This lab will not be graded - there is nothing to turn in. 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. Write out two of the sub-models that the authors used, specifically in comparing class 2 trajectory vs. class 1, and again for class 5 trajectory vs. class 1 (use the estimated coefficients when writing out the models).
  4. Which variables are significant at the \(\alpha\) = 0.05 level, and for which comparisons vs. a class 1 trajectory?
  5. Interpret the odds ratio estimates corresponding to years of education and for presence of prior TBI.
  6. Which of the raw \(\beta\) estimates when comparing class 4 trajectories to class 2 trajectories would be negative?
  7. Suppose you had a Black female patient with 12 years of education, whose TBI was due to an accident, has a positive computed tomography finding, but has no prior history of TBI, alcohol use, or psychiatric history. Rank the insomnia symptom trajectory classes by least likely to most likely in terms of predicted probability.
  8. 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.