Causal Analysis of Self-tracked Time Series Data Using a Counterfactual Framework for N-of-1 Trials*

Abstract

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.