https://rss.onlinelibrary.wiley.com/doi/pdf/10.1111/j.2517-6161.1977.tb01600.x

Maximum likelihood from incomplete data via the EM algorithm

THE DESIGN AND ANALYSIS OF EXPERIMENTS. By Oscar Kempthorne. New York, John Wiley and Sons, Inc., 1952. 631 pp. $8.50. This book by a teacher of statistics (as well as a consultant for \"experimenters\") is a comprehensive study of the philosophical background for the statistical design of experiment. It is necessary to have some facility with algebraic notation and manipulation to be able to use the volume intelligently. The problems are presented from the theoretical point of view, without such practical examples as would be helpful for those not acquainted with mathematics. The mathematical justification for the techniques is given. As a somewhat advanced treatment of the design and analysis of experiments, this volume will be interesting and helpful for many who approach statistics theoretically as well as practically. With emphasis on the \"why,\" and with description given broadly, the author relates the subject matter to the general theory of statistics and to the general problem of experimental inference. MARGARET J. ROBERTSON

The Design and Analysis of Experiments

Statistics for Spatial Data.

Free radicals, metals and antioxidants in oxidative stress-induced cancer

bevacizumab, as compared with 10.3 months in the chemotherapy-alone group (hazard ratio for death, 0.79; P = 0.003). The median progression-free survival in the two groups was 6.2 and 4.5 months, respectively (hazard ratio for disease progression, 0.66; P<0.001), with corresponding response rates of 35% and 15% (P<0.001). Rates of clinically significant bleeding were 4.4% and 0.7%, respectively (P<0.001). There were 15 treatment-related deaths in the chemotherapy-plus-bevacizumab group, including 5 from pulmonary hemorrhage. Conclusions The addition of bevacizumab to paclitaxel plus carboplatin in the treatment of selected patients with non–small-cell lung cancer has a significant survival benefit with the risk of increased treatment-related deaths. (ClinicalTrials.gov number, NCT00021060.)

/pdf/paclitaxel-carboplatin-alone-or-with-bevacizumab-for-non-4d5hxp2t6m.pdf

Paclitaxel-carboplatin alone or with bevacizumab for non-small-cell lung cancer

We consider the analysis of serial biomarkers to screen and monitor individuals in a given population for onset of a specific disease of interest. The biomarker readings are subject to error. We survey some of the existing literature and concentrate on two recently proposed models. The first is a fully Bayesian hierarchical structure for a mixed effects segmented regression model. Posterior estimates of the changepoint (onset time) distribution are obtained by Gibbs sampling. The second is a hidden changepoint model in which the onset time distribution is estimated by maximum likelihood using the EM algorithm. Both methods lead to a dynamic index that represents a strength of evidence that onset has occurred by the current time in an individual subject. The methods are applied to some large data sets concerning prostate specific antigen (PSA) as a serial marker for prostate cancer. Rules based on the indices are compared to standard diagnostic criteria through the use of ROC curves adapted for longitudinal data.

Statistical models for longitudinal biomarkers of disease onset.

We review and discuss numerical inversion of the characteristic function as a tool for obtaining cumulative distribution functions. With the availability of high-speed computing and symbolic computation software, the method is ideally suited for instructional purposes, particularly in the illustration of the inversion theorems covered in graduate probability courses. The method is also available as an alternative to asymptotic approximations, Monte Carlo, or bootstrap techniques when analytic expressions for the distribution function are not available. We illustrate the method with several examples, including one which is concerned with the detection of possible clusters of disease in an epidemiologic study.

https://www.jstor.org/stable/pdfplus/2684571.pdf

Obtaining Distribution Functions by Numerical Inversion of Characteristic Functions with Applications

There is a current trend towards clinical protocols which involve an initial “selection” phase followed by a hypothesis testing phase. The selection phase may involve a choice between competing treatments or different dose levels of a drug, between different target populations, between different endpoints, or between a superiority and a non-inferiority hypothesis. Clearly there can be benefits in elapsed time and economy in organizational effort if both phases can be designed up front as one experiment, with little downtime between phases. Adaptive designs have been proposed as a way to handle these selection/testing problems. They offer flexibility and allow final inferences to depend on data from both phases, while maintaining control of overall false positive rates. We review and critique the methods, give worked examples and discuss the efficiency of adaptive designs relative to more conventional procedures. Where gains are possible using the adaptive approach, a variety of logistical, operational, da...

Adaptive seamless designs: selection and prospective testing of hypotheses.

We consider the statistical modeling and analysis of replicated multi-type point process data with covariates. Such data arise when heterogeneous subjects experience repeated events or failures which may be of several distinct types. The underlying processes are modeled as nonhomogeneous mixed Poisson processes with random (subject) and fixed (covariate) effects. The method of maximum likelihood is used to obtain estimates and standard errors of the failure rate parameters and regression coefficients. Score tests and likelihood ratio statistics are used for covariate selection. A graphical test of goodness of fit of the selected model is based on generalized residuals. Measures for determining the influence of an individual observation on the estimated regression coefficients and on the score test statistic are developed. An application is described to a large ongoing randomized controlled clinical trial for the efficacy of nutritional supplements of selenium for the prevention of two types of skin cancer.

https://www.jstor.org/stable/info/2532445

Analysis of multi-type recurrent events in longitudinal studies; application to a skin cancer prevention trial

An important component of clinical trials in drug development is the analysis of treatment efficacy in patient subgroups (subpopulations). Because of concerns of multiplicity and of the small sample sizes often involved, such analyses can present substantial statistical challenges and may lead to misleading conclusions. As a confirmatory seamless phase II/III design, we propose an adaptive enrichment group sequential procedure whereby resources can be concentrated on subgroups most likely to respond to treatment. Stopping boundaries are defined through upper and lower spending functions. The procedure is presented in terms of the efficient score, enabling the analysis of normal, binary, or time-to-event data. It addresses the dilution effect by eliminating populations at the first stage that appear likely to derive no therapeutic benefit. It subsequently proceeds with the definitive assessment of treatment efficacy among the remaining pooled populations using a group sequential design. The procedure provides strong protection of familywise type I error rate, and we employ a bootstrap algorithm to obtain point and interval estimates that are adjusted for the selection bias. We give examples to demonstrate how the design is used. We make comparisons with adaptive two-stage combination test procedures and with a group sequential test that does not account for the presence of subgroups. Numerical results show that the procedure has high power to detect subgroup-specific effects and the use of multiple interim analysis points can lead to substantial sample size savings.

Bruce W. Turnbull

Papers

Statistical models for longitudinal biomarkers of disease onset.

Obtaining Distribution Functions by Numerical Inversion of Characteristic Functions with Applications

Adaptive seamless designs: selection and prospective testing of hypotheses.

Analysis of multi-type recurrent events in longitudinal studies; application to a skin cancer prevention trial

Group sequential enrichment design incorporating subgroup selection.