CHAPTER 18 A Yes-or-No Proposition: Logistic Regression 269

Assuming a one-predictor model, the required sample size for logistic regression

also depends on the relative frequency of yes and no outcomes, and how the pre-

dictor variable is distributed. And with multiple predictors in the model, deter-

mining sample size is even more complicated. So for a rigorous sample-size

calculation for a study that will use a logistic regression model with multiple pre-

dictors, you may have no choice but to seek the help of a professional

statistician.

Here are two simple approaches you can use if your logistic model has only one

predictor. In each case, you replace the logistic regression equation with another

equation that is somewhat equivalent, and then do a sample-size calculation

based on that. It’s not an ideal solution, but it can give you an answer that’s close

enough for planning purposes.»

» ^{If the predictor is a dichotomous category (a yes/no variable), logistic}

regression gives the same p value you get from analyzing a fourfold table.

Therefore, you can use the sample-size calculations we describe in

Chapter 12.»

» ^{If the predictor is a continuous numerical quantity (like age), you can}

pretend that the outcome variable is the predictor, and age is the outcome.

We realize this flips the cause-and-effect relationship backwards, but if you

allow that conceptual flip, then you can ask whether the two different

outcome groups have different mean values for the predictor. You can test

that question with an unpaired Student t test, so you can use the sample-size

calculations we describe in Chapter 11.