Showing papers in "Biometrics in 1985"

Estimation of a common effect parameter from sparse follow-up data.

Abstract: Breslow (1981, Biometrika 68, 73-84) has shown that the Mantel-Haenszel odds ratio is a consistent estimator of a common odds ratio in sparse stratifications. For cohort studies, however, estimation of a common risk ratio or risk difference can be of greater interest. Under a binomial sparse-data model, the Mantel-Haenszel risk ratio and risk difference estimators are consistent in sparse stratifications, while the maximum likelihood and weighted least squares estimators are biased. Under Poisson sparse-data models, the Mantel-Haenszel and maximum likelihood rate ratio estimators have equal asymptotic variances under the null hypothesis and are consistent, while the weighted least squares estimators are again biased; similarly, of the common rate difference estimators the weighted least squares estimators are biased, while the estimator employing "Mantel-Haenszel" weights is consistent in sparse data. Variance estimators that are consistent in both sparse data and large strata can be derived for all the Mantel-Haenszel estimators.

Testing for qualitative interactions between treatment effects and patient subsets

Abstract: Evaluation of evidence that treatment efficacy varies substantially among different subsets of patients is an important feature of the analysis of large clinical trials. Qualitative or crossover interactions are said to occur when one treatment is superior for some subsets of patients and the alternative treatment is superior for other subsets. A non-crossover interaction arises when there is variation in the magnitude, but not in the direction, of treatment effects among subsets. Some authors use the term quantitative interaction to mean non-crossover interaction. Non-crossover interactions are usually of less clinical importance than qualitative interactions, which often have major therapeutic significance. A likelihood ratio test is developed to test for qualitative interactions. Exact critical values are determined and tabulated.

The life table and its applications

Abstract: The statistical theory of the ordinary life table is presented in this book, with its construction explained. Topics cover measures of mortality and adjustment of rates, and other areas include survival and stages of disease, reproduction, married life, antenatal life table and ecological studies.

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

Abstract: 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.

The Bias Due to Incomplete Matching

Abstract: Observational studies comparing groups of treated and control units are often used to estimate the effects caused by treatments. Matching is a method for sampling a large reservoir of potential controls to produce a control group of modest size that is ostensibly similar to the treated group. In practice, there is a trade-off between the desires to find matches for all treated units and to obtain matched treated-control pairs that are extremely similar to each other. We derive expressions for the bias in the average matched pair difference due to the failure to match all treated units--incomplete matching, and the failure to obtain exact matches--inexact matching. A practical example shows that the bias due to incomplete matching can be severe, and moreover, can be avoided entirely by using an appropriate multivariate nearest available matching algorithm, which, in the example, leaves only a small residual bias due to inexact matching.

Correspondence Analysis of Incidence and Abundance Data:Properties in Terms of a Unimodal Response Model

Abstract: Correspondence analysis is commonly used by ecologists to analyze data on the incidence or abundance of species in samples. The first few axes are interpreted as latent variables and are presumed to relate to underlying environmental variables. In this paper correspondence analysis is shown to approximate the maximum likelihood solution of explicit unimodal response models in one latent variable. These models are logistic-linear for presence/absence data and loglinear for Poisson counts, with predictors that are quadratic in the latent variable. The approximation is best when the maxima and tolerances (widths) of the response curves are equal and the species' optima and the sample values of the latent variable are equally spaced. It is still fairly good for uniformly distributed optima and sample values, as shown by simulation. For the models extended to two latent variables, the approximation is often bad because of the horseshoe effect in correspondence analysis, but improves considerably in the simulations when this effect is removed as it is in detrended correspondence analysis.

The effect of conditional dependence on the evaluation of diagnostic tests.

Abstract: The accuracy of a new diagnostic test is often determined by comparison with a reference test which also has unknown error rates. Maximum likelihood estimation of the error rates of both tests is possible if they are simultaneously applied to two populations with different disease prevalences. The estimation procedure assumes that the two tests are independent, conditional on a subject's true diagnostic status. If the tests are conditionally dependent, error rates for both tests can be substantially underestimated. Estimators for the prevalence rates in the two populations can be positively or negatively biased, depending on the relative magnitude of the two conditional covariances and the value of the prevalence parameter.

A semiparametric model for regression analysis of interval-censored failure time data.

Abstract: Left-, right-, and interval-censored response time data arise in a variety of settings, including the analyses of data from laboratory animal carcinogenicity experiments, clinical trials, and longitudinal studies. For such incomplete data, the usual regression techniques such as the Cox (1972, Journal of the Royal Statistical Society, Series B 34, 187-220) proportional hazards model are inapplicable. In this paper, we present a method for regression analysis which accommodates interval-censored data. We present applications of this methodology to data sets from a study of breast cancer patients who were followed for cosmetic response to therapy, a small animal tumorigenicity study, and a clinical trial.

Maximum likelihood estimation of variance components for a multivariate mixed model with equal design matrices.

Abstract: An algorithm is described for estimating variance and covariance components by restricted maximum likelihood for a multivariate mixed two-way classification with equal design matrices. The procedure involves a transformation to canonical scale, effectively reducing a q-variate analysis to q corresponding univariate analyses. A small numerical example is given as well as a large-scale practical application.

Two-stage analysis based on a mixed model: large-sample asymptotic theory and small-sample simulation results

Abstract: SUMMARY A two-stage analysis for the mixed model in which variance components due to the random effects are estimated and used to compute generalized least squares estimates of fixed effects is developed. Large-sample theory is used to establish asymptotic properties. An approximate t test that can be used to test linear contrasts among fixed effects is discussed. Two modest simulations, based on a model for a grazing trial (Burns, Harvey, and Giesbrecht, 1981, Proceedings of 14th International Grassland Conference, J. A. Smith and V. W. Hays (eds), 497-500, Boulder, Colorado: Westview Press; Burns et al., 1983, Agronomy Journal 75, 865-871) are used to show that the asymptotic results are reasonable for small samples.

A Bayesian approach to nonlinear random effects models.

Abstract: Nonlinear random effects models are considered from the Bayesian point of view. The method of analysis follows closely that of Lindley and Smith (1972, Journal of the Royal Statistical Society, Series B 34, 1-42). The numerical method is related to the EM algorithm.

Perpendicular Distance Models for Line Transect Sampling

Abstract: SUMMARY Perpendicular distance line transect models are examined to assess whether any single model can provide a general procedure for analysing line transect data. Of the two-parameter models considered, the hazard-rate model appears promising, whereas the exponential power series and exponential quadratic models do not. Of the nonparametric models, the Fourier series is the best developed, and is favoured by many researchers as a general model. However, for a given data set, the Fourier series estimate may be highly dependent on the number of terms selected, and so the model is not a clear improvement over the hazard-rate model. A similar variable-term model, using Hermite polynomials, is considered, and is shown to be less dependent on the number of terms selected. There has been some debate about whether the derivative of the density function of perpendicular distances evaluated at 0 should be 0, so that the function has a "shoulder." The problem is examined in detail, and it is argued that reliable estimation is not possible from line transect data unless a shoulder exists. Many data sets appear to exhibit no shoulder; possible reasons are examined.

Markov models for covariate dependence of binary sequences

Abstract: Suppose that a heterogeneous group of individuals is followed over time and that each individual can be in state 0 or state 1 at each time point. The sequence of states is assumed to follow a binary Markov chain. In this paper we model the transition probabilities for the 0 to 0 and 1 to 0 transitions by two logistic regressions, thus showing how the covariates relate to changes in state. With p covariates, there are 2(p + 1) parameters including intercepts, which we estimate by maximum likelihood. We show how to use transition probability estimates to test hypotheses about the probability of occupying state 0 at time i (i = 2, ..., T) and the equilibrium probability of state 0. These probabilities depend on the covariates. A recursive algorithm is suggested to estimate regression coefficients when some responses are missing. Extensions of the basic model which allow time-dependent covariates and nonstationary or second-order Markov chains are presented. An example shows the model applied to a study of the psychological impact of breast cancer in which women did or did not manifest distress at four time points in the year following surgery.

A cox regression model for the relative mortality and its application to diabetes mellitus survival data

Abstract: A Cox-type regression model for the ratio between the mortality in a cohort and that in a reference population is introduced. By means of the model it is possible to include in the survival analysis both individual (possibly time-dependent) characteristics for the study cohort and changing trends in the mortality in the reference population. This is particularly relevant in long-term follow-up studies where there may be considerable changes in the mortality in the reference population. Estimation procedures in the model are discussed and large-sample properties of the estimators are outlined. The model is applied to the analysis of two sets of data concerning the survival among insulin-dependent diabetics in Denmark.

Parsimonious modelling of capture―mark―recapture studies

Abstract: On propose une modelisation multinomiale generale des donnees de captures-recaptures issues d'une population animale ouverte. Dans ce cadre, un certain nombre d'hypotheses possibles sont suggerees pour les probabilites de survie, d'instant de recrutement et de probabilites de capture. Pour les modeles comportant moins de parametres que celui de Jolly-Seber, les estimations doivent etre faites numeriquement

Goodness of fit tests for open capture-recapture models.

Abstract: On propose des tests generaux d'ajustement pour le modele de Jolly-Seber. Ces tests sont fondes sur des raisonnements conditionnels utilisant des statistiques minimales exhaustives. Les liens de ces tests avec les autres tests existant sont examines. La procedure de test est illustree sur des donnees de capture-recapture des campagnols

A dose-response model for teratological experiments involving quantal responses.

Abstract: This paper introduces a dose-response model for teratological quantal response data where the probability of response for an offspring from a female at a given dose varies with the litter size. The maximum likelihood estimators for the parameters of the model are given as the solution of a nonlinear iterative algorithm. Two methods of low-dose extrapolation are presented, one based on the litter size distribution and the other a conservative method. The resulting procedures are then applied to a teratological data set from the literature.

Clustering means in ANOVA by simultanuous testing

Abstract: L'inference simultanee sur un ensemble de traitements equirepetes representes par k moyennes independantes distribuees normalement avec une estimation independante de leur variance commune est un probleme usuel. On propose deux methodes de classification «encastrees» de maniere «consequente» (non contradictoire) dans des procedures de tests simultanes (STP) appropriees, l'une dans une extension d'une procedure fondee sur l'etendue studentisee et l'autre fondee sur le test F. Il s'agit de classifier les traitements en un eventuellement petit nombre de groupes distincts mais homogenes. La premiere methode est une methode hierarchique, agglomerative et du plus proche voisin avec comme mesure de distance l'etendue de la reunion de deux groupes et avec la regle d'arret basee sur l'etendue studentisee generalisee STP. La seconde methode de classification n'est pas hierarchique; elle minimise la somme des carres intragroupes et la regle d'arret est basee sur la procedure de tests simultanes generalisee a partir du F. Des exemples numeriques montrent une ressemblance frappante entre les deux classifications resultantes pour un large spectre de risques egaux. Ces methodes sont comparees a celles proposees anterieurement dans ce contexte par Scott et Knott (1974, Biometrics 30, 507-512) et par Jolliffe (1975, in Applied Statistics, R.P. Gupta (ed.), 159-168, Amsterdam: North-Holland). On conclut par une discussion sur la pertinence des methodes presentees

Confidence limits for probability of response in multistage phase II clinical trials.

Abstract: Herson (1979, Biometrics 35, 775-783) has given a method for designing one-arm k-stage phase II clinical trials, which permits early termination of the trial if the treatment is apparently ineffective, while retaining acceptable levels of power and significance. This paper gives a method for calculating the confidence limits on the response proportion, conditional on a particular study design.

A Bayesian analysis of the two-period crossover design for clinical trials.

Abstract: Statisticians have been critical of the use of the two-period crossover designs for clinical trials because the estimate of the treatment difference is biased when the carryover effects of the two treatments are not equal. In the standard approach, if the null hypothesis of equal carryover effects is not rejected, data from both periods are used to estimate and test for treatment differences; if the null hypothesis is rejected, data from the first period alone are used. A Bayesian analysis based on the Bayes factor against unequal carryover effects is given. Although this Bayesian approach avoids the "all-or-nothing" decision inherent in the standard approach, it recognizes that with small trials it is difficult to provide unequivocal evidence that the carryover effects of the two treatments are equal, and thus that the interpretation of the difference between treatment effects is highly dependent on a subjective assessment of the reality or not of equal carryover effects.

Confidence intervals for a variance ratio, or for heritability, in an unbalanced mixed linear model

Abstract: A procedure is presented for constructing an exact confidence interval for the ratio of the two variance components in a possibly unbalanced mixed linear model that contains a single set of m random effects. This procedure can be used in animal and plant breeding problems to obtain an exact confidence interval for a heritability. The confidence interval can be defined in terms of the output of a least squares analysis. It can be computed by a graphical or iterative technique requiring the diagonalization of an m X m matrix or, alternatively, the inversion of a number of m X m matrices. Confidence intervals that are approximate can be obtained with much less computational burden, using either of two approaches. The various confidence interval procedures can be extended to some problems in which the mixed linear model contains more than one set of random effects. Corresponding to each interval procedure is a significance test and one or more estimators.

A two-sample test sensitive to crossing hazards in uncensored and singly censored data.

Abstract: Savage score statistics are employed to develop a test for comparing survival distributions with right-hand singly censored data. The procedure is motivated by the interest in developing a powerful method for determining differences when true survival distributions cross. Examination of small-sample characteristics under the null hypothesis indicate that asymptotic critical values yield a slightly conservative test. Power of the test compares favorably with other criteria, including the modified Smirnov procedure, particularly if there is a single crossing of the survival curves.