Now Playing: Cox Regression (2:35)
Researchers would like to determine whether the level of a particular thyroid-controlled hormone is predictive of survival in patients following a surgical procedure. At the time of surgery, a variety of additional measurements are taken on each patient, including weight, blood pressure, and several blood count measurements.
The researchers wish to determine the sample sizes needed to obtain 90% power for detecting hazard ratios between 1.5 and 2. The log-hazard-ratios are entered into the procedure, rather than the hazard ratios themselves. The log-hazard-ratio is the regression coefficient in the Cox Model, and represents the predicted change in log (base e) hazards at one unit change in hormone level, when the other covariates are held constant.
The standard deviation of the hormone levels is expected to be in the range of 0.34 to 0.56.
Based on similar studies, the R-squared value, when regressing hormone level on the other covariates, is 0.072.
The overall event rate is assumed to be 0.43. The event rate is the proportion of subjects in which the event of interest occurs during the duration of the study.
The required sample size varies substantially across the different assumed standard deviations. It may prove useful to get a narrower estimate of the standard deviation of hormone levels.
One can also compare the sample sizes needed for the various presumed hazard ratios.