Esteban Walker

Comparing curves using additive models

Advances in technology have increased dramatically the amount of data measured in industrial processes. Thousands of measurements are often available in operations where previously only a single measurement, at a given point in time or space, was taken. These measurements allow the reconstruction of the whole profile or “signature” of the operation over time or space. Examples are the tonnage applied in a stamping press during a stroke and the density profile of particleboard. Many of these signatures have complicated forms that are not well modeled with parametric models. In this paper, a relatively new class of models called additive models is used to assess the sources of variation active on these signatures. The models used contain a nonparametric or smooth portion to model the form of the signature, and a parametric portion to incorporate other sources of variation. A table is developed to assess the magnitude of the sources of variation. These techniques are illustrated using density profiles of engineered wood boards. Instructions on the implementation of these techniques in S-Plus and SAS are given.

Should Fewer Premature Infants Be Screened for Retinopathy of Prematurity in the Managed Care Era

Objective. To determine appropriate upper limits for gestational age and birth weight when screening infants for retinopathy of prematurity (ROP). Design. Retrospective survey. Setting. Tertiary neonatal intensive care nursery. Patients. Seven hundred seven infants born July 1, 1990 to June 30, 1996 and screened for ROP according to the 1988 to 1996 American Academy of Pediatrics guidelines. Outcome Measures. Maximum stage of ROP with respect to birth weight and gestational age. Results. No ROP more than Stage 1 was observed in infants with gestational ages ≥32 weeks or birth weights ≥1500 g. All cases of threshold and Stage 4 ROP were confined to infants with gestational ages ≤30 weeks or birth weights <1200 g. Conclusions. The latest American Academy of Pediatrics screening guidelines for ROP are discretionary for infants with birth weights >1500 g or gestational ages >28 weeks. If ROP screening is limited to infants with birth weights of ≤1500 g, 34.2% fewer infants would require screening compared with the previous <1800 g recommendation, while missing no cases of ROP more than Stage 1. A gestational age cut-off of ≤28 weeks, however, is less desirable, and could potentially miss several infants with more advanced retinopathy (including Stage 4). If ROP screening criteria were instead modified to include infants of gestational ages <32 weeks, the number of patients requiring screening could be reduced 29.1% compared with the previous recommendation of <35 weeks, again without missing any cases of ROP more than Stage 1. Use of such a screening strategy (birth weight <1500 g or gestational age <32 weeks) is predicted to save in excess of 1.5 million dollars annually in the United States, while missing no cases of ROP more than Stage 1.

Influence measures in ridge regression

In regression, it is of interest to detect anomalous observations that exert an unduly large influence on the least squares analysis. Frequently, the existence of influential data is complicated by the presence of collinearity (see, e.g., Lawrence and Marsh 1984). Very little work has been done, however, on the possible effects that collinearity can have on the influence of an observation. In this article, we show that when ridge regression is used to mitigate the effects of collinearity, the influence of some observations can be drastically modifield. Approximate deletion formulas for the detection of influential points are proposed for ridge regression.

Improved fluid management utilizing humidified incubators in extremely low birth weight infants

OBJECTIVE: To compare fluid and electrolyte management in extremely low birth weight (ELBW) infants nursed in humidified versus nonhumidified incubators.STUDY DESIGN: Setting — tertiary intensive care nursery. Subjects — all infants with birth weight <1000 g admitted 1/95 to 1/99 who were treated with incubators and survived for >96 hours (N=155). Intervention — retrospective comparison of daily weights, fluid intakes, urine outputs, and serum electrolytes between group 1 (n=70, nonhumidified incubators, born 1/95 to 1/97) and group 2 (n=85, humidified incubators, born 1/97 to 1/99) over the first 4 days after birth.RESULTS: Despite similar daily weight losses between groups, group 1 infants received higher fluid intakes, had lower urine outputs, and had a higher incidence of hypernatremia, hyperkalemia, and azotemia (p<0.05). Although no differences in mortality or the incidence of patent ductus arteriosus, bronchopulmonary dysplasia, or the overall rate of nosocomial infections were observed, the proportion of gram-negative isolates increased significantly (62%, p<0.05) following the introduction of humidified incubators.CONCLUSIONS: ELBW weight infants nursed in humidified incubators have lower fluid requirements, improved electrolyte balance, and higher urine outputs during the first 4 days after birth compared to those nursed in nonhumidified incubators.

Detection of collinearity- influential observations

Collinearity is defined as the existence of near linear dependencies among the columns of the matrix. It has been found, though, that a strategically located point (i.e. a row of ) can greatly modify the collinearity structure of the data. The whole approach to regression analysis depends, largely, on the measured level of collinearity. It is, thus, crucial for the analyst to be able to detect points that modify this level significantly. The main objective of this paper is to develop a diagnostic tool for the detection of collinearity-influential points. This diagnostic is easy to compute and capable of detecting collinearity influential sets of points, Two examples are given to illustrate its use.

Burn-in to improve which measure of reliability?

Abstract Burn-in plans or screens are often used to improve the “reliability” of systems, subassemblies, and components. There are, however, different ways of measuring reliability. Sometimes contradictory results are obtained when different measures of reliability are used. This problem stems from the fact that each one of these measures is really assessing reliability from a different point of view. These differences are crucial for designing in reliability and for devising burn-in plans. It is known, for example, that a burn-in plan that optimizes (or improves) one reliability measure does not necessarily yield an optimal (or improvement) for another measure. After introducing and discussing several reliability measures, examples are presented to illustrate the behavior of different reliability measures. We stress the importance of understanding what the end user of a product needs in terms of “reliability” before the design stage, through all the developmental stages, and for burn-in plans.

Comparing Reliabilities of the Strength of Two Container Designs: A Case Study

Two designs for PET (polyethylene terephthalate) beverage bottles were compared. These bottles are used for carbonated beverages; and thus, a very critical property is their burst strength. The burst strengths of bottles from each design across 24 cavities were measured. Standard nonparametric methods suggested a highly significant difference in the reliability of the two designs. Using simple graphical techniques, it was found that the reliability data of the new design appeared to be a mixture of distributions caused by the presence of ”arly mortality,” due possibly to different failure modes. Even though they were clearly different, neither design was uniformly more reliable than the other. Standard parametric methods showed inadequate fit due to the bimodality of the strength data of the new design. The paper stresses (1) the need of operational clear definitions for ”reliability,” (2) the need of graphical exploratory analysis to discover anomalies in the data, and (3) the value of nonparametric methods, and (4) the problems of using parametric techniques when the assumptions are violated. To justify work on improvement of the new design, the potential effect of the removal of the early mortality on the new design was analyzed.

Semiparametric Regression, David Ruppert

Weisberg (1985). Also, very little recent literature (after 1984) is covered (with the exception of Sec. 7.3, which covers radial basis functions). Following Cook and Weisberg (1999, p. 432), the most important idea from the recent literature is that MLR is the study of the conditional distribution of the response variable given the predictors, and this distribution can be visualized with a plot of the fitted values versus the response variable. Texts that do not discuss this plot may be obsolete.