Consider a model with one CLASS variable A with four levels, 1, 2, 5, and 7. Details of the possible choices for the PARAM= option follow.
EFFECT | Three columns are created to indicate group membership of the nonreference levels. For the reference level, all three dummy variables have a value of ˆ’ 1. For instance, if the reference level is 7 (REF=7), the design matrix columns for A are as follows . | |||
Effect Coding | ||||
A | Design Matrix | |||
A1 | A2 | A5 | ||
1 | 1 |
|
| |
2 |
| 1 |
| |
5 |
|
| 1 | |
7 | ˆ’ 1 | ˆ’ 1 | ˆ’ 1 | |
Parameter estimates of CLASS main effects using the effect coding scheme estimate the difference in the effect of each nonreference level compared to the average effect over all four levels. |
GLM | As in PROC GLM, four columns are created to indicate group membership. The design matrix columns for A are as follows. | |||||
GLM Coding | ||||||
A | Design Matrix | |||||
A1 | A2 | A5 | A7 | |||
1 | 1 |
|
|
| ||
2 |
| 1 |
|
| ||
5 |
|
| 1 |
| ||
7 |
|
|
| 1 | ||
Parameter estimates of CLASS main effects using the GLM coding scheme estimate the difference in the effects of each level compared to the last level. |
ORDINAL | Three columns are created to indicate group membership of the higher levels of the effect. For the first level of the effect (which for A is 1), all three dummy variables have a value of 0. The design matrix columns for A are as follows. | |||
Ordinal Coding | ||||
A | Design Matrix | |||
A2 | A5 | A7 | ||
1 |
|
|
| |
2 | 1 |
|
| |
5 | 1 | 1 |
| |
7 | 1 | 1 | 1 | |
The first level of the effect is a control or baseline level. Parameter estimates of CLASS main effects using the ORDINAL coding scheme estimate the effect on the response as the ordinal factor is set to each succeeding level. When the parameters for an ordinal main effect have the same sign, the response effect is monotonic across the levels. | ||||
POLYNOMIAL POLY | Three columns are created. The first represents the linear term ( x ), the second represents the quadratic term ( x 2 ), and the third represents the cubic term ( x 3 ), where x is the level value. If the CLASS levels are not numeric, they are translated into 1, 2, 3, according to their sorting order. The design matrix columns for A are as follows. |
Polynomial Coding | |||
---|---|---|---|
Design Matrix | |||
A | APOLY1 | APOLY2 | APOLY3 |
1 | 1 | 1 | 1 |
2 | 2 | 4 | 8 |
5 | 5 | 25 | 125 |
7 | 7 | 49 | 343 |
REFERENCE REF | Three columns are created to indicate group membership of the nonreference levels. For the reference level, all three dummy variables have a value of 0. For instance, if the reference level is 7 (REF=7), the design matrix columns for A are as follows. | |||
Reference Coding | ||||
A | Design Matrix | |||
A1 | A2 | A5 | ||
1 | 1 |
|
| |
2 |
| 1 |
| |
5 |
|
| 1 | |
7 |
|
|
| |
Parameter estimates of CLASS main effects using the reference coding scheme estimate the difference in the effect of each nonreference level compared to the effect of the reference level. | ||||
ORTHEFFECT | The columns are obtained by applying the Gram-Schmidt orthogonalization to the columns for PARAM=EFFECT. The design matrix columns for A are as follows. | |||
Orthogonal Effect Coding | ||||
A | Design Matrix | |||
AOEFF1 | AOEFF2 | AOEFF3 | ||
1 | 1 . 41421 | ˆ’ . 81650 | ˆ’ . 57735 | |
2 | . 00000 | 1 . 63299 | ˆ’ . 57735 | |
5 | . 00000 | . 00000 | 1 . 73205 | |
7 | ˆ’ 1 . 41421 | ˆ’ . 81649 | ˆ’ . 57735 | |
ORTHORDINAL | The columns are obtained by applying the Gram-Schmidt orthogonalization to the columns for PARAM=ORDINAL. The design matrix columns for A are as follows. |
Orthogonal Ordinal Coding | |||
---|---|---|---|
Design Matrix | |||
A | AOORD1 | AOORD2 | AOORD3 |
1 | ˆ’ 1 . 73205 | . 00000 | . 00000 |
2 | . 57735 | ˆ’ 1 . 63299 | . 00000 |
5 | . 57735 | . 81650 | ˆ’ 1 . 41421 |
7 | . 57735 | . 81650 | 1 . 41421 |
ORTHPOLY | The columns are obtained by applying the Gram-Schmidt orthogonalization to the columns for PARAM=POLY. The design matrix columns for A are as follows. | |||
Orthogonal Polynomial Coding | ||||
A | Design Matrix | |||
AOPOLY1 | AOPOLY2 | AOPOLY5 | ||
1 | ˆ’ 1 . 153 | . 907 | ˆ’ . 921 | |
2 | ˆ’ . 734 | ˆ’ . 540 | 1 . 473 | |
5 | . 524 | ˆ’ 1 . 370 | ˆ’ . 921 | |
7 | 1 . 363 | 1 . 004 | . 368 | |
ORTHREF | The columns are obtained by applying the Gram-Schmidt orthogonalization to the columns for PARAM=REFERENCE. The design matrix columns for A are as follows. |
Orthogonal Reference Coding | |||
---|---|---|---|
Design Matrix | |||
A | AOREF1 | AOREF2 | AOREF3 |
1 | 1 . 73205 | . 00000 | . 00000 |
2 | ˆ’ . 57735 | 1 . 63299 | . 00000 |
5 | ˆ’ . 57735 | ˆ’ . 81650 | 1 . 41421 |
7 | ˆ’ . 57735 | ˆ’ . 81650 | ˆ’ 1 . 41421 |
The default method of computing the survivor function estimate is METHOD=CH which is based on the empirical cumulative hazard function estimate rather than the product-limit estimate (METHOD=PL) as in PROC PHREG. This applies to both the OUTPUT and BASELINE statements.
The OUT= data set in the OUTPUT statement contains the entire input data set along with statistics you request using the keyword= name options. Observations in the OUT= data set follow the same order as the input data set. The ORDER=SORTED option in the OUTPUT statement of PROC PHREG (see the 'OUTPUT Statement' section (page 3233) in Chapter 54, 'The PHREG Procedure,' ) is no longer available.
The BASELINE statement in PROC PHREG enables you to to predict the cumulative mean function (CMF) and the cumulative hazard function (CUMHAZ) for recurrent events models. However, such features are not yet available in the BASELINE statement of PROC TPHREG.
If you use the NOPRINT option in the PROC TPHREG statement, the procedure does not display any output. Otherwise, the displayed output of the TPHREG procedure includes the following:
the 'Model Information' table, which contains
the two-level name of the input data set
the name and label of the failure-time variable
if you specify the censoring variable,
the name and label of the censoring variable
the values that the censoring variable assumes to indicate censored times
if you use the OFFSET= option in the MODEL statement, the name and label of the offset variable
if you specify the FREQ statement, the name and label of the frequency variable
if you specify the WEIGHT statement, the name and label of the weight variable
the method of handling ties in the failure time
the 'Class Level Information' table, which shows the levels and the corresponding design variables for each CLASS explanatory variable
the 'Summary of the Number of Event and Censored Values' table, which gives, for each stratum, the breakdown of the number of events and censored values. This table is not produced if the NOSUMMARY option is specified.
if you specify the SIMPLE option in the PROC TPHREG statement, the 'Descriptive Statistics for Continuous Explanatory Variables' table for continuous explanatory variables, and the 'Frequency Distribution of CLASS Variables' table. The 'Descriptive Statistics for Continuous Explanatory Variables' table contains the mean, standard deviation, maximum and minimum of each continuous variable specified in the MODEL statement. If the WEIGHT statement is specified, the 'Frequency Distribution of Class Variables' table also contains the weight distributions of the CLASS variables.
if you specify the ITPRINT option in the MODEL statement, the 'Iteration History' table, which displays the iteration number, step size , log likelihood , and parameter estimates at each iteration The last evaluation of the gradient vector is also displayed.
the 'Model Fit Statistics' table, which gives the values of ˆ’ 2 log likelihood for fitting a model with no explanatory variable and for fitting a model with all the explanatory variables. The AIC and SBC are also given in this table.
the 'Testing Global Null Hypothesis: BETA=0' table, which displays results of the likelihood ratio test, the score test, and the Wald test
if the model contains an effect involving a CLASS variable, the 'Type 3 Tests' table, which gives the Wald chi-square statistic, the degrees of freedom, and the p -value for each effect in the model
the 'Analysis of Maximum Likelihood Estimates' table, which contains the following:
the maximum likelihood estimate of the parameter
the estimated standard error of the parameter estimate, computed as the square root of the corresponding diagonal element of the estimated covariance matrix
if you specify the COVS option in the PROC statement, the ratio of the robust standard error estimate to the model-based standard error estimate
the Wald Chi-Square statistic, computed as the square of the parameter estimate divided by its standard error estimate
the degrees of freedom of the Wald chi-square statistic. It has a value of 1 unless the corresponding parameter is redundant or infinite, in which casethevalueis0.
the p -value of the Wald chi-square statistic with respect to a chi-square distribution with one degree of freedom
the hazards ratio estimate computed by exponentiating the parameter estimate
if you specified the RISKLIMITS option in the MODEL statement, the confidence limits for the hazards ratio
if you specify SELECTION=SCORE in the MODEL statement, the 'Regression Models Selected by Score Criterion' table, which gives the number of explanatory variables in each model, the score chi-square statistic, and the names of the variables included in the model
if you use the FORWARD or STEPWISE selection method and specify the DETAILS option in the MODEL statement, the 'Effects to Enter' table, which gives the score chi-square statistic for testing the significance of each candidate effect for entry (after adjusting for the effects already in the model), the degrees of freedom of the score chi-square statistic, and the corresponding p -value. This table is produced before an effect is selected for entry.
if you use the BACKWARD or STEPWISE selection method and specify the DETAILS option in the MODEL statement, the 'Effects to Remove' table, which gives the Wald chi-square statistic for testing the significance of each candidate effect for removal, the degrees of freedom of the Wald chi-square, and the corresponding p -value. This table is produced before an effect is selected for removal.
if you use the BACKWARD, FORWARD, or STEPWISE selection method, a table summarizing the model-building process, which gives the step number, the effect entered or removed at each step, the chi-square statistic, and the corresponding p -value on which the selection is based
if you use the COVB option in the MODEL statement, the estimated covariance matrix of the parameter estimates
if you use the CORRB option in the MODEL statement, the estimated correlation matrix of the parameter estimates
if you specify a CONTRAST statement, the 'Contrast Test Results' table, which gives the result of the Wald test for each CONTRAST specified. If you specify the E option in the CONTRAST statement, then the contrast matrix is displayed. If you specify the ESTIMATE= option in the CONTRAST statement, the 'Contrast Rows Estimation and Testing Results' table is produced, which includes the point estimate and confidence interval for each row of the contrast matrix, and the corresponding Wald test as well.
if you specify a TEST statement,
the 'Linear Coefficients' table, which gives the coefficients and constants of the linear hypothesis (if the E option is specified)
the printing of the intermediate calculations of the Wald test (if the option PRINT is specified)
the 'Test Results' table, which gives the Wald chi-square statistic, the degrees of freedom, and the p -value
the 'Average Effect' table, which gives the weighted average of the parameter estimates for the variables in the TEST statement, the estimated standard error, the z-score, and the p -value (if the AVERAGE option is specified)
PROC TPHREG assigns a name to each table it creates. You can use these names to reference the table when using the Output Delivery System (ODS) to select tables and create output data sets. These names are listed in the following table.
ODS Table Name | Description | Statement | Option |
---|---|---|---|
BestSubsets | Best subset selection | MODEL | SELECTION=SCORE |
CensoredSummary | Summary of event and censored observations | MODEL | default |
ClassLevelFreq | Frequency breakdown of CLASS variables | PROC | SIMPLE (with CLASS vars) |
ClassLevelInfo | CLASS variable levels and design variables | MODEL | default (with CLASS vars) |
ClassWgt | Weight breakdown of CLASS variables | WEIGHT | SIMPLE (with CLASS vars) |
ContrastCoeff | L matrix for contrasts | CONTRAST | E |
ContrastEstimate | Individual contrast estimates | CONTRAST | ESTIMATE= |
ContrastTest | Wald test for contrasts | CONTRAST | default |
ConvergenceStatus | Convergence status | MODEL | default |
CorrB | Estimated correlation matrix of parameter estimators | MODEL | CORRB |
CovB | Estimated covariance matrix of parameter estimators | MODEL | COVB |
EffectsToEnter | Eligible effects for entry to model | MODEL | SELECTION=F/S |
EffectsToRemove | Eligible effects for removal from model | MODEL | SELECTION=B/S |
FitStatistics | Model fit statistics | MODEL | default |
GlobalScore | Global chi-square test | MODEL | NOFIT |
GlobalTests | Tests of the global null hypothesis | MODEL | default |
IterHistory | Iteration history | MODEL | ITPRINT |
LastGradient | Last evaluation of gradient | MODEL | ITPRINT |
ModelBuildingSummary | Summary of model building | MODEL | SELECTION=B/F/S |
ModelInfo | Model information | PROC | default |
NObs | Number of observations | default | |
ParameterEstimates | Maximum likelihood estimates of model parameters | MODEL | default |
ResidualChiSq | Residual chi-square | MODEL | SELECTION=F/B |
SimpleStatistics | Summary statistics for continuous explanatory variables | PROC | SIMPLE |
TestAverage | Average Effect for test | TEST | AVERAGE |
TestCoeff | coefficients for linear hypotheses | TEST | E |
TestPrint1 | L [cov( b )] L ' and Lb - c | TEST | |
TestPrint2 | Ginv( L [cov( b )] L ') and Ginv( L [cov( b )] L ')( Lb - c ) | TEST | |
TestStmts | Linear Hypotheses Test Results | TEST | default |
Type3 | Type 3 tests of effects | MODEL | default (with CLASS vars) |