Parametric Survival

Parametric regression models for censored data are used in a variety of contexts ranging from manufacturing to studies of environmental contaminants. Because of their frequent use for modeling failure time or survival data, they are often referred to as parametric survival models. In this context, they are used throughout engineering to discover reasons why engineered products fail. They are called accelerated failure time models or accelerated testing models when the product is tested under more extreme conditions than normal to accelerate its failure time.

The Parametric Survival and Life Testing dialogs fit the same type of model. The difference between the two dialogs is in the options available. The Life Testing dialog is motivated more by manufacturing applications while the Parametric Survival dialog is motivated more by biomedical applications.

Choose Statistics __image\ebd_ebd64.gif Survival __image\ebd_ebd65.gif Parametric Survival. The dialog shown below appears.

Model page

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In the Parameteric Survival dialog, the Model page has the following options:

Data

Data Set

Select a data set from the dropdown list or type the name of a data set. You can also type into the Data Set edit field any expression that evaluates to a data set.

Subset Rows

Enter an S-PLUS expression that identifies the rows to use in the analysis. To use all the rows in the data set, leave this field blank.

Omit Rows with Missing Values

Select this box to omit from the analysis any rows in the data set that contain missing values for any of the variables in the model.

Formula

Enter a formula specifying the desired model. The response indicates the survival time and event status using the Surv function. A typical formula is Surv(days, event) ~ voltage.

Create Formula

Click this to open a formula builder dialog used to construct a formula specifying the desired model. See the Cox Proportional Hazards - Formula for more information on the Formula dialog for survival functions.

Model

Distribution

Select the assumed distribution for the transformed response variable.

Scale

Specify a fixed value for the scale. By default the scale is estimated.

Fixed Parameters

Specify fixed parameter values in the format name1=value1, name2=value2. For example, the t-distribution would have a degrees of freedom parameter, specified as df = 10. Most distributions have no parameters.

Save Model Object

Save Model Object

In the Save As field, enter the name for the object in which to save the results of the analysis. If an object with this name already exists, its contents are overwritten. The model object can be used in later functions such as plotting.

Options page

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In the Parameteric Survival dialog, the Options page has the following options:

Optimization Parameters

Convergence Tolerance

Enter a number specifying the convergence tolerance. Iteration continues until the relative change in the log-likelihood is less than this number.

Initial Parameter Values

Enter a vector of initial values. If this is left blank, zero is used for each variable.

Maximum Iteration

Enter a numeric value specifying the maximum number of iterations to perform for the maximum likelihood estimation procedure. If convergence has not been reached after this number of iterations, the procedure stops. The default value appears in the field.

Results page

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In the Parameteric Survival dialog, the Results page has the following options:

Short Output for Parametric Survival

Select this to print a summary of the model results in the designated output window. This includes estimates of the coefficients, scale, degrees of freedom, and log-likelihood.

Long Output for Parametric Survival

Select this to print a long summary of the model results in the designated output window. This includes summary statistics for the deviance residuals, standard errors and z-values for the coefficients, distribution, number of iterations, and correlation of coefficients.

Saved Results

Save In

Enter the name of a data set in which a part of the analysis, such as fitted values and residuals, predictions, confidence intervals, or standard errors, is saved.

Fitted Values

Save the fitted values from the model in the object specified in Save In.

Response Residuals

Select to save the response residuals. These are the ordinary residuals (the response minus the fitted value).

Deviance Residuals

Select to save the deviance residuals. These residuals are reasonable for use in detecting observations with unduly large influence in the fitting process, since they reflect the same criterion as used in the fitting.

Working Residuals

Store the working residuals in the object specified in Save In. The working residuals are the response minus the fitted value.

Matrix Residuals

Select this to save the matrix residuals. The matrix type produces multiple columns based on derivatives of the log-likelihood function.

Related S-Plus language functions for Parametric Survival

survReg