Agnes Berger

On the theory of C[alpha]-tests

While in principle, score tests and C[alpha]-tests provide asymptotically optimal tests for composite hypotheses, in practice, these techniques often lead to intractable calculations. The tests proposed here are asymptotically equivalent to C[alpha]-tests, and require only routinely available software, thus greatly enlarging the practical reach of asymptotic theory.

Nephrosis of childhood: Statistical evaluation of the effect of adrenocortical-active therapy

Abstract In summary, the evidence now available supports the belief that prolonged and intensive use of adrenocortical-active hormone therapy in childhood nephrosis not only improves the clinical status but also extends life. Only time will tell whether it will prove curative. We have suggested the use of the sedimentation rate as an added simple criterion to help decide when to give or withdraw such treatment.

AN IMPROVED ASSAY TECHNIQUE FOR MATRONE, A MOSQUITO PHEROMONE, AND ITS APPLICATION IN ULTRAFILTRATION EXPERIMENTS*

Abstract An improved assay technique is presented for the detection of matrone, the mosquito pheromone which prevents insemination in female mosquitoes. This new technique requires 24 hours less to complete. The number of repeat tests necessary is reduced by 50% as compared to the number required utilizing the old technique and the reliability of the test is improved through the visual surveillance of the flight ability and mating activity of the females. Incorporated into this assay technique is the construction and use of a dose (dilution) response curve (calibration line) with a confidence band, establishing a threshold level of matrone activity and making it possible to assess the dilution of matrone in any non-toxic test material. Utilizing this new technique, we demonstrated by ultrafiltration that the molecular weight of matrone is between 50,000 and 100,000.

Malignant melanoma in spouses

A study of three married couples where both spouses developed malignant melanoma was undertaken at the New York University‐Bellevue Medical Center melanoma registry. An upper bound was calculated for the number of spouses expected to develop melanoma, along with the origin of the disease and its relation to nation‐wide rates of incidence. The observed number was six times greater than the bound.

Note on Cochran's Q-Test for the Comparison of Correlated Proportions

Abstract Cochrans Q-test, proposed to test the equality of three proportions for correlated observations, may have a larger asymptotic significance level than the nominal one, unless the admissible family of distributions is restricted to ensure that under the hypothesis the correlations between the observations are also equal. For a large class of such restricted families, optimal C 2(α) tests of the hypothesis are obtained, and the family for which the Q-test is an optimal C 2(α) test is identified. The use of Q for testing a related hypothesis, suggested by Madansky, is also discussed: it is shown that the Q-test is not consistent against all alternatives to Madanskys hypothesis, while the classical χ2-test provides an optimal C 4(α) test for it.

On Comparing Intensities of Association between Two Binary Characteristics in Two Different Populations

Abstract Asymptotically favorable methods for testing the equality of certain measures of association in different four-fold tables are deduced from the general theory of χ2-tests as given by Neyman and generalized by Anderson, Goodman and Gold. The tests turn out to be also obtainable by an intuitive use of maximum likelihood estimates as suggested by Walds large sample theory and include one proposed by Lancaster for testing the second order interaction in a complex contingency table. Applications in the field of drug research and health surveys are indicated.

On the Asymptotic Power of Tests for Comparing K Correlated Proportions

Abstract The limit distribution of Cochrans Q statistic for testing the equality of k proportions in matched samples is obtained for sequences of Pitman alternatives. Comparison of the asymptotic power of the test based on the Q statistic with that of the test based on Walds statistic for the same asymptotic level shows that neither test is uniformly better than the other. We study by simulation a modified Q test using an estimated critical value obtained from a Satterthwaite-type approximation for cases when the proportions to be compared are near one-half and k = 4. The operating characteristics agree closely with estimated values in samples of 50 and 100, while the agreement with the Wald statistics was occasionally poor.

On the Question of Whether a Disease is Familial

Abstract In trying to determine whether a disease is familial, epidemiologists often locate a source of cases and compare the proportion of affected relatives of these cases with that of the relatives of controls by the usual fourfold table techniques. In the model considered here, following Haenszel [5], the probability of being affected is a random variable, ρ, which is constant for members of the same “family” but which may vary from family to family. The usual tests are examined under a sampling scheme designed to simulate actual epidemiological practice, and it is found that if ρ is the same for all families, the proportions of affected relatives in the two groups are distributed as binomial proportions from the same universe. If ρ is not constant, the proportions are no longer binomial, but the tests used are shown to be consistent nevertheless. A large sample confidence interval for Eρ is derived.

Weighted Logrank Tests to Detect a Transient Improvement in Survivorship

In investigating whether an intervention has an effect on survival, we exploit the flexibility of weighted logrank tests for constructing optimal tests sensitive to specified patterns of changes in the ratios or differences of the hazards as a function of time. The tests presented seem appropriate if either the intervention on trial imposes changes in life style, such as a diet modification or an exercise regimen, or if the effect of therapy itself is limited in duration, such as in the case of drugs for AIDS that may induce drug resistant viruses. For such problems, we postulate no difference between the hazards of the two groups initially, increased discrepancies as time goes on, and an eventual leveling-off of the discrepancies in hazards perhaps due to compliance problems or to adoption of the behavior change under study by individuals in the control group. We suggest a quadratic weight function for such problems and show how to evaluate the power of the proposed tests as well as their efficiency relative to other logrank tests. Other uses of quadratic weight functions, for example for evaluating effects with lag times, and for some parametric procedures are also described. Additive and multiplicative models are presented and both discrete and continuous times are considered.

On comparing survival probabilities from discrete observations under unequal censoring

In this paper C([alpha]) tests are derived for the discrete Markov chain set-up that are locally asymptotically most powerful (LAMP) against alternatives with constant odds ratios for the comparison of survival rates under possibly unequal censoring.