Showing papers in "Biometrics in 1980"

Design and analysis of experiments in the animal and medical sciences

Abstract: Design and analysis of experiments in the animal and medical sciences , Design and analysis of experiments in the animal and medical sciences , مرکز فناوری اطلاعات و اطلاع رسانی کشاورزی

Estimating the Error Rates of Diagnostic Tests

Abstract: It is often required to evaluate the accuracy of a new diagnostic test against a standard test with unknown error rates. If the two tests are applied simultaneously to the same individuals from two populations with different disease prevalences, then assuming conditional independence of the errors of the two tests, the error rates of both tests and the true prevalences in both populations can be estimated by a maximum likelihood procedure. Generalizations to several tests applied in several populations are also possible.

Bias Reduction Using Mahalanobis-Metric Matching

Abstract: SUMMARY Monte Carlo methods are used to study the ability of nearest available Mahalanobis metric matching to make the means of matching variables more similar in matched samples than in random samples.

The crossover experiment for clinical trials.

Abstract: The two-period crossover or changeover design for clinical trials is compared with other simple designs in terms of statistical precision and cost. The sensitivity of the crossover to bias due to carryover effects is examined. The feasibility of using the crossover data to test for the existence of carryover effects is investigated and found to be uneconomical. A numerical example is presented.

The analysis of rates and of survivorship using log-linear models.

Abstract: Models are considered in which the underlying rate at which events occur has a log-linear relationship with covariates. It is shown that the estimation of parameters involves the solution of identical systems of equations for data from either a Poisson process, an exponential distribution, a survival model or a generalized log-linear model. This enables one to use algorithms for fitting log-linear models, such as iterative proportional fitting (IPF), for the analysis of rates or survivorship.

A simple approximation for calculating sample sizes for comparing independent proportions.

Abstract: A simple approximation is provided to the formula for the sample sizes needed to detect a difference between two binomial probabilities with specified significance level and power The formula for equal sample sizes was derived by Casagrande, Pike and Smith (1978, Biometrics 34 , 483-486) and can be easily generalized to the case of unequal sample sizes It is shown that over fairly wide ranges of parameter values and ratios of sample sizes, the percentage error which results from using the approximation is no greater than 1% The approximation is especially useful for the inverse problem of estimating power when the sample sizes are given

The estimation of intraclass correlation in the analysis of family data.

Abstract: The maximum likelihood estimator of the intraclass correlation coefficient rho in samples of unequal size from a multivariate normal distribution has been derived and compared to several other estimators, using Monte Carlo simulation. It is recommended that maximum likelihood be used if no prior knowledge concerning the value of rho is thought to be high. Fow low to moderate values of rho it is recommended that the analysis of variance estimator be used, with those families having only one member deleted from the analysis.

A comparison of tests for Hardy-Weinberg equilibrium.

Abstract: The various tests for the goodness of fit of a population to Hardy-Weinberg equilibrium are compared with respect to their power and the accuracy of their distributional approximations. The tests are similar in terms of power. However, when one or more alleles are rare (with frequencies of less than .45 to .21 for n = 10 and 200, respectively) some of the tests are not able to detect outbreeding. When all but one allele are rare (frequencies of less than .40 to .15 for n = 10 and 200, respectively) none of the tests are able to detect outbreeding. In terms of distributional assumptions, there are two situations: (i) Test of hypothesis (when a preset significance level is chosen and the null hypothesis accepted or rejected at that level); here the chi square test with conditional expectations, the Freeman-Tukey test and the Mantel-Li test, all without continuity correction, were found to be best; they were closely followed by the chi square test and conditional chi square test, both with a continuity correction of 1/4, and by the Elston-Forthofer average test. (ii) Test of significance (when the obtained level of significance is used as strength against the null hypothesis); here the chi square test and conditional chi square test, both with a continuity correction of 1/4, and the average test were found to be best.

Modified Kolmogorov-Smirnov Test Procedures with Application to Arbitrarily Right-Censored Data

Abstract: The classical Kolmogorov one-sample goodness-of-fit and Smirnov two-sample test procedures are modified in an attempt to obtain increased power when applied to uncensored data. Both are then generalized for use with arbitrarily right-censored data. Motivation for the formulation of the generalized procedures is provided heuristically by appealing to the basic concept upon which the procedures for uncensored data are based; a theoretical motivation is provided by asymptotic weak convergence results. The size and power of the generalized Smirnov two-sample procedure are evaluated for small and moderate sample sizes using Monte Carlo simulations. Results of the simulations are also used to make comparisons with the Gehan-Wilcoxon and logrank two-sample test procedures. The generalized Smirnov procedure is found to maintain the size of the test in nearly all the cases studied, although it is conservative in small samples of heavily censored data. It is found to be more powerful than both the Gehan-Wilcoxon and the logrank procedures for the non-Lehmann alternatives considered.

Extension of the Kappa Coefficient

Abstract: An extension of the kappa coefficient is proposed which is appropriate for use with multiple observations per subject (not necessarily an equal number) and for multiple response choices per observation. Computational methods and nonasymptotic, nonnull distribution theory are discussed. The proposed method is applied to previously published data, not only to compare results with those in earlier methods, but to illustrate new approaches to difficult problems in evaluation of reliability. The effect of using an 'Other' response category is examined. Strategies to enhance reliability are evaluated, including empirical investigation of the Spearman-Brown formula as applied to nominal response measures.

Estimation of Variance Using Judgment Ordered Ranked Set Samples

Abstract: Ranked set sampling has been shown by Dell and Clutter (1972, Biometrics 28, 545-553) to be a useful technique for improving estimates of the mean when actual measurement of the observations is diflicult but ranking of the elements in a sample is relatively easy. The technique is extended here to show an estimator of variance, which is asymptotically unbiased regardless of the presence of errors in ranking. Furthermore, the asymptotic efficiency of these estimators, relative to those based on the same number of quantified observations from a random sample, is greater than unity for any underlying distribution, even if ranking errors occur.

A treatment allocation procedure for sequential clinical trials.

Abstract: A dynamic treatment allocation procedure is proposed for clinical trials which require balancing across several prognostic factors. The treatment allocation decision is based on the minimization of a function which is an easily evaluated approximation to the variance of the treatment effect in a linear model relating the outcome variable to the chosen prognostic factors and selected interactions. By use of simulations, the procedure is shown to be superior to ad hoc procedures proposed by Pocock and Simon (1975, Biometrics 31, 103-115), over a variety of reasonable experimental situations. It is shown that it is feasible to evaluate the procedure by hand calculations and that it is extremely easy if a small programmable calculator is available. Practical problems relating to implementation of the procedure are discussed with special reference to multi-institutional clinical trials.

An analysis of comparative carcinogenesis experiments based on multiple times to tumor.

Abstract: Methods are given for the comparison of two treatment groups in experiments giving rise to multiple tumors. Methods based on the gaps in time between successive tumors are emphasized, but, for comparison, one method based directly on times to tumor is also presented. When applied to the results of an experimental animal carcinogenesis study, these analyses show that a diet supplemented with retinyl acetate reduces the hazard of mammary tumors, compared with controls, in every gap, and they allow one to combine evidence from the several gaps to obtain a powerful test for treatment effect.

Why data bases should not replace randomized clinical trials.

Abstract: Advances in computer technology have made it possible to store large amounts of observational data concerning treatment of patients for medical disorders. It has been suggested that these data banks might replace randomized clinical trials as a means of evaluating the efficacy of therapies. A review of the methodological problems likely to arise in analyzing such data for the purpose of comparing treatments suggests that sound inferences would not generally be possible because of difficulties with bias in treatment assignment, nonstandard definitions, definitions changing in time, specification of groups to be compared, missing data, and multiple comparisons.

Optimum Age-Specific Harvesting in a Nonlinear Population Model

Abstract: The age-specific harvesting policy for maximizing equilibrium yield in a discrete-time, selfregenerating, age-structured population model is determined. The model assumes that survival of animals in their first year of life is density-dependent, while survival, growth and fecundity at other ages are density-independent. The optimal policy is of the 'two-age' type. Other forms of age-selective harvesting, which are practically more feasible, are discussed, and an example using data for Arcto-Norwegian cod is provided to demonstrate the possibility of increasing yields from fisheries by such methods.

The probability of losing an allele when diploid genotypes are sampled.

Abstract: Given the genotypic frequencies for a single gene locus with an arbitrary number of alleles in a hypothetically infinite population, the probability of losing at least one of the alleles in a sample of genotypes from this population is derived. The sensitivity of this probability to changes in the population frequencies of heterozygotes and of alleles has been investigated and has proved to be in accord with intuitive expectations. Least upper bounds for this probability, in cases where only the allelic frequencies or the minimum allelic frequency of alpha is known, have been found and the correspondence of these bounds to the situation of sampling of gametes rather than genotypes has been pointed out. It has been proved that the latter bound is also the least upper bound of the probability of losing at least one of the alleles with frequencies greater than or equal to alpha in a sample of genotypes or gametes if neither the number of alleles in the population nor the genotypic frequencies are known. This result has been used for the compilation of a table of the minimum sample sizes required to assure that all alleles with frequencies greater than or equal to alpha are detected with probability 1-sigma for the different values of alpha or sigma.

A new approach to the analysis of clinical drug trials with withdrawals.

Abstract: In clinical drug trials which require observation of patients for more than a few days or weeks, some patients may withdraw before completing the planned course of the trial for reasons that are related to the therapy, for example adverse experiences or lack of therapeutic effect. If the number of such withdrawals is material, then analysis of the data from these trials should account for these withdrawals. Ignoring them in the analyses or using the last recorded value before withdrawl can lead to misleading conclusions. If the response outcomes can be ordered so that, for instance, adverse withdrawals can be regarded as "bad" outcomes, then the withdrawals can be incorporated into the analyses straightforwardly. The method is described and illustrated, and several issues arising in its application are discussed.

Generalized Odds Ratios for Ordinal Data

Abstract: We consider properties of the ordinal measure of association defined by the ratio of the proportions of concordant and discordant pairs. For 2 x 2 cross-classification tables, the measure simplifies to the odds ratio. The generalized measure can be used to summarize the difference between two stochastically ordered distributions of an ordinal categorical variable. The ratio of its values for two groups constitutes an odds ratio defined in terms of pairs of observations. Unlike the odds ratio measures proposed by Clayton (1974, Bionxetrika 61, 525-531) for similar purposes, this measure is not linked to specific model assumptions and hence it is more widely applicable as a descriptive measure.

On Sampling Spatial Patterns by Distance Methods

Abstract: 'Distance' or 'nearest neighbour' methods are often used as alternatives to counting plants within squares ('quadrat' methods) either to estimate the number of plants in a study region or to test the 'randomness' of their pattern.To be specific we will consider trees; Figure 1 illustrates a 10 metre square plot of pines (from Strand, 1972). The suggested procedures for density estirnation and for testing have been compared by Diggle (1975 1977), Diggle, Besag and Gleaves (1976), and Hines and Hines (1979). The method suggested by Hopkins (1954) invelves measuring the following squared distances: u from a random point to the nearest tree and v from a randomly chosen tree to its nearest neighbour. Edge effects should be made negligible by placillg the study region from which random points and plants are to be selected well within the region of interest. Hopkins' method has generally been preferred in comparison studies but is usually regarded as impracticable since, to find a random tree, all trees in the study regioIl should be counted and a randomly numbered tree chosen. Squared distances arise because the areas swept out in searches for the nearest trees are Fru and Frv, if the search is thought of in concentric circles about the chosen point or tree. The distribution tlleory assulnes that for a Poisson process the areas ru and xv will be independent. For this to hold it should be checked that the areas searched do not overlap, which constrains the number of samples that can be taken. We consider bounds on the sampling intensity and we introduce a semisystematic sampling scheme which allows a higher sampling intensity and permits Hopkins' method to be used without complete enumeration of the study region. A new test for 'randomness' related to Hopkins' test is introduced; a Monte Carlo study shows that this test and

A reparameterization of a genetic selection index to locate its sampling properties.

Abstract: A transformation is proposed of the variables used for constructing genetic selection indices, such that the reparameterized phenotypic covariance matrix is identity and the genetic covariance matrix is diagonal. These diagonal elements play the role of heritabilities of the transformed variables. The reparameterization enables sampling properties of the index weights to be easily computed and formulae are given for data from half-sib families. The index is likely to be least stable when the transformed variables of low heritability have high economic weights, and the weights will have highest sampling variance when these heritabilities are nearly equal. It is suggested that the sample roots of the determinantal equation be inspected when constructing an index in order to give some guide to its accuracy.

Assessing laboratory evidence for neoplastic activity.

Abstract: A variety of statistical issues which arise in the analysis of tumorigenesis assay data are reviewed. Tumor acceleration appeared as a possibility in the Red Dye 40 situation and that phenomenon is discussed. Experimental design considerations covered include sex, cage locations, and whether there is complete randomization, or whether littermates are stratified across doses, or whether, as in multigeneration studies, all littermates are treated alike. Whichever, the statistical analysis should be appropriate. Statistical techniques must take into account the time-to-response aspect in the detection of palpable tumors along with the complication of censored observation due to interim mortality. A logrank technique for accomplishing this must be further adjusted so as to handle tumors detectable only on necropsy. Dosage effects may be sought in a variety of ways, including alternative procedures for identifying progressive dosage effects. Separate analyses may be conducted for separate tumor sites or types, introducing a multiple-testing aspect. Because of the sparseness of data for many individual tumor sites, the usual multiple-testing procedures have to be modified. Statistical analysis, however, is only a guide to the careful interpretation of results, and the need to take action as a result of that interpretation remains.

Estimation of the Mean for Lognormal Data Containing Zeroes and Left-Censored Values, with Applications to the Measure- ment of Worker Exposure to Air Contaminants

Abstract: SUMMARY The robustness to certain deviations from model assumptions of two methods of estimating the mean for lognormal data containing zeroes and left-censored values are compared on the basis of mean squared error for small sample sizes. Using Monte Carlo simulation techniques, comparisons of the performance of the two estimators are made for three situations in which the underlying distributions generate data consisting of: (i) uncensored lognormal data augmented with zeroes, (ii) censored and uncensored lognormal data with no zeroes, and (iii) lognormal data with zeroes and censored values. In all three cases the minimum variance unbiased estimator for the delta distribution given by Aitchison (1955: Journal of the American Statistical Association 50, 901-908) is superior to a censored lognormal estimator based on the parameter estimation methods in Aitchison and Brown (1969: The Lognormal Distribution. Cambridge: Cambridge University Press). The results of the simulations are applied to a data set collected for the purpose of estimating the average exposure of industrial workers to an air contaminant.