Using Bayes' rule to define the value of evidence from syndromic surveillance

In this work we propose the adoption of a statistical framework used in the evaluation of forensic evidence as a tool for evaluating and presenting circumstantial "evidence" of a disease outbreak from syndromic surveillance. The basic idea is to exploit the predicted distributions of reported cases to calculate the ratio of the likelihood of observing n cases given an ongoing outbreak over the likelihood of observing n cases given no outbreak. The likelihood ratio defines the Value of Evidence (V). Using Bayes' rule, the prior odds for an ongoing outbreak are multiplied by V to obtain the posterior odds. This approach was applied to time series on the number of horses showing clinical respiratory symptoms or neurological symptoms. The separation between prior beliefs about the probability of an outbreak and the strength of evidence from syndromic surveillance offers a transparent reasoning process suitable for supporting decision makers. The value of evidence can be translated into a verbal statement, as often done in forensics or used for the production of risk maps. Furthermore, a Bayesian approach offers seamless integration of data from syndromic surveillance with results from predictive modeling and with information from other sources such as disease introduction risk assessments.

Twenty questions with noise: Bayes optimal policies for entropy loss

We consider the problem of twenty questions with noisy answers, in which we seek to find a target by repeatedly choosing a set, asking an oracle whether the target lies in this set, and obtaining an answer corrupted by noise. Starting with a prior distribution on the target's location, we seek to minimize the expected entropy of the posterior distribution. We formulate this problem as a dynamic program and show that any policy optimizing the one-step expected reduction in entropy is also optimal over the full horizon. Two such Bayes optimal policies are presented: one generalizes the probabilistic bisection policy due to Horstein and the other asks a deterministic set of questions. We study the structural properties of the latter, and illustrate its use in a computer vision application.

Random Sampling with Interspike-Intervals of the Exponential Integrate and Fire Neuron: A Computational Interpretation of UP-States

Oscillations between high and low values of the membrane potential (UP and DOWN states respectively) are an ubiquitous feature of cortical neurons during slow wave sleep and anesthesia. Nevertheless, a surprisingly small number of quantitative studies have been conducted only that deal with this phenomenon’s implications for computation. Here we present a novel theory that explains on a detailed mathematical level the computational benefits of UP states. The theory is based on random sampling by means of interspike intervals (ISIs) of the exponential integrate and fire (EIF) model neuron, such that each spike is considered a sample, whose analog value corresponds to the spike’s preceding ISI. As we show, the EIF’s exponential sodium current, that kicks in when balancing a noisy membrane potential around values close to the firing threshold, leads to a particularly simple, approximative relationship between the neuron’s ISI distribution and input current. Approximation quality depends on the frequency spectrum of the current and is improved upon increasing the voltage baseline towards threshold. Thus, the conceptually simpler leaky integrate and fire neuron that is missing such an additional current boost performs consistently worse than the EIF and does not improve when voltage baseline is increased. For the EIF in contrast, the presented mechanism is particularly effective in the high-conductance regime, which is a hallmark feature of UP-states. Our theoretical results are confirmed by accompanying simulations, which were conducted for input currents of varying spectral composition. Moreover, we provide analytical estimations of the range of ISI distributions the EIF neuron can sample from at a given approximation level. Such samples may be considered by any algorithmic procedure that is based on random sampling, such as Markov Chain Monte Carlo or message-passing methods. Finally, we explain how spike-based random sampling relates to existing computational theories about UP states during slow wave sleep and present possible extensions of the model in the context of spike-frequency adaptation.

LC-MS/MS based assay and reference intervals in children and adolescents for oxysterols elevated in Niemann-Pick diseases

BACKGROUND Niemann-Pick type C (NP-C) is a rare progressive neurodegenerative lipid storage disorder with heterogeneous clinical presentation and challenging diagnostic procedures. Recently oxysterols have been reported to be specific biomarkers for NP-C but knowledge on the intra-individual variation and on reference intervals in children and adolescents are lacking. METHODS We established a LC-MS/MS assay to measure Cholestane-3β, 5α, 6β-triol (C-triol) and 7-Ketocholesterol (7-KC) following Steglich esterification. To assess reference intervals and intra-individual variation we determined oxysterols in 148 children and adolescents from 0 to 18 years and repeat measurements in 19 of them. RESULTS The reported method is linear (r>0.99), sensitive (detection limit of 0.03 ng/mL [0.07 nM] for C-triol, and 0.54 ng/mL [1.35 nM] for 7-KC) and precise, with an intra-day imprecision of 4.8% and 4.1%, and an inter-day imprecision of 7.0% and 11.0% for C-triol (28 ng/ml, 67 nM) and 7-KC (32 ng/ml, 80 nM), respectively. Recoveries for 7-KC and C-triol range between 93% and 107%. The upper reference limit obtained for C-triol is 40.4 ng/mL (95% CI: 26.4-61.7 ng/mL, 96.0 nM, 95% CI: 62.8-146.7 nM) and 75.0 ng/mL for 7-KC (95% CI: 55.5-102.5 ng/mL, 187.2 nM, 95% CI: 138.53-255.8 nM), with no age or gender dependency. Both oxysterols have a broad intra-individual variation of 46%±23% for C-triol and 52%±29% for 7-KC. Nevertheless, all Niemann-Pick patients showed increased C-triol levels including Niemann-Pick type A and B patients. CONCLUSIONS The LC-MS/MS assay is a robust assay to quantify C-triol and 7-KC in plasma with well documented reference intervals in children and adolescents to screen for NP-C in the pediatric population. In addition our results suggest that especially the C-triol is a biomarker for all three Niemann-Pick diseases.

The cystatin C/creatinine ratio, a marker of glomerular filtration quality: associated factors, reference intervals, and prediction of morbidity and mortality in healthy seniors.

The ratio of cystatin C (cysC) to creatinine (crea) is regarded as a marker of glomerular filtration quality associated with cardiovascular morbidities. We sought to determine reference intervals for serum cysC-crea ratio in seniors. Furthermore, we sought to determine whether other low-molecular weight molecules exhibit a similar behavior in individuals with altered glomerular filtration quality. Finally, we investigated associations with adverse outcomes. A total of 1382 subjectively healthy Swiss volunteers aged 60 years or older were enrolled in the study. Reference intervals were calculated according to Clinical & Laboratory Standards Institute (CLSI) guideline EP28-A3c. After a baseline exam, a 4-year follow-up survey recorded information about overall morbidity and mortality. The cysC-crea ratio (mean 0.0124 ± 0.0026 mg/μmol) was significantly higher in women and increased progressively with age. Other associated factors were hemoglobin A1c, mean arterial pressure, and C-reactive protein (P < 0.05 for all). Participants exhibiting shrunken pore syndrome had significantly higher ratios of 3.5-66.5 kDa molecules (brain natriuretic peptide, parathyroid hormone, β2-microglobulin, cystatin C, retinol-binding protein, thyroid-stimulating hormone, α1-acid glycoprotein, lipase, amylase, prealbumin, and albumin) and creatinine. There was no such difference in the ratios of very low-molecular weight molecules (urea, uric acid) to creatinine or in the ratios of molecules larger than 66.5 kDa (transferrin, haptoglobin) to creatinine. The cysC-crea ratio was significantly predictive of mortality and subjective overall morbidity at follow-up in logistic regression models adjusting for several factors. The cysC-crea ratio exhibits age- and sex-specific reference intervals in seniors. In conclusion, the cysC-crea ratio may indicate the relative retention of biologically active low-molecular weight compounds and can independently predict the risk for overall mortality and morbidity in the elderly.

Intervals for the assessment of measurement agreement: Similarities, differences, and consequences of incorrect interpretations

Several intervals have been proposed to quantify the agreement of two methods intended to measure the same quantity in the situation where only one measurement per method and subject is available. The limits of agreement are probably the most well-known among these intervals, which are all based on the differences between the two measurement methods. The different meanings of the intervals are not always properly recognized in applications. However, at least for small-to-moderate sample sizes, the differences will be substantial. This is illustrated both using the width of the intervals and on probabilistic scales related to the definitions of the intervals. In particular, for small-to-moderate sample sizes, it is shown that limits of agreement and prediction intervals should not be used to make statements about the distribution of the differences between the two measurement methods or about a plausible range for all future differences. Care should therefore be taken to ensure the correct choice of the interval for the intended interpretation.

Gestation-specific reference intervals for comprehensive spot urinary steroid hormone metabolite analysis in normal singleton pregnancy and 6 weeks postpartum

BACKGROUND: Normal pregnancy depends on pronounced adaptations in steroid hormone concentrations. Although in recent years, the understanding of these hormones in pregnancy has improved, the interpretation is hampered by insufficient reference values. Our aim was to establish gestation-specific reference intervals for spot urinary steroid hormone levels in normal singleton pregnancies and 6 weeks postpartum. METHODS: Cross-sectional multicentre observational study. Women recruited between 2008 and 2013 at 3 University Hospitals in Switzerland (Bern), Scotland (Glasgow) and Austria (Graz). Spot urine was collected from healthy women undergoing a normal pregnancy (age, 16-45 years; mean, 31 years) attending routine antenatal clinics at gestation weeks 11, 20, and 28 and approximately 6 weeks postpartum. Urine steroid hormone levels were analysed using gas-chromatography mass spectrometry. Creatinine was also measured by routine analysis and used for normalisation. RESULTS: From the results, a reference interval was calculated for each hormone metabolite at each trimester and 6 weeks postpartum. Changes in these concentrations between trimesters and postpartum were also observed for several steroid hormones and followed changes proposed for index steroid hormones. CONCLUSIONS: Normal gestation-specific reference values for spot urinary steroid hormones throughout pregnancy and early postpartum are now available to facilitate clinical management and research approaches to steroid hormone metabolism in pregnancy and the early postpartum period.

Visual-auditory differences in duration discrimination of intervals in the subsecond and second range

A common finding in time psychophysics is that temporal acuity is much better for auditory than for visual stimuli. The present study aimed to examine modality-specific differences in duration discrimination within the conceptual framework of the Distinct Timing Hypothesis. This theoretical account proposes that durations in the lower milliseconds range are processed automatically while longer durations are processed by a cognitive mechanism. A sample of 46 participants performed two auditory and visual duration discrimination tasks with extremely brief (50-ms standard duration) and longer (1000-ms standard duration) intervals. Better discrimination performance for auditory compared to visual intervals could be established for extremely brief and longer intervals. However, when performance on duration discrimination of longer intervals in the 1-s range was controlled for modality-specific input from the sensory-automatic timing mechanism, the visual-auditory difference disappeared completely as indicated by virtually identical Weber fractions for both sensory modalities. These findings support the idea of a sensory-automatic mechanism underlying the observed visual-auditory differences in duration discrimination of extremely brief intervals in the millisecond range and longer intervals in the 1-s range. Our data are consistent with the notion of a gradual transition from a purely modality-specific, sensory-automatic to a more cognitive, amodal timing mechanism. Within this transition zone, both mechanisms appear to operate simultaneously but the influence of the sensory-automatic timing mechanism is expected to continuously decrease with increasing interval duration.