Cox Proportional Hazards

The Cox proportional hazards model is the most commonly used regression model for survival data. It allows the estimation of nonparametric survival curves (such as Kaplan-Meier curves) in the presence of covariates. The effect of the covariates upon survival is usually of primary interest.

To perform Cox regression modeling

Choose Statistics __image\ebd_ebd62.gif Survival __image\ebd_ebd63.gif Cox Proportional Hazards. The dialog shown below appears.

Model page

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In the Cox Proportional Hazards 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.

Weights

Enter the column that specifies weights to be applied to all observations used in the analysis. To weight all rows equally, leave this blank.

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

Formula

In the Formula field, enter a formula specifying the desired model. In its simplest form a formula consists of the response variable, a tilde (~), and a list of predictor variables separated by "+"s. An intercept is automatically included by default.

Create Formula

Click the Create Formula button to open a formula builder dialog used to construct a formula specifying the desired model. See the online Help section Building Formulas for more information.

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 Cox Proportional Hazards 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.

Allow Collinearity

Select this to allow for collinearity in the model matrix; columns that are linear combinations of earlier columns are skipped. Coefficients for such columns are missing (NA) and the variance matrix contains zeroes. Missing coefficients are treated as zeros for ancillary calculations.

Model Options

Model Options

Method for Ties Select a method for handling ties: efron, breslow, and exact. The exact method computes the exact partial likelihood, which is equivalent to a conditional logistic model.

Robust Variance Estimate Select this to calculate a robust variance estimate. This is the default if the model, as defined in the Formula field, contains a cluster operative.

Results page

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In the Cox Proportional Hazards dialog, the Results page has the following options:

Short Output for Cox Proportional Hazards

Select this to print a short summary of the fit. This includes the call, model coefficients, and a likelihood ratio test.

Long Output for Cox Proportional Hazards

Select this to print a long summary of the fit. This includes the call, model coefficients, standards errors of the estimates, a confidence interval for the relative risk of each coefficient, a likelihood ratio test, Wald's test, and the efficient score test.

Plot page

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In the Cox Proportional Hazards dialog, the Plot page has the following options:

Plots

Survival Curves

Select this to plot survival curves for the current survival model.

Curve Type

Select the type of survival estimate: aalen or kaplan-meier. The Aalen estimate of survival, which is equivalent to the Tsiatis estimate, is used by default.

New Data

New Data Set

Enter the name of a data set with the same variable names as those that appear in the formula on the model page. The curves produced are representative of a cohort whose covariates correspond to the values in this data set. If left blank, the survival curves are based on the mean of the covariates used in the cox regression fit.

Only One Individual

Select this to indicate that Data Set represents different time epochs for only one individual. When checked, only one curve is produced. By default, multiple rows indicate multiple individuals and there is one curve generated per row in Data Set.

Confidence Intervals

Show Confidence Intervals

Select this to plot two-sided confidence intervals. For Nonparametric Survival the confidence interval level can be set on the Options page.

Confidence Interval Type

Select a confidence interval type.

. log: for intervals based on the cumulative hazard or log(survival). This is the default.

. plain: for standard intervals.

. log-log: for intervals based on the log hazard or log(-log(survival)).

Curve Options

Curve Options

Line Colors Enter a list of integers using either the name of an existing S-PLUS vector or a comma-delimited list. If the number of curves to be plotted is greater than the length of the list, the line colors cycle through the list.

Line Types Enter a list of integers using either the name of an existing S-PLUS vector or a comma-delimited list. If the number of curves to be plotted is greater than the length of the list, the line types cycle through the list.

Line Widths Enter a list of integers using either the name of an existing S-PLUS vector or a comma-delimited list. If the number of curves to be plotted is greater than the length of the list, the line widths cycle through the list.

Axis Options

Axis Options

Log Axis for Y Select this to plot the y-axis on the log scale.

X-Axis Style Select the x-axis style.

standard scale or extend the maximum survival time, creating an axis with extended labels on the right side of the plot. This is the default.

tight create an axis labeled internal to the data values.

extended create an axis whose numeric labels are more extreme than any data values.

Scale Factor for X-Axis Tick Labels Enter a number used to multiply the labels on the x-axis. For example, a value of 365.25 gives labels in years instead of the original days.

Scale Factor for Y-Axis Tick Labels Enter a number used to multiply the labels on the y-axis. For example a value of 100 yields a percent scale.

X-Axis Label Enter a label for the x-axis.

Y-Axis Label Enter a label for the y-axis.

Predict page

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In the Cox Proportional Hazards dialog, the Predict page has the following options:

New Data

Enter the name of a data set containing the specification of future covariate history for the patients in question. The columns of the data set must have the same names as those used in the model formula.

Save

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.

Predictions

Select this to save predictions to the data set specified in Save In.

Standard Errors

Store the pointwise standard errors for the predictions in the object specified in Save In.

Prediction Type

Choose the type of model predictions: lp (linear predictors), risk, expected, or terms.

Variable Over Which to Collapse

Enter the name of a grouping variable over which to collapse the predictions. The program sums the predictions for each level of this variable.

Related S-Plus language functions for Cox regression

coxph, print.coxph, plot.coxph, predict.coxph, coxph.fit, residuals.coxph, summary.coxph, survfit.coxph

Other related S-Plus language functions

cluster, strata, Surv, survfit