Coefficients table for Fit Cox Model in a Counting Process Form

Find definitions and interpretation guidance for every statistic in the Coefficients table.

In This Topic

Coef
SE Coef
Confidence interval for coefficient (95% CI)
Z-value
P-Value

Coef

A regression coefficient describes the size and direction of the relationship between a predictor and the risk score. Coefficients are the numbers by which the values of the term are multiplied in a regression equation.

Interpretation

Use the coefficient to determine whether a change in a predictor variable makes the event more likely or less likely. Generally, positive coefficients make the event more likely and negative coefficients make the event less likely. An estimated coefficient near 0 implies that the effect of the predictor is small. For a categorical predictors, the interpretation depends on the coding.

Continuous predictors: The estimated coefficient for a predictor represents the change in the risk score for each unit change in the predictor, while the other predictors in the model are held constant.
Categorical predictors with 1,0 coding: The coefficient is the estimated change in the risk score when you change from the reference level to the level of the coefficient. For example, a categorical variable has the levels Fast and Slow. The reference level is Slow. If the coefficient for Fast is 1.3, then a change in the variable from Slow to Fast increases the risk score by 1.3.
Categorical predictors with 1, 0, -1 coding: The coefficient is the estimated change in the risk score when you change from the mean of the risk score to the level of the coefficient. For example, a categorical variable has the levels Before Change and After Change. If the coefficient for After Change is −2.1, then the risk score decreases by 2.1 from the average when the variable equals After Change.

SE Coef

The standard error of the coefficient estimates the variability between coefficient estimates that you would obtain if you took samples from the same population again and again. The calculation assumes that the sample size and the coefficients to estimate would remain the same if you sampled again and again.

Interpretation

Use the standard error of the coefficient to measure the precision of the estimate of the coefficient. The smaller the standard error, the more precise the estimate.

Confidence interval for coefficient (95% CI)

These confidence intervals (CI) are ranges of values that are likely to contain the true value of the coefficient for each term in the model. The calculation of the confidence intervals uses the normal distribution. The confidence interval is accurate if the sample size is large enough that the distribution of the sample coefficient follows a normal distribution.

Because samples are random, two samples from a population are unlikely to yield identical confidence intervals. However, if you take many random samples, a certain percentage of the resulting confidence intervals contain the unknown population parameter. The percentage of these confidence intervals that contain the parameter is the confidence level of the interval.

The confidence interval is composed of the following two parts:

Point estimate: This single value estimates a population parameter by using your sample data. The confidence interval is centered around the point estimate.
Margin of error: The margin of error defines the width of the confidence interval and is determined by the observed variability in the sample, the sample size, and the confidence level. To calculate the upper limit of the confidence interval, the margin of error is added to the point estimate. To calculate the lower limit of the confidence interval, the margin of error is subtracted from the point estimate.

Interpretation

Use the confidence interval to assess the estimate of the population coefficient for each term in the model.

For example, with a 95% confidence level, you can be 95% confident that the confidence interval contains the value of the coefficient for the population. The confidence interval helps you assess the practical significance of your results. Use your specialized knowledge to determine whether the confidence interval includes values that have practical significance for your situation. If the interval is too wide to be useful, consider increasing your sample size.

Z-value

The Z-value is a test statistic that measures the ratio between the coefficient and its standard error.

Interpretation

Minitab uses the Z-value to calculate the p-value, which you use to make a decision about the statistical significance of the terms and the model. The test is accurate when the sample size is large enough that the distribution of the sample coefficients follows a normal distribution.

A Z-value that is sufficiently far from 0 indicates that the coefficient estimate is both large and precise enough to be statistically different from 0. Conversely, a Z-value that is close to 0 indicates that the coefficient estimate is too small or too imprecise to be certain that the term has an effect on the risk score.

P-Value

The p-value is a probability that measures the evidence against the null hypothesis. Lower probabilities provide stronger evidence against the null hypothesis.

Interpretation

To determine whether the association between the risk score and each term in the model is statistically significant, compare the p-value for the term to your significance level to assess the null hypothesis. The null hypothesis is that the term's coefficient is equal to zero, which implies that there is no association between the term and the risk score. Usually, a significance level (denoted as α or alpha) of 0.05 works well. A significance level of 0.05 indicates a 5% risk of concluding that an association exists when there is no actual association.

P-value ≤ α: The association is statistically significant: If the p-value is less than or equal to the significance level, you can conclude that there is a statistically significant association between the risk score and the term.
P-value > α: The association is not statistically significant: If the p-value is greater than the significance level, you cannot conclude that there is a statistically significant association between the risk score and the term. You may want to refit the model without the term.; If there are multiple predictors without a statistically significant association with the risk score, you can reduce the model by removing terms one at a time. For more information on removing terms from the model, go to Model reduction.

If a model term is statistically significant, the interpretation depends on the type of term. The interpretations are as follows:

If a categorical factor is significant, you can conclude that the factor has an effect on the time to the event.
If a continuous predictor is significant, you can conclude that changes in the value of the predictor are associated with changes in the risk that the subject experiences the event.
If an interaction term is significant, the relationship between a factor and the response depends on the level of the other factors in the term. In this case, you should not interpret the main effects without considering the interaction effect.
If a coefficient for a polynomial term is significant, you can conclude that the data contain curvature.