Makio Ishiguro

Bootstrapping Log Likelihood and EIC, an Extension of AIC

Akaike (1973, 2nd International Symposium on Information Theory, 267-281,Akademiai Kiado, Budapest) proposed AIC as an estimate of the expected loglikelihood to evaluate the goodness of models fitted to a given set of data.The introduction of AIC has greatly widened the range of application ofstatistical methods. However, its limit lies in the point that it can beapplied only to the cases where the parameter estimation are performed bythe maximum likelihood method. The derivation of AIC is based on theassessment of the effect of data fluctuation through the asymptoticnormality of MLE. In this paper we propose a new information criterion EICwhich is constructed by employing the bootstrap method to simulate the datafluctuation. The new information criterion, EIC, is regarded as an extensionof AIC. The performance of EIC is demonstrated by some numerical examples.

Bootstrap approach for constructing confidence intervals for population pharmacokinetic parameters. I: a use of bootstrap standard error

In population pharmacokinetic studies, one of the main objectives is to estimate population pharmacokinetic parameters specifying the population distributions of pharmacokinetic parameters. Confidence intervals for population pharmacokinetic parameters are generally estimated by assuming the asymptotic normality, which is a large-sample property, that is, a property which holds for the cases where sample sizes are large enough. In actual clinical trials, however, sample sizes are limited and not so large in general. Likelihood functions in population pharmacokinetic modelling include a multiple integral and are quite complicated. We hence suspect that the sample sizes of actual trials are often not large enough for assuming the asymptotic normality and that the asymptotic confidence intervals underestimate the uncertainties of the estimates of population pharmacokinetic parameters. As an alternative to the asymptotic normality approach, we can employ a bootstrap approach. This paper proposes a bootstrap standard error approach for constructing confidence intervals for population pharmacokinetic parameters. Comparisons between the asymptotic and bootstrap confidence intervals are made through applications to a simulated data set and an actual phase I trial.

A bayesian approach to binary response curve estimation

SummaryThe purpose of the present paper is to propose a practical procedure for the estimation of the binary response curve. The procedure is based on a model which approximates the response curve by a finely segmented piecewise constant function. To obtain a stable estimate we assume a prior distribution of the parameters of the model. The prior distribution has several parameters (hyper-parameters) which are chosen to minimize an information criterion ABIC. The procedure is applicable to data consisting of observations of a binary response variable and a single explanatory variable. The practical utility of the procedure is demonstrated by examples of applications to the dose response curve estimation, to the intensity function estimation of a point process and to the analysis of social survey data. The application of the procedure to the discriminant analysis is also briefly discussed.

Bootstrap approach for constructing confidence intervals for population pharmacokinetic parameters. II : A bootstrap modification of standard two-stage (STS) method for phase I trial

For population pharmacokinetics in phase I trials, the standard two-stage (STS) method is quite appealing, especially to non-statisticians, because the method is theoretically and computationally simple. The method, however, does not take into account the uncertainty in estimating individual-specific parameters and gives biased estimates for population variances of pharmacokinetic parameters. This is one of the main reasons why the STS method is not generally recommended. This paper proposes a simple bootstrap modification of the STS method for estimating confidence intervals of population means and standard deviations of pharmacokinetic parameters in phase I trials. The proposed approach adopts a bootstrap bias correction in estimating population variances of pharmacokinetic parameters. Applications are given to a simulated data set and an actual phase I trial to show how the proposed approach works in practice.

A bayesian approach to the probability density estimation

SummaryA Bayesian procedure for the probability density estimation is proposed. The procedure is based on the multinomial logit transformations of the parameters of a finely segmented histogram model. The smoothness of the estimated density is guaranteed by the introduction of a prior distribution of the parameters. The estimates of the parameters are defined as the mode of the posterior distribution. The prior distribution has several adjustable parameters (hyper-parameters), whose values are chosen so that ABIC (Akaikes Bayesian Information Criterion) is minimized.The basic procedure is developed under the assumption that the density is defined on a bounded interval. The handling of the general case where the support of the density function is not necessarily bounded is also discussed. The practical usefulness of the procedure is demonstrated by numerical examples.

Better grading systems for evaluating the degree of lymph node invasion in cancer of the thoracic esophagus

To evaluate the quality of various grading systems for lymph node invasion in cancer of the thoracic esophagus, the surgical results of 142 patients who underwent systematic lymph node dissection with curative intent were analyzed. The survival probability of patients in the same grade was modeled using a Weibull distribution and the parameters were estimated by the maximum likelihood principle. The quality of each grading system was measured by the Akaike Information Criterion (AIC) of the estimated statistical model, by which the smaller the AIC of a grading system, the smaller the loss of information for predicting outcomes. The AIC of the TNM grading of the International Union Against Cancer, the grading of the Japanese Society for Esophageal Diseases, and the grading designed according to the total number of positive lymph nodes became substantially smaller in that order. The AIC of grading systems variously designed on rather simple criteria were examined with the aim of creating a better grading system. It was concluded that a grading system based on the total number of positive nodes and the state of the paratracheal and/or middle mediastinal node groups was better than the other systems examined.

A Note on Sample Size Determination for Akaike Information Criterion (AIC) Approach to Clinical Data Analysis

ABSTRACT Because of its flexibility and usefulness, Akaike Information Criterion (AIC) has been widely used for clinical data analysis. In general, however, AIC is used without paying much attention to sample size. If sample sizes are not large enough, it is possible that the AIC approach does not lead us to the conclusions which we seek. This article focuses on the sample size determination for AIC approach to clinical data analysis. We consider a situation in which outcome variables are dichotomous and propose a method for sample size determination under this situation. The basic idea is also applicable to the situations in which outcome variables have more than two categories or outcome variables are continuous. We present simulation studies and an application to an actual clinical trial.

Anatomical Architecture and Responses to Acidosis of a Novel Respiratory Neuron Group in the High Cervical Spinal Cord (HCRG) of the Neonatal Rat

It has been postulated that there exists a neuronal mechanism that generates respiratory rhythm and modulates respiratory output pattern in the high cervical spinal cord. Recently, we have found a novel respiratory neuron group in the ventral portion of the high cervical spinal cord, and named it the high cervical spinal cord respiratory group (HCRG). In the present study, we analyzed the detailed anatomical architecture of the HCRG region by double immunostaining of the region using a neuron-specific marker (NeuN) and a marker for motoneurons (ChAT) in the neonatal rat. We found a large number of small NeuN-positive cells without ChAT-immunoreactivity, which were considered interneurons. We also found two and three clusters of motoneurons in the ventral portion of the ventral horn at C1 and C2 levels, respectively. Next, we examined responses of HCRG neurons to respiratory and metabolic acidosis in vitro by voltage-imaging together with cross correlation techniques, i.e., by correlation coefficient imaging, in order to understand the functional role of HCRG neurons. Both respiratory and metabolic acidosis caused the same pattern of changes in their spatiotemporal activation profiles, and the respiratory-related area was enlarged in the HCRG region. After acidosis was introduced, preinspiratory phase-dominant activity was recruited in a number of pixels, and more remarkably inspiratory phase-dominant activity was recruited in a large number of pixels. We suggest that the HCRG composes a local respiratory neuronal network consisting of interneurons and motoneurons and plays an important role in respiratory augmentation in response to acidosis.

Kullback-leibler information approach to the optimum measurement point for bayesian estimation

When an appropriate parametric model and a prior distribution of its parameters are given to describe clinical time courses of a dynamic biological process, Bayesian approaches allow us to estimate the entire profiles from a few or even a single observation per subject. The goodness of the estimation depends on the measurement points at which the observations were made. The number of measurement points per subject is generally limited to one or two. The limited measurement points have to be selected carefully. This paper proposes an approach to the selection of the optimum measurement point for Bayesian estimations of clinical time courses. The selection is made among given candidates, based on the goodness of estimation evaluated by the Kullback-Leibler information. This information measures the discrepancy of an estimated time course from the true one specified by a given appropriate model. The proposed approach is applied to a pharmacokinetic analysis, which is a typical clinical example where the sele...

A novel statistical analysis of voltage-imaging data by structural time series modeling and its application to the respiratory neuronal network.

The respiratory neuronal network activity can be optically recorded from the ventral medulla of the in vitro brainstem-spinal cord preparation using a voltage-sensitive dye. To assess the synchronicity between respiratory-related neurons and the breath-by-breath variability of respiratory neuronal activity from optical signals, we developed a novel method by which we are able to analyze respiratory-related optical signals without cycle-triggered averaging. The model, called the sigmoid and transfer function model, assumes a respiratory motor activity as the output and optical signals of each pixel as the input, and activity patterns of respiratory-related regions are characterized by estimated model parameter values. We found that rats intermittently showing multi-peaked respiratory motor activities had a relatively low appearance frequency of respiratory-related pixels. Further, correlations between respiratory-related pixels in rats with such unstable respiratory motor activities were poor. The poor correlations were caused by respiratory neurons recruited in the late inspiratory phase. These results suggest that poor synchronicity between respiratory neurons, which are recruited at various timings of inspiration, causes intermittent multi-peaked respiratory motor output. In conclusion, analyses of respiratory-related optical signals without cycle-triggered averaging are feasible by using the proposed method. This approach can be widely applied to the analysis of event-related optical signals.