Inference of dynamic systems from noisy and sparse data via manifold-constrained Gaussian processes

Parameter estimation for nonlinear dynamic system models, represented by ordinary differential equations (ODEs), using noisy and sparse data, is a vital task in many fields. We propose a fast and accurate method, manifold-constrained Gaussian process inference (MAGI), for this task. MAGI uses a Gaussian process model over time series data, explicitly conditioned on the manifold constraint that derivatives of the Gaussian process must satisfy the ODE system. By doing so, we completely bypass the need for numerical integration and achieve substantial savings in computational time. MAGI is also suitable for inference with unobserved system components, which often occur in real experiments. MAGI is distinct from existing approaches as we provide a principled statistical construction under a Bayesian framework, which incorporates the ODE system through the manifold constraint. We demonstrate the accuracy and speed of MAGI using realistic examples based on physical experiments.

Dynamic systems, represented as a set of ordinary differential equations (ODEs), are commonly used to model behaviors in scientific domains, such as gene regulation (1), biological rhythms (2), spread of disease (3), ecology (4), etc. We focus on models specified by a set of ODEsx˙(t)=dx(t)dt=f(x(t),θ,t), t∈[0,T],[1]where the vector x(t) contains the system outputs that evolve over time t and θ is the vector of model parameters to be estimated from experimental/observational data. When f is nonlinear, solving x(t) given initial conditions x(0) and θ generally requires a numerical integration method, such as Runge–Kutta.Historically, ODEs have mainly been used for conceptual or theoretical understanding rather than data fitting as experimental data were limited. Advances in experimental and data collection techniques have increased the capacity to follow dynamic systems closer to real time. Such data will generally be recorded at discrete times and subject to measurement error. Thus, we assume that we observe y(τ)=x(τ)+ϵ(τ) at a set of observation time points τ with error ϵ governed by noise level σ. Our focus here is inference of θ given y(τ), with emphasis on nonlinear f where specialized methods that exploit a linear structure (e.g., refs. 5 and 6), are not generally applicable. We shall present a coherent, statistically principled framework for dynamic system inference with the help of Gaussian processes (GPs). The key to our method is to restrict the GPs on a manifold that satisfies the ODE system: Thus, we name our method MAGI (manifold-constrained Gaussian process inference). Placing a GP on x(t) facilitates inference of θ without numerical integration, and our explicit manifold constraint is the key idea that addresses the conceptual incompatibility between the GP and the specification of the ODE model, as we shall discuss shortly when overviewing our method. We show that the resulting parameter inference is computationally efficient, statistically principled, and effective in a variety of practical scenarios. MAGI particularly works in the cases when some system component(s) is/are unobserved. To the best of our knowledge, none of the current available software packages that do not use numerical integration can analyze systems with unobserved component(s).     

The development of theoretical sampling in practice

Problem

Theoretical sampling is a key research process within grounded theory. However, whilst methodological texts provide a definition, it is difficult to find examples of how theoretical sampling is undertaken as a study develops. The lack of clear exemplars has caused confusion amongst researchers, with many grounded theory studies providing no evidence of theoretical sampling.

Pain,Please: An Investigation of Sampling Bias in Pain Research

Experimental pain research frequently relies on the recruitment of volunteers. However, because experimental pain research often involves unpleasant and painful sensations, it may be especially susceptible to sampling bias. That is, volunteers in experimental pain research might differ from nonvolunteers on several relevant variables that could affect the generalizability and external validity of the research. We conducted 2 studies to investigate potential sampling bias in experimental pain research. In study 1 we assessed participants' (N?=?275; age = 17–30 years) perceived likelihood of participating in pain research. Pain catastrophizing, fear of pain, illness and injury sensitivity, depression, anxiety, sensation-seeking, gender identity, body appreciation, and social desirability were also assessed as potential predictors of the likelihood to participate. In study 2, participants (N?=?87; Age = 18–31 years) could sign up for 2 nearly identical studies, with only one involving painful sensations. Thirty-six participants signed up for the pain study and 51 participants signed up for the no-pain study. Study 1 showed that lower levels of fear of pain, higher levels of sensation-seeking, and older age predicted the perceived likelihood of participating in pain research. Study 2 showed significantly higher levels of sensation-seeking in participants who signed up for the pain study compared with those who signed up for the no-pain study. The implications of these findings for future research, as well as the clinical conclusions on the basis of experimental pain research, are discussed.

Arterial stimulation with simultaneous venous sampling for localizing insulinomas

Purpose: The present study aimed to assess the accuracies of arterial stimulation with simultaneous venous sampling (ASVS) in preoperative localization of insulinomas.Materials and Methods: A cohort consisting of 6 males and 14 females (median age, 48.5y; range, 28–62y) with pathologically proven insulinomas were included in this study. Selective angiographies were performed with the superior mesenteric artery (SMA), gastroduodenal artery (GDA), proximal splenic artery, and midsplenic artery in all individuals. Then ASVS procedures were followed after angiographies for these arteries. Clinical characteristics of the patient and the tumor number, location, and size were recorded. The accuracy of preoperative localization of insulinomas was tested.Results: A total of 22 tumors were identified by histopathological diagnosis. The mean size of the tumor was 1.40±0.60cm. Five tumors were in the head/neck region and 17 in the body/tail region. ASVS accurately localized 17/20 (85%) cases with only biochemical data and 19/20 (95%) cases with biochemical data and angiography images. Variant pancreatic arterial anatomy was revealed in 2 false cases with inferior pancreatic artery replaced by the superior mesenteric artery.Conclusion: ASVS was highly accurate in localizing insulinomas and should be performed in most of the patients with suspected insulinomas before the operation.     

Heat-assisted slurry sampling GFAAS method for determination of lead in food standard reference materials

A valid method based on heat-assisted slurry sampling graphic furnace atomic absorption spectrometry (HASS-GFAAS) was developed for the accurate determination of trace Pb in food standard reference materials (SRMs). The HASS technique significantly improved Pb recovery and precision compared to conventional slurry sampling techniques. The optimized HASS procedure was performed as follows: first, the sample (particle size ≤ 150 μm) was diluted with 0.05% (v/v) Triton X-100 containing 2% HNO₃ and 1% H₂O₂ followed by heating for 20 min at 120 °C on a heating block. Next, the obtained slurry was sonicated in an autosampler cup, and finally, the slurry was introduced into a graphite tube and analyzed by the GFAAS with a Pb electrodeless discharge lamp (EDL). Calibration with aqueous standard solutions was used for Pb determination in food samples. The characteristic mass and limit of detection for Pb based on the integrated absorbance for a 2% (m/v) sample were 12 ± 0.6 pg and 0.003 mg kg⁻¹, respectively. The accuracy (95.1–102% recovery) and good precision (0.1–3.6%) of this procedure are illustrated by the results obtained for the 12 food reference materials. The proposed method is suitable for determination of trace Pb in solid food samples.     

Impact of sampling time deviations on the prediction of the area under the curve using regression limited sampling strategies

The regression limited sampling strategy approach (R‐LSS), which is based on a small number of blood samples drawn at selected time points, has been used as an alternative method for the estimation of the area under the concentration–time curve (AUC). However, deviations from planned sampling times may affect the performance of R‐LSS, influencing related therapeutic decisions and outcomes. The aim of this study was to investigate the impact of different sampling time deviation (STD) scenarios on the estimation of AUC by the R‐LSS using a simulation approach. Three types of scenarios were considered going from the simplest case of fixed deviations, to random deviations and then to a more realistic case where deviations of mixed nature can occur. In addition, the sensitivity of the R‐LSS to STD in each involved sampling point was evaluated. A significant impact of STD on the performance of R‐LSS was demonstrated. The tolerance of R‐LSS to STD was found to depend not only on the number of sampling points but more importantly on the duration of the sampling process. Sensitivity analysis showed that sampling points at which rapid concentration changes occur were relatively more critical for AUC prediction by R‐LSS. As a practical approach, nomograms were proposed, where the expected predictive performance of R‐LSS was provided as a function of STD information. The investigation of STD impact on the predictive performance of R‐LSS is a critical element and should be routinely performed to guide R‐LSS selection and use. Copyright © 2015 John Wiley & Sons, Ltd.     

If You Are Not Counted,You Don’t Count: Estimating the Number of African-American Men Who Have Sex with Men in San Francisco Using a Novel Bayesian Approach

African-American men who have sex with men (AA MSM) have been disproportionately infected with and affected by HIV and other STIs in San Francisco and the USA. The true scope and scale of the HIV epidemic in this population has not been quantified, in part because the size of this population remains unknown. We used the successive sampling population size estimation (SS-PSE) method, a new Bayesian approach to population size estimation that incorporates network size data routinely collected in respondent-driven sampling (RDS) studies, to estimate the number of AA MSM in San Francisco. This method was applied to data from a 2009 RDS study of AA MSM. An estimate from a separate study of local AA MSM was used to model the prior distribution of the population size. Two-hundred and fifty-six AA MSM were included in the RDS survey. The estimated population size was 4917 (95 % CI 1267–28,771), using a flat prior estimated 1882 (95 % CI 919–2463) as a lower acceptable bound, and a large prior estimated 6762 (95 % CI 1994–13,863) as an acceptable upper bound. Point estimates from the SS-PSE were consistent with estimates from multiplier methods using external data. The SS-PSE method is easily integrated into RDS studies and therefore provides a simple and appealing tool to rapidly produce estimates of the size of key populations otherwise difficult to reach and enumerate.     

Sampling Males Who Inject Drugs in Haiphong,Vietnam: Comparison of Time-Location and Respondent-Driven Sampling Methods

Accurate measurements of HIV prevalence and associated risk factors among hidden and high-risk groups are vital for program planning and implementation. However, only two sampling methods are purported to provide representative estimates for populations without sampling frames: time-location sampling (TLS) and respondent-driven sampling (RDS). Each method is subject to potential biases and questionable reliability. In this paper, we evaluate surveys designed to estimate HIV prevalence and associated risk factors among people who inject drugs (PWID) sampled through TLS versus RDS. In 2012, males aged ≥16 years who reported injecting drugs in the previous month and living in Haiphong, Vietnam, were sampled using TLS or RDS. Data from each survey were analyzed to compare HIV prevalence, related risk factors, socio-demographic characteristics, refusal estimates, and time and expenditures for field implementation. TLS (n = 432) and RDS (n = 415) produced similarly high estimates for HIV prevalence. Significantly lower proportions of PWID sampled through RDS received methadone treatment or met an outreach worker. Refusal estimates were lower for TLS than for RDS. Total expenditures per sample collected and number of person-days of staff effort were higher for TLS than for RDS. Both survey methods were successful in recruiting a diverse sample of PWID in Haiphong. In Vietnam, surveys of PWID are conducted throughout the country; although the refusal estimate was calculated to be much higher for RDS than TLS, RDS in Haiphong appeared to sample PWID with less exposure to services and required fewer financial and staff resources compared with TLS.     

Evaluation of Respondent-Driven Sampling in a Study of Urban Young Men Who Have Sex with Men

Evidence suggests that respondent-driven sampling (RDS) is an efficient approach to sampling among varied populations of adult men who have sex with men (MSM) both in the USA and abroad, although no studies have yet evaluated its performance among younger MSM, a population with a steep rise in HIV infection in recent years. Young MSM (YMSM) may differ in terms of their connectedness to other YMSM (e.g., due to evolving sexual identity, internalization of sexual minority stigma, and lack of disclosure to others) and mobility (e.g., due to parental monitoring) which may inhibit the sampling process. The aims of this study were to evaluate the efficiency and effectiveness of RDS-based sampling among young urban MSM and to identify factors associated with recruitment success. We hypothesized that demographic, social, behavioral, and network factors, including racial/ethnic minority status, homelessness (i.e., as an indicator of socioeconomic marginalization), HIV-positive status, substance use problems, gay community connectedness, and network size would be positively related to recruitment productivity, while sexual minority stigmatization, environmental barriers (e.g., parental monitoring), and meeting sex partners on the internet (i.e., virtual venue) would be negatively related to recruitment productivity. Between December 2009 and February 2013, we used RDS to recruit a sample of 450 YMSM, ages 16–20. Findings suggest that the use of RDS for sampling among YMSM is challenging and may not be feasible based on the slow pace of recruitment and low recruitment productivity. A large number of seeds (38 % of the sample, n = 172) had to be added to the sample to maintain a reasonable pace of recruitment, which makes use of the sample for RDS-based population estimates questionable. In addition, the prevalence of short recruitment chains and segmentation in patterns of recruitment by race/ethnicity further hamper the network recruitment process. Thus, RDS was not particularly efficient in terms of the rate of recruitment or effective in generating a representative sample. Hypotheses regarding factors associated with recruitment success were supported for network size and internalized stigma (but not other factors), suggesting that participants with larger network sizes or high levels of internalized stigma may have more and less success recruiting others, respectively.