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 P values

Although not shown by default, Prism provides the option to calculate and report a P value for each parameter estimate (and hazard ratio) of a Cox proportional hazards regression model. These P values are generated by testing the null hypothesis that the true parameter estimate (beta) is equal to zero (this is tested individually for each parameter estimate). Note that if the true parameter estimate were actually zero, any increase or decrease in the associated predictor variable would have no effect on the hazard rate.

When thinking about hazard ratios instead of parameter estimates, the null hypothesis is that the true hazard ratio is equal to one. Because hazard ratios are multiplicative, a hazard ratio equal to 1.0 says that a change in the associated predictor variable would not affect the hazard rate.

Whether you prefer to think in terms of beta coefficients or hazard ratios, the same effective null hypothesis is used. This is due to the relationship of beta coefficients and hazard ratios. Recall that hazard ratios are calculated by taking the exponent of the corresponding beta coefficient (HRi = exp(βi)). Thus, testing if a beta coefficient is equal to zero is the same as testing if the hazard ratio is equal to exp(0) = 1. Either way, the null hypothesis asserts that the value of the associated predictor variable does not impact the hazard rate.

For each reported predictor value, the calculated P value answers the question: if the null hypothesis (above) were true and all of the analysis assumptions are reasonable, what is the probability of observing a parameter estimate of this magnitude or more extreme than this? If the P value is small enough (smaller than the specified alpha level, generally set to 0.05), then the null hypothesis (that the parameter estimate is zero) is rejected.

For these tests, we always generate two-sided (two-tailed) P values, since we’d be equally interested in parameter estimates that were greater or less than zero (or hazard ratios that are greater or less than one). If you wanted a one-sided P value:

you must have predicted the direction of the effect (Hazard ratio greater or less than one, or parameter estimate greater or less than zero) in your experimental design

If the actual direction matches the prediction, the one-tailed P value is equal to the two-tailed P value divided by two

If the actual direction is opposite of the prediction, the one-tailed P value is equal to 1-(two-tailed P value/2)

REMEMBER: failing to reject the null hypothesis that the parameter estimate is zero, does not confirm this hypothesis!! All that can be said is that the hypothesis cannot be rejected given the data.

When the P value option is selected in the analysis parameters dialog, Prism will report:

The absolute value of Z, calculated as the parameter estimate divided by its standard error

The P value which is determined from Z

A P value summary, reported as “ns” (for not significant) or as one or multiple asterisks