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

This paper presents control and coordination algorithms for groups of vehicles. The focus is on autonomous vehicle networks performing distributed sensing tasks where each vehicle plays the role of a mobile tunable sensor. The paper proposes gradient descent algorithms for a class of utility functions which encode optimal coverage and sensing policies. The resulting closed-loop behavior is adaptive, distributed, asynchronous, and verifiably correct.

Coverage control for mobile sensing networks

Colorectal tumours that are wild type for KRAS are often sensitive to EGFR blockade, but almost always develop resistance within several months of initiating therapy. The mechanisms underlying this acquired resistance to anti-EGFR antibodies are largely unknown. This situation is in marked contrast to that of small-molecule targeted agents, such as inhibitors of ABL, EGFR, BRAF and MEK, in which mutations in the genes encoding the protein targets render the tumours resistant to the effects of the drugs. The simplest hypothesis to account for the development of resistance to EGFR blockade is that rare cells with KRAS mutations pre-exist at low levels in tumours with ostensibly wild-type KRAS genes. Although this hypothesis would seem readily testable, there is no evidence in pre-clinical models to support it, nor is there data from patients. To test this hypothesis, we determined whether mutant KRAS DNA could be detected in the circulation of 28 patients receiving monotherapy with panitumumab, a therapeutic anti-EGFR antibody. We found that 9 out of 24 (38%) patients whose tumours were initially KRAS wild type developed detectable mutations in KRAS in their sera, three of which developed multiple different KRAS mutations. The appearance of these mutations was very consistent, generally occurring between 5 and 6 months following treatment. Mathematical modelling indicated that the mutations were present in expanded subclones before the initiation of panitumumab treatment. These results suggest that the emergence of KRAS mutations is a mediator of acquired resistance to EGFR blockade and that these mutations can be detected in a non-invasive manner. They explain why solid tumours develop resistance to targeted therapies in a highly reproducible fashion.

/pdf/the-molecular-evolution-of-acquired-resistance-to-targeted-32q0mio6j2.pdf

The molecular evolution of acquired resistance to targeted EGFR blockade in colorectal cancers

Clonal evolution in cancer

Major efforts to sequence cancer genomes are now occurring throughout the world. Though the emerging data from these studies are illuminating, their reconciliation with epidemiologic and clinical observations poses a major challenge. In the current study, we provide a mathematical model that begins to address this challenge. We model tumors as a discrete time branching process that starts with a single driver mutation and proceeds as each new driver mutation leads to a slightly increased rate of clonal expansion. Using the model, we observe tremendous variation in the rate of tumor development—providing an understanding of the heterogeneity in tumor sizes and development times that have been observed by epidemiologists and clinicians. Furthermore, the model provides a simple formula for the number of driver mutations as a function of the total number of mutations in the tumor. Finally, when applied to recent experimental data, the model allows us to calculate the actual selective advantage provided by typical somatic mutations in human tumors in situ. This selective advantage is surprisingly small—0.004 ± 0.0004—and has major implications for experimental cancer research.

/pdf/accumulation-of-driver-and-passenger-mutations-during-tumor-56vc5al4md.pdf

Accumulation of driver and passenger mutations during tumor progression

In many carcinogenicity studies, the time to disease occurrence is not clinically observable; a survival/sacrifice experiment is considered for nonparametric inference about the rate of disease occurrence. A multistate model for disease development and death is considered and an algorithm of the EM type for maximum likelihood estimation is obtained. Questions of identifiability and estimability are addressed. Under the model, interval hazards for disease occurrence are identifiable for intervals defined by the sacrifice times. A score test is developed appropriate for the comparison of two groups with respect to disease development without need of any assumption concerning lethality of the disease concerned.

Nonparametric methods for survival/sacrifice experiments.

We develop extensions of the Luria–Delbruck model that explicitly consider non-exponential growth of normal cells and a birth–death process with mean exponential or Gompertz growth of mutants Death of mutant cells can be important in clones arising during cancer progression The use of a birth–death process for growth of mutant cells, as opposed to a pure birth process as in previous work on the Luria–Delbruck model, leads to a large increase in the extra Poisson variation in the size of the mutant cell populations, which needs to be addressed in statistical analyses We also discuss connections with previous work on carcinogenesis models

A generalized Luria-Delbrück model.

SUMMARY The modified log rank test for competing risks with missing failure type suggested by Goetghebeur & Ryan (1990) is derived from a partial likelihood which leaves out some information. This extra information is incorporated to give a new partial likelihood and hence a new test statistic.

A note on a test for competing risks with missing failure type

The traveling salesman problem (TSP) is one of the classical combinatorial optimization problems and has wide application in various fields of science and technology. In the present paper, we propose a new algorithm for solving the TSP that uses the variable neighborhood search (VNS) algorithm coupled with a stochastic approach for finding the optimal solution. Such neighborhood search with various other local search algorithms, named as VNS-1 and VNS-2, has been reported in the literature. The proposed algorithm is compared in detail with these algorithms, in the light of two benchmark TSP problems (one being symmetric while the other is asymmetric) suggested in the TSPLIB dataset in programming language R , along with two asymmetric problems obtained through simulation experiment. The present algorithm has been found to perform better than the conventional algorithms implemented in R for solving TSP's, and also, on an average, found to be more effective than the VNS-1 and the VNS-2 algorithms. The performance of the proposed algorithm has also been tested on 60 benchmark symmetric TSPs from the TSPLIB dataset. Apart from solving the TSP, the flexibility of the proposed hybrid algorithm to solve some other optimization problems related to other disciplines has also been discussed.

Improving variable neighborhood search to solve the traveling salesman problem

Background: Hierarchical Bayesian methods have been used in previous papers to estimate national mean effects of air pollutants on daily deaths in time-series analyses.

Objectives: We obtained maximum likelihood estimates of the common national effects of the criteria pollutants on mortality based on time-series data from ≤ 108 metropolitan areas in the United States.

Methods: We used a subsampling bootstrap procedure to obtain the maximum likelihood estimates and confidence bounds for common national effects of the criteria pollutants, as measured by the percentage increase in daily mortality associated with a unit increase in daily 24-hr mean pollutant concentration on the previous day, while controlling for weather and temporal trends. We considered five pollutants [PM10, ozone (O3), carbon monoxide (CO), nitrogen dioxide (NO2), and sulfur dioxide (SO2)] in single- and multipollutant analyses. Flexible ambient concentration–response models for the pollutant effects were considered as well. We performed limited sensitivity analyses with different degrees of freedom for time trends.

Results: In single-pollutant models, we observed significant associations of daily deaths with all pollutants. The O3 coefficient was highly sensitive to the degree of smoothing of time trends. Among the gases, SO2 and NO2 were most strongly associated with mortality. The flexible ambient concentration–response curve for O3 showed evidence of nonlinearity and a threshold at about 30 ppb.

Conclusions: Differences between the results of our analyses and those reported from using the Bayesian approach suggest that estimates of the quantitative impact of pollutants depend on the choice of statistical approach, although results are not directly comparable because they are based on different data. In addition, the estimate of the O3-mortality coefficient depends on the amount of smoothing of time trends.

Anup Dewanji

Papers

Nonparametric methods for survival/sacrifice experiments.

A generalized Luria-Delbrück model.

A note on a test for competing risks with missing failure type

Improving variable neighborhood search to solve the traveling salesman problem

Time-Series Analyses of Air Pollution and Mortality in the United States: A Subsampling Approach