Conventional randomized clinical trials provide a powerful and scientifically rigorous method for comparing medical therapies, but designs using 50-50 randomization (or any other constant assignment probabilities) can raise ethical difficulties when there is strong evidence, either a priori or from study data, that one of the therapies may offer great benefit to individual patients. This article describes such a situation, the evaluation of extracorporeal membrane oxygenation (ECMO) for treatment of persistent pulmonary hypertension of the newborn (PPHN). For many years, the mortality rate among infants with severe PPHN treated with conventional medical therapy (CMT) was 80${\tt\%}$ or higher. ECMO treatment of PPHN was introduced in 1977 and, by 1985, several centers had reported survival rates of 80${\tt\%}$ or better in infants treated with ECMO. Only one randomized trial was reported by the end of 1985. This trial used a randomized play-the-winner design. Eleven patients received ECMO therapy and all survived. Only one patient received CMT and this patient died. In part because of the success of ECMO therapy, this trial provided very little comparative data on the two therapies. The author and medical colleagues reviewed these data in 1985 and concluded that they did not justify routine use of ECMO without further study. A review of historical experience at two Harvard hospitals showed, however, that 13 infants had developed severe PPHN in 1982 and 1983 and 11 (85${\tt\%}$) had died. All received CMT. Thus, there was a strong possibility that a randomized trial would show large differences in survival rates in the ECMO and CMT groups. To balance ethical and scientific concerns, we designed a clinical trial with a treatment assignment procedure that would begin as conventional randomization but switch to a single therapy study when a prespecified number of deaths was observed in either group. This article describes the study design and results. Nineteen (19) patients were enrolled during the randomized phase; 6 of 10 survived in the CMT group and 9 of 9 in the ECMO group. In the second nonrandomized phase, 20 patients were assigned to ECMO therapy and 19 survived. The survival rates in the two treatment groups were significantly different $(P < .05$ with curtailed sampling) and the profile likelihood for the difference in survival rates between the ECMO and CMT groups gave a one-sided 95${\tt\%}$ confidence interval with a lower limit of .131. We conclude that ECMO therapy increases survival relative to CMT therapy in patients with severe PPHN.

This paper offers a glimpse into the theory of empirical processes. Two asymptotic problems are sketched as motivation for the study of maximal inequalities for stochastic processes made up of properly standardized sums of random variables--empirical processes. The exposition develops the technique of Gaussian symmetrization, which is the least technical of the techniques to have evolved during the last decade of empirical process research. The resulting maximal inequalities are useful because they depend on quantities that can be bounded using simple methods. These methods, which extend the concept of a Vapnik-Cervonenkis class of sets, are demonstrated by use of the two motivating asymptotic problems. The paper is not intended as a complete survey of the state of empirical process theory; it certainly does not present the whole range of available techniques. It is written as an attempt to convey the look and feel of a very powerful, very useful, and tractable tool of contemporary mathematical statistics.

Several methods of analyzing extreme values are now known, most based on the extreme value limit distributions or related families. This paper reviews these techniques and proposes some extensions based on the point-process view of high-level exceedances. These ideas are illustrated with a detailed analysis of ozone data collected in Houston, Texas. There is particular interest in whether they is any trend in the data. The analysis reveals no trend in the overall levels of the series, but a marked downward trend in the extreme values.

This expository paper deals with the role of iterative generalized least squares as an algorithm for the computation of statistical estimators. Relationships between various algorithms, such as Newton-Raphson, Gauss-Newton, and scoring, are studied. A parallel is made between statistical properties of the model and the structure of the numerical algorithm employed to find parameter estimates. In particular a general linearizability property that extends the concept of link function in generalized linear models is considered and its computational meaning is discussed. Maximum quasilikelihood estimators are reinterpreted so that they may exist even when there is no quasilikelihood function.

Many scientific phenomena are now investigated by complex computer models or codes. A computer experiment is a number of runs of the code with various inputs. A feature of many computer experiments is that the output is deterministic--rerunning the code with the same inputs gives identical observations. Often, the codes are computationally expensive to run, and a common objective of an experiment is to fit a cheaper predictor of the output to the data. Our approach is to model the deterministic output as the realization of a stochastic process, thereby providing a statistical basis for designing experiments (choosing the inputs) for efficient prediction. With this model, estimates of uncertainty of predictions are also available. Recent work in this area is reviewed, a number of applications are discussed, and we demonstrate our methodology with an example.