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J J Gart

Publications and source records attributed to J J Gart.

At least 19 recordsLinked to original sources
PubMed1992

Improved and extended exact and asymptotic methods for the combination of 2 x 2 tables.

Exact and approximate methods for analyzing the common odds ratio in the combination of 2 x 2 tables are programmed. The approximate methods are improved by incorporating bias and skewness corrections in testing and estimation. Exact methods are done more efficiently by employing network theory. This makes more feasible the exact analyses of sparse data, large numbers of 2 x 2 tables each based on small numbers. Additional tests of interaction, particularly for sparse data, are added. Another feature is the point and interval estimation of the attributable risk. The various aspects of the program are illustrated in three numerical examples. An executable version of this program, for IBM compatible PCs, requires about 314K for up to 500 tables. It is available from the authors upon submission of a PC diskette formatted with MS-DOS.

Aged↗
PubMed1991

Simple tests of homogeneity of controls in matched studies.

Consider matched case-control studies with a pair of distinguishable controls, say neighbourhood and hospital, wherein one of the controls may be missing. Liang and Stewart derive an efficient test for the possible difference in controls for the complete data case. They suggest inefficient tests for the situation where some triplets are incomplete. Levin, and Risch and Tibshirani, derive efficient tests for the incomplete triplet case by the methods of maximum likelihood estimator (Wald) tests and likelihood ratio tests, respectively. All these tests require the use of compute algorithms. Using score theory, we derive a simple efficient test for complete triplets which only requires solving a quadratic equation. Furthermore, we show that the usual normal approximation to McNemar's test is equivalent to the score test and is thus fully efficient as well. For incomplete triplets, score theory leads to a fully efficient test which only requires the solution of a cubic equation. We propose a nearly efficient test which is even more simply computed. The example of Liang and Stewart illustrates application of the results.

Case-Control Studies↗
PubMed1990

Approximate interval estimation of the difference in binomial parameters: correction for skewness and extension to multiple tables.

Recently, Beal (1987, Biometrics 43, 941-950) found Mee's modification of Anbar's approximate interval estimation for the difference in binomial parameters to be a good choice in small sample sizes. As this method can be derived from the score theory of Bartlett, it is easily corrected for skewness. Exact numerical evaluation shows that this correction is not as important for this case as for the ratio of binomial parameters (Gart and Nam, 1988, Biometrics 44, 323-338). The score theory is also used to extend this method to the stratified or multiple-table case. Thus, good approximate interval estimates for differences, ratios, and odds ratios of binomial parameters can all be derived from the same general theory.

Binomial Distribution↗
PubMed1989

Significance tests for cancer screening trials.

The goal of a cancer screening program is to reduce cancer mortality by detecting tumors at earlier stages of their development. For some types of cancer, screening tests may allow the preclinical detection of benign precursors of a tumor, and thus a screening program could result in reductions in both cancer incidence and mortality. For other types of cancer, a screening program will not reduce cancer incidence, and thus the expected outcome in a randomized cancer screening trial would be equal cancer incidence rates in control and study groups, but reduced cancer mortality in the study group. For the latter situation, we employ a variety of Poisson models for cancer incidence and mortality to derive optimal tests for equality of cancer mortality rates in a cancer screening trial, and we compare the asymptotic relative efficiencies of the test statistics under various alternatives. We demonstrate that testing equality of case mortality rates using Fisher's exact test or its Pearson chi-square approximation is nearly optimal when cancer incidence rates are equal and is fully efficient when cancer incidence rates are unequal. When valid, this comparison of case mortality rates in the study and control groups can be considerably more powerful than the standard comparison of population mortality rates. We illustrate the results using data from a clinical trial of a breast cancer screening program.

Adult↗
PubMed1988

The equivalence of two tests and models for HLA data with no observed double blanks.

Gart and Nam (1984, Biometrics 40, 887-894) consider the analysis of an ABO-like model based on the Hardy-Weinberg law in the commonly occurring case of human leukocyte antigen (HLA) data where there are no double blanks, that is, no recessive homozygotes. They derive a score test, based on the truncated likelihood, of the hypothesis that the true recessive gene (or allele) frequency is zero. Yasuda (1968, Biometrics 24, 915-935) considers a similar codominant system wherein the true recessive gene frequency is assumed zero, but the Hardy-Weinberg law does not hold. In particular, he considers the possibility of a nonzero inbreeding coefficient. We show that the two models are equivalent; each likelihood can be shown to be a reparameterization of the other. Furthermore, the score test of the zero gene frequency in Gart and Nam is identical to the score test for a zero inbreeding coefficient given by Yasuda. The results are applied to an example wherein it appears that the Hardy-Weinberg model is appropriate. Thus, it is not possible in this population to identify homozygous individuals without error from phenotypic data alone.

Consanguinity↗
PubMed1988

Approximate interval estimation of the ratio of binomial parameters: a review and corrections for skewness.

Various methods for finding confidence intervals for the ratio of binomial parameters are reviewed and evaluated numerically. It is found that the method based on likelihood scores (Koopman, 1984, Biometrics 40, 513-517; Miettinen and Nurminen, 1985, Statistics in Medicine 4, 213-226) performs best in achieving the nominal confidence coefficient, but it may distribute the tail probabilities quite disparately. Using general theory of Bartlett (1953, Biometrika 40, 306-317; 1955, Biometrika 42, 201-203), we correct this method for asymptotic skewness. Following Gart (1985, Biometrika 72, 673-677), we extend this correction to the case of estimating the common ratio in a series of two-by-two tables. Computing algorithms are given and applied to numerical examples. Parallel methods for the odds ratio and the ratio of Poisson parameters are noted.

Algorithms↗
PubMed1987

On the efficiency of age-adjusted tests in animal carcinogenicity experiments.

Based on asymptotic relative efficiency calculations, Ryan (1985, Biometrics 41, 525-531) concludes that, in the analysis of animal carcinogenicity experiments, age-adjusted tests of tumor rates should be routinely preferred to simple proportions tests for both lethal and nonlethal tumors. We recalculate the asymptotic efficiencies of the simple proportions test relative to the log-rank test for the lethal tumor case. For a simplified model it is shown that the relative efficiency may be easily computed as a function of the crude tumor rate and the survival rate at the time of terminal sacrifice. More generally, we calculate by numerical quadrature the asymptotic relative efficiency for all models considered by Ryan and, using simulations, examine the relevance of asymptotic efficiencies to typical sample sizes. Contrary to the numerical results of Ryan, we find, for experiments with good survival and typical tumor rates, that the relative efficiencies are greater than 95%, usually about 99%. In the nonlethal tumor case, similar results follow from Ryan for tumor rates and survival rates typically encountered in practice. As it is often difficult to determine whether or not a tumor is lethal, we conclude for equal interim mortality rates, that the simple proportions test is usually adequate in evaluating animal carcinogenicity experiments.

Age Factors↗
PubMed1987

On two tests of fit for HLA data with no double blanks.

Stevens suggests a test of fit, based on Bernstein's estimators, of the Hardy-Weinberg law for the ABO system. Nam and Gart extend this test to the generalized ABO-like system and apply it to HLA data. When the recessive gene is rare, Huether and Murphy recall Haldane's point that its Bernstein's estimator is negatively biased and go on to suggest novel corrected versions of it. With the identification of more HLA antigens, it is not uncommon to find, in certain populations, that the sample data contain no double blanks; that is, every individual reacts to at least one antigen for a given locus. Gart and Nam give a simple score test of a zero true recessive-gene frequency for such situations. Here we examine the extended test of Stevens as a test of this hypothesis. We find that it is fully efficient for two codominant alleles but that when the number exceeds two its efficiency may be 50% or lower or as high as 100%, depending on the number of alleles and the pattern of gene frequencies. The tests are applied to a set of HLA data.

ABO Blood-Group System↗
PubMed1985

The ML estimation and testing of generalized ABO-like data with no observed double recessives.

The general method of the discrepancy or heterogeneity chi-square is applied to ABO-like data in which there are no observed double blanks in either the disease or the control group. When the recessive gene frequency is assumed zero, this method leads to an approximate chi-square test identical to that suggested by Smouse and Williams (1982, Biometrics 38, 757-768). When this assumption is relaxed, there arise two cases which are determined by whether the maximum likelihood estimate of this frequency is zero or not. It is shown that the value of the simple score statistic of Gart and Nam (1984, Biometrics 40, 887-894) discriminates between the two cases. The various omnibus test statistics for comparing groups are shown to differ little in several practical examples. However, under the more general assumption the appropriate degrees of freedom is one more than the number previously suggested.

ABO Blood-Group System↗
PubMed1979

Statistical analyses of the relative risk.

Let P1 be the probability of a disease in one population and P2 be the probability of a disease in a second population. The ratio of these quantities, R = P1/P2, is termed the relative risk. We consider first the analyses of the relative risk from retrospective studies. The relation between the relative risk and the odds ratio (or cross-product ratio) is developed. The odds ratio can be considered a parameter of an exponential model possessing sufficient statistics. This permits the development of exact significance tests and confidence intervals in the conditional space. Unconditional tests and intervals are also considered briefly. The consequences of misclassification errors and ignoring matching or stratifying are also considered. The various methods are extended to combination of results over the strata. Examples of case-control studies testing the association between HL-A frequencies and cancer illustrate the techniques. The parallel analyses of prospective studies are given. If P1 and P2 are small with large samples sizes the appropriate model is a Poisson distribution. This yields a exponential model with sufficient statistics. Exact conditional tests and confidence intervals can then be developed. Here we consider the case where two populations are compared adjusting for sex differences as well as for the strata (or covariate) differences such as age. The methods are applied to two examples: (1) testing in the two sexes the ratio of relative risks of skin cancer in people living in different latitudes, and (2) testing over time the ratio of the relative risks of cancer in two cities, one of which fluoridated its drinking water and one which did not.

Age Factors↗
PubMed1979

Statistical issues in interpretation of chronic bioassay tests for carcinogenicity.

The interpretation of chronic bioassay tests for carcinogenicity requires that the data be appropriately recorded. A "case history" for each animal links the pathology data for each organ of each animal to the length of its life. This information can be used in interpretation of the tumor incidences in light of the survival information. The role of historical controls was discussed, and the use of significance tests in a multidisciplinary approach to the assessment of the pattern of tumor response was suggested. Multiple comparison methods valid for the interpretation of continuous (or measurement) data do not apply to the discrete data analyses used in these studies. The ideas and methods of these studies were applied to an animal study of chloroform.

Animals↗
PubMed1979

Mathematical models and the statistical analyses of cell transformation experiments.

Statistical methods are developed and applied to the fitting of the one-hit curves to chemically induced transformations in Syrian hamster colonies. Data from several experiments in two laboratories are shown to fit the model well at all but the highest doses of benzo(a)pyrene. The ratio of the estimated parameters of the one-hit curves ("transformicities") is proposed as a measure of the enhancement by X-irradiation. Statistical tests for possible nonrandom variation among dishes are developed for the situation where a sample of dishes is used to estimate the total number of surviving cells. The methods of fitting and estimation are also extended to this case. Further analyses exclude selection as an explanation for the observed increase in transformation frequency with increased carcinogen concentration. The reproducibility of the fit of the one-hit model and the radiation enhancement measures is ascribed to the uniqueness of this in vitro system in which the direct target cell-insult interaction is not modulated by host intervention.

Animals↗
PubMed1977

Cell cycle of Saccharomycescerevisiae in populations growing at different rates.

The cell cycle of Saccharomyces cerevisiae in populations growing at different rates was analyzed by flow microflourometry. The results demonstrate that (i) variation in growth rate of the population depends mainly on variation in the G1 phase of the cell cycle, and (ii) atall growth rates initiation of DNA synthesis occurs concomitantly with initiation of budding.

Cell Cycle↗
PubMed1976

Relative activity of alpha-tocopherol and gamma-tocopherol in preventing oxidative red cell hemolysis.

The purpose of this study was to compare the antioxidant activities of alpha-tocopherol and gamma-tocopherol in protecting the red cell membrane against lipid peroxidation. Tocopherols were incorporated into the red cell membrane by incubating cells with solutions of the tocopherols in bovine albumin. The cells were then washed and subjected to the dialuric acid hemolysis test. Analysis of variance of the response curves revealed that gamma-tocopherol had 38% of the activity of alpha-tocopherol. No evidence was found for an interaction between the two tocopherols when present in the red cell membranes simultaneously.

Animals↗
PubMed1976

Bernstein's and gene-counting methods in generalized ABO-like systems.

Although the simple and adjusted Bernstein's methods are fully efficient for m=2 and m=3 (ABO system) respectively, their efficiency declines for larger values of m. For m greater than or equal to 4, the adjusted or modified Bernstein's method with a single counting iteration leads to a nearly efficient estimator. A single degree of freedom chi-square test of the Hardy-Weinberg law for all m is derived. Some findings on the statistical efficiency of typing various numbers of antigens are given. All the results are illustrated in numerical examples.

ABO Blood-Group System↗