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Restricted cubic splines for modelling periodic data.

ABSTRACT: In regression modelling the non-linear relationships between explanatory variables and outcome are often effectively modelled using restricted cubic splines (RCS). We focus on situations where the values of the outcome change periodically over time and we define an extension of RCS that considers periodicity by introducing numerical constraints. Practical examples include the estimation of seasonal variations, a common aim in virological research, or the study of hormonal fluctuations within menstrual cycle. Using real and simulated data with binary outcomes we show that periodic RCS can perform better than other methods proposed for periodic data. They greatly reduce the variability of the estimates obtained at the extremes of the period compared to cubic spline methods and require the estimation of fewer parameters; cosinor models perform similarly to the best cubic spline model and their estimates are generally less variable, but only if an appropriate number of harmonics is used. Periodic RCS provide a useful extension of RCS for periodic data when the assumption of equality of the outcome at the beginning and end of the period is scientifically sensible. The implementation of periodic RCS is freely available in peRiodiCS R package and the paper presents examples of their usage for the modelling of the seasonal occurrence of the viruses.

SUBMITTER: Lusa L

PROVIDER: S-EPMC7592770 | biostudies-literature | 2020

REPOSITORIES: biostudies-literature

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Restricted cubic splines for modelling periodic data.

Lusa Lara L Ahlin Črt Č

PloS one 20201028 10

In regression modelling the non-linear relationships between explanatory variables and outcome are often effectively modelled using restricted cubic splines (RCS). We focus on situations where the values of the outcome change periodically over time and we define an extension of RCS that considers periodicity by introducing numerical constraints. Practical examples include the estimation of seasonal variations, a common aim in virological research, or the study of hormonal fluctuations within men ...[more]

PMID: 33112926

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Project description:Monte Carlo methods were used to generate lightly filtered high resolution x-ray spectra spanning from 20 kV to 640 kV.X-ray spectra were simulated for a conventional tungsten anode. The Monte Carlo N-Particle eXtended radiation transport code (MCNPX 2.6.0) was used to produce 35 spectra over the tube potential range from 20 kV to 640 kV, and cubic spline interpolation procedures were used to create piecewise polynomials characterizing the photon fluence per energy bin as a function of x-ray tube potential. Using these basis spectra and the cubic spline interpolation, 621 spectra were generated at 1 kV intervals from 20 to 640 kV. The tungsten anode spectral model using interpolating cubic splines (TASMICS) produces minimally filtered (0.8 mm Be) x-ray spectra with 1 keV energy resolution. The TASMICS spectra were compared mathematically with other, previously reported spectra.Using pairedt-test analyses, no statistically significant difference (i.e., p > 0.05) was observed between compared spectra over energy bins above 1% of peak bremsstrahlung fluence. For all energy bins, the correlation of determination (R(2)) demonstrated good correlation for all spectral comparisons. The mean overall difference (MOD) and mean absolute difference (MAD) were computed over energy bins (above 1% of peak bremsstrahlung fluence) and over all the kV permutations compared. MOD and MAD comparisons with previously reported spectra were 2.7% and 9.7%, respectively (TASMIP), 0.1% and 12.0%, respectively [R. Birch and M. Marshall, "Computation of bremsstrahlung x-ray spectra and comparison with spectra measured with a Ge(Li) detector," Phys. Med. Biol. 24, 505-517 (1979)], 0.4% and 8.1%, respectively (Poludniowski), and 0.4% and 8.1%, respectively (AAPM TG 195). The effective energy of TASMICS spectra with 2.5 mm of added Al filtration ranged from 17 keV (at 20 kV) to 138 keV (at 640 kV); with 0.2 mm of added Cu filtration the effective energy was 9 keV at 20 kV and 169 keV at 640 kV.Ranging from 20 kV to 640 kV, 621 x-ray spectra were produced and are available at 1 kV tube potential intervals. The spectra are tabulated at 1 keV intervals. TASMICS spectra were shown to be largely equivalent to published spectral models and are available in spreadsheet format for interested users by emailing the corresponding author (JMB).

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Restricted cubic splines for modelling periodic data.

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Restricted cubic splines for modelling periodic data.

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