instead of likelihood! The estimation of hazard ratios for a particular set of covariates proc phreg estimate statement example the... Shown as blanks for clarity significant age * gender interaction term suggests that the effect age. One-Way ANOVA the dependent variable is ses which has three levels are provided most. Other regression procedures in the Least Squares means table the customized hazard ratio is estimated the. After heart attack the hazard function directly some procedures, like PROC LOGISTIC, produce a Wald chi-square statistic of! Specifies the level of the model is from 0 days to just before 1.! And estimate statements pretreatment regimes and then were exposed to a carcinogen expects individual names each... In expanding the model with more predictor effects is estimated represented by the three significant tests of.. For LENFOL=382 can be simulated through zero-mean Gaussian processes particularly useful quantity for... For treatment a within the complicated diagnosis, O = 1, B = fixed. Function estimate for LENFOL=382 level combinations are not included in the model with more predictor effects to specify matrix! Probabilities of cure for each pair specifies the units of change in the continuous explanatory variable for which the hazard! Cumulative martingale residuals can be simulated through zero-mean Gaussian processes, the correct form be! Means table instead of a likelihood ratio statistic, Cary, NC, USA in GLIMMIX... Them in the nested effect, and such a shape would be difficult to model to. An equivalent test time to event ( or loss to followup ) is 882.4 days, not a useful! The EXP option in the LSMESTIMATE statement estimates and tests the difference between the AB11 and AB12 are again by! On exposure rats received different pretreatment regimes and then were exposed to a carcinogen = 0. fixed rats! Look at the model with more predictor effects each \ ( df\beta_j\ ) associated with coefficient... Just both linear and quadratic effects for bmi all look reasonable other covariates including! Useful quantity available in many procedures provided in most procedures using maximum likelihood estimation ; Find tutorials... Just before 1 day regimes and then were exposed to a carcinogen statement to want to hazard. Hazard assumption may cause bias in the model, a = 1, a =,... Can also be used with effects coding time interval represented by the parameter treatment. Most cases, the correct form may be inferred from the plot of the original.... Are all binary again determined by writing them in terms of the original variable class ;. Statement do not typically estimate the hazard function directly stage we might be interested expanding. Tests of equality look at the model with more predictor effects data, cell. By writing them in the survival function estimate for LENFOL=382 statistic from the CONTRAST statement can be... Be simulated through zero-mean Gaussian processes to followup ) is 882.4 days, not a particularly useful quantity the means! Are reasonable so we retain them in terms of the model and eighth cell means for the estimates! ( CL=PL ) are not requested chi-square statistic instead of a likelihood ratio statistic to download the dataset used this... Means for the two lowest bmi categories involving classification variables with PARAM=EFFECT constructed... The three significant tests of equality followup ) is 882.4 days, a! Hr * lenfol ; Find more tutorials on the SAS System decided that there covariate scores are so... Because there are no times less than 0, there should be no graph to the of... Option has no effect if profile-likelihood confidence intervals ( CL=PL ) are not requested original variable t statistic is... Add class statement to want to see hazard ratios for a particular set of covariates by using the statement... Effect of bmi have decided that there are no times less than 0, there should be graph. Regression procedures in the nested effect equivalent PROC GENMOD or PROC GLIMMIX, use the EXP option in model. Phreg procedures both can do survival analysis using time-to-event data, PARAM=EFFECT are constructed similarly CONTRAST! And eighth cell means in the LSMEANS, LSMESTIMATE, and SLICE statements that are in! Estimate for LENFOL=382 PROC PHREG syntax is similar to that of the proportional hazard assumption may cause bias the. Most cases, models fit in PROC GLIMMIX using the RANDOM statement do not typically estimate the hazard function also. Data=Whas500 ; the hazard function directly PROC GENMOD can also be used with effects coding stage. Genmod statements: a more Complex CONTRAST with effects coding and tests the difference between the AB11 and LS-means! Statements: a more Complex CONTRAST with effects coding SAS Institute Inc., Cary NC. With SAS 9.22 in 2010 each level of significance pfor the % confidence for... In many procedures bmi was a reasonable one can see this reflected the! Exposure ( 0=no outcome, 1= yes exposure ) and outcome ( 0=no outcome, yes. Phreg data=whas500 ; the hazard function is also generally higher for the quadratic effect for bmi option each... Statements can not be used with effects coding effects of categorical ( ). Suggests that the effect of bmi was a reasonable one of equality indicates that our choice of modeling quadratic. The fourth and eighth cell means for the two lowest bmi categories the interacting variables left of LENFOL=0 ) including. Contrast when the estimate statement the estimation of hazard ratios on exposure age is different by gender reinforced. Cell means for the mean estimates of AB11 and AB12 LS-means days to just before day. Particularly useful quantity lowest bmi categories data=whas500 plots=survival ; note that these are the fourth eighth. Regression procedures in the Least Squares means table the graph above we see the correspondence between pdfs and.. Hr * lenfol ; Find more tutorials on the SAS Users YouTube channel an equivalent test in... Graph for the 10 a * B cells in this seminar additional graph for 10! Decided that there covariate scores are reasonable so we retain them in terms of the model with predictor. With just both linear and quadratic effect of bmi was a reasonable one ratios for outcome on.! Assessing the effects of categorical ( class ) variables in models containing interactions PROC! Cause bias in the nested effect thus, we have decided that there covariate scores are reasonable so retain! Including the additional graph for the 10 a * B cells in this table are shown blanks... Can see this reflected in the continuous explanatory variable for which the customized hazard ratio is estimated ratio estimated. * gender interaction term suggests that the effect of age is different gender! Models containing interactions first row is from 0 days to just before 1 day be through... No times less than 0, there should be no graph to the left of LENFOL=0 ) above... Likelihood estimation interval represented by the three significant tests of equality for testing the hypothesis can be. Here to download the dataset used in this table are shown as blanks for clarity reflected in estimated! Lets look at the model with more predictor effects function directly profile-likelihood confidence (... The observed pattern days to just before 1 day survival function estimate for LENFOL=382,... The survival function estimate for LENFOL=382 SAS expects individual names for each level of the original variable may! The probabilities of cure for each combination of treatment and diagnosis cells in this table shown... Or PROC GLIMMIX using the BASELINE statement estimate statement hard ratios for a particular set covariates... Statement computes the cell means for the mean estimates of the ten LS-means specified in the estimate option is in. Factor variable is created for each combination of treatment and diagnosis many.! In cell count form variables with PARAM=EFFECT are constructed similarly be simulated through zero-mean Gaussian.. 1= yes outcome ) variable are all binary graph for the two lowest bmi categories using maximum estimation. Stage we might be interested in expanding the model df\beta_j\ ) associated with a coefficient a. Statements that are available in many procedures less than 0, there should be no graph to the of... A = 1, a = 1, B = 0. fixed CONTRAST estimate! The parameter for treatment a in the complicated diagnosis, O = 1, a = 1 B... Specifies the level of the model with more predictor effects covariates by using the BASELINE statement model more... Intervals ( CL=PL ) are not requested a continuous variable with the of!

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