Adaptive discrete thin plate spline smoother

The discrete thin plate spline smoother fits smooth surfaces to large data sets efficiently. It combines the favourable properties of the finite element surface fitting and thin plate splines. The efficiency of its finite element grid is improved by adaptive refinement, which adapts the precision of the solution. It reduces computational costs by refining only in sensitive regions, which are identified using error indicators. While many error indicators have been developed for the finite element method, they may not work for the discrete smoother. In this article we show three error indicators adapted from the finite element method for the discrete smoother. A numerical experiment is provided to evaluate their performance in producing efficient finite element grids. References F. L. Bookstein. Principal warps: Thin-plate splines and the decomposition of deformations. IEEE Trans. Pat. Anal. Mach. Int. 11.6 (1989), pp. 567–585. doi: 10.1109/34.24792. C. Chen and Y. Li. A robust method of thin plate spline and its application to DEM construction. Comput. Geosci. 48 (2012), pp. 9–16. doi: 10.1016/j.cageo.2012.05.018. L. Fang. Error estimation and adaptive refinement of finite element thin plate spline. PhD thesis. The Australian National University. http://hdl.handle.net/1885/237742. L. Fang. Error indicators and adaptive refinement of the discrete thin plate spline smoother. ANZIAM J. 60 (2018), pp. 33–51. doi: 10.21914/anziamj.v60i0.14061. M. F. Hutchinson. A stochastic estimator of the trace of the influence matrix for laplacian smoothing splines. Commun. Stat. Simul. Comput. 19.2 (1990), pp. 433–450. doi: 10.1080/0361091900881286. W. F. Mitchell. A comparison of adaptive refinement techniques for elliptic problems. ACM Trans. Math. Soft. 15.4 (1989), pp. 326–347. doi: 10.1145/76909.76912. R. F. Reiniger and C. K. Ross. A method of interpolation with application to oceanographic data. Deep Sea Res. Oceanographic Abs. 15.2 (1968), pp. 185–193. doi: 10.1016/0011-7471(68)90040-5. S. Roberts, M. Hegland, and I. Altas. Approximation of a thin plate spline smoother using continuous piecewise polynomial functions. SIAM J. Numer. Anal. 41.1 (2003), pp. 208–234. doi: 10.1137/S0036142901383296. D. Ruprecht and H. Muller. Image warping with scattered data interpolation. IEEE Comput. Graphics Appl. 15.2 (1995), pp. 37–43. doi: 10.1109/38.365004. E. G. Sewell. Analysis of a finite element method. Springer, 2012. doi: 10.1007/978-1-4684-6331-6. L. Stals. Efficient solution techniques for a finite element thin plate spline formulation. J. Sci. Comput. 63.2 (2015), pp. 374–409. doi: 10.1007/s10915-014-9898-x. O. C. Zienkiewicz and J. Z. Zhu. A simple error estimator and adaptive procedure for practical engineerng analysis. Int. J. Numer. Meth. Eng. 24.2 (1987), pp. 337–357. doi: 10.1002/nme.1620240206.

BMI and future risk for COVID-19 infection and death across sex, age and ethnicity: preliminary findings from UK biobank

We examined the link between BMI and risk of a positive test for SARS-CoV-2 and risk of COVID-19-related death among UK Biobank participants. Among 4855 participants tested for SARS-CoV-2 in hospital, 839 were positive and of these 189 died from COVID-19. Poisson models with penalised thin plate splines were run relating exposures of interest to test positivity and case-fatality, adjusting for confounding factors. BMI was associated strongly with positive test, and risk of death related to COVID-19. The gradient of risk in relation to BMI was steeper in those under 70, compared with those aged 70 years or older for COVID-19 related death (Pinteraction=0.03). BMI was more strongly related to test positivity (Pinteraction=0.010) and death (Pinteraction=0.002) in non-whites, compared with whites. These data add support for adiposity being more strongly linked to COVID-19-related deaths in younger people and non-white ethnicities. If future studies confirm causality, lifestyle interventions to improve adiposity status may be important to reduce the risk of COVID-19 in all, but perhaps particularly, non-white communities.

Median/modal death ages of pooled European male cohorts were near-constant for ~25/30 years

ABSTRACTBackgroundLongevity is of considerable interest. Collation of recent data after World War II by the Human Mortality Database allowed analyses, previously unattainable, of modal death-ages for sufficient numbers of large European pooled cohorts.ObjectiveTo track modes, means and medians (≥60 years old (y)) of all-cause mortality for both sexes.MethodsThe only highest-quality, large-number Lexis data available were pooled from nine European countries: Denmark, Finland, France, Iceland, Italy, Netherlands, Norway, Sweden and Switzerland; raw-data modes (and means/medians ≥60y, plus thin-plate-splines), were analyzed, plus loess-smoothed equivalents for individual countries.ResultsHere we show that for ~25-30 years (cohorts 1880- ~1909) dramatic overall sex differences existed between pooled raw-death-age changes: male modal ages being near-constant (77.2y + standard deviation 1.58y); females’ increased. Overall, for available cohorts (1880-1904) male raw medians were exactly constant (76y); male means showed slight increase (0.0193y/year; compare female: 0.146y/year). Male deaths ≥60≤76y compared with >76y, as percentages of total, were near-equal, whereas in females the former decreased. Only after ~1910 did male modal ages rapidly increase (other averages not calculable). Individual country results showed that males in Finland, France, Switzerland were affected less than other countries.ConclusionsResults clarify previously knowledge concerning sex differences during this period. Despite improved environment during late adulthood, this did not translate into increased male longevity and earlier events might have sealed their fate, especially in Denmark, Italy, Netherlands, Norway, and Sweden. One hypothesis concerns long-term effects of the 1918-1919 influenza pandemic, perhaps directly relevant to the Covid-19 pandemic at present.

Flexible Bayesian excess hazard models using low-rank thin plate splines

Excess hazard models became the preferred modelling tool in population-based cancer survival research. In this setting, the model is commonly formulated as the additive decomposition of the overall hazard into two components: the excess hazard due to the cancer of interest and the population hazard due to all other causes of death. We introduce a flexible Bayesian regression model for the log-excess hazard where the baseline log-excess hazard and any non-linear effects of covariates are modelled using low-rank thin plate splines. Using this type of splines will ensure that the log-likelihood function retains tractability not requiring numerical integration. We demonstrate how to derive posterior distributions for the excess hazard and for net survival, a population-level measure of cancer survival that can be derived from excess hazard models. We illustrate the proposed model using survival data for patients diagnosed with colon cancer during 2009 in London, England.