Osvaldo Marrero

L'analyse de la variation saisonniére quand l'amplitude et la taille sont faibles

Studies of seasonal variation are valuable in biomedical research because they can help to discover the etiology of diseases that are not well understood. Generally in these studies the data have certain characteristics that require specialized tests and methods for the statistical analysis. But the effectiveness of these specialized tests is variable, especially according to the seasonal variation, the dimension of the amplitude in the seasonal variation, and the sample size. The purpose of this paper is to present a test and methods appropriate for the analysis and modeling of data whose seasonal variation has small amplitude and whose sample size is small. This test can detect different kinds of seasonal variation. The results from a simulation study show that the test performs very well. The application of these methods is illustrated by two examples.

Multigroup analysis of seasonal variation : Assessing the homogeneity of multiple cyclically ordered multinomial distributions

A procedure is presented for the analysis of seasonal variation in multiple groups. The proposed method includes two tests. One is a multigroup test for seasonality that is capable of detecting simultaneously different seasonal variations in different groups. The other is a test for homogeneity of multiple multinomial distributions with cyclically ordered categories. These tests are obtained by a geometric approach that helps both to understand the statistical analyses and to communicate the results. Mathematical expressions are given to facilitate the data analysis, and two examples are presented.

Seasonal and Geographic Variation in Adverse Event Reporting

BackgroundMany illnesses demonstrate seasonal and geographic variations. Pharmacovigilance is unique among public health surveillance systems in terms of the clinical diversity of the events under surveillance. Since many pharmacovigilance signal detection methodologies are geared towards looking for increased frequency of spontaneous adverse drug event (ADE) reporting over variable time frames, seasonality of ADEs may have implications for signal detection.ObjectiveThe aim of this study was to investigate whether a set of illnesses that might be expected to display seasonality in general, did so when spontaneously reported as ADEs.MethodsWe performed our analysis with the publically available US FDA Adverse Event Reporting System (FAERS) data. We selected a convenience sample of events possibly triggered by seasonal factors (hypothermia, Raynaud’s phenomenon, photosensitivity reaction, heat exhaustion, heat stroke, and sunburn) and events for which previous literature experience suggests seasonality (anencephaly and interstitial lung disease). Our statistical procedures can be explained in terms of a simple physicogeometric setting: the unit circle divided into 6 (semiannual sinusoidal) or 12 (annual sinusoidal) arcs. When reporting frequencies (weights) are more or less evenly distributed across months, the center of mass of the circle would not be significantly displaced from the origin (0, 0). Distinct seasonal patterns will significantly displace the center of mass of the circle.ResultsVarious patterns of seasonality were identified for some, but not all, events and region–event pairs. USA displayed the most instances of seasonality. Scandinavia did not display seasonality for any events. Seasonality was usually annual sinusoidal. Possible explanations for failure to observe seasonality are briefly considered.ConclusionsUnderstanding seasonality of spontaneous ADE reporting may have public health policy and research implications and may mitigate false-positive and missed true-positive pharmacovigilance signals. More systematic study of seasonality of spontaneous ADE reporting, including additional events with more or less biological rationale for seasonality, is a logical extension of this analysis.

Seasonal Variation in Epidemiology.

Summary Seasonality analyses are important in medical research. If the incidence of a disease shows a seasonal pattern, then an environmental factor must be considered in its etiology. We discuss a method for the simultaneous analysis of seasonal variation in multiple groups. The nuts and bolts are explained using simple trigonometry, an elementary physical model, and several graphics. Two examples show how the method is applied.

A Surprising MLE for Interval-Censored Binomial Data

We derive the maximum likelihood estimator of the binomial success probability when the number of trials is known, but the number of successes is only known to fall in some interval. This estimator has a surprisingly simple form. Specifically, the maximum likelihood estimate of the log odds of success is the mean of the maximum likelihood estimates of the log odds of success that are obtained by letting the number of successes take on each integer value in the interval. An application is suggested.

A test statistic whose derivation is simple and unusual

Teaching students how to derive test statistics is an important part of an introductory course in mathematical statistics. Typically the course material includes both the development and the performance of likelihood-ratio tests. Thus, students learn the theoretical foundation for many of the standard tests. But students should also have the opportunity early on to see that sometimes a problem can lend itself well to the development of a specialized test statistic, tailor-made to a particular situation. One such development is given in this paper. Easy to visualize and understand, the derivation of the test statistic is based on simple geometrical and physical ideas. An example is given. Well received by students, this material is useful in mathematical-statistics courses.

Sequences of Chords and of Parabolic Segments Enclosing Proportional Areas

The graph of y = x and a line tangent to it enclose an area. In [1] it is shown that the areas determined by successive such tangent lines are proportional to one another. In the left-hand side of the figure, the first tangent line encloses the region shaded in black, and the second tangent line encloses the gray region which has 16 times as much area. This motivated our consideration of similar problems for the family of parabolas y = cx. For a parabola, tangent lines enclose no such areas; thus, it was natural for us to consider instead areas determined by secant lines, and that’s what we did. Specifically, we considered a parabola, and, beginning at the origin, we found a sequence of points {pn} on it such that the areas enclosed by the parabola and by the chords joining successive pairs of points in the sequence were proportional. The right-hand side of the figure shows the first two chords when the proportionality constant is 1. In this case, the point p2 is chosen so that the area of the gray region is equal to the area of the black region. We then examined the lengths of these chords and the lengths of the parabolic segments joining consecutive points, as well as the ratios of such lengths. It was the limit of some of these ratios as n → ∞ that we found to be surprising.

The Right-Hand Derivative of an Integral

In this note, we provide a general result that explains the examples contained in [1], [3], [4], and [5]. We also observe with interest that this problem seems to have been proposed anew at nearly regular intervals of ten to fifteen years. The article [2] also contains a discussion of this problem. Using the notation in [3], suppose that f is a real-valued function defined on the interval [0, 1] such that (a) f is bounded on [0, 1], (b) f is continuous on (0, 1], and (c) lim,,o+ f (x) does not exist. Then let F(x) = fJx f (t) dt for x in [0, 1]. The question is whether or not the right-hand derivative

Row Coincidences in Nonsingular Binary Matrices

We present best possible bounds for the number of coincidences of ones between two distinct rows of a nonsingular binary matrix of constant row sum. The lower bound is shown best possible by examples. We construct two classes of matrices that show the upper bound is best possible.ResumeNous etudions le nombre de coi#x0308;ncidences des chiffres uns dans chaque paire de lignes differentes d?une matrice binaire et inversible dont toutes les lignes contiennent la meme quantite d?unites. Nous presentons des bornes pour ce nombre, et nous demontrons que ces bornes peuvent etre atteintes. Que la borne inferieure peut etre realisee est demontre par moyen des exemples. Quant a la borne superieure, nous presentons la construction de deux familles de matrices pour lesquelles cette borne est atteinte.

Affine Transformations, Polynomials, and Proportionality

In the articles [1] and [3], standard tools and techniques of calculus are used to establish a variety of proportionality results concerning areas defined by the lines tangent to a cubic curve, and by the lengths of certain arcs of a parabola, where the arcs themselves are determined by an area-proportionality criterion. We demonstrate here that these results can be viewed as consequences of some basic facts about affine transformations in the plane.