Piecewise Linear Spline Function Research Articles

Evaluating the impact of heat stress as measured by temperature-humidity index (THI) on test-day milk yield of small holder dairy cattle in a sub-Sahara African climate

This study evaluates the effect of heat stress on milk production and describes the pattern of response of milk yield to increasing heat load, using temperature-humidity index (THI) on test-day milk records of small holder dairy cattle herds in the sub-Saharan African climate of Tanzania. Climate data obtained from aWhere, an agricultural weather data platform (http://www.awhere.com) was analysed with 14,367 first lactation test day milk records of 3511 dairy cows collected between 2016 and 2019. THI was calculated from daily maximal temperatures and daily minimum humidity. Three sets of analysis were performed. In the first and second analysis, two mixed effect repeatability models were fitted with THI treated as a categorical variable grouped into 5 classes (THI1= [61 - 66], THI2= [67 - 71], THI3= [72 - 78], THI4=[79 - 81], THI5=[82 - 86]), to obtain least squares estimates of THI effect on milk production, and as a continuous variable within THI classes to identify THI thresholds at which milk yield started to decline. In the third analyses, one quadratic polynomial regression (POL) and three regression spline functions namely piecewise linear spline function (PLF), natural splines function (NSF) and cubic splines function (CSF) were fitted to determine the average effect of THI on milk yield in the population and describe the pattern of response of milk yield to increasing head load.The results show that heat stress reduced milk yield by 4.16% to 14.42% across THI groups, with daily milk yield being the highest in THI1 (7.40±0.39 litres) and the lowest in THI4 (6.33±0.32).Regression coefficients within groups showed significant daily milk yield decrease in THI2 (-0.09) and THI3 (-0.06), but not for other THI classes, indicating that cows experienced heat stress between THI values of 67 and 76 and milk loss plateaued afterwards, suggesting that the animals acclimatized to heat stress conditions beyond THI value of 76. At the population level, THI and its squared term were significantly negatively and positively (-0.61, 0.004) associated with milk production, indicating a non-linear relationship between milk yield and THI. The CSF model showed better goodness of fit and predictive ability than other models for predicting future population response of milk yield to heat stress in small holder dairy farms in Tanzania.Herd management strategies and animal husbandry measures are needed in small holder dairy farms in Tanzania to minimize the impact of heat stress on milk yield and income of the farmers.

Non-linear return to human capital for workers of productive sectors in Indonesia

This study is aimed to investigate a typical return to human capital for workers of productive economic sectors in Indonesia. Instead of satisfying Mincer’s linearity assumption, we use a piecewise linear spline function in order to trace marginal returns to education and job tenure and to find out how large the returns to both variables could be moderated by certain variables. The research is conducted on 2609 individuals who work for Indonesian top-five productive sectors in 2016, as recorded in National Work Force Survey (SAKERNAS). We implement quantile regression analysis to produce three levels earning model. The result shows that the return to education varies across schooling level and apparently negative for academy schooling. We also find that job training participation does not always enhance the return to education especially for higher earning workers. The return to job tenure is found to diminish during career length. However, graduating from certain college majors significantly slowdown the diminishing return to job tenure and thus promoting better career. Based on these findings, we outline several ideas concerned to developing higher education and job training provision in national scale for more efficient supply of human capital in the productive sectors.

The use of piecewise linear spline function on dose-response meta-analysis.

Does-response meta-analysis is widely used in observational-based meta-analysis since proposed by Greenland et al . (1-4). The method works well in most of the situation, especially for the nonlinear trend approximating. Our argument is the linear slope insert within the function: by setting the parameters of quadratic and cubic term as zero. Linear relationship usually acts as main analysis when non-linear trend is non-significant or as additional analysis when non-linear trend is significant. Actually, only part of the linear slopes fit well (5). For J-shaped, U-shaped, S-shaped, and V-shaped curves, the linear slope fit bad since these slopes differ across pieces. We introduce a piecewise linear spline function that may be a solution for this issue (5,6). We assume log relative risks (LogRR) as dependent variable and exposure (X) as independent variable. Then a piecewise linear regression can be established as X against LogRR, with K indicates the cut points (knots) of the slopes.

Study on the association between ambient temperature and mortality using spatially resolved exposure data

There are many studies that have posited an association between extreme temperature and increased mortality. However, most studies use temperature at a single station per city as the reference point to analyze deaths. This leads to exposure misclassification and usually the exclusion of exurban, small town, and rural populations. In addition, few studies control for confounding by PM2.5, which is expected to induce upward bias. The high-resolution temperature and PM2.5 data at a resolution of 1km2 were derived from satellite images and other land use sources.To capture the nonlinear association of temperature with mortality we fit a piecewise linear spline function for temperature, with a change in slope at −1°C and 28°C, the temperature threshold at which mortality in Georgia, North Carolina, and South Carolina increases due to cold and heat, respectively. We conducted stratified analyses by age group, sex, race, education, and urban vs nonurban, as well as sensitivity analyses of different temperature threshold and covariate sets.We found a 0.19% (95% CI=−0.98, 1.34%) increase in mortality for each 1°C decrease in temperature below −1°C and a 2.05% (95% CI=0.87, 3.24%) increase in mortality for each 1°C increase in temperature above 28°C, a 79.8% larger effect size for heat compared to the station-based metric. The effect estimates relying on the monitoring stations were 0.09% (95% CI=−0.79, 0.95%) and 1.14% (95% CI=0.08, 1.57%) for the equivalent temperature changes. The estimates were not confounded by PM2.5. Children under 15 years of age had the largest percentage increase per 1°C increase in temperature (8.19%, 95% CI=−0.38 to 17.49%) followed by Blacks (4.35%, 95% CI=2.22 to 6.53%). Higher education was a protective factor for the effect of extreme temperature on mortality. There was a suggestion that people in less urban areas were more susceptible to extreme temperature. The relationship between temperature and mortality was stronger when using exposure data with more spatial variability than using exposure data based on existing monitors alone.

CALIBRATION OF THE NuSTAR HIGH-ENERGY FOCUSING X-RAY TELESCOPE

We present the calibration of the \textit{Nuclear Spectroscopic Telescope Array} (\nustar) X-ray satellite. We used the Crab as the primary effective area calibrator and constructed a piece-wise linear spline function to modify the vignetting response. The achieved residuals for all off-axis angles and energies, compared to the assumed spectrum, are typically better than $\pm 2$\% up to 40\,keV and 5--10\,\% above due to limited counting statistics. An empirical adjustment to the theoretical 2D point spread function (PSF) was found using several strong point sources, and no increase of the PSF half power diameter (HPD) has been observed since the beginning of the mission. We report on the detector gain calibration, good to 60\,eV for all grades, and discuss the timing capabilities of the observatory, which has an absolute timing of $\pm$ 3\,ms. Finally we present cross-calibration results from two campaigns between all the major concurrent X-ray observatories (\textit{Chandra}, \textit{Swift}, \textit{Suzaku} and \textit{XMM-Newton}), conducted in 2012 and 2013 on the sources 3C\,273 and PKS\,2155-304, and show that the differences in measured flux is within $\sim$10\% for all instruments with respect to \nustar.

Association between high temperature and work-related injuries in Adelaide, South Australia, 2001–2010

Objectives(1) To investigate the association between temperature and work-related injuries and (2) to identify groups of workers at high risk of work-related injuries in hot environments in Adelaide, South Australia.MethodsWorkers’...

366 The association between heat exposure and work-related injuries in South Australia, 2001–2010

ObjectiveTo investigate the association between work-related injuries and temperature, to identify the groups of workers at high risk of heat-related injuries, and to explore the possible lagged effects of extreme...

362 Updated results on the risk of death from lung cancer by silica dust in German Wismut uranium miners, 1946–2008

ObjectivesTo investigate the exposure-response relationship between silica dust and lung cancer mortality within German uranium miners in the extended follow-up period from 1946 to 2008. The cohort consists of 58,672...

Quantitative relationship between silica exposure and lung cancer mortality in German uranium miners, 1946–2003

Background:In 1996 and 2009, the International Agency for Research on Cancer classified silica as carcinogenic to humans. The exposure–response relationship between silica and lung cancer risk, however, is still debated. Data from the German uranium miner cohort study were used to further investigate this relationship.Methods:The cohort includes 58 677 workers with individual information on occupational exposure to crystalline silica in mg m−3-years and the potential confounders radon and arsenic based on a detailed job-exposure matrix. In the follow-up period 1946–2003, 2995 miners died from lung cancer. Internal Poisson regression with stratification by age and calendar year was used to estimate the excess relative risk (ERR) per dust-year. Several models including linear, linear quadratic and spline functions were applied. Detailed adjustment for cumulative radon and arsenic exposure was performed.Results:A piecewise linear spline function with a knot at 10 mg m−3-years provided the best model fit. After full adjustment for radon and arsenic no increase in risk <10 mg m−3-years was observed. Fixing the parameter estimate of the ERR in this range at 0 provided the best model fit with an ERR of 0.061 (95% confidence interval: 0.039, 0.083) >10 mg m−3-years.Conclusion:The study confirms a positive exposure–response relationship between silica and lung cancer, particularly for high exposures.