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Biomedical subjects

J W Tukey

Publications and source records attributed to J W Tukey.

15 recordsLinked to original sources
PubMed2000

Efficacy estimates from parasite count data that include zero counts.

Because of the positive skewness of parasite distributions and the greater constancy of percentage of response of therapy in animal populations, parasite count data are conventionally transformed logarithmically before combining results from different animals, either all controls or all treated. Observations of zero counts raise difficulties, since the logarithm of zero is not useful. In this study, several types of zero count adjustments are compared. Two systems for assigning values to zero counts were considered: a fixed system, which assigns the same value to all zero counts regardless of the proportion of such counts in a treatment group, and a variable system, which replaces zero counts with a value based on the proportion of zero counts in the group. The values assigned by either system are then adjusted to reflect aliquot size. An evaluation was performed by using 32 compound Poisson lognormal distributions, three sample sizes, and three representatives of each zero count adjustment system. The Poisson lognormal distribution provides a convenient method with which to provide variability greater than Poisson. Expected values of the sample estimate of the (known) population mean were calculated for each of the 576 combinations of these factors, and the bias associated with each combination was derived. The bias associated with the three representatives of the variable adjustment system was similar. The variable adjustment system had a lower overall bias than any representatives of the fixed adjustment system.

Animals↗
PubMed2000

A sensible formulation of the significance test.

The conventional procedure for null hypothesis significance testing has long been the target of appropriate criticism. A more reasonable alternative is proposed, one that not only avoids the unrealistic postulation of a null hypothesis but also, for a given parametric difference and a given error probability, is more likely to report the detection of that difference.

Confidence Intervals↗
PubMed1996

Urbanicity-related trends in lung cancer mortality in US counties: white females and white males, 1970-1987.

BACKGROUND: The effect of urbanization on age-adjusted lung cancer mortality rates in US counties is investigated. The data come from National Cancer Institute, and urban trends are estimated in time periods 1970-1979 and 1980-1987, for both white males and white females. To account for possibly different gradients in different parts of the country, the 48 contiguous states are divided into seven regions. METHODS: A measure of urbanness, urbanicity, is defined and is used to stratify counties. A multiplicative model is proposed that relates county mortality rates to urbanicity. The residuals from this multiplicative model serve as age- and urban-adjusted rates. RESULTS: Urban-rural gradients are significant for nearly all regions for both white males and white females, diminishing slightly in the latter time period for white males but becoming stronger for white females. CONCLUSIONS: The age- and urban-adjusted rates may be used in mapping to investigate geographical patterns that remain after removal of the urban factor.

Female↗
PubMed1993

Tests for qualitative treatment-by-centre interaction using a 'pushback' procedure.

In multicentre clinical trials using a common protocol, the centres are usually regarded as being a fixed factor, thus allowing any treatment-by-centre interaction to be omitted from the error term for the effect of treatment. However, we feel it necessary to use the treatment-by-centre interaction as the error term if there is substantial evidence that the interaction with centres is qualitative instead of quantitative. To make allowance for the estimated uncertainties of the centre means, we propose choosing a reference value (for example, the median of the ordered array of centre means) and converting the individual centre results into standardized deviations from the reference value. The deviations are then reordered, and the results 'pushed back' by amounts appropriate for the corresponding order statistics in a sample from the relevant distribution. The pushed-back standardized deviations are then restored to the original scale. The appearance of opposite signs among the destandardized values for the various centres is then taken as 'substantial evidence' of qualitative interaction. Procedures are presented using, in any combination: (i) Gaussian, or Student's t-distribution; (ii) order-statistic medians or outward 90 per cent points of the corresponding order statistic distributions; (iii) pooling or grouping and pooling the internally estimated standard deviations of the centre means. The use of the least conservative combination--Student's t, outward 90 per cent points, grouping and pooling--is recommended.

Clinical Trials as Topic↗
PubMed1993

Evaluation of multicentre clinical trial data using adaptations of the Mosteller-Tukey procedure.

Two procedures, based on proposals discussed by Mosteller and Tukey, are described for obtaining a combined estimate of the difference between two treatment means and its confidence interval from multicentre clinical trial data. Both procedures provide estimates in the possible presence of heteroscedasticity. The first procedure is designated the primary analysis for efficacy assessment. It omits treatment-by-centre interaction from the error term for treatment, unless there is substantial evidence of qualitative interaction (Ciminera et al.) or other special circumstances. The second procedure is the primary analysis whenever there is substantial evidence of qualitative interaction, and can be used whenever there are other reasons to make an analysis allowing for interaction.

Asthma↗
PubMed1993

Tightening the clinical trial.

Randomized clinical trials adhere more closely to pre-agreed-on protocols than almost any other type of experiment, yet we can tighten up their analysis if we desire. If we convert the analysis into a randomization analysis--where the one set of data is analyzed many times--once as though each acceptable assignment has been employed, we can eliminate any dependence of the analysis on statistical or probabilistic assumptions. To do this effectively when many assignments could be acceptable, we can go to double randomization, in which a subset, usefully kept balanced, of acceptable assignments is selected (perhaps randomly) before data acquisition. If we have one covariate, adjustment for which answers a question that is at least as appropriate, we can easily build on this. Imperfect covariance adjustments can help almost as much as perfect ones. If it is appropriate to work with many covariate(s), it is often desirable to first construct a (few) compound covariate(s) and then work with it (them). Often we can base the coefficients in our compound covariate on the univariate regressions of response on single covariates. Doing this within each arm of the trial and pooling keeps the fitting of the final adjustment unbiased. Since we can prespecify how the compounds are to be calculated and fitted, we can do all this while retaining rigid prespecification. Prespecification, randomization, and intelligent use of covariates combined to make the resulting significance analysis of platinum standard quality. (If we want confidence statements, as we ordinarily should, it may make sense, for technical reasons, to plan for somewhat less than platinum standard quality).

Humans↗
PubMed1989

Adjusting the 1980 census of population and housing.

"In 1980, several cities and states sued the U.S. Census Bureau to correct census results. This correction would adjust for the differential undercounting of Blacks and Hispanics, especially in cities. In this article, the authors, each of whom testified for New York City and State in their joint lawsuit against the Census Bureau, describe the likely pattern of the undercount and present a method to adjust for it." The authors describe available methods for data adjustment and introduce a regression-based composite method of adjustment, which is used to estimate the undercounts for 66 areas. "As expected, we find that the highest undercount rates are in large cities, and the lowest are in states and state remainders with small percentages of Blacks and Hispanics. Next, we analyze how sensitive our estimates are to changes in data and modeling assumptions. We find that these changes do not affect the estimates very much. Our conclusion is that regardless of whether we use one of the simple methods or the composite method and regardless of how we vary the assumptions of the composite method, an adjustment reliably reduces population shares in states with few minorities and increases the shares of large cities."

Black or African American↗
PubMed1985

Testing the statistical certainty of a response to increasing doses of a drug.

Experiments in which the treatments are composed of a series of doses of a compound and a zero dose control are often used in animal toxicity studies. A test procedure is proposed to assess trends in the response variable. The notion of a no-statistical-significance-of-trend (NOSTASOT) dose is introduced, and questions of multiplicity of statistical tests in this context are addressed.

Animals↗
PubMed1978

Inversion of articulatory-to-acoustic transformation in the vocal tract by a computer-sorting technique.

We present numerical methods for studying the relationship between the shape of the vocal tract and its acoustic output. For a stationary vocal tract, the articulatory-acoustic relationship can be represented as a multidimensional function of a multidimensional argument: y=f(x), where x, y are vectors describing the vocal-tract shape and the resulting acoustic output, respectively. Assuming that y may be computed for any x, we develop a procedure for inverting f(x). Inversion by computer sorting consists of computing y for many values of x and sorting the resulting (y,x) pairs into a convenient order according to y; x for a given y is then obtained by looking up y in the sorted data. Application of this method for determining parameters of an articulatory model corresponding to a given set of formant frequencies is presented. A method is also described for finding articulatory regions (fibers) which map into a single point in the acoustic space. The local nature of f(x) is determined by linearization in a small neighborhood. Larger regions are explored by extending the linear neighborhoods in small steps. This method was applied for the study of compensatory articulation. Sounds produced by various articulations along a fiber were synthesized and were compared by informal listening tests. These tests show that, in many cases of interest, a given sound could be produced by many different vocal-tract shapes.

Acoustics↗
PubMed1977

Some thoughts on clinical trials, especially problems of multiplicity.

Problems of statistical and conceptual design of experiments are exacerberated by ethical issues in many, if not most, clinical trials. Statutory requirements of demonstrated effectiveness are far from being clearly resolved--either qualitatively or quantitatively. Ethics, bolstered by informed consent, are likely to keep us from ever learning the answer to many questions. Unbalanced boundaries, focusing-down designs, historical controls, and not-very-sequential designs are among the possible consequences.

Bayes Theorem↗
PubMed1975

An improved Mantel-Bryan procedure for "safety" testing of carcinogens.

A published method by Mantel and Bryan for calculating "safe" doses of carcinogens is updated by incorporating several improvements. These improvements include more effective procedures for taking into account any spontaneous tumor rate and for combining data at several dose levels. An added feature is that it permits the combining of data from several experiments by postulating that it is only the spontaneous rate that differs between experiments. The improved method is illustrated with data from five hypothetical experiments, using a risk level of 10-8, a conservative slope of one probit or normal deviate per tenfold dose increase, and a nominal assurance level of 99%. The hypothetical experiments were geared to bring out particular pointsas, for example, the applicability of the model in the absence of control data. A large variety of issues involved in the determination of "safe" doses are discussed, including questions of experiment design and extrapolitan between species. A statistical appendix is provided, laying the framework for the calculating procedure and detailing complications therein. The "safe" dose approach helps resolve certain dilemmas in questions relating to food additives. A "no-detectable-level" prescription for chemical residues may be dangerous to the public where detection techniques are insufficiently sensitive, but it can become far too restrictive as exquisitely sensitive detection techniquesare developed. Only levels in excess of the "safe" dose would require detection. Calculated values for the "safe" dose could be updated and increased as more clear evidence of safety becomes available.

Animals↗
PubMed1975

Higher-order diagnosis of two-way tables, illustrated on two sets of demographic empirical distributions.

Two-way tables of all kinds often require diagnosis, usually of the residuals after some simple fit such as row-PLUS-column or row-TIMES-column. The first step in diagnosis is likely to be either one-degree-of-freedom-for-non-additivity or a diagnositic plot (for which the former is the linear regression term). Not all diagnoses can be made at the first step. Some diagnostic plots appear like a diagonal cross, or, when such an appearance is not quite clear, become converted to oppositely tilted pictures when we look only at points with high fitted values and, separately, at those with low fitted values. Such behavior diagnoses a need for a more subtle re-expression than powers and logs, in our examples a need for a re-expression like plamda -(1 - p)lamda. The appearance and treatment of such diagnoses, in two examples, lead into the use of letter-value displays and the associated plots to study the character of non-normality, instances of the effect of the method of fitting on the shape of the distribution of residuals, and convenient algorithms for the iterative, recursive fitting of a variety of additive, multiplicative, and mixed additive-multiplicative models to any kind of two-way table, APL programs for which are appended.

Adolescent↗