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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↗
PubMed1984

A score test for the possible presence of recessive alleles in generalized ABO-like genetic systems.

In generalized ABO-like genetic systems, particularly for certain human leukocyte antigen (HLA) loci, it is quite likely, even for large sample sizes, that no double recessives (or 'double blanks') may be found. It has been suggested that all such data should be analyzed as if the true recessive gene frequency were 0. We derive an easily computed score [or C(alpha)] statistic which tests for the possibility that, in such instances, this frequency may exceed 0. An associated point estimator is suggested. The methods are applied to the data analyzed by Smouse and Williams (1982, Biometrics 38, 757-768).

ABO Blood-Group System↗
PubMed1983

Dietary habits and lung cancer risk.

A previously reported negative association between a high index of dietary vitamin A and lung cancer incidence was confirmed in an extended follow-up, covering 11 1/2 years, of 13,785 men and 2,928 women, Responses to a postal questionnaire provided the dietary information. Relationships between the major dietary items and lung cancer were explored for various diagnostic subsets of the 168 lung cancer cases diagnosed among the study subjects. Analyses were stratified for sex, age, residence characteristics, cigarette smoking and, at times, socioeconomic group. Although the data do not permit a firm interpretation in terms of risk enhancement by a marginal retinoid deficiency, we found that the apparent protection afforded by higher intakes of vitamin A or its provitamins was particularly strong for lung cancer appearing as squamous-cell carcinoma and among those with higher alcohol intakes. The individual food items which showed the strongest negative association with lung cancer were carrots and milk. These two items made a major contribution to the vitamin A index and its variation among the respondents.

Age Factors↗
PubMed1983

Stratified trend and homogeneity analyses of proportions and life table data.

Tests for linear trend and homogeneity among proportions and analogous time adjusted tests for life table data are programmed for stratified data. For proportions, the maximum likelihood estimator of the common logistic slope and its approximate standard error is given. This parameter is related to the relative risk for the factor under test. The model is a simpler and more relevant subcase of the general linear multiple logistic model. Tests of fit include a chi-square test of departure from trend for both types of data, and, for proportions, a test for the equality of slopes among groups of strata. The program is particularly useful for large prospective studies in epidemiology, but may also prove helpful for case-control studies, clinical trials, and combining animal studies. Several optional analyses are included. The program generalizes most aspects of a previously published program by Thomas, Breslow, and Gart (Trend and homogeneity analyses of proportions and life table data. Comp. Biomed. Res. 10, 373 (1977)). A FORTRAN card deck with documentation is available upon request.

Actuarial Analysis↗
PubMed1982

The performance of three approximate confidence limit methods for the odds ratio.

The performance of three approximate confidence limit methods for the odds ratio, R, is studied at the 95% level in the unconditional sample space. There are: the method proposed by Cornfield (Proceedings of the 3rd Berkeley Symposium 1956;4:135-48), the logit method with 1/2 corrections first considered by Woolf (Ann Hum Genet 1955;19:251-3), and the test-based method proposed by Miettinen (Am J Epidemiol 1976;103:226-35). Cornfield's method comes closest to attaining the normal confidence coefficient. The logit method typically has actual confidence coefficients somewhat too large with disparate tail areas. The latter is ascribed in part to the enhanced skewness induced by the logit transformation itself. The test-based method has actual coefficients uniformly less than nominal when R not equal to 1. This underestimation is worse in finite samples than Halperin found it to be asymptotically. Although the Cornfield and test-based methods have the same confidence coefficients for R = 1, the test-based method is more likely to cover distant values of R not equal to 1 when in fact R = 1. It is concluded that Cornfield's method without the continuity correction is the preferred approximate method in the unconditional space as, with the continuity correction, it was previously found to be in the conditional space.

Abnormalities, Drug-Induced↗
PubMed1981

Carcinogenicity tests of certain environmental and industrial chemicals.

Fourteen chemicals of varied uses were tested for carcinogenicity by oral administration in male and female Charles River CD rats. Under the conditions of the tests, propane sultone, propylene imine, and ethylenethiourea, in addition to the positive control N-2-fluorenylacetamide, were carcinogenic. Avadex, bis(2-chloroethyl) ether, the potassium salt of bis(2-hydroxyethyl) dithiocarbamic acid, ethylene carbonate, and semicarbazide hydrochloride were not carcinogenic under the test conditions. Dithiooxamide, glycerol alpha-monochlorohydrin, and thiosemicarbazide gave somewhat ambiguous results, though administered at high enough dose levels to be toxic. An inadequate number of animals survived treatments with sodium azide, sodium bisulfide, and vinylene carbonate, or the animals may not have received sufficiently high doses of the test chemicals to provide maximum test sensitivity. However, there were no indications that these three chemicals were carcinogenic under the test conditions.

2-Acetylaminofluorene↗
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↗