### Department of Biostatistics Seminar/Workshop Series

# **Probability-scale Residuals**

## Bryan Shepherd, PhD

##### Associate Professor, Department of Biostatistics, Vanderbilt School of Medicine

In prior work, Chun Li and I developed a new residual for ordered categorical outcomes. The residual is P(Y<y) - P(Y>y), where y is an observed outcome, Y is a random variable from the fitted distribution, and P(.) designates a probability function. I will spend some time describing this probability-scale residual, why we developed it, its implementation in medical studies, why you should be using it in your applied work, and software that will help you use it. The residual also has several nice properties when the outcome is continuous, ordered discrete (e.g., binary or count data), or censored (e.g., time-to-event outcomes). These properties make it useful for model diagnostics and tests of conditional independence across a wide variety of settings. I will describe these properties and demonstrate the probability-scale residual's use with both simulated and real data.