Testing unit root non-stationarity in the presence of missing data in univariate time series of mobile health studies.

The use of digital devices to collect data in mobile health studies introduces a novel application of time series methods, with the constraint of potential data missing at random or missing not at random (MNAR). In time-series analysis, testing for stationarity is an important preliminary step to inform appropriate subsequent analyses. The Dickey-Fuller test evaluates the null hypothesis of unit root non-stationarity, under no missing data. Beyond recommendations under data missing completely at random for complete case analysis or last observation carry forward imputation, researchers have not extended unit root non-stationarity testing to more complex missing data mechanisms. Multiple imputation with chained equations, Kalman smoothing imputation, and linear interpolation have also been used for time-series data, however such methods impose constraints on the autocorrelation structure and impact unit root testing. We propose maximum likelihood estimation and multiple imputation using state space model approaches to adapt the augmented Dickey-Fuller test to a context with missing data. We further develop sensitivity analyses to examine the impact of MNAR data. We evaluate the performance of existing and proposed methods across missing mechanisms in extensive simulations and in their application to a multi-year smartphone study of bipolar patients.

Assessing Mobility in Patients With Glioblastoma Using Digital Phenotyping-Piloting the Digital Assessment in Neuro-Oncology.

BACKGROUND AND OBJECTIVES: Digital phenotyping (DP) enables objective measurements of patient behavior and may be a useful tool in assessments of quality-of-life and functional status in neuro-oncology patients. We aimed to identify trends in mobility among patients with glioblastoma (GBM) using DP. METHODS: A total of 15 patients with GBM enrolled in a DP study were included. The Beiwe application was used to passively collect patient smartphone global positioning system data during the study period. We estimated step count, time spent at home, total distance traveled, and number of places visited in the preoperative, immediate postoperative, and late postoperative periods. Mobility trends for patients with GBM after surgery were calculated by using local regression and were compared with preoperative values and with values derived from a nonoperative spine disease group. RESULTS: One month postoperatively, median values for time spent at home and number of locations visited by patients with GBM decreased by 1.48 h and 2.79 locations, respectively. Two months postoperatively, these values further decreased by 0.38 h and 1.17 locations, respectively. Compared with the nonoperative spine group, values for time spent at home and the number of locations visited by patients with GBM 1 month postoperatively were less than control values by 0.71 h and 2.79 locations, respectively. Two months postoperatively, time spent at home for patients with GBM was higher by 1.21 h and locations visited were less than nonoperative spine group values by 1.17. Immediate postoperative values for distance traveled, maximum distance from home, and radius of gyration for patients with GBM increased by 0.346 km, 2.24 km, and 1.814 km, respectively, compared with preoperative values. CONCLUSIONS: :Trends in patients with GBM mobility throughout treatment were quantified through the use of DP in this study. DP has the potential to quantify patient behavior and recovery objectively and with minimal patient burden.

The relationship of rate and pause features to the communicative participation of people living with ALS.

INTRODUCTION/AIMS: Many people living with amyotrophic lateral sclerosis (PALS) report restrictions in their day-to-day communication (communicative participation). However, little is known about which speech features contribute to these restrictions. This study evaluated the effects of common speech symptoms in PALS (reduced overall speaking rate, slowed articulation rate, and increased pausing) on communicative participation restrictions. METHODS: Participants completed surveys (the Communicative Participation Item Bank-short form; the self-entry version of the ALS Functional Rating Scale-Revised) and recorded themselves reading the Bamboo Passage aloud using a smartphone app. Rate and pause measures were extracted from the recordings. The association of various demographic, clinical, self-reported, and acoustic speech features with communicative participation was evaluated with bivariate correlations. The contribution of salient rate and pause measures to communicative participation was assessed using multiple linear regression. RESULTS: Fifty seven people living with ALS participated in the study (mean age = 61.1 years). Acoustic and self-report measures of speech and bulbar function were moderately to highly associated with communicative participation (Spearman rho coefficients ranged from rs = 0.48 to rs = 0.77). A regression model including participant age, sex, articulation rate, and percent pause time accounted for 57% of the variance of communicative participation ratings. DISCUSSION: Even though PALS with slowed articulation rate and increased pausing may convey their message clearly, these speech features predict communicative participation restrictions. The identification of quantitative speech features, such as articulation rate and percent pause time, is critical to facilitating early and targeted intervention and for monitoring bulbar decline in ALS.

Heterogeneity in suicide risk: Evidence from personalized dynamic models.

Most theories of suicide propose within-person changes in psychological states cause suicidal thoughts/behaviors; however, most studies use between-person analyses. Thus, there are little empirical data exploring current theories in the way they are hypothesized to occur. We used a form of statistical modeling called group iterative multiple model estimation (GIMME) to explore one theory of suicide: The Interpersonal Theory of Suicide (IPTS). GIMME estimates personalized statistical models for each individual and associations shared across individuals. Data were from a real-time monitoring study of individuals with a history of suicidal thoughts/behavior (adult sample: participants = 111, observations = 25,242; adolescent sample: participants = 145, observations = 26,182). Across both samples, none of theorized IPTS effects (i.e., contemporaneous effect from hopeless to suicidal thinking) were shared at the group level. There was significant heterogeneity in the personalized models, suggesting there are different pathways through which different people come to experience suicidal thoughts/behaviors. These findings highlight the complexity of suicide risk and the need for more personalized approaches to assessment and prediction.

Tracking amyotrophic lateral sclerosis disease progression using passively collected smartphone sensor data.

BACKGROUND: Passively collected smartphone sensor data provide an opportunity to study physical activity and mobility unobtrusively over long periods of time and may enable disease monitoring in people with amyotrophic lateral sclerosis (PALS). METHODS: We enrolled 63 PALS who used Beiwe mobile application that collected their smartphone accelerometer and GPS data and administered the self-entry ALS Functional Rating Scale-Revised (ALSFRS-RSE) survey. We identified individual steps from accelerometer data and used the Activity Index to summarize activity at the minute level. Walking, Activity Index, and GPS outcomes were then aggregated into day-level measures. We used linear mixed effect models (LMMs) to estimate baseline and monthly change for ALSFRS-RSE scores (total score, subscores Q1-3, Q4-6, Q7-9, Q10-12) and smartphone sensor data measures, as well as the associations between them. FINDINGS: The analytic sample (N = 45) was 64.4% male with a mean age of 60.1 years. The mean observation period was 292.3 days. The ALSFRS-RSE total score baseline mean was 35.8 and had a monthly rate of decline of -0.48 (p-value <0.001). We observed statistically significant change over time and association with ALSFRS-RSE total score for four smartphone sensor data-derived measures: walking cadence from top 1 min and log-transformed step count, step count from top 1 min, and Activity Index from top 1 min. INTERPRETATION: Smartphone sensors can unobtrusively track physical changes in PALS, potentially aiding disease monitoring and future research.

Accounting for contact network uncertainty in epidemic inferences.

When modeling the dynamics of infectious disease, the incorporation of contact network information allows for the capture of the non-randomness and heterogeneity of realistic contact patterns. Oftentimes, it is assumed that the underlying contact pattern is known with perfect certainty. However, in realistic settings, the observed data often serves as an imperfect proxy of the actual contact patterns in the population. Furthermore, the epidemic in the real world are often not fully observed; event times such as infection and recovery times may be missing. In order to conduct accurate inferences on parameters of contagion spread, it is crucial to incorporate these sources of uncertainty. In this paper, we propose the use of Mixture Density Network compressed ABC (MDN-ABC) to learn informative summary statistics for the available data. This method will allow for Bayesian inference on the epidemic parameters of a contagious process, while accounting for imperfect observations on the epidemic and the contact network. We will demonstrate the use of this method on simulated epidemics and networks, and extend this framework to analyze the spread of Tattoo Skin Disease (TSD) among bottlenose dolphins in Shark Bay, Australia.

Menarche and Time to Cycle Regularity Among Individuals Born Between 1950 and 2005 in the US.

Importance: Early menarche is associated with adverse health outcomes. Trends toward earlier menarche have been observed in the US, but data remain limited on differences by sociodemographic factors and body mass index (BMI). Time from menarche to cycle regularity is another understudied early-life characteristic with health implications. Objectives: To evaluate the temporal trends and disparities in menarche and time to regularity and explore early-life BMI as a mediator. Design, Setting, and Participants: This ongoing cohort study enrolled participants from an ongoing mobile application-based US cohort from November 14, 2019, to March 20, 2023. Exposures: Birth year (categorized as 1950-1969, 1970-1979, 1980-1989, 1990-1999, and 2000-2005). Main Outcomes and Measures: Main outcomes were age at menarche and time to regularity, which were self-recalled at enrollment. In addition, early (aged <11 years), very early (aged <9 years), and late (aged ≥16 years) age at menarche was assessed. Results: Among the 71 341 female individuals who were analyzed (mean [SD] age at menarche, 12.2 [1.6] years; 2228 [3.1%] Asian, 3665 [5.1%] non-Hispanic Black, 4918 [6.9%] Hispanic, 49 518 [69.4%] non-Hispanic White, and 8461 [11.9%] other or multiple races or ethnicities), 5223 were born in 1950 to 1969, 12 226 in 1970 to 1979, 22 086 in 1980 to 1989, 23 894 in 1990 to 1999, and 7912 in 2000 to 2005. The mean (SD) age at menarche decreased from 12.5 (1.6) years in 1950 to 1969 to 11.9 (1.5) years in 2000 to 2005. The number of individuals experiencing early menarche increased from 449 (8.6%) to 1223 (15.5%), the number of individuals experiencing very early menarche increased from 31 (0.6%) to 110 (1.4%), and the number of individuals experiencing late menarche decreased from 286 (5.5%) to 137 (1.7%). For 61 932 participants with reported time to regularity, the number reaching regularity within 2 years decreased from 3463 (76.3%) to 4075 (56.0%), and the number not yet in regular cycles increased from 153 (3.4%) to 1375 (18.9%). The magnitude of the trend toward earlier menarche was greater among participants who self-identified as Asian, non-Hispanic Black, or other or multiple races (vs non-Hispanic White) (P = .003 for interaction) and among participants self-rated with low (vs high) socioeconomic status (P < .001 for interaction). Within a subset of 9865 participants with data on BMI at menarche, exploratory mediation analysis estimated that 46% (95% CI, 35%-61%) of the temporal trend in age at menarche was explained by BMI. Conclusions and Relevance: In this cohort study of 71 341 individuals in the US, as birth year increased, mean age at menarche decreased and time to regularity increased. The trends were stronger among racial and ethnic minority groups and individuals of low self-rated socioeconomic status. These trends may contribute to the increase in adverse health outcomes and disparities in the US.

Irregular Cycles, Ovulatory Disorders, and Cardiometabolic Conditions in a US-Based Digital Cohort.

Importance: Polycystic ovary syndrome (PCOS), characterized by irregular menstrual cycles and hyperandrogenism, is a common ovulatory disorder. Having an irregular cycle is a potential marker for cardiometabolic conditions, but data are limited on whether the associations differ by PCOS status or potential interventions. Objective: To evaluate the association of PCOS, time to regularity since menarche (adolescence), and irregular cycles (adulthood) with cardiometabolic conditions. Design, Setting, and Participants: This cross-sectional study used a large, US-based digital cohort of users of the Apple Research application on their iPhone. Eligibility criteria were having ever menstruated, living in the US, being at age of consent of at least 18 years (or 19 years in Alabama and Nebraska or 21 years in Puerto Rico), and being able to communicate in English. Participants were enrolled between November 14, 2019, and December 13, 2022, and completed relevant surveys. Exposures: Self-reported PCOS diagnosis, prolonged time to regularity (not spontaneously establishing regularity within 5 years of menarche), and irregular cycles. Main Outcomes and Measures: The primary outcome was self-reported cardiometabolic conditions, including obesity, prediabetes, type 1 and 2 diabetes, high cholesterol, hypertension, metabolic syndrome, arrhythmia, congestive heart failure, coronary artery disease, heart attack, heart valve disease, stroke, transient ischemic attack (TIA), deep vein thrombosis, and pulmonary embolism measured using descriptive statistics and logistic regression to estimate prevalence odds ratios (PORs) and 95% CIs. Effect modification by lifestyle factors was also estimated. Results: The study sample (N = 60 789) had a mean (SD) age of 34.5 (11.1) years, with 12.3% having PCOS and 26.3% having prolonged time to regularity. Among a subset of 25 399 participants who completed the hormonal symptoms survey, 25.6% reported irregular cycles. In covariate-adjusted logistic regression models, PCOS was associated with a higher prevalence of all metabolic and several cardiovascular conditions, eg, arrhythmia (POR, 1.37; 95% CI, 1.20-1.55), coronary artery disease (POR, 2.92; 95% CI, 1.95-4.29), heart attack (POR, 1.79; 95% CI, 1.23-2.54), and stroke (POR, 1.66; 95% CI, 1.21-2.24). Among participants without PCOS, prolonged time to regularity was associated with type 2 diabetes (POR, 1.24; 95% CI, 1.05-1.46), hypertension (POR, 1.09; 95% CI, 1.01-1.19), arrhythmia (POR, 1.20; 95% CI, 1.06-1.35), and TIA (POR, 1.33; 95% CI, 1.01-1.73), and having irregular cycles was associated with type 2 diabetes (POR, 1.36; 95% CI, 1.08-1.69), high cholesterol (POR, 1.17; 95% CI, 1.05-1.30), arrhythmia (POR, 1.21; 95% CI, 1.02-1.43), and TIA (POR, 1.56; 95% CI, 1.06-2.26). Some of these associations were modified by high vs low body mass index or low vs high physical activity. Conclusions and Relevance: These findings suggest that PCOS and irregular cycles may be independent markers for cardiometabolic conditions. Early screening and intervention among individuals with irregular menstrual cycles may be beneficial.

Approximate inference for longitudinal mechanistic HIV contact network.

Network models are increasingly used to study infectious disease spread. Exponential Random Graph models have a history in this area, with scalable inference methods now available. An alternative approach uses mechanistic network models. Mechanistic network models directly capture individual behaviors, making them suitable for studying sexually transmitted diseases. Combining mechanistic models with Approximate Bayesian Computation allows flexible modeling using domain-specific interaction rules among agents, avoiding network model oversimplifications. These models are ideal for longitudinal settings as they explicitly incorporate network evolution over time. We implemented a discrete-time version of a previously published continuous-time model of evolving contact networks for men who have sex with men and proposed an ABC-based approximate inference scheme for it. As expected, we found that a two-wave longitudinal study design improves the accuracy of inference compared to a cross-sectional design. However, the gains in precision in collecting data twice, up to 18%, depend on the spacing of the two waves and are sensitive to the choice of summary statistics. In addition to methodological developments, our results inform the design of future longitudinal network studies in sexually transmitted diseases, specifically in terms of what data to collect from participants and when to do so.

Precision Assessment of Real-World Associations Between Stress and Sleep Duration Using Actigraphy Data Collected Continuously for an Academic Year: Individual-Level Modeling Study.

BACKGROUND: Heightened stress and insufficient sleep are common in the transition to college, often co-occur, and have both been linked to negative health outcomes. A challenge concerns disentangling whether perceived stress precedes or succeeds changes in sleep. These day-to-day associations may vary across individuals, but short study periods and group-level analyses in prior research may have obscured person-specific phenotypes. OBJECTIVE: This study aims to obtain stable estimates of lead-lag associations between perceived stress and objective sleep duration in the individual, unbiased by the group, by developing an individual-level linear model that can leverage intensive longitudinal data while remaining parsimonious. METHODS: In total, 55 college students (n=6, 11% second-year students and n=49, 89% first-year students) volunteered to provide daily self-reports of perceived stress via a smartphone app and wore an actigraphy wristband for the estimation of daily sleep duration continuously throughout the academic year (median usable daily observations per participant: 178, IQR 65.5). The individual-level linear model, developed in a Bayesian framework, included the predictor and outcome of interest and a covariate for the day of the week to account for weekly patterns. We validated the model on the cohort of second-year students (n=6, used as a pilot sample) by applying it to variables expected to correlate positively within individuals: objective sleep duration and self-reported sleep quality. The model was then applied to the fully independent target sample of first-year students (n=49) for the examination of bidirectional associations between daily stress levels and sleep duration. RESULTS: Proof-of-concept analyses captured expected associations between objective sleep duration and subjective sleep quality in every pilot participant. Target analyses revealed negative associations between sleep duration and perceived stress in most of the participants (45/49, 92%), but their temporal association varied. Of the 49 participants, 19 (39%) showed a significant association (probability of direction>0.975): 8 (16%) showed elevated stress in the day associated with shorter sleep later that night, 5 (10%) showed shorter sleep associated with elevated stress the next day, and 6 (12%) showed both directions of association. Of note, when analyzed using a group-based multilevel model, individual estimates were systematically attenuated, and some even reversed sign. CONCLUSIONS: The dynamic interplay of stress and sleep in daily life is likely person specific. Paired with intensive longitudinal data, our individual-level linear model provides a precision framework for the estimation of stable real-world behavioral and psychological dynamics and may support the personalized prioritization of intervention targets for health and well-being.

Flexible Bayesian inference on partially observed epidemics.

Individual-based models of contagious processes are useful for predicting epidemic trajectories and informing intervention strategies. In such models, the incorporation of contact network information can capture the non-randomness and heterogeneity of realistic contact dynamics. In this article, we consider Bayesian inference on the spreading parameters of an SIR contagion on a known, static network, where information regarding individual disease status is known only from a series of tests (positive or negative disease status). When the contagion model is complex or information such as infection and removal times is missing, the posterior distribution can be difficult to sample from. Previous work has considered the use of Approximate Bayesian Computation (ABC), which allows for simulation-based Bayesian inference on complex models. However, ABC methods usually require the user to select reasonable summary statistics. Here, we consider an inference scheme based on the Mixture Density Network compressed ABC, which minimizes the expected posterior entropy in order to learn informative summary statistics. This allows us to conduct Bayesian inference on the parameters of a partially observed contagious process while also circumventing the need for manual summary statistic selection. This methodology can be extended to incorporate additional simulation complexities, including behavioural change after positive tests or false test results.

Upper limb movements as digital biomarkers in people with ALS.

BACKGROUND: Objective evaluation of people with amyotrophic lateral sclerosis (PALS) in free-living settings is challenging. The introduction of portable digital devices, such as wearables and smartphones, may improve quantifying disease progression and hasten therapeutic development. However, there is a need for tools to characterize upper limb movements in neurologic disease and disability. METHODS: Twenty PALS wore a wearable accelerometer, ActiGraph Insight Watch, on their wrist for six months. They also used Beiwe, a smartphone application that collected self-entry ALS Functional Rating Scale-Revised (ALSFRS-RSE) survey responses every 1-4 weeks. We developed several measures that quantify count and duration of upper limb movements: flexion, extension, supination, and pronation. New measures were compared against ALSFRS-RSE total score (Q1-12), and individual responses to specific questions related to handwriting (Q4), cutting food (Q5), dressing and performing hygiene (Q6), and turning in bed and adjusting bed clothes (Q7). Additional analysis considered adjusting for total activity counts (TAC). FINDINGS: At baseline, PALS with higher Q1-12 performed more upper limb movements, and these movements were faster compared to individuals with more advanced disease. Most upper limb movement metrics had statistically significant change over time, indicating declining function either by decreasing count metrics or by increasing duration metric. All count and duration metrics were significantly associated with Q1-12, flexion and extension counts were significantly associated with Q6 and Q7, supination and pronation counts were also associated with Q4. All duration metrics were associated with Q6 and Q7. All duration metrics retained their statistical significance after adjusting for TAC. INTERPRETATION: Wearable accelerometer data can be used to generate digital biomarkers on upper limb movements and facilitate patient monitoring in free-living environments. The presented method offers interpretable monitoring of patients' functioning and versatile tracking of disease progression in the limb of interest. FUNDING: Mitsubishi-Tanabe Pharma Holdings America, Inc.

The Pain Intervention & Digital Research Program: an operational report on combining digital research with outpatient chronic disease management.

Chronic pain affects up to 28% of U.S. adults, costing ∼$560 billion each year. Chronic pain is an instantiation of the perennial complexity of how to best assess and treat chronic diseases over time, especially in populations where age, medical comorbidities, and socioeconomic barriers may limit access to care. Chronic disease management poses a particular challenge for the healthcare system's transition from fee-for-service to value and risk-based reimbursement models. Remote, passive real-time data from smartphones could enable more timely interventions and simultaneously manage risk and promote better patient outcomes through predicting and preventing costly adverse outcomes; however, there is limited evidence whether remote monitoring is feasible, especially in the case of older patients with chronic pain. Here, we introduce the Pain Intervention and Digital Research (Pain-IDR) Program as a pilot initiative launched in 2022 that combines outpatient clinical care and digital health research. The Pain-IDR seeks to test whether functional status can be assessed passively, through a smartphone application, in older patients with chronic pain. We discuss two perspectives-a narrative approach that describes the clinical settings and rationale behind changes to the operational design, and a quantitative approach that measures patient recruitment, patient experience, and HERMES data characteristics. Since launch, we have had 77 participants with a mean age of 55.52, of which n = 38 have fully completed the 6 months of data collection necessitated to be considered in the study, with an active data collection rate of 51% and passive data rate of 78%. We further present preliminary operational strategies that we have adopted as we have learned to adapt the Pain-IDR to a productive clinical service. Overall, the Pain-IDR has successfully engaged older patients with chronic pain and presents useful insights for others seeking to implement digital phenotyping in other chronic disease settings.

Returning Individual Research Results from Digital Phenotyping in Psychiatry.

Psychiatry is rapidly adopting digital phenotyping and artificial intelligence/machine learning tools to study mental illness based on tracking participants' locations, online activity, phone and text message usage, heart rate, sleep, physical activity, and more. Existing ethical frameworks for return of individual research results (IRRs) are inadequate to guide researchers for when, if, and how to return this unprecedented number of potentially sensitive results about each participant's real-world behavior. To address this gap, we convened an interdisciplinary expert working group, supported by a National Institute of Mental Health grant. Building on established guidelines and the emerging norm of returning results in participant-centered research, we present a novel framework specific to the ethical, legal, and social implications of returning IRRs in digital phenotyping research. Our framework offers researchers, clinicians, and Institutional Review Boards (IRBs) urgently needed guidance, and the principles developed here in the context of psychiatry will be readily adaptable to other therapeutic areas.

Open-Source, Step-Counting Algorithm for Smartphone Data Collected in Clinical and Nonclinical Settings: Algorithm Development and Validation Study.

BACKGROUND: Step counts are increasingly used in public health and clinical research to assess well-being, lifestyle, and health status. However, estimating step counts using commercial activity trackers has several limitations, including a lack of reproducibility, generalizability, and scalability. Smartphones are a potentially promising alternative, but their step-counting algorithms require robust validation that accounts for temporal sensor body location, individual gait characteristics, and heterogeneous health states. OBJECTIVE: Our goal was to evaluate an open-source, step-counting method for smartphones under various measurement conditions against step counts estimated from data collected simultaneously from different body locations ("cross-body" validation), manually ascertained ground truth ("visually assessed" validation), and step counts from a commercial activity tracker (Fitbit Charge 2) in patients with advanced cancer ("commercial wearable" validation). METHODS: We used 8 independent data sets collected in controlled, semicontrolled, and free-living environments with different devices (primarily Android smartphones and wearable accelerometers) carried at typical body locations. A total of 5 data sets (n=103) were used for cross-body validation, 2 data sets (n=107) for visually assessed validation, and 1 data set (n=45) was used for commercial wearable validation. In each scenario, step counts were estimated using a previously published step-counting method for smartphones that uses raw subsecond-level accelerometer data. We calculated the mean bias and limits of agreement (LoA) between step count estimates and validation criteria using Bland-Altman analysis. RESULTS: In the cross-body validation data sets, participants performed 751.7 (SD 581.2) steps, and the mean bias was -7.2 (LoA -47.6, 33.3) steps, or -0.5%. In the visually assessed validation data sets, the ground truth step count was 367.4 (SD 359.4) steps, while the mean bias was -0.4 (LoA -75.2, 74.3) steps, or 0.1%. In the commercial wearable validation data set, Fitbit devices indicated mean step counts of 1931.2 (SD 2338.4), while the calculated bias was equal to -67.1 (LoA -603.8, 469.7) steps, or a difference of 3.4%. CONCLUSIONS: This study demonstrates that our open-source, step-counting method for smartphone data provides reliable step counts across sensor locations, measurement scenarios, and populations, including healthy adults and patients with cancer.

Flexible Bayesian Inference on Partially Observed Epidemics.

Individual-based models of contagious processes are useful for predicting epidemic trajectories and informing intervention strategies. In such models, the incorporation of contact network information can capture the non-randomness and heterogeneity of realistic contact dynamics. In this paper, we consider Bayesian inference on the spreading parameters of an SIR contagion on a known, static network, where information regarding individual disease status is known only from a series of tests (positive or negative disease status). When the contagion model is complex or information such as infection and removal times is missing, the posterior distribution can be difficult to sample from. Previous work has considered the use of Approximate Bayesian Computation (ABC), which allows for simulation-based Bayesian inference on complex models. However, ABC methods usually require the user to select reasonable summary statistics. Here, we consider an inference scheme based on the Mixture Density Network compressed ABC (MDN-ABC), which minimizes the expected posterior entropy in order to learn informative summary statistics. This allows us to conduct Bayesian inference on the parameters of a partially observed contagious process while also circumventing the need for manual summary statistic selection. This methodology can be extended to incorporate additional simulation complexities, including behavioral change after positive tests or false test results.

Cost-based feature selection for network model choice.

Selecting a small set of informative features from a large number of possibly noisy candidates is a challenging problem with many applications in machine learning and approximate Bayesian computation. In practice, the cost of computing informative features also needs to be considered. This is particularly important for networks because the computational costs of individual features can span several orders of magnitude. We addressed this issue for the network model selection problem using two approaches. First, we adapted nine feature selection methods to account for the cost of features. We show for two classes of network models that the cost can be reduced by two orders of magnitude without considerably affecting classification accuracy (proportion of correctly identified models). Second, we selected features using pilot simulations with smaller networks. This approach reduced the computational cost by a factor of 50 without affecting classification accuracy. To demonstrate the utility of our approach, we applied it to three different yeast protein interaction networks and identified the best-fitting duplication divergence model. Supplemental materials, including computer code to reproduce our results, are available online.

Framework for converting mechanistic network models to probabilistic models.

There are two prominent paradigms for the modelling of networks: in the first, referred to as the mechanistic approach, one specifies a set of domain-specific mechanistic rules that are used to grow or evolve the network over time; in the second, referred to as the probabilistic approach, one describes a model that specifies the likelihood of observing a given network. Mechanistic models (models developed based on the mechanistic approach) are appealing because they capture scientific processes that are believed to be responsible for network generation; however, they do not easily lend themselves to the use of inferential techniques when compared with probabilistic models. We introduce a general framework for converting a mechanistic network model (MNM) to a probabilistic network model (PNM). The proposed framework makes it possible to identify the essential network properties and their joint probability distribution for some MNMs; doing so makes it possible to address questions such as whether two different mechanistic models generate networks with identical distributions of properties, or whether a network property, such as clustering, is over- or under-represented in the networks generated by the model of interest compared with a reference model. The proposed framework is intended to bridge some of the gap that currently exists between the formulation and representation of mechanistic and PNMs. We also highlight limitations of PNMs that need to be addressed in order to close this gap.

Maximum likelihood estimation for reversible mechanistic network models.

Mechanistic network models specify the mechanisms by which networks grow and change, allowing researchers to investigate complex systems using both simulation and analytical techniques. Unfortunately, it is difficult to write likelihoods for instances of graphs generated with mechanistic models, and thus it is near impossible to estimate the parameters using maximum likelihood estimation. In this paper, we propose treating the node sequence in a growing network model as an additional parameter, or as a missing random variable, and maximizing over the resulting likelihood. We develop this framework in the context of a simple mechanistic network model, used to study gene duplication and divergence, and test a variety of algorithms for maximizing the likelihood in simulated graphs. We also run the best-performing algorithm on one human protein-protein interaction network and four nonhuman protein-protein interaction networks. Although we focus on a specific mechanistic network model, the proposed framework is more generally applicable to reversible models.