A Bayesian test for seasonality in medical data

In medical research, the results from seasonality analyses provide valuable information that eventually can help to clarify the etiology of poorly understood diseases. We present a Bayesian procedure for the analysis of seasonal variation in medical data. The method is a Bayesian version of a frequentist test that performs very well. Statistical seasonality analyses of medical data often involve a short time series, 12 observations with small amplitude and small sample size. Among the specialized procedures already developed for such analyses, only one is Bayesian; the method we present in this paper appears to be the second such Bayesian procedure. Easy to understand and apply, the method is versatile because it can be used to analyze different types of seasonal variation. We illustrate the procedure’s application with two examples of real data.

Studies of the Seasonal Pattern of Multiple Maternities

The seasonality of population data has been of great interest in demographic studies. When seasonality is analyzed, the population at risk plays a central role. In a study of the monthly number of births and deaths, the population at risk is the product of the size of the population and the length of the month. Usually, the population can be assumed to be constant, and consequently, the population at risk is proportional to the length of the month. Hence, the number of cases per day has to be analyzed. If one studies the seasonal variation in twin or multiple maternities, the population at risk is the total number of monthly confinements, and the study should be based on the rates of the multiple maternities. Consequently, if one considers monthly twinning rates, the monthly number of birth data is eliminated and one obtains an unaffected seasonality measure of the twin maternities. The strength of the seasonality is measured by a chi-squared test or by the standard deviation. When seasonal models are applied, one must pay special attention to how well the model fits the data. If the goodness of fit is poor, it can erroneously result in a statement that the seasonality is slight, although the observed seasonal fluctuations are marked.

Statistical analysis of the seasonal variation in the twinning rate

There have been few secular analyses of the seasonal variation in human twinning and the results are conflicting. One reason for this is that the seasonal pattern of twinning varies in different populations and at different periods. Another reason is that the statistical methods used are different. The changing pattern of seasonal variation in twinning rates and total maternities in Denmark was traced for three periods (1855–69, 1870–94, and 1937–84). Two alternative methods of analysis are considered. The method of Walter and Elwood and a trigonometric regression model give closely similar results. The seasonal distribution of twin maternities for the periods in the 19th century showed highly significant departures. For both twin and general maternities, the main peaks can be seen from March to June and a local peak in September. During the spring– summer season the twinning rates were higher than the total birth rates, indicating a stronger seasonal variation for the twin maternities than for the general maternities. For 1937–84, there was a similar, but less accentuated, pattern. Studies of other populations are compared with the Danish results. The more accentuated seasonal variation of twinning in the past indicate that some factors in the past affected women during summer–autumn and around Christmas time, making them more fecund and particularly to be more prone to polyovulation and/or more able to complete a gestation with multiple embryos.

Testing for seasonality using circular distributions based on non-negative trigonometric sums as alternative hypotheses

In medical and epidemiological studies, the importance of detecting seasonal patterns in the occurrence of diseases makes testing for seasonality highly relevant. There are different parametric and non-parametric tests for seasonality. One of the most widely used parametric tests in the medical literature is the Edwards test. The Edwards test considers a parametric alternative that is a sinusoidal curve with one peak and one trough. The Cave and Freedman test is an extension of the Edwards test that is also frequently applied and considers a sinusoidal curve with two peaks and two troughs as the alternative hypothesis. The Kuiper, Hewitt and David and Newell are common non-parametric tests. Fernández-Durán (2004) developed a family of univariate circular distributions based on non-negative trigonometric (Fourier) sums (series) (NNTS) that can account for an arbitrary number of peaks and troughs. In this article, this family of distributions is used to construct a likelihood ratio test for seasonality considering parametric alternative hypotheses that are NNTS distributions.

Infectious exposure in the first years of life and risk of central nervous system tumours in children: analysis of birth order, childcare attendance and seasonality of birth

Background:

An infective, mostly viral basis has been found in different human cancers. To test the hypothesis of a possible infectious aetiology for central nervous system (CNS) tumours in children, we investigated the associations with proxy measures of exposure to infectious disease.

Methods:

In a large case–control study nested in the populations of Denmark, Norway, Sweden, and Finland of 4.4 million children, we studied the association of birth order and seasonal variation of birth with subsequent risk for CNS tumours. We identified 3983 children from the national cancer registries, and information on exposure was obtained from the high-quality national administrative health registries. We investigated the association between childcare attendance during the first 2 years of life and the risk for CNS tumours in a subset of Danish children with CNS tumours, using information from the Danish Childcare database.

Results:

We observed no association between birth order and risk of CNS tumours overall (odds ratio (OR) for second born or later born vs first born, 1.03; 95% confidence interval (CI), 0.96–1.10) or by histological subgroup, and children with CNS tumours did not show a seasonal variation of birth that was distinct from that of the background population. Childcare attendance compared with homecare showed a slightly increased OR (1.29; 95% CI, 0.90–1.86) for CNS tumours, with the highest risk observed in children attending a crèche. The strongest association was observed for embryonal CNS tumours. We found no effect of age at enrolment or duration of enrolment in childcare.

Conclusion:

These results do not support the hypothesis that the burden of exposure to infectious disease in early childhood has an important role in the aetiology of paediatric CNS tumours.

Seasonality of birth month of children with celiac disease differs from that in the general population and between sexes and is linked to family history and environmental factors

BACKGROUND

Patients with autoimmune diseases, such as type 1 diabetes mellitus, atopic dermatitis, autoimmune thyroid diseases, and multiple sclerosis have a different seasonality of month of birth (MOB) from the general population. This study was undertaken to determine the seasonality of MOB in children with celiac disease (CD), an autoimmune-mediated enteropathy.

PATIENTS AND METHODS

The medical records of 431 children with CD (239 girls, 192 boys) were included in the study; 138 girls and 81 boys were under the age of 24 months. Data were analyzed by the cosinor method, which, in addition to statistical significance, provides parameters of rhythms. Statistical differences between groups were also analyzed by the chi test.

RESULTS

Patients with CD showed different patterns from that in the general population, which peaks in September. Boys and girls with CD were found to have a different seasonality of MOB (P < 0.02). Girls whose CD was diagnosed before age 24 months (peak July-August) had a different seasonality of MOB from those whose CD was diagnosed after age 24 months (no rhythm; P < 0.005) and showed a different seasonality from boys whose CD was diagnosed above 24 months (peak July; P < 0.02). In addition, we found a different seasonality of MOB in children with a family history of CD compared with those with no family history (P < 0.001).

CONCLUSIONS

Girls with the diagnosis of CD and patients of both sexes with a family history of CD have a different pattern of seasonality of birth from the general population. This is suggestive of a perinatal virus infection as a plausible candidate for the primary trigger.

Seasonality of birth in children with central nervous system tumours in Denmark, 1970-2003

We investigated possible seasonal variation of births among children <20 years with a central nervous system tumour in Denmark (N=1640), comparing them with 2,582,714 children born between 1970 and 2003. No such variation was seen overall, but ependymoma showed seasonal variation.

Simple estimators of the intensity of seasonal occurrence

Background

Edwards's method is a widely used approach for fitting a sine curve to a time-series of monthly frequencies. From this fitted curve, estimates of the seasonal intensity of occurrence (i.e., peak-to-low ratio of the fitted curve) can be generated.

Methods

We discuss various approaches to the estimation of seasonal intensity assuming Edwards's periodic model, including maximum likelihood estimation (MLE), least squares, weighted least squares, and a new closed-form estimator based on a second-order moment statistic and non-transformed data. Through an extensive Monte Carlo simulation study, we compare the finite sample performance characteristics of the estimators discussed in this paper. Finally, all estimators and confidence interval procedures discussed are compared in a re-analysis of data on the seasonality of monocytic leukemia.

Results

We find that Edwards's estimator is substantially biased, particularly for small numbers of events and very large or small amounts of seasonality. For the common setting of rare events and moderate seasonality, the new estimator proposed in this paper yields less finite sample bias and better mean squared error than either the MLE or weighted least squares. For large studies and strong seasonality, MLE or weighted least squares appears to be the optimal analytic method among those considered.

Conclusion

Edwards's estimator of the seasonal relative risk can exhibit substantial finite sample bias. The alternative estimators considered in this paper should be preferred.

Seasonality of month of birth differs between type 1 diabetes patients with pronounced beta-cell autoimmunity and individuals with lesser or no beta-cell autoimmunity

OBJECTIVE

To establish whether children with type 1 diabetes mellitus (T1D) with signs of pronounced beta-cell-specific autoimmunity as reflected by high autoantibody titers or positivity for several beta-cell-specific autoantibodies show a different pattern of month of birth (MOB) compared with children with T1D and low beta-cell autoimmunity and that of the general population.

RESEARCH DESIGN AND METHODS

Cosinor analysis was used to analyze MOB rhythmicity in Swedish children with new onset T1D (n = 572), in whom the glutamate decarboxylase autoantibody (GAD65Ab) titer was determined and compared with that in 833 healthy children, and in 505 children with T1D in Berlin, in whom the titers of autoantibodies to insulin, GAD65, and islet antigen-2 were compared with the MOB pattern in the general population (n = 446 571).

RESULTS

In both cohorts of children with T1D, we found that children with either a high GAD65Ab titer (above the 80th percentile) or positivity for three beta-cell-specific autoantibodies differed in their pattern of MOB from the healthy population.

CONCLUSIONS

Our past and present observations support the hypothesis that the autoimmune process leading to childhood T1D is in part triggered in the perinatal period by viral infections in genetically susceptible individuals. The present study suggests that the process is linked to titer levels of autoantibodies.

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

This paper describes an approach to summarize the data arising from studies investigating the pattern of disease onset within a calendar year. Such data have been traditionally summarized into monthly counts summated over the complete years studied and patterns often examined by use of Pearson's chi(2) tests with 11 degrees of freedom. This test and others commonly used in practice are reviewed. As an alternative, we suggest that by first representing the date of onset for an individual as a point on a unit circle that the von Mises distribution with a single peak may provide a useful description of such data. Further an extension to angular regression including covariates, analogous to that used routinely in other areas of clinical research, potentially allows a more systematic and detailed investigation of possible seasonal patterns in patient subgroups. The methodology is applied to examples from the date of onset of primary angle-closure glaucoma and date of diagnosis of acute lymphoblastic leukaemia and examines in both situations how the peak onset varies with covariates. Difficulties associated with convergence to the maximum likelihood estimates of the associated parameters are described. Finally, we emphasize the need for individualized (rather than grouped) patient data to be available for study, a clear specification of the particular 'onset' time studied, and suggest that further case studies are required to evaluate the approach.

Diamond Blackfan anaemia in the UK: clinical and genetic heterogeneity

A detailed family study was undertaken of patients notified to the UK Diamond Blackfan Anaemia (DBA) Registry. RPS19 mutations were detected in 16 of 104 families, including two patients with deletions detected by intragenic loss of heterozygosity of tightly linked polymorphisms. In two further cases, polymorphisms were used to determine the parental allele of origin of RPS19 point mutations. A review of clinical details of patients with mutations and patients in the literature having identical or equivalent mutations revealed evidence for a genotype:phenotype correlation with respect to the prevalence of physical anomalies, and the occurrence of mild or variable haematological severity. Nine of 60 patients had a known family history of DBA. Haematological abnormalities, including raised red cell adenosine deaminase activity, were found in first-degree relatives of 16 of 51 (31%) of patients not previously considered to have familial DBA. Results of both parents and any siblings were normal in only 35 of 60 (58%) of cases, who were therefore assumed to have sporadic de novo DBA. The classical inheritance pattern for DBA is autosomal dominant; however, 12 of 60 families (20%) had more than one affected child despite normal results in both parents. These results have important implications for genetic counselling, and for the selection of potential sibling bone marrow donors.

Use of statistical techniques in studies of suicide seasonality, 1970 to 1997

The effect of seasons on suicides has been suggested repeatedly. In order to reveal a true seasonal pattern, an appropriate statistical technique, which is sensitive to a specific type of cyclic variation in the data, must be chosen. This study is a review of the use of statistical techniques for seasonality and of some important characteristics of study samples that were evaluated from 46 original suicide seasonality articles published in major psychiatric journals. The results showed that statistical techniques were applied in a majority of articles, but they were commonly lacking regarding analyses, which compared seasonal patterns among subgroups of a population. In recent studies more sophisticated statistical techniques were utilized for seasonality, like spectral analyses, as compared with earlier studies, in which the emphasis was on chi-square tests. Lack of reporting essential features of the data, such as the sample size and monthly values of suicides, were frequent. The calendar effect was adjusted only in 11 studies. Some recommendations concerning the methodological and reporting issues are summarized for future articles on the seasonal affect on suicides.

Cryptorchidism: seasonal variations in Greece do not support the theory of light

To examine seasonal trends of cryptorchidism in Greece, 583 males with true isolated cryptorchidism were analyzed. All 208 912 live-born boys born during the same period were used as a comparison group. Seasonality by month of birth was evaluated using both Edwards' model with adjusted frequencies and exact theta(i), and Walter-Elwood method with exact theta(i). Both tests resulted in consistent findings. The incidence of cryptorchid births in Greece follows a documented cyclic pattern of simple harmonic type with spring being the season of statistical predominance (peak in March with a second, almost equivalent, peak in May). In contrast, in autumn the incidence of cryptorchid births was considerably lower (trough in September). Given the fact that no significant differences in daylight length are found among seasons in Greece, the detection of a significant seasonal variation suggests that factors other than light are involved in the pathogenesis of cryptorchidism. Low environmental temperature is proposed as a causative factor negatively influencing the maternal hCG profiles and the inguinoscrotal phase of testicular descent. This is further supported by: (i) the similarity of our results to those reported by other European countries of different longitude and geographical width and (ii) our data showing significantly smaller maternal hCG profiles at the 26th week of gestation during winter compared with summer.

Seasonality of birth for cancer in Northern England, UK

Environmental factors operating around the time of birth may influence the subsequent development of childhood cancer, particularly leukaemia. Certain factors may vary with season (e.g. infections), and we therefore investigated whether there was any evidence of seasonality of month of birth, based on data from 4199 children diagnosed with cancer under the age of 15 years. We extracted details of (i) children born 1960-95 and diagnosed 1968-95 from two population-based registries, covering the Northern (n = 2053) and Yorkshire (n = 1977) Regional Health Authority and (ii) children born in Cumbria 1950-93 and diagnosed anywhere in the UK before 1994 from a birth cohort database (n = 397). The following diagnostic categories were analysed: 0-14 years--all cancers, leukaemias, acute lymphoblastic leukaemias, central nervous system tumours, all other solid tumours; 1-6 years--leukaemias, acute lymphoblastic leukaemias. Seasonal variation was tested using Walter and Elwood's test, and logistic regression analysis allowing for cyclical variation in month of birth. No evidence of seasonality was present for any group except acute lymphoblastic leukaemia diagnosed among 1- to 6-year-olds. Seasonal trends varied by region: in the Northern and Cumbrian datasets, seasonality patterns were significant and similar (P < 0.05) with a predicted peak in early spring, whereas in Yorkshire there was less strong evidence of seasonality (P = 0.08) with a peak predicted in late summer. These findings suggest that local seasonal environmental factors operating around the time of birth are not associated with the totality of childhood cancer, but possible links with acute lymphoblastic leukaemia are supportive of a hypothesis of an infectious aetiology.

Spectral analysis of clinical signals: an interface between medical statisticians and medical engineers

This paper reviews the current use of spectral analysis in clinical medicine. We cover the problems of aliasing and estimation of the spectrum using windowing and autoregressive techniques. These techniques are modified for nonstationary data to include evolutionary spectral analysis and recursive autoregressive methods. The relationship between evolutionary spectral analysis and the time-frequency methods such as the Wigner-Ville distribution is discussed. Other techniques covered are Walsh Transforms and cosinor analysis. The methods are shown to apply in the analysis of signals from heart rate, blood pressure, EEG, other electrical signals and hormone levels. The engineering and statistical approaches are contrasted.

Season of birth: issues, approaches and findings for autism

Rates of birth in the general population show seasonal fluctuations for reasons that are ill understood. Variations from these general population patterns have been reported for several psychiatric conditions and used as the basis for aetiological hypotheses. In this paper, the evidence for alterations in the expected seasonal fluctuation in birth dates of autistic people is evaluated. A national sample of 1435 autistic individuals and a clinic sample of 196 subjects are compared to general population figures and to 121 sibling controls. Compared with the general population, the national sample showed significant deviations from the expected rate of birth by month. In the clinic sample, differences from the anticipated monthly pattern were only evident when this sample was compared to the sibling controls. A variety of models for seasonal trends, including year quarters, temperature and sine wave forms, were fitted to these variations but no consistent picture emerged.

The choice of a statistic for testing hypotheses regarding seasonality

This paper discusses statistical methods for testing hypotheses of seasonality in births across one year, using monthly frequencies. It argues that the Freedman test, a variant of the Kolmogorov-Smirnov one-sample test, and the Edwards test and its modifications are most appropriate for this purpose. These tests take into account the order of the monthly frequencies and have a higher power than the ordinary chi-square goodness-of-fit test, regarding seasonality. The paper addresses some points mentioned in earlier papers by McCullough, and O'Brien and Holbert.

Seasonal prevalence of major congenital malformations in the Fylde of Lancashire 1957-1981

The seasonal prevalence of major congenital malformations was studied in a prospective survey of 88,449 children born in the circumscribed Fylde of Lancashire to residents there over 25 years. Ascertainment was thought to be as complete as was practically possible because cases were recorded daily by one, and for 17 years the only, paediatrician and a very high rate of necropsies was maintained. The number of malformations were classified by month of maternal last menstrual period and seasonal variation was assessed by three statistical models. Neural tube defects showed a significant seasonal variation in month of last menstrual period but not in month of birth. From May 1956 to April 1968, when the prevalence of neural tube defects was high (5.5 per 1000 total births), conceptions were significantly more common in December to May. For anencephaly alone the figures were not significant, but spina bifida and cranium bifidum were more common in March to May. From May 1968 to April 1981, when the prevalence of neural tube defects fell below the national average, the significant variations disappeared. Seasonality for spina bifida and cranium bifidum was seen only in "singles" (cases with no other major lesion), but for anencephaly it was seen only in "multiples" (cases with other lesions). The three types of cardiac septal defect and persistent ductus each showed a higher prevalence of conceptions at some time during May to October. In contrast the commonest group of cyanotic cases showed no such pattern but with greater numbers in winter. There was evidence of a seasonal variation for bilateral renal agenesis and for vesicoureteric reflux as ascertained. Seasonal prevalence in an aetiological factor for certain malformations of the central nervous system, cardiac and urinary systems.

Incidence and differences in urban-rural seasonal variation of type 1 (insulin-dependent) diabetes in Wisconsin

In a hospital-based records study of Type 1 (insulin-dependent) diabetes mellitus among persons aged 0 to 29 years in two Wisconsin, USA counties (1970-79), the age-adjusted yearly incidence rate for white males (16.4/100,000) was significantly higher than for white females (11.6/100,000) (p = 0.006). Overall age-adjusted rates are similar to rates previously reported for the United States and the northern European countries of Denmark and Norway. Seasonal variation in diagnosis was found for total cases and males aged 10 to 19 years. A striking difference also was found in seasonal diagnosis between urban and rural cases. A diagnosis peak in the third and fourth quarter among rural cases contrasted with even quarterly distribution among urban cases. In addition, 52% of rural male cases aged 10 to 19 years were diagnosed during the fourth quarter while no seasonal pattern occurred among urban males the same ages. These findings identify subgroups for focus of future etiologic investigations.

Seasonality of thyrotoxicosis

Study of a large and representative series of thyrotoxic patients showed a higher frequency of diagnosis in the spring and summer. The median interval between onset and diagnosis was 12 weeks, indicating a peak in onset of the disease from January to June. The seasonality of thyrotoxicosis may be related to seasonal variations in iodine intake.

Exact significance levels for Hewitt's test for seasonality

Hewitt proposed an easily computed test for seasonality in ranked monthly data. This paper provides a tabulation of the exact distribution of the test statistic, which previously could be estimated only from simulated data. The use of this test when ties may occur in the data is also discussed.

The use of a Kolmogorov--Smirnov type statistic in testing hypotheses about seasonal variation

This paper presents a non-parametric method for testing departures from a uniform seasonal variation in incidence of disease. The method may be used either with exact dates of incidence when they are available or with monthly totals. It is equally valid for sinusoidal and non-sinusoidal departures from uniformity. A simulation study shows it to be much more powerful than other non-parametric alternatives and nearly as powerful as Edwards's test in detecting sinusoidal departures.