On the application of the von Mises distribution and angular regression methods to investigate the seasonality of disease onset

Analyses of lambing dates in sheep breeds using von Mises distribution

Regular changes in the environment and biological responses generate seasonal patterns in the reproduction in small ruminants. Breeding seasonality is a significant constraint impacting efficiency of lamb production. However, seasonality-related traits present a special peculiarity from a statistical point of view being circular data (day of year running 1:365). Recently, circular mixed models have been developed on the basis of the von Mises distribution and were applied to analyse lambing day distribution recorded from five major Canadian sheep breeds (Rideau Arcott, Romanov, Dorset, Suffolk and Polypay). In a simulation study, the linear model was not able to capture the variance components simulated under the circular paradigm; however, the von Mises model evidenced its ability to infer the variance components of simulated circular records. Using real data of sheep, mostly negligible variances were observed for additive genetic effect when using a linear model on circular data values. In contrast, when using the von Mises model, genetic variances were different across breeds, and it raises the possibility to delay the peak of reproduction and to change the seasonality of the ewes. However, a large variance was captured by flock-year effects emphasizing the strong influence of management in lambing seasons for Canadian sheep populations. Finally, the results suggest the potential of using the von Mises model to analyse circular data, and further research is needed for better understand the complexity of this trait and the von Mises models.

Seasonal variations and climatic factors on acute primary angle-closure admission in southern China: a 5-year hospital-based retrospective study

PURPOSE

To delineate the seasonality of acute primary angle-closure (APAC) admission in a coastal city of southern China and its association with climatic factors.

METHODS

A total of 1155 Chinese subjects with principal diagnosis of APAC attack were recruited from 2012 to 2016, and their medical records were retrieved. Monthly climatic factors were obtained from the Meteorological Bureau of Shantou. Monthly and seasonal APAC admissions were compared, and its correlation with climatic factors was evaluated.

RESULTS

APAC admission was higher in female subjects (75.9%) with an overall mean age of 64.7 ± 9.3 years. APAC admission was highest in summer with the peak onset in June. The peak of APAC admission for female subjects aged ≤ 65 years was in June, and that for> 65 years was in July. The peak of APAC admission for male subjects aged > 65 years was in August. Precipitation was positively correlated with APAC admission rate for both aged ≤ 65 (β = 0.415, p = 0.001) and > 65 years old (β = 0.364, p = 0.004) female subjects. In contrast, surface temperature was positively correlated with APAC admission rate for male subjects aged > 65 years (β = 0.441, p < 0.001). No climatic factor was correlated with APAC admission rate for male subjects ≤ 65 years.

CONCLUSIONS

This study revealed the peak season of APAC admission in summer, and surface temperature and precipitation are the associated factors. Close monitoring of climate changes could help to reduce the incidence of APAC attack.

A mixture of linear-linear regression models for a linear-circular regression

We introduce a new approach to a linear-circular regression problem that relates multiple linear predictors to a circular response. We follow a modelling approach of a wrapped normal distribution that describes angular variables and angular distributions and advances them for a linear-circular regression analysis. Some previous works model a circular variable as projection of a bivariate Gaussian random vector on the unit square, and the statistical inference of the resulting model involves complicated sampling steps. The proposed model treats circular responses as the result of the modulo operation on unobserved linear responses. The resulting model is a mixture of multiple linear-linear regression models. We present two EM algorithms for maximum likelihood estimation of the mixture model, one for a parametric model and another for a nonparametric model. The estimation algorithms provide a great trade-off between computation and estimation accuracy, which was numerically shown using five numerical examples. The proposed approach was applied to a problem of estimating wind directions that typically exhibit complex patterns with large variation and circularity.

The Seasonality of Acute Attack of Primary Angle-Closure Glaucoma in Beijing, China

In this study, the seasonality of acute attack of primary angle-closure glaucoma (PACG) was analysed. This retrospective case series included 283 patients (200 women, 83 men; mean age, 68.2 ± 10.3 years; range, 37–96 years) with acute attack of PACG from a university-based clinic over 4 years. Patients’ age and sex, and the date and season of onset of PACG attack, were analysed. Descriptive analysis and von Mises distribution were used for statistical analysis. The highest incidence of acute attack of PACG was observed in those aged 60–69 years (34.6%). Descriptive analysis showed that the incidence was greater in June and July for men, November for women, and November for the entire sample. An angular plot (using von Mises distribution) of the individual dates of onset revealed the estimated peak onset on September 11, November 8, and October 28 for men, women, and both, respectively. Integration of the results from the two analyses revealed the incidence to be higher in the summer and winter for men, and in the winter for women and for the entire sample. More females than males were affected. Monthly and seasonal variations in onset were observed, which might be related to weather changes.

Association of lifestyle-related factors with circadian onset patterns of acute myocardial infarction: a prospective observational study in Japan

OBJECTIVE

The onset of acute myocardial infarction (AMI) shows characteristic circadian variations involving a definite morning peak and a less-defined night-time peak. However, the factors influencing the circadian patterns of AMI onset and their influence on morning and night-time peaks have not been fully elucidated.

DESIGN, SETTING AND PARTICIPANTS

An analysis of patients registered between 1998 and 2008 in the Osaka Acute Coronary Insufficiency Study, which is a prospective, multicentre observational study of patients with AMI in the Osaka region of Japan. The present study included 7755 consecutive patients with a known time of AMI onset.

MAIN OUTCOMES AND MEASURES

A mixture of two von Mises distributions was used to examine whether a circadian pattern of AMI had uniform, unimodal or bimodal distribution, and the likelihood ratio test was then used to select the best circadian pattern among them. The hierarchical likelihood ratio test was used to identify factors affecting the circadian patterns of AMI onset. The Kaplan-Meier method was used to estimate survival curves of 1-year mortality according to AMI onset time.

RESULTS

The overall population had a bimodal circadian pattern of AMI onset characterised by a high and sharp morning peak and a lower and less-defined night-time peak (bimodal p<0.001). Although several lifestyle-related factors had a statistically significant association with the circadian patterns of AMI onset, serum triglyceride levels had the most prominent association with the circadian patterns of AMI onset. Patients with triglyceride ≥150 mg/dL on admission had only one morning peak in the circadian pattern of AMI onset during weekdays, with no peaks detected on weekends, whereas all other subgroups had two peaks throughout the week.

CONCLUSIONS

The circadian pattern of AMI onset was characterised by bimodality. Notably, several lifestyle-related factors, particularly serum triglyceride levels, had a strong relation with the circadian pattern of AMI onset.

TRIAL REGISTRATION NUMBER

UMIN000004575.

Poisson regression models outperform the geometrical model in estimating the peak-to-trough ratio of seasonal variation: a simulation study

INTRODUCTION

Several statistical methods of assessing seasonal variation are available. Brookhart and Rothman [3] proposed a second-order moment-based estimator based on the geometrical model derived by Edwards [1], and reported that this estimator is superior in estimating the peak-to-trough ratio of seasonal variation compared with Edwards' estimator with respect to bias and mean squared error. Alternatively, seasonal variation may be modelled using a Poisson regression model, which provides flexibility in modelling the pattern of seasonal variation and adjustments for covariates.

METHOD

Based on a Monte Carlo simulation study three estimators, one based on the geometrical model, and two based on log-linear Poisson regression models, were evaluated in regards to bias and standard deviation (SD). We evaluated the estimators on data simulated according to schemes varying in seasonal variation and presence of a secular trend. All methods and analyses in this paper are available in the R package Peak2Trough[13].

RESULTS

Applying a Poisson regression model resulted in lower absolute bias and SD for data simulated according to the corresponding model assumptions. Poisson regression models had lower bias and SD for data simulated to deviate from the corresponding model assumptions than the geometrical model.

CONCLUSION

This simulation study encourages the use of Poisson regression models in estimating the peak-to-trough ratio of seasonal variation as opposed to the geometrical model.

From a different angle: a novel approach to health valuation

The value of a health state is typically described relative to the value of an optimal state, specifically as a ratio ranging from unity (equal to optimal health) to negative infinity. Incorporating potentially infinite values is a challenging issue in the econometrics of health valuation. In this paper, we apply a directional statistics approach based on the assumption of wavering preference. Unlike ratio statistics, directional statistics are based on polar coordinates (angle, radius). The range of angles is bounded between 45 degrees (unity) and negative 90 degrees (i.e., negative infinity); therefore, mean angles are well behaved and negate the impetus behind arbitrary data manipulations. Using time trade-off (TTO) responses from the seminal Measurement and Valuation of Health study, we estimate 243 EQ-5D health state values by minimizing circular variance with and without radial weights. For states with published values greater than zero (i.e., better-than-death), the radially weighted estimates are nearly identical to the published values (Mean Absolute Difference 0.07; Lin's rho 0.94). For worse-than-death states, the estimates are substantially lower than the published values (Mean Absolute Difference 0.186; Lin's rho 0.576). For the worst EQ-5D state (33333), the published value is -0.59 and the directional estimate is -1.11. By taking a directional statistics approach, we circumvent problems inherent to ratio statistics and the systematic bias introduced by arbitrary data manipulations. The predictions suggest that published estimates overvalue severe states. This paper examines TTO responses; however, it may be extended to all forms of health valuation.

On the evidence for seasonal variation in the onset of acute lymphoblastic leukemia (ALL)

Inconsistent seasonal patterns in peak presentation of acute lymphoblastic leukemia have been reported but no formal synthesis of published reports has been attempted to date. We extracted monthly tabulations of cases from publications and reanalysed using an angular methodology and the von Mises distribution. Twenty-four articles from 11 countries in locations ranging from 35.05 degrees S to 65.01 degrees N were identified. Formal synthesis established weak evidence for seasonality in adults and children. Were seasonality present, and arising from a climatic determinant, one might anticipate peaks of an increasing magnitude as the associated latitude moved away from the equator. No such pattern was apparent.