the siren song of the linear model

Prepare for a really dorky blog entry.

I was very struck by Kendler, Kuhn, & Prescott's 2004 article--not necessarily because of their conclusions about risk factors for depressive episodes but because of how they got there. In other words, I appreciated their approach to various statistical issues, especially model building and the use of raw probabilities. Admittedly, I am still a quantitative infant, but I particularly appreciated their deliberate decision to compare additive versus multiplicative models of risk. It is often tempting to try to fit any dataset to a linear model, not for any theoretical reason, but simply for reasons of convenience. Much can be gained, however, from considering the implications of fitting data to different mathematical functions; in this case, for instance, fitting a multiplicative model of risk suggests processes that differ in important ways from the ones that would operate in an additive model of risk. Just because linear models are easy to construct and analyze does not mean that they are the best way to understand our data!

I also appreciated Kendler et al.'s discussion of their decision to use raw probabilities as opposed to transforming them, perhaps to log(raw probability). Using a logarithmic transformation may indeed have made the process of statistical analysis easier but it also would have disguised one of the most interesting features of these data, which is the nonlinear relationship between risk of a depressive episode and contextual threat X neuroticism. I agree with the "public health argument" and I also think that it would have been much more difficult to interpret log(hazard ratio) than it is to interpret the raw probabilities. Despite the statistical convenience that transformation to a log scale can provide, it can lead to results that are difficult to interpret. Here, sticking with the raw probabilities makes the patterns Kendler et al. wish to highlight much more clear.


P.S. Jim--you wanted me to remind you to get me the reference(s) on doing meta-analyses of single-case studies.

me and my incoherent brain

While reading Voelker's brief article on proposed links between sleep disruptions and depression in college students, I flashed back to vivid memories of college friends dealing with depression who felt unable to get up in the morning despite multiple alarm clocks--who stayed asleep in bed until 4 or 5 pm, missing all their classes. Their problems with depression seemed intimately tied to abnormal sleep patterns and an inability to establish a healthy sleep-wake rhythm. Sleep problems can be devastating to individuals' daily functioning (lost jobs, failed classes...), so I'd be interested to know the statistics on abnormal sleep patterns in persons with depression. [Armitage's observation of poor coherence during the sleep of some individuals with depression was certainly provocative, but I'd be interested to see the findings replicated.]

Thinking along these lines, it seems to me that incorporating sleep hygiene goals in a behavioral activation therapy program for depression could be highly useful. Bootzin & Epstein discuss establishing appropriate discriminative stimuli for falling asleep by reserving the bed and bedroom for sleep only; along with establishing appropriate cues for sleep, they recommend certain daytime activities as well: avoiding naps, engaging in light, regular exercise, and exposing oneself to bright light. It seems to me that the stimulus control instructions would mesh well with goals for behavioral activation; developing simple goals early in therapy such as "I will not stay in bed for more than 15 minutes after waking in the morning" and "I will not use my bed for purposes other than sleeping (or sexual activity)" and moving on to more challenging goals such as "I will avoid naps" and "I will spend 15 minutes a day doing [fill in form of light exercise here]" as therapy progresses could help the client both to "activate" and to resolve sleep disturbances--which, in turn, would likely assist the client in activating yet further.

Certainly, resolving sleep problems will not automatically resolve depression, but it seems to me that these issues may, for many individuals, have a reciprocal relationship; anxiety or catastrophizing may feed insomnia, but then insomnia may further feed anxiety. Certain depressed persons might be predisposed to certain kinds of sleep disturbances, and these sleep disturbances may lead to impaired performance at school or at work--which may worsen a depressed individual's perception of their own efficacy. It seems to me that it would only make sense to tackle these problems together. I'd be interested to see any research that tackled this question empirically.