Tilman M. Davies

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.

Symmetric adaptive smoothing regimens for estimation of the spatial relative risk function

The spatial relative risk function is now regarded as a standard tool for visualising spatially tagged case-control data. This function is usually estimated using the ratio of kernel density estimates. In many applications, spatially adaptive bandwidths are essential to handle the extensive inhomogeneity in the distribution of the data. Earlier methods have employed separate, asymmetrical smoothing regimens for case and control density estimates. However, we show that this can lead to potentially misleading methodological artefacts in the resulting estimates of the log-relative risk function. We develop a symmetric adaptive smoothing scheme that addresses this problem. We study the asymptotic properties of the new log-relative risk estimator, and examine its finite sample performance through an extensive simulation study based on a number of problems adapted from real life applications. The results are encouraging.

Identification of high-risk regions for schistosomiasis in the Guichi region of China: an adaptive kernel density estimation-based approach.

Identification of high-risk regions of schistosomiasis is important for rational resource allocation and effective control strategies. We conducted the first study to apply the newly developed method of adaptive kernel density estimation (KDE)-based spatial relative risk function (sRRF) to detect the high-risk regions of schistosomiasis in the Guichi region of China and compared it with the fixed KDE-based sRRF. We found that the adaptive KDE-based sRRF had a better ability to depict the heterogeneity of risk regions, but was more sensitive to altering the user-defined smoothing parameters. Specifically, the impact of bandwidths on the estimated risk value and risk significance (P value) was higher for the adaptive KDE-based sRRF, but lower on the estimated risk variation standard error (s.e.) compared with the fixed KDE-based sRRF. Based on this application the adaptive and fixed KDE-based sRRF have their respective advantages and disadvantages and the joint application of the two approaches can warrant the best possible identification of high-risk subregions of diseases.

Modelling dichotomously marked muscle fibre configurations

Human skeletal muscle consists of contractile elements (fibres) that may be differentiated according to their physiological and biochemical properties. The different types of fibre are distributed throughout each muscle, with the pattern (when viewed as a cross-section) of cell distribution being an important determinant of the functional properties of each muscle. It is well known that the proportions and distributions of muscle fibre types change with advancing age or disease, but few studies have quantitatively investigated these changes. A better knowledge of the nature of changes in muscle fibre distributions is an essential requirement for future development of therapies and interventions directed at maintaining or restoring good muscle function. In this work, we examine several statistical methods designed to gauge the departure of a dichotomously labelled muscle fibre distribution from that of a random fibre-type dispersal. These methods are also applicable to a wide range of biological investigations in which the spatial distribution of cells or specimens underpins an important biological principle. This work includes the proposal of a novel technique, based on weighted kernel-smoothed density ratios, which can account for the variable areas of the individual fibres. We illustrated the methodology by using a number of real-data examples, and we employed a comprehensive set of simulations to assess the empirical power and false-positive rates of these tests.

Student injuries in the dissecting room.

Cadaver dissection is the first opportunity for many students to practice handling human tissue and is their first exposure to the occupational hazards involved with this task. Few studies examine dissection room injuries to ascertain the dangers associated with dissecting. We performed a retrospective cohort analysis of dissection room injuries from four student cohorts over an eleven‐year period (2001–2011), including second‐year medical students, third‐year medical students, second‐year dental students, and third‐year science students. Injury data included activity causing injury, object responsible, and injury site. A total of 163 injuries during 70,039 hours of dissection were recorded, with 66 in third‐year medical students, 42 in second‐year medical students, 36 in third‐year science students, and 16 in second‐year dental students. The overall rate was 2.87 injuries per 1,000 dissection hours, with second‐year medical students most frequently injured (5.5 injuries per 1,000 hours); third‐year medical students were least frequently injured (1.3 injuries per 1,000 hours). A significant difference in injury rates between student groups indicated a higher than expected injury rate to second‐year medical students and lower than expected rates to third‐year medical students. Injury rates increased for most groups between 2001–2006 and 2007–2011 periods. Most injuries (79%) were from scalpel cuts to the finger or thumb. This study provides injury rates for dissection room injuries to students, indicating differences in injury frequency between cohorts and an increase in injury rate over time. As scalpel cuts were the most likely injury mechanism, targeting scalpel handling with preventative strategies may reduce future injury risk. Anat Sci Educ 6: 404–409.

Fast computation of spatially adaptive kernel estimates

Kernel smoothing of spatial point data can often be improved using an adaptive, spatially varying bandwidth instead of a fixed bandwidth. However, computation with a varying bandwidth is much more demanding, especially when edge correction and bandwidth selection are involved. This paper proposes several new computational methods for adaptive kernel estimation from spatial point pattern data. A key idea is that a variable-bandwidth kernel estimator for d-dimensional spatial data can be represented as a slice of a fixed-bandwidth kernel estimator in

Comment on Makino et al. and observations on spatial modeling.

(d+1)