Semiparametric Methods for Semi-competing Risks Problem with Censoring and Truncation

Studies of chronic life-threatening diseases often involve both mortality and morbidity. In observational studies, the data may also be subject to administrative left truncation and right censoring. Since mortality and morbidity may be correlated and mortality may censor morbidity, the Lynden-Bell estimator for left truncated and right censored data may be biased for estimating the marginal survival function of the non-terminal event. We propose a semiparametric estimator for this survival function based on a joint model for the two time-to-event variables, which utilizes the gamma frailty specification in the region of the observable data. Firstly, we develop a novel estimator for the gamma frailty parameter under left truncation. Using this estimator, we then derive a closed form estimator for the marginal distribution of the non-terminal event. The large sample properties of the estimators are established via asymptotic theory. The methodology performs well with moderate sample sizes, both in simulations and in an analysis of data from a diabetes registry.

Kernel Estimation of Rate Function for Recurrent Event Data

Recurrent event data are largely characterized by the rate function but smoothing techniques for estimating the rate function have never been rigorously developed or studied in statistical literature. This paper considers the moment and least squares methods for estimating the rate function from recurrent event data. With an independent censoring assumption on the recurrent event process, we study statistical properties of the proposed estimators and propose bootstrap procedures for the bandwidth selection and for the approximation of confidence intervals in the estimation of the occurrence rate function. It is identified that the moment method without resmoothing via a smaller bandwidth will produce curve with nicks occurring at the censoring times, whereas there is no such problem with the least squares method. Furthermore, the asymptotic variance of the least squares estimator is shown to be smaller under regularity conditions. However, in the implementation of the bootstrap procedures, the moment method is computationally more efficient than the least squares method because the former approach uses condensed bootstrap data. The performance of the proposed procedures is studied through Monte Carlo simulations and an epidemiological example on intravenous drug users.

[Herd problem: udder health. Retrospective study of farms assessed by the Swiss Bovine Health Service (BHS) from 1999 to 2004]

Data from 59 farms with complaints of udder health problems and insufficient quality of delivered milk that had been assessed by the Swiss Bovine Health Service (BHS) between 1999 and 2004 were retrospectively analysed. Data evaluated included farm characteristics such as farm size, herd size, average milk yield, milking system and housing system, deficits of the milking equipment and the milking practices, and bacteriological results of milk samples from all cows in lactation. The average size of the farms assessed by the BHS was larger than the size of the were evaluated, 42 showed obvious failures which the farm managers could have noticed. Only 5 of the 57 milkers carried out their work according to the generally valid guidelines of the National Mastitis Council. More than 2 basic mistakes were observed in the milking practices of 36 milkers. In 51 farms, mixed infections with several problem bacteria (those present in at least 20 % of the tested cows on a farm) were found. Staphylococcus aureus proved to be the most common problem germ. As the bacteria responsible for the herd problem (the sole problem bacteria detectable on a particular farm) Staphylococcus aureus was detected in 4 farms. The current study revealed that education in the area of milking techniques and milking practices of farmers should be improved in order to reduce the incidence of udder health problems on herd level. Staphylococcus aureus is the most important problem bacteria involved in herds with udder health problems in Switzerland. Staphylococcus aureus might be used in practice as the indicator germ for early recognition of management problems in dairy farms.

Virtopsy - the concept of a centralized database in forensic medicine for analysis and comparison of radiological and autopsy data

Recent developments in clinical radiology have resulted in additional developments in the field of forensic radiology. After implementation of cross-sectional radiology and optical surface documentation in forensic medicine, difficulties in the validation and analysis of the acquired data was experienced. To address this problem and for the comparison of autopsy and radiological data a centralized database with internet technology for forensic cases was created. The main goals of the database are (1) creation of a digital and standardized documentation tool for forensic-radiological and pathological findings; (2) establishing a basis for validation of forensic cross-sectional radiology as a non-invasive examination method in forensic medicine that means comparing and evaluating the radiological and autopsy data and analyzing the accuracy of such data; and (3) providing a conduit for continuing research and education in forensic medicine. Considering the infrequent availability of CT or MRI for forensic institutions and the heterogeneous nature of case material in forensic medicine an evaluation of benefits and limitations of cross-sectional imaging concerning certain forensic features by a single institution may be of limited value. A centralized database permitting international forensic and cross disciplinary collaborations may provide important support for forensic-radiological casework and research.

Accurate and robust reconstruction of proximal femur from sparse intraoperative data and dense point distribution model for surgical navigation

Constructing a 3D surface model from sparse-point data is a nontrivial task. Here, we report an accurate and robust approach for reconstructing a surface model of the proximal femur from sparse-point data and a dense-point distribution model (DPDM). The problem is formulated as a three-stage optimal estimation process. The first stage, affine registration, is to iteratively estimate a scale and a rigid transformation between the mean surface model of the DPDM and the sparse input points. The estimation results of the first stage are used to establish point correspondences for the second stage, statistical instantiation, which stably instantiates a surface model from the DPDM using a statistical approach. This surface model is then fed to the third stage, kernel-based deformation, which further refines the surface model. Handling outliers is achieved by consistently employing the least trimmed squares (LTS) approach with a roughly estimated outlier rate in all three stages. If an optimal value of the outlier rate is preferred, we propose a hypothesis testing procedure to automatically estimate it. We present here our validations using four experiments, which include 1 leave-one-out experiment, 2 experiment on evaluating the present approach for handling pathology, 3 experiment on evaluating the present approach for handling outliers, and 4 experiment on reconstructing surface models of seven dry cadaver femurs using clinically relevant data without noise and with noise added. Our validation results demonstrate the robust performance of the present approach in handling outliers, pathology, and noise. An average 95-percentile error of 1.7-2.3 mm was found when the present approach was used to reconstruct surface models of the cadaver femurs from sparse-point data with noise added.

The exchange of radiotherapy data as part of an electronic patient-referral system

PURPOSE: To describe the implementation and use of an electronic patient-referral system as an aid to the efficient referral of patients to a remote and specialized treatment center. METHODS AND MATERIALS: A system for the exchange of radiotherapy data between different commercial planning systems and a specially developed planning system for proton therapy has been developed through the use of the PAPYRUS diagnostic image standard as an intermediate format. To ensure the cooperation of the different TPS manufacturers, the number of data sets defined for transfer has been restricted to the three core data sets of CT, VOIs, and three-dimensional dose distributions. As a complement to the exchange of data, network-wide application-sharing (video-conferencing) technologies have been adopted to provide methods for the interactive discussion and assessment of treatments plans with one or more partner clinics. RESULTS: Through the use of evaluation plans based on the exchanged data, referring clinics can accurately assess the advantages offered by proton therapy on a patient-by-patient basis, while the practicality or otherwise of the proposed treatments can simultaneously be assessed by the proton therapy center. Such a system, along with the interactive capabilities provided by video-conferencing methods, has been found to be an efficient solution to the problem of patient assessment and selection at a specialized treatment center, and is a necessary first step toward the full electronic integration of such centers with their remotely situated referral centers.

Simulating dioxane transport in a heterogeneous glacial aquifer system (Washtenaw County, Michigan) using publicly available models and data

The primary challenge in groundwater and contaminant transport modeling is obtaining the data needed for constructing, calibrating and testing the models. Large amounts of data are necessary for describing the hydrostratigraphy in areas with complex geology. Increasingly states are making spatial data available that can be used for input to groundwater flow models. The appropriateness of this data for large-scale flow systems has not been tested. This study focuses on modeling a plume of 1,4-dioxane in a heterogeneous aquifer system in Scio Township, Washtenaw County, Michigan. The analysis consisted of: (1) characterization of hydrogeology of the area and construction of a conceptual model based on publicly available spatial data, (2) development and calibration of a regional flow model for the site, (3) conversion of the regional model to a more highly resolved local model, (4) simulation of the dioxane plume, and (5) evaluation of the model's ability to simulate field data and estimation of the possible dioxane sources and subsequent migration until maximum concentrations are at or below the Michigan Department of Environmental Quality's residential cleanup standard for groundwater (85 ppb). MODFLOW-2000 and MT3D programs were utilized to simulate the groundwater flow and the development and movement of the 1, 4-dioxane plume, respectively. MODFLOW simulates transient groundwater flow in a quasi-3-dimensional sense, subject to a variety of boundary conditions that can simulate recharge, pumping, and surface-/groundwater interactions. MT3D simulates solute advection with groundwater flow (using the flow solution from MODFLOW), dispersion, source/sink mixing, and chemical reaction of contaminants. This modeling approach was successful at simulating the groundwater flows by calibrating recharge and hydraulic conductivities. The plume transport was adequately simulated using literature dispersivity and sorption coefficients, although the plume geometries were not well constrained.

Hermitian curve interpolation for CT-data re-sampling

Purpose: Development of an interpolation algorithm for re‐sampling spatially distributed CT‐data with the following features: global and local integral conservation, avoidance of negative interpolation values for positively defined datasets and the ability to control re‐sampling artifacts. Method and Materials: The interpolation can be separated into two steps: first, the discrete CT‐data has to be continuously distributed by an analytic function considering the boundary conditions. Generally, this function is determined by piecewise interpolation. Instead of using linear or high order polynomialinterpolations, which do not fulfill all the above mentioned features, a special form of Hermitian curve interpolation is used to solve the interpolation problem with respect to the required boundary conditions. A single parameter is determined, by which the behavior of the interpolation function is controlled. Second, the interpolated data have to be re‐distributed with respect to the requested grid. Results: The new algorithm was compared with commonly used interpolation functions based on linear and second order polynomial. It is demonstrated that these interpolation functions may over‐ or underestimate the source data by about 10%–20% while the parameter of the new algorithm can be adjusted in order to significantly reduce these interpolation errors. Finally, the performance and accuracy of the algorithm was tested by re‐gridding a series of X‐ray CT‐images. Conclusion: Inaccurate sampling values may occur due to the lack of integral conservation. Re‐sampling algorithms using high order polynomialinterpolation functions may result in significant artifacts of the re‐sampled data. Such artifacts can be avoided by using the new algorithm based on Hermitian curve interpolation

Movement control of manipulative tasks in patients with Gilles de la Tourette syndrome

When a hand-held object is moved, grip and load force are accurately coordinated for establishing grasp stability. In the present work, the question was raised whether patients with Gilles de la Tourette syndrome (TS), who show tic-like movements, are impaired in grip-load force control when executing a manipulative task. To this end, we assessed force regulation during action patterns that required rhythmical unimanual or bimanual (iso-directional/anti-directional) movements. Results showed that the profile of grip-load force ratio was characterized by maxima and minima that were realized at upward and downward hand positions, respectively. TS patients showed increased force ratios during unimanual and bimanual movements, compared with control subjects, indicative of an inaccurate specification of the precision grip. Functional imaging data complemented the behavioural results and revealed that secondary motor areas showed no (or greatly reduced) activation in TS patients when executing the movement tasks as compared with baseline conditions. This indicates that the metabolic level in the secondary motor areas was equal during rest and task performance. At the neuronal level, this observation suggests that these cortical areas were continuously involved in movement preparation. Based on these data, we conclude that the ongoing activation of secondary motor areas may be explained by the TS patients' involuntary urges to move. Accordingly, interference will prevent an accurate planning of voluntary behaviour. Together, these findings reveal modulations in movement organization in patients with TS and exemplify degrading consequences for manual function.

Data-driven estimates of the number of clusters in multivariate time series

An important problem in unsupervised data clustering is how to determine the number of clusters. Here we investigate how this can be achieved in an automated way by using interrelation matrices of multivariate time series. Two nonparametric and purely data driven algorithms are expounded and compared. The first exploits the eigenvalue spectra of surrogate data, while the second employs the eigenvector components of the interrelation matrix. Compared to the first algorithm, the second approach is computationally faster and not limited to linear interrelation measures.

A Surface Displacement Analysis for Volcan Pacaya from October 2001 through March 2013 by Means of 3-D Modeling of Precise Position GPS Data

Volcán Pacaya is one of three currently active volcanoes in Guatemala. Volcanic activity originates from the local tectonic subduction of the Cocos plate beneath the Caribbean plate along the Pacific Guatemalan coast. Pacaya is characterized by generally strombolian type activity with occasional larger vulcanian type eruptions approximately every ten years. One particularly large eruption occurred on May 27, 2010. Using GPS data collected for approximately 8 years before this eruption and data from an additional three years of collection afterwards, surface movement covering the period of the eruption can be measured and used as a tool to help understand activity at the volcano. Initial positions were obtained from raw data using the Automatic Precise Positioning Service provided by the NASA Jet Propulsion Laboratory. Forward modeling of observed 3-D displacements for three time periods (before, covering and after the May 2010 eruption) revealed that a plausible source for deformation is related to a vertical dike or planar surface trending NNW-SSE through the cone. For three distinct time periods the best fitting models describe deformation of the volcano: 0.45 right lateral movement and 0.55 m tensile opening along the dike mentioned above from October 2001 through January 2009 (pre-eruption); 0.55 m left lateral slip along the dike mentioned above for the period from January 2009 and January 2011 (covering the eruption); -0.025 m dip slip along the dike for the period from January 2011 through March 2013 (post-eruption). In all bestfit models the dike is oriented with a 75° westward dip. These data have respective RMS misfit values of 5.49 cm, 12.38 cm and 6.90 cm for each modeled period. During the time period that includes the eruption the volcano most likely experienced a combination of slip and inflation below the edifice which created a large scar at the surface down the northern flank of the volcano. All models that a dipping dike may be experiencing a combination of inflation and oblique slip below the edifice which augments the possibility of a westward collapse in the future.

Past is Prologue: Montana’s Historic Women’s Movement Re-emerges in the Progressive 1970s -- Dorothy Bradley, Marilyn Wessel & Jane Jelinski “In the Crucible of Change”

One-hundred years ago, in 1914, male voters in Montana (MT) extended suffrage (voting rights) to women six years before the 19th Amendment to the US Constitution was ratified and provided that right to women in all states. The long struggle for women’s suffrage was energized in the progressive era and Jeanette Rankin of Missoula emerged as a leader of the campaign; in 1912 both major MT political party platforms supported women suffrage. In the 1914 election, 41,000 male voters supported woman suffrage while nearly 38,000 opposed it. MT was not only ahead of the curve on women suffrage, but just two years later in 1916 elected Jeanette Rankin as the first woman ever elected to the United States Congress. Rankin became a national leader for women's equality. In her commitment to equality, she opposed US entry into World War I, partially because she said she could not support men being made to go to war if women were not allowed to serve alongside them. During MT’s initial progressive era, women in MT not only pursued equality for themselves (the MT Legislature passed an equal pay act in 1919), but pursued other social improvements, such as temperance/prohibition. Well-known national women leaders such as Carrie Nation and others found a welcome in MT during the period. Women's role in the trade union movement was evidenced in MT by the creation of the Women's Protective Union in Butte, the first union in America dedicated solely to women workers. But Rankin’s defeat following her vote against World War I was used as a way for opponents to advocate a conservative, traditionalist perspective on women's rights in MT. Just as we then entered a period in MT where the “copper collar” was tightened around MT economically and politically by the Anaconda Company and its allies, we also found a different kind of conservative, traditionalist collar tightened around the necks of MT women. The recognition of women's role during World War II, represented by “Rosie the Riveter,” made it more difficult for that conservative, traditionalist approach to be forever maintained. In addition, women's role in MT agriculture – family farms and ranches -- spoke strongly to the concept of equality, as farm wives were clearly active partners in the agricultural enterprises. But rural MT was, by and large, the bastion of conservative values relative to the position of women in society. As the period of “In the Crucible of Change” began, the 1965 MT Legislature included only three women. In 1967 and 1969 only one woman legislator served. In 1971 the number went up to two, including one of our guests, Dorothy Bradley. It was only after the Constitutional Convention, which featured 19 women delegates, that the barrier was broken. The 1973 Legislature saw 9 women elected. The 1975 and 1977 sessions had 14 women legislators; 15 were elected for the 1979 session. At that time progressive women and men in the Legislature helped implement the equality provisions of the new MT Constitution, ratified the federal Equal Rights Amendment in 1974, and held back national and local conservatives forces which sought in later Legislatures to repeal that ratification. As with the national movement at the time, MT women sought and often succeeded in adopting legal mechanisms that protected women’s equality, while full equality in the external world remained (and remains) a treasured objective. The story of the re-emergence of Montana’s women’s movement in the 1970s is discussed in this chapter by three very successful and prominent women who were directly involved in the effort: Dorothy Bradley, Marilyn Wessel, and Jane Jelinski. Their recollections of the political, sociological and cultural path Montana women pursued in the 1970s and the challenges and opposition they faced provide an insider’s perspective of the battle for equality for women under the Big Sky “In the Crucible of Change.” Dorothy Bradley grew up in Bozeman, Montana; received her Bachelor of Arts Phi Beta Kappa from Colorado College, Colorado Springs, in 1969 with a Distinction in Anthropology; and her Juris Doctor from American University in Washington, D.C., in 1983. In 1970, at the age of 22, following the first Earth Day and running on an environmental platform, Ms. Bradley won a seat in the 1971 Montana House of Representatives where she served as the youngest member and only woman. Bradley established a record of achievement on environmental & progressive legislation for four terms, before giving up the seat to run a strong second to Pat Williams for the Democratic nomination for an open seat in Montana’s Western Congressional District. After becoming an attorney and an expert on water law, she returned to the Legislature for 4 more terms in the mid-to-late 1980s. Serving a total of eight terms, Dorothy was known for her leadership on natural resources, tax reform, economic development, and other difficult issues during which time she gained recognition for her consensus-building approach. Campaigning by riding her horse across the state, Dorothy was the Democratic nominee for Governor in 1992, losing the race by less than a percentage point. In 1993 she briefly taught at a small rural school next to the Northern Cheyenne Indian Reservation. She was then hired as the Director of the Montana University System Water Center, an education and research arm of Montana State University. From 2000 - 2008 she served as the first Gallatin County Court Administrator with the task of collaboratively redesigning the criminal justice system. She currently serves on One Montana’s Board, is a National Advisor for the American Prairie Foundation, and is on NorthWestern Energy’s Board of Directors. Dorothy was recognized with an Honorary Doctorate from her alma mater, Colorado College, was named Business Woman of the Year by the Bozeman Chamber of Commerce and MSU Alumni Association, and was Montana Business and Professional Women’s Montana Woman of Achievement. Marilyn Wessel was born in Iowa, lived and worked in Los Angeles, California, and Washington, D.C. before moving to Bozeman in 1972. She has an undergraduate degree in journalism from Iowa State University, graduate degree in public administration from Montana State University, certification from the Harvard University Institute for Education Management, and served a senior internship with the U.S. Congress, Montana delegation. In Montana Marilyn has served in a number of professional positions, including part-time editor for the Montana Cooperative Extension Service, News Director for KBMN Radio, Special Assistant to the President and Director of Communications at Montana State University, Director of University Relations at Montana State University and Dean and Director of the Museum of the Rockies at MSU. Marilyn retired from MSU as Dean Emeritus in 2003. Her past Board Service includes Montana State Merit System Council, Montana Ambassadors, Vigilante Theater Company, Montana State Commission on Practice, Museum of the Rockies, Helena Branch of the Ninth District Federal Reserve Bank, Burton K. Wheeler Center for Public Policy, Bozeman Chamber of Commerce, and Friends of KUSM Public Television. Marilyn’s past publications and productions include several articles on communications and public administration issues as well as research, script preparation and presentation of several radio documentaries and several public television programs. She is co-author of one book, 4-H An American Idea: A History of 4-H. Marilyn’s other past volunteer activities and organizations include Business and Professional Women, Women's Political Caucus, League of Women Voters, and numerous political campaigns. She is currently engaged professionally in museum-related consulting and part-time teaching at Montana State University as well as serving on the Editorial Board of the Bozeman Daily Chronicle and a member of Pilgrim Congregational Church and Family Promise. Marilyn and her husband Tom, a retired MSU professor, live in Bozeman. She enjoys time with her children and grandchildren, hiking, golf, Italian studies, cooking, gardening and travel. Jane Jelinski is a Wisconsin native, with a BA from Fontbonne College in St. Louis, MO who taught fifth and seventh grades prior to moving to Bozeman in 1973. A stay-at-home mom with a five year old daughter and an infant son, she was promptly recruited by the Gallatin Women’s Political Caucus to conduct a study of Sex-Role Stereotyping in K Through 6 Reading Text Books in the Bozeman School District. Sociologist Dr. Louise Hale designed the study and did the statistical analysis and Jane read all the texts, entered the data and wrote the report. It was widely disseminated across Montana and received attention of the press. Her next venture into community activism was to lead the successful effort to downzone her neighborhood which was under threat of encroaching business development. Today the neighborhood enjoys the protections of a Historic Preservation District. During this time she earned her MPA from Montana State University. Subsequently Jane founded the Gallatin Advocacy Program for Developmentally Disabled Adults in 1978 and served as its Executive Director until her appointment to the Gallatin County Commission in 1984, a controversial appointment which she chronicled in the Fall issue of the Gallatin History Museum Quarterly. Copies of the issue can be ordered through: http://gallatinhistorymuseum.org/the-museum-bookstore/shop/. Jane was re-elected three times as County Commissioner, serving fourteen years. She was active in the Montana Association of Counties (MACO) and was elected its President in 1994. She was also active in the National Association of Counties, serving on numerous policy committees. In 1998 Jane resigned from the County Commission 6 months before the end of her final term to accept the position of Assistant Director of MACO, from where she lobbied for counties, provided training and research for county officials, and published a monthly newsletter. In 2001 she became Director of the MSU Local Government Center where she continued to provide training and research for county and municipal officials across MT. There she initiated the Montana Mayors Academy in partnership with MMIA. She taught State and Local Government, Montana Politics and Public Administration in the MSU Political Science Department before retiring in 2008. Jane has been married to Jack for 46 years, has two grown children and three grandchildren.

Prevalence of halitosis in the population of the city of Bern, Switzerland: a study comparing self-reported and clinical data

Epidemiological data on halitosis are rare. In this study we evaluated the prevalence of halitosis in the population of the city of Bern, Switzerland, using a standardized questionnaire and clinical examination. First of all, a standardized questionnaire was filled out by all 419 participants. In the clinical examination, 'objective' values for halitosis were gathered through two different organoleptic assessments and by the measurement of volatile sulfur compounds (VSC). Additionally, tongue coating and the modified periodontal screening index (PSI) were evaluated for each participant. The questionnaire revealed that 32% of all subjects sometimes or often experienced halitosis. The organoleptic evaluation (grade 0-5) identified 48 persons with grade 3 and higher. Measurement of VSC identified 117 subjects (28%) with readings of >or= 75 parts per billion (ppb). Tongue coating, modified PSI, and smoking were significantly associated with higher organoleptic scores, and tongue coating and smoking were associated with higher VSC values. For about one-third of the Bernese city population, halitosis seems to pose an oral health problem. Only a weak correlation between self-reported halitosis and either organoleptic or VSC measurements could be detected.

Prevalence of halitosis in young male adults: a study in swiss army recruits comparing self-reported and clinical data

BACKGROUND: Sound epidemiologic data on halitosis are rare. We evaluated the prevalence of halitosis in a young male adult population in Switzerland using a standardized questionnaire and clinical examination. METHODS: Six hundred twenty-six Swiss Army recruits aged 18 to 25 years (mean: 20.3 years) were selected as study subjects. First, a standardized questionnaire focusing on dental hygiene, self-reported halitosis, smoking, and alcohol consumption was filled out by all participants. In the clinical examination, objective values for the presence of halitosis were gathered through an organoleptic assessment of the breath odor and the measurement of volatile sulfur compounds (VSCs). Additionally, tongue coating, plaque index, and probing depths were evaluated for each recruit. RESULTS: The questionnaire revealed that only 17% of all included recruits had never experienced halitosis. The organoleptic evaluation (grades 0 to 3) identified eight persons with grade 3, 148 persons with grade 2, and 424 persons with grade 1 or 0. The calculation of the Pearson correlation coefficient to evaluate the relationship among the three methods of assessing halitosis revealed little to no correlation. The organoleptic score showed high reproducibility (kappa = 0.79). Tongue coating was the only influencing factor found to contribute to higher organoleptic scores and higher VSC values. CONCLUSIONS: Oral malodor seemed to pose an oral health problem for about one-fifth of 20-year-old Swiss males questioned. No correlation between self-reported halitosis and organoleptic or VSC measurements could be detected. Although the organoleptic method described here offers a high reproducibility, the lack of correlation between VSC values and organoleptic scores has to be critically addressed. For further studies assessing new organoleptic scores, a validated index should always be included as a direct control.

Quantifying the periodicty of Inter Movement Intervals of Leg Movements

ims: Periodic leg movements in sleep (PLMS) are a frequent finding in polysomnography. Most patients with restless legs syndrome (RLS) display PLMS. However, since PLMS are also often recorded in healthy elderly subjects, the clinical significance of PLMS is still discussed controversially. Leg movements are seen concurrently with arousals in obstructive sleep apnoea (OSA) may also appear periodically. Quantitative assessment of the periodicity of LM/PLM as measured by inter movement intervals (IMI) is difficult. This is mainly due to influencing factors like sleep architecture and sleep stage, medication, inter and intra patient variability, the arbitrary amplitude and sequence criteria which tend to broaden the IMI distributions or make them even multi-modal. Methods: Here a statistical method is presented that enables eliminating such effects from the raw data before analysing the statistics of IMI. Rather than studying the absolute size of IMI (measured in seconds) we focus on the shape of their distribution (suitably normalized IMI). To this end we employ methods developed in Random Matrix Theory (RMT). Patients: The periodicity of leg movements (LM) of four patient groups (10 to 15 each) showing LM without PLMS (group 1), OSA without PLMS (group 2), PLMS and OSA (group 3) as well as PLMS without OSA (group 4) are compared. Results: The IMI of patients without PLMS (groups 1 and 2) and with PLMS (groups 3 and 4) are statistically different. In patients without PLMS the distribution of normalized IMI resembles closely the one of random events. In contrary IMI of PLMS patients show features of periodic systems (e.g. a pendulum) when studied in normalized manner. Conclusions: For quantifying PLMS periodicity proper normalization of the IMI is crucial. Without this procedure important features are hidden when grouping LM/PLM over whole nights or across patients. The clinical significance of PLMS might be eluded when properly separating random LM from LM that show features of periodic systems.