Error Of Second Kind Research Articles

Early prediction of bronchopulmonary dysplasia in extremely premature infants: a cohort study

Objective. To develop the model for early prediction of clinically significant bronchopulmonary dysplasia in extremely premature infants. Materials and methods. 226 premature infants with gestational age less than 31 weeks, birth weight from 490 to 999 g, age from 0 to 7 days, and respiratory failure requiring ventilatory support (ventilator support) were included into a retrospective study conducted in the Perm Regional Perinatal Center. Machine learning algorithms such as logistic regression, support vector machine, random forest method, and gradient boosting method were used for the prognostic model building. Five variables were used: birth weight, Apgar score in the 5th minute of life, Silverman score, number of days of invasive ventilatory support, median oxygen fraction in the inhaled air measured daily during the first seven days of life. Results. In the 36th week of postconceptional age 148 out of 182 infants (81.3%) in the study cohort developed bronchopulmonary dysplasia (BPD), among them 15.4% had a mild form, 29.7% a moderate one, and in 36.3% of patient it was severe. Among the four studied prediction algorithms, logistic regression model was chosen as the final model with metrics: AUC=0.840, accuracy 0.818, sensitivity 0.972, specificity 0.666. The practical application of the modeling results was implemented in the form of a probability calculator. Conclusions. In the early neonatal period of extremely premature infants, a combination of clinical predictors such as birth weight, Apgar score in the 5th minute of life, Silverman score, number of days of invasive ventilatory support, median oxygen fraction in the inhaled air measured during the first seven days of life can be used to predict the development of bronchopulmonary dysplasia. The logistic regression model shows high sensitivity that minimizes the probability of an error of second kind. Thus, its application is useful in the early prediction of bronchopulmonary dysplasia in premature infants.

Sharp minimax adaptation over Sobolev ellipsoids in nonparametric testing

We consider testing for presence of a signal in Gaussian white noise with intensity 1/sqrt(n), when the alternatives are given by smoothness ellipsoids with an L2-ball of (squared) radius rho removed. It is known that, for a fixed Sobolev type ellipsoid of smoothness beta and size M, a rho which is of order n to the power -4 beta/(4 beta+1)} is the critical separation rate, in the sense that the minimax error of second kind over alpha-tests stays asymptotically between 0 and 1 strictly (Ingster, 1982). In addition, Ermakov (1990) found the sharp asymptotics of the minimax error of second kind at the separation rate. For adaptation over both beta and M in that context, it is known that a loglog-penalty over the separation rate for rho is necessary for a nonzero asymptotic power. Here, following an example in nonparametric estimation related to the Pinsker constant, we investigate the adaptation problem over the ellipsoid size M only, for fixed smoothness degree beta. It is established that the sharp risk asymptotics can be replicated in that adaptive setting, if rho tends to zero slower than the separation rate. The penalty for adaptation here turns out to be a sequence tending to infinity arbitrarily slowly.

About One Method of On-Line Signature Verification Using Radial Basis Function

The article is devoted to the study of a possibility of on-line signature verification using the wavelet transform with the radial basis function. Representation of the signature in the form of function, invariant concerning a position, – the signature is replaced by a broken curve and is described using the angles between the adjacent links – is offered. Using the wavelet transforms for the signature description, comparison of expansion coefficients of functions of signatures by the radial basis function to verify signatures is described in detail. In the result of application of the offered method the magnitude of error of first kind has made 4.4%, the magnitude of error of second kind – 2.8%.

Sensitivity of dose-finding studies to observation errors

The purpose of Phase I designs is to estimate the MTD (maximum tolerated dose, in practice a dose with some given acceptable rate of toxicity) while, at the same time, minimizing the number of patients treated at doses too far removed from the MTD. Our purpose here is to investigate the sensitivity of conclusions from dose-finding designs to recording or observation errors. Certain toxicities may go undetected and, conversely, certain non-toxicities may be incorrectly recorded as dose-limiting toxicities. Recording inaccuracies would be expected to have an influence on final and within trial recommendations and, in this paper, we study in greater depth this question. We focus, in particular on three designs used currently; the standard ‘3 + 3’ design, the grouped up-and-down design [M. Gezmu, N. Flournoy, Group up-and-down designs for dose finding. Journal of Statistical Planning and Inference 2006; 136 (6): 1749–1764.] and the continual reassessment method (CRM, [J. O'Quigley, M. Pepe, L. Fisher, Continual reassessment method: a practical design for phase 1 clinical trials in cancer. Biometrics 1990; 46 (1): 33–48.]). A non-toxicity incorrectly recorded as a toxicity (error of first kind) has a greater influence in general than the converse (error of second kind). These results are illustrated via figures which suggest that the standard ‘3 + 3’ design in particular is sensitive to errors of the second kind. Such errors can have a very important impact on drug development in that, if carried through to the Phase 2 and Phase 3 studies, we can significantly increase the probability of failure to detect efficacy as a result of having delivered an inadequate dose.

Asymptotic Properties of Neyman-Pearson Tests for Infinite Kullback-Leibler Information

In the present paper we will improve the results concerning the rate of convergence of the error of second kind of the Neyman-Pearson test if the Kullback-Leibler information $K(P_0,P_1)$ is infinite. It is pointed out that in certain cases the sequence $exp(-q_\infty,n)$ is the correct rate of convergence if $-q_\infty,n$ denotes the logarithm of the critical value of the Neyman-Pearson test of level and sample size n. Therefore we generalize the classical results of Stein, Chernoff, and Rao which deal with the error probability of second kind and state that $q_\infty,n\tilde nK(P_0,P_1)$ if the Kullback-Leibler information is finite. Moreover the relation between $q_\infty,n$ and the local behavior of the Laplace transform of the log-likelihood distribution with respect to the hypothesis is studied. The results can be applied to one-sided test problems for exponential families if the hypothesis consists of a single point. In this case it may happen that $q_\infty,n$ is of the order $n^{1/p}$ for some p, 0<p<1.