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 Options for Cox proportional hazards regression

The options tab for Cox proportional hazards regression provides a number of controls and optional results that Prism can report from this analysis. Many of the same techniques for testing and reporting best-fit values and model diagnostics are similar to other techniques such as multiple linear regression and multiple logistic regression.

## How precise are the best-fit values of the parameters?

After fitting a Cox proportional hazards regression model, Prism will report the estimated regression coefficients (beta coefficients) as well as the hazard ratios (exponentiated beta coefficients) for each of the predictor variables in the model. Prism can also optionally report the standard error for the beta coefficients, confidence intervals for coefficients and hazard ratios, and P values for each predictor (note that a P value for a given parameter coefficient is the same as the P value for the associated hazard ratio). These values can be used to assess how stable the coefficient estimates are. Large standard errors for the parameter estimates (which subsequently mean large confidence intervals) imply that there is considerable uncertainty with regards to the point estimate. The P values provide an assessment for whether the true value of the beta coefficient is zero (equivalent to testing whether the true value of the hazard ratio is 1.0). If the true value of a coefficient is zero (or hazard ratio is one), then the value of the corresponding predictor variable would have no effect on the hazard as calculated by the model.

## Are the variables intertwined or redundant?

Prism provides the option of including a parameter covariance matrix as part of the analysis results to show how much each parameter is correlated with each other parameter. If the “Correlation matrix” option is selected, Prism will generate an additional results tab with the parameter correlations, and will also generate a heatmap of the correlations. Additionally, Prism can quantify multicollinearity -- how well each variable can be predicted from the other variables. This process is the same for Cox proportional hazards regression as it is for multiple linear and multiple logistic regression, and more details can be found here.

## Comparative model diagnostics

There are four options that can be enabled in this section of the dialog, including:

Akaike's Information Criterion (AIC)

Partial log-likelihood (LL)

Negative two times partial log-likelihood (-2*LL)

Pseudo R squared

When enabled, each of these will report a value for the selected diagnostic for both the model specified on the Model tab of the dialog and the null model (the model with no covariates/predictor variables) fit to the data. By default, AIC is the only option enabled. This page provides additional details on how each of these diagnostics are calculated.

## Calculations

Specify the confidence level that Prism should use when reporting values in the results. By default, this is set to 95%

## Additional variables for graphing (Graphs of residuals only)

Choose optional variables to customize the residual graphs generated by Cox proportional hazards regression:

Labels - row identifiers such as the row numbers, names, or ID numbers

Symbol fill color - The color of each symbol is determined by the value of this variable, which is often not part of the calculations. Color-coding the symbols this way can show more details of your data on the graph.

Symbol size - used for scaling the size of the symbols on the output graph. Refine the rules for converting value to size on the Format Graph dialog

## Output

Use these controls to specify the number of significant digits for Prism to report in the results (for all values except P values), and to specify the P value style to use when reporting P values in the results.