Maintained Individual Data Distributed Likelihood Estimation (MIDDLE)

Abstract

Maintained Individual Data Distributed Likelihood Estimation (MIDDLE) is a novel paradigm for research in the behavioral, social, and health sciences. The MIDDLE approach is based on the seemingly impossible idea that data can be privately maintained by participants and never revealed to researchers, while still enabling statistical models to be fit and scientific hypotheses tested. MIDDLE rests on the assumption that participant data should belong to, be controlled by, and remain in the possession of the participants themselves. Distributed likelihood estimation refers to fitting statistical models by sending an objective function and vector of parameters to each participant's personal device (e.g., smartphone, tablet, computer), where the likelihood of that individual's data is calculated locally. Only the likelihood value is returned to the central optimizer. The optimizer aggregates likelihood values from responding participants and chooses new vectors of parameters until the model converges. A MIDDLE study provides significantly greater privacy for participants, automatic management of opt-in and opt-out consent, lower cost for the researcher and funding institute, and faster determination of results. Furthermore, if a participant opts into several studies simultaneously and opts into data sharing, these studies automatically have access to individual-level longitudinal data linked across all studies.

Keywords: data sharing, distributed computation, ecological momentary assessment, privacy, smart phones.

Figure 1

Traditional experimental design. In traditional designs for human subjects research, steps are performed sequentially, data are stored centrally, and statistical analysis is conducted only after the data collection portion of the experiment is concluded. This leads to long intervals between experiment replication and/or hypothesis revision as well as barriers to data sharing.

Figure 2

Simplified flowcharts for traditional full information maximum likelihood (FIML) estimation and distributed likelihood estimation (DLE). (a) In FIML, the data are centralized into a data matrix and the likelihood of each row of the data matrix contributes to the summed log likelihood. Parameters are adjusted until the summed likelihood is at a maximum. (b) In DLE, the data resides on participants’ personal devices. The personal device receives model parameters from the central optimizer, calculates the likelihood of a participant’s data, and passes only the likelihood back to the central optimizer. The central optimizer calculates the summed log likelihood, and if necessary, chooses new parameters to redistribute to the personal devices. We use FIML as an example although Bayesian or other optimization methods for parameter estimation can be used in DLE.

Figure 3

Flowchart of a MIDDLE experiment including a MIDDLE Host for disseminating Maintained Individual Data (MID) experiments and managing requests for Distributed Likelihood Evaluation (DLE). Participants and research labs communicate through the MIDDLE Host, which acts as something of an App Store for Science.

Figure 4

Results of one simulated MIDDLE experiment estimated using two different optimization criteria. For panels (a), (b), and (c), each query of the distributed devices was paired with one major iteration of the optimizer occurred. For panels (d), (e), and (f), each time the distributed devices were queried, the optimizer was allowed to come to complete maximum likelihood convergence. Note: mean(I), mean(S), var(I), var(S), and cov(I,S) refer to the simulated Latent Growth Curve mean, variance, and covariance of the latent intercept and slope.

Figure 5

Means and standard deviations of 100 simulated MIDDLE experiments. Each query of the distributed devices was accompanied by (a) one major iteration of the optimizer or (b) the optimizer was allowed to reach maximum likelihood convergence. Note: mean(I), mean(S), var(I), var(S), and cov(I,S) refer to the simulated Latent Growth Curve mean, variance, and covariance of the latent intercept and slope.

Figure 6

Clinicians and hospitals could use the MIDDLE approach to calculate likelihood of patient health problems from daily observations recorded by home health monitors. These predictive models could be directly accessed from a MIDDLE Host accelerating the translation of research into clinical practice.