Using linear and natural cubic splines, SITAR, and latent trajectory models to characterise nonlinear longitudinal growth trajectories in cohort studies

Longitudinal data analysis can improve our understanding of the influences on health trajectories across the life-course. There are a variety of statistical models which can be used, and their fitting and interpretation can be complex, particularly where there is a nonlinear trajectory. This paper provides a guide to describing nonlinear growth trajectories for repeatedly measured continuous outcomes using linear mixed-effects (LME) models with linear splines and natural cubic splines, nonlinear mixed effects Super Imposition by Translation and Rotation (SITAR) models, and latent trajectory models. The underlying model for each of the four approaches, the similarities and differences between models, and their advantages and disadvantages are described. Their applications and correct interpretation are illustrated by analysing repeated bone mass measures across three cohort studies with 8,500 individuals and 37,000 measurements covering ages 5-40 years. Linear and natural cubic spline LME models and SITAR provided similar descriptions of the mean bone growth trajectory and growth velocity, and the sex differences in growth patterns. Latent trajectory models identified up to four subgroups of individuals with distinct trajectories during adolescence and similar trajectories in childhood and adulthood. Recommendations for choosing a modelling approach are provided along with a discussion and signposting on further modelling extensions for analysing trajectory exposures and outcomes, and multiple cohorts. In summary, we present a resource for characterising nonlinear longitudinal growth trajectories, that could be adapted for other complex traits. Scripts and synthetic datasets are provided so readers can replicate trajectory modelling and visualisation using the open-source R software.

A Statistical Approach to Evaluating Wheel-Rail Contact Dynamics

This paper provides a statistical analysis of the effects of wheel load, angle of attack (AoA), and creepage on longitudinal traction force at the wheel-rail contact using experimental data collected on the Virginia Tech-Federal Railroad Administration (VT-FRA) Roller Rig. The VT-FRA Roller Rig is a unique piece of equipment designed and built with the specific goal of evaluating the wheel-rail contact mechanics and dynamics with a high degree of precision. Longitudinal traction forces are of great importance to the railroad industry since they provide the motive power needed to move a train. Various experiments are conducted in different settings to study the relationship between the aforementioned variables and the longitudinal traction force. The test data is split into “training” and “testing” sets, and the training sets (a total of four) are used to entertain statistical models in a standard parametric regression framework. The study carefully assesses whether the assumptions of the classical linear regression model hold by studying the empirical histogram and the normal Q-Q plot of the residuals. In the case of non-linearities, different transformations are applied to the explanatory variable to find the closest functional form that captures the relationship between the response and the explanatory variables. The developed models are then compared with their non-parametric counterparts such as natural cubic splines in terms of goodness of fit, and prediction error on the testing set. The study develops regression models that are able to accurately explain the relationship between longitudinal traction and creepage and AoA. The models are intended to be used for predicting traction under various operating conditions.

Optimal doses of heart failure medication in women and men: perspective from daily clinical care

Background Heart failure (HF) guidelines recommend equal target doses for women and men. Recently, these recommendations have been challenged as research suggested that women with HF with reduced Ejection Fraction (HFrEF) may reach optimal treatment effect at half of the guideline-recommended dose while men may require the full dose. However, it is unclear how often women and men reach guideline-recommended target doses in daily practice. Purpose To evaluate whether women and men with HF reach guideline-recommended target doses for Angiotensin-converting enzyme inhibitors (ACEI)/angiotensin II receptor blocker (ARB), β-blockers (BB) and mineralocorticoid receptor antagonists (MRA) in daily practice. Methods We extracted data from 13 outpatient cardiology clinics for all individuals diagnosed with HF within 14 days leading up to their visit who were prescribed at least one guideline-recommended HF medication. HF was defined based on a combination of the cardiologist's diagnosis and left ventricular systolic or diastolic dysfunction determined during echocardiography. Guideline-recommended medication groups and target doses were taken from the 2016 ESC HF guidelines or from literature for medications not mentioned in the guidelines. To enable comparison between medications and medication groups, daily dose was converted to percentage of target dose. Mean change in percentage of target dose over consecutive medication prescriptions was modelled for men and women using natural cubic splines. Results We included 1254 patients with HF (48% women). Women were on average older at diagnosis (71 vs 67 years) and more often had hypertension (54.9 vs 44.3%), but less often had diabetes mellitus (13.5 vs 19.4%), a history of coronary heart disease (7.8 vs 19.6%,) or past cardiovascular interventions (8.7 vs 23.0%) than men. In total, 1069 patients were prescribed an ACEI/ARB (46% women), 920 a BB (48% women) and 243 an MRA (43% women). Women were more often prescribed only one medication than men (39.6 vs 33.2%, p=0.014). Approximately 14% of first prescriptions for all medications were at 100% of target dose or higher for both women and men, with the majority of prescriptions being either at 1–49% of target dose (47.2 vs 45.5%, respectively) or 50–99% of target dose (39.1 vs 40.8%, respectively). The natural cubic splines showed that this distribution did not change over consecutive drug prescriptions in either women or men. Only MRA prescriptions for men showed an upward trend and reached 100% of target dose. Conclusion In daily practice, both women and men were unlikely to reach guideline-recommended target doses for both ACEI/ARBs and BBs. For MRAs, women were less likely to reach target dose than men. Optimal dosing in HF is difficult for both sexes, but in light of recent evidence, the challenge in daily practice seems to lie more in undertreatment of men than overtreatment of women. Figure 1 (women in red, men in blue) Funding Acknowledgement Type of funding source: Public Institution(s). Main funding source(s): ZonMw

4878Different relationships between blood pressures and clinical events in SPRINT and ACCORD-BP trial

Introduction SPRINT showed that intensive control of systolic blood pressure (SBP) <120mmHg was beneficial when compared to the standard treatment (SBP <140mmHg). In contrast, ACCORD-BP trial failed to prove the benefit of intensive SBP lowering in diabetic patients. J-curve phenomenon might be the key to help understanding the different results of two trials. Methods SPRINT and ACCORD-BP databases were obtained via BioLINCC. Since BP changes along with the time, timing at which BP became stable after treatment were chosen at 9 months for SPRINT and 1 year for ACCORD BP. The final analytic datasets consisted of 8,787 and 4,306 event-free patients at the time of stable BP, respectively. Clinical events were defined at the primary composite endpoint for each trial. The effects of BP on clinical events were modeled using natural cubic splines in Cox regression models. Degrees of freedom of splines curves were chosen using Akaike Information Criterion. Results Analyzing SPRINT database, the spline-based hazard ratio (HR) curve showed a J-curve, which means lowering DBP below 77mmHg could be harmful, while SBP had a linear relationship (HR 1.13 per 10mmHg increase, 95% confidence interval [CI] 1.06∼1.20, p<0.0001; Figure). In ACCORD-BP trial, no J-curve phenomenon was observed. The effect of SBP was linear and almost the same to the result of SPRINT with HR 1.13 (95% CI 1.06∼1.20, p=0.0003). The relationship between DBP and clinical events was non-significant with a negative trend, which means the lower, the worse (HR 0.91, 95% CI 0.82∼1.01 p=0.071). Conclusions Despite the different results regarding the benefit of intensive BP control, the effects of SBP on clinical events were quite similar in SPRINT and ACCORD-BP trial. Instead,differences existed in the relationships between DBP and clinical events. Understanding the meaning of different patterns of relationships including J-curve might be the key to determine the optimal BP control.

Fast Frequency Sweep Technique Based on Segmentation for the Acceleration of the Electromagnetic Analysis of Microwave Devices

The characterization of communication devices in a certain frequency band can be accelerated if a fast frequency sweep technique is used instead of a discrete frequency sweep. Existing fast frequency sweep techniques are either complex or specific for a certain electromagnetic solver. In this work, a new fast frequency sweep method is proposed that consists in segmenting the device under analysis into simple building blocks. Each building block is characterized with a generalized (multimode) circuital matrix whose elements present a simple and flat frequency response that is interpolated using natural cubic splines with very few points. In this way, the response of each block along the whole frequency band is obtained efficiently and accurately with as many frequency points as desired. Then, the circuital matrices of all the blocks are cascaded and the circuital matrix of the whole device in obtained. The new fast frequency sweep was successfully applied to the analysis of different types of devices (all metallic rectangular waveguide filter, dielectric loaded rectangular waveguide filter, and substrate integrated waveguide filter). The computational times were reduced to 15% or 19%, depending on the device, when compared with a discrete frequency sweep using the same electromagnetic solver.

Prevailing Clusters of Canine Behavioural Traits in Historical US Demand for Dog Breeds (1926–2005)

Drawing on American Kennel Club (AKC) puppy registration numbers for approximately 82 varieties of pedigree dogs between 1926 and 2005, the current article analyses behavioural reports on 32,005 dogs of these varieties reported through the Canine Behavioural Assessment and Research Questionnaire (C-BARQ). Cluster analysis of C-BARQ scores indicates that the 82 breeds fell into six clusters. Average scores for each of the 14 behavioural subscales and 22 miscellaneous traits in C-BARQ were calculated for each cluster, and the breeds in each cluster with average scores most similar to the cluster averages were selected as titular breeds. Titular breeds for each cluster were the Maltese terrier, the Great Dane, the Akita, the Australian shepherd, the American Staffordshire terrier, and the Weimaraner. Using the AKC data, we tracked longitudinal trends in annual registration numbers of breeds of each cluster over the period from 1926 to 2005. This period was subdivided into periods with differing overall trends by fitting natural cubic splines to the overall raw trend and considering both the spline and its derivative curves. Differences in the absolute numbers of dogs and trends in registrations over nearly 80 years were identified: an Early period (1926–1944, during which total registration numbers were very low); a Mid-Century Period (1945–1971, during which total registration numbers were tending to rise from year to year); a First Decline (1972–1979, a brief period during which registration numbers experienced a trend of more gradual decline); a Recovery (1980–1992, where registration numbers began to gradually rise again); and a Second Decline (1993–2005, a second sustained period of falling registration numbers, more dramatic than the first decline). The current article describes the ways in which the clustered behaviour of dogs associate with these trends. That said, there is no compelling evidence that shifts in the popularity within or between the clusters reflect consumer canine behavioural preferences. Understanding historic trends in the demand for certain canine behavioural traits could help veterinary and urban animal management stakeholders to anticipate future needs for education and infrastructure.