Summary
Background: Many of an individual’s historically recorded personal measurements vary over time,
thereby forming a time series (e.g., wearable-device data, self-tracked fitness or
nutrition measurements, regularly monitored clinical events or chronic conditions).
Statistical analyses of such n-of-1 (i.e., single-subject) observational studies (N1OSs)
can be used to discover possible cause-effect relationships to then self-test in an
n-of-1 randomized trial (N1RT). However, a principled way of determining how and when
to interpret an N1OS association as a causal effect (e.g., as if randomization had
occurred) is needed.
Objectives: Our goal in this paper is to help bridge the methodological gap between risk-factor
discovery and N1RT testing by introducing a basic counterfactual framework for N1OS
design and personalized causal analysis.
Methods and Results: We introduce and characterize what we call the average period treatment effect (APTE),
i.e., the estimand of interest in an N1RT, and build an analytical framework around
it that can accommodate autocorrelation and time trends in the outcome, effect carryover
from previous treatment periods, and slow onset or decay of the effect. The APTE is
loosely defined as a contrast (e.g., difference, ratio) of averages of potential outcomes
the individual can theoretically experience under different treatment levels during
a given treatment period. To illustrate the utility of our framework for APTE discovery
and estimation, two common causal inference methods are specified within the N1OS
context. We then apply the framework and methods to search for estimable and interpretable
APTEs using six years of the author’s self-tracked weight and exercise data, and report
both the preliminary findings and the challenges we faced in conducting N1OS causal
discovery.
Conclusions: Causal analysis of an individual’s time series data can be facilitated by an N1RT
counterfactual framework. However, for inference to be valid, the veracity of certain
key assumptions must be assessed critically, and the hypothesized causal models must
be interpretable and meaningful.
Keywords
Causal inference - counterfactual - n-of-1 trial - single subject - time series
