# Cox Visualizations

The following tables and options are available for Cox visualizations.

**Case Processing Summary table**

Shows the counts and percentages of cases or records used in the analysis, including the numbers of events and censored observations. Also shows the numbers and percentages not used in the analysis due to missing data, negative values for the time measure or being censored prior to the first event time within a given stratum (since only observations that remain in the risk set at event times contribute to the partial likelihood function maximized by the Cox regression model).

**Stratum Status table**

Appearing only when a stratification or grouping field has been specified, shows the numbers of events and censored observations, as well as the percentage of observations censored, within each stratum and overall.

**Categorical Variable Codings table**

If any categorical features or predictor variables are specified, this table shows the numbers of observations at each level and how each level is represented in computations by one or more coded numeric features. The coded values would be the values used when scoring observations using the regression coefficients from the Cox regression model.

**Omnibus Tests of Model Coefficients table**

Gives -2 times the log-likelihood for the model and usually three chi-square tests at each stage in model building. The Overall (score) statistic tests the null hypothesis that all model coefficients are 0. The tests for Change from Previous Step and Change from Previous Block use likelihood-ratio tests to compare the current model to either the previous step or the previous block, which refers to the null model with no predictors. These provide tests for the additional parameters added at a given step or cumulatively for the block tests.

**Variables in the Equation table**

Shows estimated regression coefficients (B), standard errors, Wald chi-square test statistics, degrees of freedom, significance or p values, risk or hazard ratios (Exp(B) column), and optionally confidence interval values for risk or hazard ratios, for each predictor or coded categorical predictor in the model. If a stepwise model-building method has been used, results are presented for all steps in the process. Large B coefficients accompanied by very large standard errors and small Wald statistics may indicate problems in model fitting warranting attention.

**Variables not in the Equation table**

At each stage in the stepwise fitting of a model this table shows Score chi-square tests for any features or predictors not included in the current model, estimating the p value or significance for each excluded predictor if added to the model.

**Model if Term Removed table**

At each stage in stepwise fitting of a model this table shows likelihood-ratio (LR) chi-square tests for each predictor currently included in the model.

**Correlation Matrix of Regression Coefficients table**

Shows correlations among estimated regression coefficients in the final fitted model. Very high correlations among predictor coefficients indicate possible instability in estimation and may warrant attention.

**Survival Table table**

For each event time (within each stratum if stratification is in effect) shows the estimated baseline cumulative hazard function, as well as the estimated survival function, its standard error and the estimated cumulative hazard function at the mean of all covariates (including coded values representing categorical predictors). Note that while survival function values can be interpreted in terms of estimated probabilities of survival beyond a certain time, cumulative hazards are expressed in rates per unit of time and are not interpretable as probability estimates.

**Covariate Means (and Pattern Values) table**

Contains the means for all predictors used in the model (including those considered for inclusion in a stepwise method but not included in the final model), including means of coded values representing categorical predictors. These are the values at which predictors are fixed in producing any plots or survival or related functions indicating “at mean of covariates” in their titles. If plots have been requested with separate lines for each value of a categorical variable and/or at specific values of predictors, additional columns appear, labeled as Patterns, giving the specific values at which survival or related functions are plotted in additional plots.

**Survival Function plot**

Plots estimated cumulative survival probability on the vertical axis vs. elapsed time on the horizontal axis, either at the mean of all predictors or at specified pattern values (see Covariate Means and Patterns table for pattern values).

**One Minus Survival Function plot**

Plots estimated cumulative survival probability subtracted from 1 on the vertical axis vs. elapsed time on the horizontal axis, either at the mean of all predictors or at specified pattern values (see Covariate Means and Patterns table for pattern values). This provides estimated probabilities of failure over time.

**Hazard Function plot**

Plots estimated cumulative hazard on the vertical axis vs. elapsed time on the horizontal axis, either at the mean of all predictors or at specified pattern values (see Covariate Means and Patterns table for pattern values). Note that cumulative hazards are estimated in rates per unit time and are not interpretable as probabilities.

**LML Function plot**

Plots the natural log of the negative of the natural log of the estimated cumulative survival probability on the vertical axis vs. elapsed time on the horizontal axis, either at the mean of all predictors or at specified pattern values (see Covariate Means and Patterns table for pattern values). This plot is useful when stratification is in effect and separate lines are plotted for each stratum. Parallel functions across strata indicate validity of the proportional hazards assumption and thus the stratification variable can be used as a predictor rather than to produce separate baseline hazards.

## Next steps

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