Confidence Corridors Research Articles

A Confidence Corridor for Sparse Longitudinal Data Curves

Longitudinal data analysis is a central piece of statistics. The data are curves and they are observed at random locations. This makes the construction of a simultaneous confidence corridor (SCC) (confidence band) for the mean function a challenging task on both the theoretical and the practical side. Here we propose a method based on local linear smoothing that is implemented in the sparse (i.e., low number of nonzero coefficients) modelling situation. An SCC is constructed based on recent results obtained in applied probability theory. The precision and performance is demonstrated in a spectrum of simulations and applied to growth curve data. Technically speaking, our paper intensively uses recent insights into extreme value theory that are also employed to construct a shoal of confidence intervals (SCI).

Stochastic modelling for determining zooplankton abundance

The most reliable method for studying the dynamic behaviour of a population of organisms in a marine pelagic environment is to analyse the biomass or the abundance spectra. The spectra presented in semi logarithmic scale features the measurement variability as a reversed cone embodying the recorded abundances. This distribution in data variability motivated us to propose the existence of a process uncertainty. To analyse abundance spectra in stochastic context, we propose a compartmental configuration in which, at a given time, marine organisms are located according to their size in the compartments of a compartmental chain. The movement of organisms across compartments is described in probabilistic terms expressing transfer probabilities. The model considered at steady state allows the expression of the process uncertainty and the construction of the confidence corridors embodying the abundance spectra data. The developed model may be used for comparison of several collections of data, for analysis of environmental factors influencing the marine populations, or for new developments involving longitudinal data.

Seasonality of births and childhood inflammatory bowel disease

In some geographical areas, including Slovakia, children with diabetes mellitus type 1 are born more often in summer than in late autumn and winter. Does this also apply to another autoimmune disorder - inflammatory bowel disease - in Slovakia? The month of birth was recorded for 30 boys and 36 girls with Crohn disease and 23 boys and 40 girls with ulcerative colitis. The monthly numbers of births were adapted to the length of the given month, divided by the number of boys or girls born in the whole Slovak children population in the same calendar month in comparable years, transformed to moving averages from three successive values each, and expressed as the fraction of the yearly total, which was equal to 1. According to the null hypothesis, there should be equal probability (1/12) of being born in any month. The significance of departures from this value was evaluated with cosinor regression using two sinusoidal functions with period lengths of 12 and 6 months. The most illustrative measure is the relation of the corridor of 95% confidence for the total approximating function to the midline estimating statistic of rhythm (the mesor) (1/12). Significant departures up or down are recognized as nonoverlapping of the mesor straight line by the confidence corridor. These were similar to those reported for childhood diabetes mellitus type 1. In our sample of Crohn disease, the number of births was markedly higher between June and October and lower between December and March. In ulcerative colitis, there was a slight increase between June and August and a decrease between December and February. The seasonal effect on births of children with later childhood-onset Crohn disease is similar to that described for diabetes mellitus type 1, i.e., maximal frequency of births in summer.