Cooper statistics

Some endpoints cannot be measured on a continuous scale, or for scientific or regulatory purposes can only be divided into two or more qualitative classes, for instance active/inactive. Goodness of fit can be described by the Cooper statistics, introduced to assess the significance of carcinogenicity tests.The goodness of fit parameters for a 2-level classification are shown in Table 9.3. This table is often, and very aptly, entitled a confusion matrix. 

The Cooper statistics express the performance of a classification model, based on 

The positive and negative predictivities focus on the effects on individual chemicals, since they act as conditional probabilities. Thus the positive predictivity is the probability that a chemical classified as active is really active, while the negative predictivity gives the probability that a classified nonactive chemical is really non-active. 

The focus on a particular Cooper statistic depends on how the model is to be used. 

---

B E Cooper Statistics for Experimentalists, Pergamon Press, Oxford, 1975... 

The predictive performance of a CM is often expressed in terms of a contingency table (Table 18.1) containing the numbers of true and false positive and negative predictions made by the CM, and in terms of the CM s Cooper statistics, which are derived from the contingency table. Definitions of the Cooper statistics are provided in Table 18.2. 

CM 18.1 to CM 18.3 were assessed in terms of their Cooper statistics, which define an upper limit to predictive performance. In addition, cross-validated Cooper statistics, which provide a more realistic indication of a model s capacity to predict the classifications of independent data, were obtained by applying the threefold cross-validation procedure to the best-sized CTs. In the threefold cross-validation procedure, the data set is randomly divided into three approximately equal parts, the CT is re-parameterized using two thirds of the data, and predicted classifications are made for the remaining third of the data. The cross-validated Cooper statistics are the mean values of the usual Cooper statistics, taken over the three iterations of the cross-validation procedure. The Cooper statistics for CM 18.1 to CM 18.3 are summarized in Table 18.6. 

Finally, Cooper statistics for the application of 4 sequences of CMs and for the application of the EPISKIN PM alone are given in Table 18.10. The statistics in Table 18.10 were calculated from the data in Table 18.9, using the definitions of the Cooper statistics given in Table 18.2. 

The Cooper statistics do not consider the prevalence within the training set, which will introduce a bias in the ability of the model to predict one or other class. For example, if the training set has 75% actives relative to inactives, the null probability will be three times as likely to predict a compound as active rather than an inactive compound. Cohen defined the kappa index to overcome the problem of prevalence when assessing the significance of classification... 

Table 9.3 2x2 contingency table and definition of the Cooper statistics. 

W. G. Heid, U.S. Wheat Industy, Agricultural Economics Report No. 432, U.S. Department of Agricultural Economics, Statistics and Cooperative Service, Washington, D.C., 1979. 

The reason(s) for the success of ISM has to do with the fact that sequence space has been confined to defined locations in the protein that are most likely to respond positively in an additive or cooperative manner. In sharp contrast, when performing several rounds of epPCR (4—8 are typical ), the whole protein is addressed repeatedly although only a fraction of the amino acid positions are important. Owing to statistical reasons, a given improved mutant (hit) evolved by ISM is not... 

New application of modem statistical mechaiucal methods to the description of stmctured continua and snpramolecnlar flnids have made it possible to treat many-body problems and cooperative phenomena in snch systems. The increasing availability of high-speed compntation and the development of vector and parallel processing teclmiqnes for its implementation are making it possible to develop more refined descriptions of the complex many-body systems. 

USDA. 1978. Farmers use of pesticides in 1976. Agricultural economic report No. 418. Washington, DC Report to U.S. Department of Agriculture by Economics, Statistics, and Cooperative Services, 16. 

Theoretically, the problem has been attacked by various approaches and on different levels. Simple derivations are connected with the theory of extrathermodynamic relationships and consider a single and simple mechanism of interaction to be a sufficient condition (2, 120). Alternative simple derivations depend on a plurality of mechanisms (4, 121, 122) or a complex mechanism of so called cooperative processes (113), or a particular form of temperature dependence (123). Fundamental studies in the framework of statistical mechanics have been done by Riietschi (96), Ritchie and Sager (124), and Thorn (125). Theories of more limited range of application have been advanced for heterogeneous catalysis (4, 5, 46-48, 122) and for solution enthalpies and entropies (126). However, most theories are concerned with reactions in the condensed phase (6, 127) and assume the controlling factors to be solvent effects (13, 21, 56, 109, 116, 128-130), hydrogen bonding (131), steric (13, 116, 132) and electrostatic (37, 133) effects, and the tunnel effect (4,... 

Evaluation of the results Evaluation of the results consists of (i) technical scrutiny of the consistency and of the quality of the data the acceptance, on technical (not statistical) grounds, of data to be used to calculate the certified value and its uncertainty, (2) the calculation (using the appropriate statistical techniques) of the certified value and its uncertainty. The approach indudes technical discussion of the results among all cooperators, rejection of outliers, statistical evaluation, and calculation of the certified value and uncertainties. 

A cohort mortality study was conducted to compare the mortality rates due to chronic renal disease in 4,519 battery plant workers and 2,300 lead production or smelter workers from 1947 to 1980 (Cooper 1988 Cooper et al. 1985). The mortality data for these workers were compared with national mortality rates for white males. Environmental lead levels and PbB levels were available for only about 30% of all workers for varying time periods from 1947 to 1972. Statistically significant increases in mortality from "other hypertensive disease" and "chronic nephritis" were seen in both lead cohorts. Limitations of this study include the fact that various confounding factors, such as smoking, were not accounted for, and the workers were probably exposed to other toxic chemicals. 

Telesurveys Research Associates of Houston conducted the public opinion survey. Rosie Zamora, Dick Jaffe, and Barry Petree demonstrated patience and good cheer through the numerous revisions of the survey instrument. Dr. Eun-Sul Lee of the University of Texas-Houston School of Public Health and Dr. Sharon P. Cooper, now at the Texas A M University School of Rural Public Health, were the statistical consultants on the survey. 

National Food Review," Economics, Statistics and Cooperatives, Service A. NFR-9 (Winter), 1980, p. 51. 

I first approached my theoretition friend and co-worker of many years, R. Simha, for statistical-mechanical assistance, and we obtained further the cooperation of H. Frisch, then just completing his Ph.D. at the Polytechnic Institute. The model we evolved was that of a macromolecule in solution colliding first with one of its segnents with a solvent-solid interface, becoming adsorbed when a complicated set of energetics becomes negative. 

---