Shrinkage estimators of the spatial relative risk function.

The spatial relative risk function describes differences in the geographical distribution of two types of points, such as locations of cases and controls in an epidemiological study. It is defined as the ratio of the two underlying densities. Estimation of spatial relative risk is typically done using kernel estimates of these densities, but this procedure is often challenging in practice because of the high degree of spatial inhomogeneity in the distributions. This makes it difficult to obtain estimates of the relative risk that are stable in areas of sparse data while retaining necessary detail elsewhere, and consequently difficult to distinguish true risk hotspots from stochastic bumps in the risk function. We study shrinkage estimators of the spatial relative risk function to address these problems. In particular, we propose a new lasso-type estimator that shrinks a standard kernel estimator of the log-relative risk function towards zero. The shrinkage tuning parameter can be adjusted to help quantify the degree of evidence for the existence of risk hotspots, or selected to optimize a cross-validation criterion. The performance of the lasso estimator is encouraging both on a simulation study and on real-world examples.

Extending statistical models for source attribution of zoonotic diseases: a study of campylobacteriosis.

Preventing and controlling zoonoses through the design and implementation of public health policies requires a thorough understanding of transmission pathways. Modelling jointly the epidemiological data and genetic information of microbial isolates derived from cases provides a methodology for tracing back the source of infection. In this paper, the attribution probability for human cases of campylobacteriosis for each source, conditional on the extent to which each case resides in a rural compared to urban environment, is estimated. A model that incorporates genetic data and evolutionary processes is applied alongside a newly developed genetic-free model. We show that inference from each model is comparable except for rare microbial genotypes. Further, the effect of 'rurality' may be modelled linearly on the logit scale, with increasing rurality leading to the increasing likelihood of ruminant-sourced campylobacteriosis.

Tutorial on kernel estimation of continuous spatial and spatiotemporal relative risk.

Kernel smoothing is a highly flexible and popular approach for estimation of probability density and intensity functions of continuous spatial data. In this role, it also forms an integral part of estimation of functionals such as the density-ratio or "relative risk" surface. Originally developed with the epidemiological motivation of examining fluctuations in disease risk based on samples of cases and controls collected over a given geographical region, such functions have also been successfully used across a diverse range of disciplines where a relative comparison of spatial density functions has been of interest. This versatility has demanded ongoing developments and improvements to the relevant methodology, including use spatially adaptive smoothers; tests of significantly elevated risk based on asymptotic theory; extension to the spatiotemporal domain; and novel computational methods for their evaluation. In this tutorial paper, we review the current methodology, including the most recent developments in estimation, computation, and inference. All techniques are implemented in the new software package sparr, publicly available for the R language, and we illustrate its use with a pair of epidemiological examples.

Modelling retinal pulsatile blood flow from video data.

Modern day datasets continue to increase in both size and diversity. One example of such 'big data' is video data. Within the medical arena, more disciplines are using video as a diagnostic tool. Given the large amount of data stored within a video image, it is one of most time consuming types of data to process and analyse. Therefore, it is desirable to have automated techniques to extract, process and analyse data from video images. While many methods have been developed for extracting and processing video data, statistical modelling to analyse the outputted data has rarely been employed. We develop a method to take a video sequence of periodic nature, extract the RGB data and model the changes occurring across the contiguous images. We employ harmonic regression to model periodicity with autoregressive terms accounting for the error process associated with the time series nature of the data. A linear spline is included to account for movement between frames. We apply this model to video sequences of retinal vessel pulsation, which is the pulsatile component of blood flow. Slope and amplitude are calculated for the curves generated from the application of the harmonic model, providing clinical insight into the location of obstruction within the retinal vessels. The method can be applied to individual vessels, or to smaller segments such as 2 × 2 pixels which can then be interpreted easily as a heat map.

Testing for changes in spatial relative risk.

The spatial relative risk function is a useful tool for describing geographical variation in disease incidence. We consider the problem of comparing relative risk functions between two time periods, with the idea of detecting alterations in the spatial pattern of disease risk irrespective of whether there has been a change in the overall incidence rate. Using case-control datasets for each period, we use kernel smoothing methods to derive a test statistic based on the difference between the log-relative risk functions, which we term the log-relative risk ratio. For testing a null hypothesis of an unchanging spatial pattern of risk, we show how p-values can be computed using both randomization methods and an asymptotic normal approximation. The methodology is applied to data on campylobacteriosis from 2006 to 2013 in a region of New Zealand. We find clear evidence of a change in the spatial pattern of risk between those years, which can be explained in differences by response to a public health initiative between urban and rural communities. Copyright © 2017 John Wiley & Sons, Ltd.

Retinal venous pulsation: Expanding our understanding and use of this enigmatic phenomenon.

Retinal vein pulsation was first noted soon after the invention of the ophthalmoscope 170 years ago and was seen to change with cerebrospinal fluid pressure (CSFP) variation in the 1920s. The classical explanation for vein pulsation was that the cardiac cycle induced systolic peak in intraocular pressure (IOP) tended to intermittently collapse the retinal vein close to its exit in the central optic disk, causing pulsation to be counter-phase to IOP. Recently, improved ophthalmodynamometry and video recording techniques have allowed us to explore the fundamentals of retinal vein pulsation. This demonstrates that retinal venous collapse is in phase with both IOP and CSFP diastole, indicating the dependence upon CSFP pulse. We describe in some detail the mathematical and physical models of Starling resistors and how their results can be applied to understand the physiology of retinal vein pulsation. We discuss various techniques for measuring retinal venous pulsation, including a novel modified photo-plethysmographic technique developed in our laboratory. With these techniques, non-invasive measurement of CSFP is beginning to look feasible. Venous pulsation properties also have significant prognostic value in predicting long-term outcomes for both glaucoma and central retinal vein occlusion, as well as utility in other retinal vasculopathies and orbital disease. We demonstrate the potential use of modified photo-plethysmographic images in assessing these various disorders. A revised understanding of retinal vein pulse wave transmission along with improved measurement techniques may generate useful clinical tools for assessing these disorders.

Intraocular Pressure Reduction Is Associated with Reduced Venous Pulsation Pressure.

PURPOSE: To explore whether alterations in intraocular pressure (IOP) affect vein pulsation properties using ophthalmodynamometric measures of vein pulsation pressure. PATIENTS AND METHODS: Glaucoma patients had two retinal vein pulsation pressure (VPP) measurements from upper and lower hemiveins performed by ophthalmodynamometry at least 3 months apart. All subjects had VPP and IOP recorded at two visits, with standard automated perimetry, central corneal thickness (CCT) recorded at the initial visit. Where venous pulsation was spontaneous ophthalmodynamometry could not be performed and VPP was considered equal to IOP. Change in VPP was calculated and binarized with reduction in pressure scored 1 and no change or increase scored as 0. Data analysis used a mixed logistic regression model with change in VPP as response variable and change in IOP, visual field loss (mean deviation), CCT and time interval as explanatory variables. RESULTS: 31 subjects (20 females) with mean age 60 years (sd 11) were examined with change in VPP being significantly associated with change in IOP (odds ratio 1.6/mmHg, 95% CI 1.2 to 2.1 in the glaucoma patients but not suspect patients (p = 0.0005). CONCLUSION: Change in VPP is strongly associated with change in IOP such that a reduced intraocular pressure is associated with a subsequent reduction in VPP. This indicates that reduced IOP alters some retinal vein properties however the nature and time course of these changes is not known.

Bayesian methods of confidence interval construction for the population attributable risk from cross-sectional studies.

Population attributable risk measures the public health impact of the removal of a risk factor. To apply this concept to epidemiological data, the calculation of a confidence interval to quantify the uncertainty in the estimate is desirable. However, because perhaps of the confusion surrounding the attributable risk measures, there is no standard confidence interval or variance formula given in the literature. In this paper, we implement a fully Bayesian approach to confidence interval construction of the population attributable risk for cross-sectional studies. We show that, in comparison with a number of standard Frequentist methods for constructing confidence intervals (i.e. delta, jackknife and bootstrap methods), the Bayesian approach is superior in terms of percent coverage in all except a few cases. This paper also explores the effect of the chosen prior on the coverage and provides alternatives for particular situations. Copyright © 2016 John Wiley & Sons, Ltd.

Relaxed Observance of Traditional Marriage Rules Allows Social Connectivity without Loss of Genetic Diversity.

Marriage rules, the community prescriptions that dictate who an individual can or cannot marry, are extremely diverse and universally present in traditional societies. A major focus of research in the early decades of modern anthropology, marriage rules impose social and economic forces that help structure societies and forge connections between them. However, in those early anthropological studies, the biological benefits or disadvantages of marriage rules could not be determined. We revisit this question by applying a novel simulation framework and genome-wide data to explore the effects of Asymmetric Prescriptive Alliance, an elaborate set of marriage rules that has been a focus of research for many anthropologists. Simulations show that strict adherence to these marriage rules reduces genetic diversity on the autosomes, X chromosome and mitochondrial DNA, but relaxed compliance produces genetic diversity similar to random mating. Genome-wide data from the Indonesian community of Rindi, one of the early study populations for Asymmetric Prescriptive Alliance, are more consistent with relaxed compliance than strict adherence. We therefore suggest that, in practice, marriage rules are treated with sufficient flexibility to allow social connectivity without significant degradation of biological diversity.

Objective detection of retinal vessel pulsation.

PURPOSE: Retinal venous pulsation detection is a subjective sign, which varies in elevated intracranial pressure, venous obstruction and glaucoma. To date no method can objectively measure and identify pulsating regions. METHOD: Using high resolution video-recordings of the optic disk and retina we measured fluctuating light absorption by haemoglobin during pulsation. Pulsation amplitude was calculated from all regions of the retinal image video-frames in a raster pattern. Segmented retinal images were formed by objectively selecting regions with amplitudes above a range of threshold values. These were compared to two observers manually drawing an outline of the pulsating areas while viewing video-clips in order to generate receiver operator characteristics. RESULTS: 216,515 image segments were analysed from 26 eyes in 18 research participants. Using data from each eye, the median area under the receiver operator curve (AU-ROC) was 0.95. With all data analysed together the AU-ROC was 0.89. We defined the ideal threshold amplitude for detection of any pulsating segment being that with maximal sensitivity and specificity. This was 5 units (95% confidence interval 4.3 to 6.0) compared to 12 units before any regions were missed. A multivariate model demonstrated that ideal threshold amplitude increased with increased variation in video-sequence illumination (p = 0.0119), but between the two observers (p = 0.0919) or other variables. CONCLUSION: This technique demonstrates accurate identification of retinal vessel pulsating regions with no areas identified manually being missed with the objective technique. The amplitude values are derived objectively and may be a significant advance upon subjective ophthalmodynamometric threshold techniques.

Photoplethysmographic measurement of various retinal vascular pulsation parameters and measurement of the venous phase delay.

PURPOSE: Retinal vein pulsation properties are altered by glaucoma, intracranial pressure (ICP) changes, and retinal venous occlusion, but measurements are limited to threshold measures or manual observation from video frames. We developed an objective retinal vessel pulsation measurement technique, assessed its repeatability, and used it to determine the phase relations between retinal arteries and veins. METHODS: Twenty-three eyes of 20 glaucoma patients had video photograph recordings from their optic nerve and peripapillary retina. A modified photoplethysmographic system using video recordings taken through an ophthalmodynamometer and timed to the cardiac cycle was used. Aligned video frames of vessel segments were analyzed for blood column light absorbance, and waveform analysis was applied. Coefficient of variation (COV) was calculated from data series using recordings taken within ±1 unit ophthalmodynamometric force of each other. The time in cardiac cycles and seconds of the peak (dilation) and trough (constriction) points of the retinal arterial and vein pulse waveforms were measured. RESULTS: Mean vein peak time COV was 3.4%, and arterial peak time COV was 4.4%. Lower vein peak occurred at 0.044 cardiac cycles (0.040 seconds) after the arterial peak (P = 0.0001), with upper vein peak an insignificant 0.019 cardiac cycles later. No difference in COV for any parameter was found between upper or lower hemiveins. Mean vein amplitude COV was 12.6%, and mean downslope COV was 17.7%. CONCLUSIONS: This technique demonstrates a small retinal venous phase lag behind arterial pulse. It is objective and applicable to any eye with clear ocular media and has moderate to high reproducibility. ( http://www.anzctr.org.au number, ACTRN12608000274370.).

Generalizing the spatial relative risk function.

The spatial relative risk function is defined as the ratio of densities describing respectively the spatial distribution of cases and controls. It has proven to be an effective tool for visualizing spatial variation in risk in many epidemiological applications over the past 20 years. We discuss the generalization of this function to spatio-temporal case-control data, and also to situations where there are covariates available that may affect the spatial patterns of disease. We examine estimation of the generalized relative risk functions using kernel smoothing, including asymptotic theory and data-driven bandwidth selection. We also consider construction of tolerance contours. Our methods are illustrated on spatio-temporal data describing the 2001 outbreak of foot-and-mouth disease in the United Kingdom, with farm size as a covariate.

Spatial modeling of visual field data for assessing glaucoma progression.

PURPOSE: In order to reduce noise and account for spatial correlation, we applied disease mapping techniques to visual field (VF) data. We compared our calculated rates of progression to other established techniques. METHODS: Conditional autoregressive (CAR) priors, weighted to account for physiologic correlations, were employed to describe spatial and spatiotemporal correlation over the VF. Our model is extended to account for several physiologic features, such as the nerve fibers serving adjacent loci on the VF not mapping to the adjacent optic disc regions, the presence of the blind spot, and large measurement fluctuation. The models were applied to VFs from 194 eyes and fitted within a Bayesian framework using Metropolis-Hastings algorithms. RESULTS: Our method (SPROG for Spatial PROGgression) showed progression in 42% of eyes. Using a clinical reference, our method had the best receiver operating characteristics compared with the point-wise linear regression methods. Because our model intrinsically accounts for the large variation of VF data, by adjusting for spatial correlation, the effects of outliers are minimized, and spurious trends are avoided. CONCLUSIONS: by using CAR priors, we have modeled the spatial correlation in the eye. combining this with physiologic information, we are able to provide a novel method for VF analysis. model diagnostics, sensitivity, and specificity show our model to be apparently superior to CURRENT POINT-wise linear regression methods. (http://www.anzctr.org.au number, ACTRN12608000274370.).

Adaptive kernel estimation of spatial relative risk.

Kernel smoothing is routinely used for the estimation of relative risk based on point locations of disease cases and sampled controls over a geographical region. Typically, fixed-bandwidth kernel estimation has been employed, despite the widely recognized problems experienced with this methodology when the underlying densities exhibit the type of spatial inhomogeneity frequently seen in geographical epidemiology. A more intuitive approach is to utilize a spatially adaptive, variable smoothing parameter. In this paper, we examine the properties of the adaptive kernel estimator by both asymptotic analysis and a simulation study, finding advantages over the fixed kernel approach in both the cases. We also look at practical issues with implementation of the adaptive relative risk estimator (including bandwidth choice and boundary correction), and develop a computationally inexpensive method for generating tolerance contours to highlight areas of significantly elevated risk.

Inference based on kernel estimates of the relative risk function in geographical epidemiology.

Kernel smoothing is a popular approach to estimating relative risk surfaces from data on the locations of cases and controls in geographical epidemiology. The interpretation of such surfaces is facilitated by plotting of tolerance contours which highlight areas where the risk is sufficiently high to reject the null hypothesis of unit relative risk. Previously it has been recommended that these tolerance intervals be calculated using Monte Carlo randomization tests. We examine a computationally cheap alternative whereby the tolerance intervals are derived from asymptotic theory. We also examine the performance of global tests of hetereogeneous risk employing statistics based on kernel risk surfaces, paying particular attention to the choice of smoothing parameters on test power.

Descriptive spatial epidemiology of subclinical Salmonella infection in finisher pig herds: application of a novel method of spatially adaptive smoothing.

We describe the spatial epidemiological features of the 6.8 million meat-juice serological tests that were conducted between 1995 and 2004 as part of the Danish swine Salmonella control programme. We investigated pig and farm density using edge-corrected kernel estimations. Pigs were aggregated at the county level to assess county-level risk, and then we investigated farm-level risk by giving farms a case or non-case label using a cut-off of 40% of pigs positive. Conditional probability surfaces, correcting for the underlying population at risk, were produced for each year of the study period using a novel kernel estimator with a spatially adaptive smoothing bandwidth. This approach improves on previous methods by allowing focussed estimation of risk in areas of high population density while maintaining stable estimates in regions where the data are sparse. Two spatial trends in the conditional probability of a farm being a case were evident: (1) over the whole country, with the highest risk in the west compared to the east; and (2) on the Jutland peninsula with the highest risk in the north and south. At the farm-level a consistent area of risk was the south-west of Jutland. Case farms tended to aggregate indicating spatial dependency in the data. We found no association between pig or farm density and Salmonella risk. We generated hypotheses for this spatial pattern of risk and we conclude that this spatial pattern should be considered in the development of surveillance strategies and as a basis for further, more detailed analyses of the data.

Kernel estimation of risk surfaces without the need for edge correction.

Kernel estimates of relative risk surfaces can be used to examine the geographical variation of disease risk. These surfaces can be expressed as ratios of bivariate kernel density estimates constructed from case and control data, but care must be taken to avoid excessive bias at the boundaries of the region under study. It is possible to correct this bias, without the complications of explicit edge correction, through the use of a specific smoothing regimen.

Value of retinal vein pulsation characteristics in predicting increased optic disc excavation.

BACKGROUND: Retinal vein pulsation is often absent in glaucoma, but can be induced by applying a graded ophthalmodynamometric force (ODF) to the eye, which is elevated in glaucoma. AIM: To assess whether ODF has a predictive value in determining glaucoma progression. METHODS: 75 patients with glaucoma and suspected glaucoma were examined prospectively in 1996, and then re-examined at a mean of 82 months later. All subjects had intraocular pressure, visual fields, stereo optic disc photography and ODF measured on their initial visit. When venous pulsation was spontaneous, the ODF was said to be 0 g. At re-examination, central corneal thickness and blood pressure were also measured. Initial and subsequent optic disc photographs were compared and graded into those that had increased excavation and those that had remained stable. The relationship between increased excavation (recorded as a binary response) and the measured variables was modelled using a multiple mixed effects logistic regression. RESULTS: ODF at the initial visit was strongly predictive of increased excavation (p = 0.004, odds ratio 1.16/g, range 0-60 g), with greater predictive value in women than in men (p = 0.004). Visual field mean deviation was predictive of increased excavation (p = 0.044), as was optic nerve haemorrhage in association with older age (p = 0.038). Central corneal thickness was not significantly predictive of increased excavation (p = 0.074) after having adjusted for other variables. CONCLUSION: ODF measurement seems to be strongly predictive of the patient's risk for increased optic disc excavation. This suggests that ODF measurement may have predictive value in assessing the likelihood of glaucoma progression.

Tutorial in biostatistics: spline smoothing with linear mixed models.

The semi-parametric regression achieved via penalized spline smoothing can be expressed in a linear mixed models framework. This allows such models to be fitted using standard mixed models software routines with which many biostatisticians are familiar. Moreover, the analysis of complex correlated data structures that are a hallmark of biostatistics, and which are typically analysed using mixed models, can now incorporate directly smoothing of the relationship between an outcome and covariates. In this paper we provide an introduction to both linear mixed models and penalized spline smoothing, and describe the connection between the two. This is illustrated with three examples, the first using birth data from the U.K., the second relating mammographic density to age in a study of female twin-pairs and the third modelling the relationship between age and bronchial hyperresponsiveness in families. The models are fitted in R (a clone of S-plus) and using Markov chain Monte Carlo (MCMC) implemented in the package WinBUGS.