# N=1 experiments and multilevel models

February 6, 2018
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(This article was originally published at Statistical Modeling, Causal Inference, and Social Science, and syndicated at StatsBlogs.)

N=1 experiments are the hot new thing. Here are some things to read:

Design and Implementation of N-of-1 Trials: A User’s Guide, edited by Richard Kravitz and Naihua Duan for the Agency for Healthcare Research and Quality, U.S. Department of Health and Human Services (2014).

Single-patient (n-of-1) trials: a pragmatic clinical decision methodology for patient-centered comparative effectiveness research, by Naihua Duan, Richard Kravitz, and Chris Schmid, for the Journal of Clinical Epidemiology (2013).

And a particular example:

The PREEMPT study – evaluating smartphone-assisted n-of-1 trials in patients with chronic pain: study protocol for a randomized controlled trial by Colin Barr et al., for Trials (2015), which begins:

Chronic pain is prevalent, costly, and clinically vexatious. Clinicians typically use a trial-and-error approach to treatment selection. Repeated crossover trials in a single patient (n-of-1 trials) may provide greater therapeutic precision. N-of-1 trials are the most direct way to estimate individual treatment effects and are useful in comparing the effectiveness and toxicity of different analgesic regimens.

This can also be framed as the problem of hierarchical modeling when the number of groups is 1 or 2, and this issue comes up, that once you go beyond N=1, you’re suddenly allowing more variation. One way to handle this is to include this between-person variance component even for an N=1 study. It’s just necessary to specify the between-person variance a priori—but that’s better than just setting it to 0. Similarly, once we have N=2 we can fit a hierarchical model but we’ll need strong prior info on the between-person variance parameter.

This relates to some recent work of ours in pharmacology—in this case, the problem is not N=1 patient, but N=1 study, and it also connects to a couple discussions we’ve had on this blog regarding the use of multilevel models to extrapolate to new scenarios; see here and here and here from 2012. We used to think of multilevel models as requiring 3 or more groups, but that’s not so at all; it’s just that when you have fewer groups, there’s more to be gained by including prior information on group-level variance parameters.

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