There is no repository for today’s lab; it will focus on statistical literacy and understanding published work.

Introduction

Wickwire et al. (2002) published an analysis that examined the trajectories of insomnia in adults after traumatic brain injury (TBI). In their article, the authors classified patients into one of five groups based on their trajectories of insomnia symptoms one year after TBI among approximately two thousand adults.

The authors’ full paper is available here. We won’t worry about how they created the trajectories or conducted variable selection - the important thing to note is that there were five patient trajectories identified, and the authors used a multinomial regression model to examine odds of patients belonging to certain trajectories based on their clinical and demographic characteristics.

Exercises

  1. Describe the outcome variable - how many categories were there? Describe each of the outcomes (specifically referencing Figure 2).
  2. Do you think the authors’ use of a multinomial model was appropriate? Compare this model to an ordinal regression model. Do you think that this outcome could have been an ordinal one instead? If so, what would the natural ordering be?
  3. Interpret the odds ratio estimates corresponding to years of education and for presence of prior TBI.
  4. Which of the raw \(\beta\) estimates when comparing class 4 trajectories to class 2 trajectories would be negative?
  5. Suppose a Black female patient with 12 years of education, whose TBI was due to an accident, has a positive computed tomography finding, but with no prior history of TBI, alcohol use, or psychiatric history presented to the clinic. Rank the insomnia symptom trajectory classes by least likely to most likely in terms of predicted probability using this model.
  6. The authors state the results of our multinomial regression model found that female sex, Black race, history of TBI, and psychiatric history were all associated with severe persistent insomnia. Do you agree with this statement given their analysis and results? Explain.