Showing papers in "Journal of the royal statistical society series b-methodological in 1983"
TL;DR: In this article, the authors proposed a simple technique for assessing the range of plausible causal con- fusions from observational studies with a binary outcome and an observed categorical covariate, under several sets of assumptions about u. The technique assesses the sensitivity of conclusions to assumptions about an unobserved binary covariate relevant to both treatment assignment and response.
Abstract: This paper proposes a simple technique for assessing the range of plausible causal con- clusions from observational studies with a binary outcome and an observed categorical covariate. The technique assesses the sensitivity of conclusions to assumptions about an unobserved binary covariate relevant to both treatment assignment and response. A medical study of coronary artery disease is used to illustrate the technique. Inevitably, the results of clinical studies are subject to dispute. In observational studies, one basis for dispute is obvious: since patients were not assigned to treatments at random, patients at greater risk may be over-represented in some treatment groups. This paper proposes a method for assess- ing the sensitivity of causal conclusions to an unmeasured patient characteristic relevant to both treatment assignment and response. Despite their limitations, observational studies will continue to be a valuable source of information, and therefore it is prudent to develop appropriate methods of analysis for them. Our sensitivity analysis consists of the estimation of the average effect of a treatment on a binary outcome variable after adjustment for observed categorical covariates and an unobserved binary covariate u, under several sets of assumptions about u. Both Cornfield et al. (1959) and Bross (1966) have proposed guidelines for determining whether an unmeasured binary covariate having specified properties could explain all of the apparent effect of a treatment, that is, whether the treatment effect, after adjustment for u could be zero. Our method has two advantages: first, Cornfield et al. (1959) and Bross (1966) adjust only for the unmeasured binary covariate u, whereas we adjust for measured covariates in addition to the unmeasured covariate u. Second, Cornfield et al. (1959) and Bross (1966, 1967) only judge whether the effect of the treatment could be zero having adjusted for u, where Cornfield et al. (1959) employ an implicit yet extreme assumption about u. In contrast, we provide actual estimates of the treatment effect adjusted for both u and the observed categorical covariates under any assumption about u. In principle, the ith of the N patients under study has both a binary response r1i that would have resulted if he had received the new treatment, and a binary response ro0 that would have resulted if he had received the control treatment. In this formulation, treatment effects are comparisons of r1i and roi, such as r1i - roi. Since each patient receives only one treatment, either rli or ro0 is observed, but not both, and therefore comparisons of rli and roi imply some degree of speculation. Treatment effects defined as comparisons of the two potential responses, r1i and roi, of individual patients are implicit in Fisher's (1953) randomization test of the sharp null
1,005 citations
TL;DR: In this article, the cross-validated smoothing spline can be used to estimate g non-parametrically from a smooth function, where the error of the spline is independent with G 2 unknown.
Abstract: SUMMARY We consider the model Y(t) =g(ti) + ei, i = 17 2, . . ., n, where g(t), t [0, 1] is a smooth function and the {ei) are independent N(0, a2 ) errors with G2 unknown. The cross-validated smoothing spline can be used to estimate g non-parametrically from
617 citations
556 citations
TL;DR: In this paper, a general method of estimating parameters in continuous univariate distributions is proposed, which is especially suited to cases where one of the parameters is an unknown shifted origin and is shown to give consistent estimators with asymptotic efficiency equal to ML estimators when these exist.
Abstract: SUMMARY A general method of estimating parameters in continuous univariate distributions is proposed. It is especially suited to cases where one of the parameters is an unknown shifted origin. This occurs, for example, in the three-parameter lognormal, gamma and Weibull models. For such distributions it is known that maximum likelihood (ML) estimation can break down because the likelihood is unbounded and this can lead to inconsistent estimators. Properties of the proposed method are described. In particular it is shown to give consistent estimators with asymptotic efficiency equal to ML estimators when these exist. Moreover it gives consistent, asymptotically efficient estimators in situations where ML fails. Examples are given including numerical ones showing the advantages of the method.
482 citations
341 citations
206 citations
TL;DR: The spatial median is defined as the bivariate location measure to minimize the sum of absolute distances to observations by Gower as mentioned in this paper, and its asymptotic efficiency relative to the sample mean vector with normal data is shown to exceed the usual univariate 2/ir = 0.637.
Abstract: The spatial median, called the mediancentre in an earlier paper by J. C. Gower, is defined as the bivariate location measure to minimize the sum of absolute distances to observations. Its asymptotic efficiency relative to the sample mean vector with normal data is shown to exceed the usual univariate 2/ir = 0.637. Its estimating equations have an angular aspect and are used to develop "angle tests", which are analogues of sign tests in one dimension.
161 citations
136 citations
TL;DR: In this article, the authors give a general formula for the expected value of the likelihood ratio statistic for generalized linear models, corrected up to terms of order n -1, where n is the size of the sample.
Abstract: SUMMARY This paper gives a general formula for the expected value of the likelihood ratio statistic for generalized linear models, corrected up to terms of order n -1, where n is the size of the sample. The application of this formula to some models is illustrated.
100 citations
TL;DR: Anscombe, Chow and Robbins as discussed by the authors proposed the large sample theory, which enables the number of samphng operations to be reduced by any predetermined factor, at the expense of only a slight increase in the expected sample size.
Abstract: Anscombe, Chow and Robbins. It enables the number of samphng operations to be reduced by any predetermined factor, at the expense of only a slight increase in the expected sample size. The large sample theory is outlined, and some numerical computations provided to demonstrate the practicality of the procedure for smaller samples.
75 citations
TL;DR: In this paper, the authors explore the structure of some further models and apply their results to the statistical analysis of bivariate spatial point patterns, which represent the locations of objects as points in an essentially planar region.
Abstract: SUMMARY From certain points of view, the range of probability models currently available for describing the joint behaviour of two point processes is rather limited. In this paper we explore the structure of some further models and apply our results to the statistical analysis of bivariate spatial point patterns. In many branches of science there is interest in the study and description of data which represent the locations of objects as points in an essentially planar region. In the present paper we assume that the objects are of two qualitatively distinguishable types and refer to the data as a bivariate spatial point pattern. A statistical analysis of such data should seek to provide some meaningful summary descriptions of the separate point patterns for each of the two types of object, and of any possible inter-relationship between these two patterns. For example, Fig. 1 shows the locations of 173 newly emergent and 155 1-year-old bramnble 0*~~~~~~ a . A * * tv t * * to~~~~~~~~~~0 , * X *t *.#**. .
TL;DR: In this paper, three simple approaches to rounding error in least square regression are considered: the first treats the rounded data as if they were unrounded, the second adds an adjustment to the diagonal of the covariance matrix of the variables, and the third subtracts an adjustment from the diagonal.
Abstract: : We consider three simple approaches to rounding error in least squares regression. The first treats the rounded data as if they were unrounded, the second adds an adjustment to the diagonal of the covariance matrix of the variables, and the third subtracts an adjustment from the diagonal. The third, Sheppard's corrections, can be motivated as maximum likelihood with small rounding error and either (1) joint normal data or (2) normal residuals, regular independent variables, and large samples. Although an example and theory suggest that the third approach is usually preferable to the first two, a generally satisfactory attack on rounding error in regression requires the specification of the full distribution of variables, and convenient computational methods for this problem are not currently available. (Author)
TL;DR: In this paper, the authors considered the combinatorial possibilities of semi-Latin squares and classified them into "species" or "main classes", akin to the species of Latin squares.
Abstract: SUMMARY A semi-Latin square for t = kn symbols is a rectangular arrangement with n rows and t columns, these latter being grouped into sets each containing k consecutive columns; each symbol occurs exactly once in each row and exactly once in each set of columns (Yates, 1935). Previous authors seem not to have considered the combinatorial possibilities of semi-Latin squares. For each pair of values k and t, the semi-Latin squares can be classified into "species" or "main classes", akin to the species of Latin squares. The classification considered in this note disregards the ordering of the k symbols to be fouind where any row intersects any set of columns; for k = 2 and t = 4, 6 and 8, the numbers of species are 1, 2 and 10 respectively. The relationship between semi-Latin squares, Trojan squares and certain partially balanced incomplete block designs with two associate classes is discussed. The relevant semi-regular designs of Clatworthy (1973) are examined to see which can be obtained from semi-Latin (Trojan) squares, and some enumerations of squares obtainable from the semi-regular designs are reported.
TL;DR: In this article, prior beliefs of association and independence in a two-way contingency table are discussed, and estimators of the cell probabilities are proposed which can incorporate this prior information.
Abstract: SUMMARY Prior beliefs of association and independence in a two-way contingency table are discussed, and estimators of the cell probabilities are proposed which can incorporate this prior information. In the 2 x 2 table where the cell counts are assumed to have a multinomial distribution, estimators are developed which can incorporate prior beliefs about the correlation coefficient and the cross-product ratio. In the I x 2 table in which one set of marginal totals is fixed, estimators are developed which reflect prior information about the similarity of a set of cell probabilities. Numerical examples are given to illustrate the use of these estimators.
TL;DR: In this article, the authors discuss procedures for assessing multivariate normality based on properties of radii and angles of the multivariate normal distribution, and suggest that different procedures may be efficiently combined in order to achieve omnibus tests.
Abstract: SUMMARY We discuss procedures for assessing multivariate normality based on properties of radii and angles of the multivariate normal distribution, and suggest that different procedures may be efficiently combined in order to achieve omnibus tests. The assumption of population multivariate normality underlies many multivariate data analytic procedures. Unfortunately, however, there are relatively few formal methods available for assess- ing the validity of this underlying assumption. Gnanadesikan (1977, Section 5.4.2) and Cox and Small (1978) have extensively reviewed various formal and informal procedures proposed for testing the multinormality hypothesis, and it is not our purpose to survey the procedures anew. Rather, we suggest in this note that different characteristics of multivariate normality can be examined with different procedures, which may thereafter be combined to obtain omnibus tests for the multinormality hypothesis.
TL;DR: In this paper, the generalized cyclic method of construction is used to construct row-column block designs, and it is shown how the confounding schemes and efficiency factors of such designs are obtained.
Abstract: Factorial experiments can be set out in row-column designs using the generalized cyclic method of construction. From parallel results on block designs, it is shown how the confounding schemes and efficiency factors of such designs are obtained. Simple rules for constructing useful designs are given.
TL;DR: In this paper, a simple and useful representation for the asymptotic behaviour of the Pearson X2 test of independence in two-way contingency tables is given, which is used to analyse the statistic when the data are generated by Markov chains.
Abstract: SUMMARY A simple and useful representation is given for the asymptotic behaviour of the Pearson X2 test of independence in two-way contingency tables. This is used to analyse the statistic when the data are generated by Markov chains. A robustness result, showing when the Markov dependence has no effect on the usual limiting x2 distribution, is also given.
TL;DR: In this paper, the authors extended previous results on competition of epidemics to the case of the general epidemic and used Coupling techniques for the stochastic model to carry the result over to the deterministic case.
Abstract: SUMMARY Previous results on competition of epidemics are extended to the case of the general epidemic. Coupling techniques are used for the stochastic model. A result of Kurtz is used to carry the result over to the deterministic case.
TL;DR: In this article, it was shown that parameters corresponding to those used for partially balanced incomplete block designs can be defined for certain designs with m distinct concurrences, leading to a new upper bound for the efficiency factor which is attained if a PBIB (2) design exists.
Abstract: SUMMARY Incomplete block designs can be regarded as being in some sense approximately partially balanced. In this paper, we show that parameters Pjk corresponding to those used for partially balanced designs can be defined for certain designs with m distinct concurrences. These parameters have properties analogous to those for m associate-class partially balanced incomplete block (PBIB (m)) designs and have proved useful in searching for optimal designs. This leads to a new upper bound for the efficiency factor which, for given PJk values, is attained if a PBIB (2) design exists. Some results on complement and dual designs are also given.
TL;DR: In this article, an information criterion for the test of a composite null hypothesis against a composite separate alternative is developed. But the criterion is not applicable to the Cox test, and it cannot be used to test a composite alternative.
Abstract: SUMMARY An information criterion is developed for the test of a composite null hypothesis against a composite separate alternative. The intuitive and interpretative appeal of the criterion is emphasized and comparisons with the Cox test invoked.
TL;DR: In this article, the authors consider experimental settings requiring usage of a block design in which v treatments are to be tested in b blocks of size k. The block design is called MV-optimal in such a setting if the maximal variance with which it estimates elementary treatment differences is minimal among all available designs.
Abstract: SUMMARY In this paper we consider experimental settings requiring usage of a block design in which v treatments are to be tested in b blocks of size k. A block design is called MV-optimal in such a setting if the maximal variance with which it estimates elementary treatment differences is minimal among all available designs. MV-optimal designs are particularly useful in exploratory experiments where as much information as possible is desired on the effects of all treatments being studied. Some sufficient conditions are derived which can be used to establish the MV-optimality of certain types of generalized group divisible designs as defined in Jacroux (1982) and some easy methods for constructing such MV-optimal designs are given.
TL;DR: In this paper, a generalization of the equivalence of a system of exponential order statistics to a model of Plackett (1975) is given, which is a generalisation of Henery's equivalence.
Abstract: SUMMARY A generalization of the equivalence noted by Henery (1981) of a system of exponential order statistics to a model of Plackett (1975) is given.
TL;DR: In this article, the authors considered the problem of estimating the signed ranks of the within pair differences of independent matched pairs using the signed rank test of Wilcoxon or the half-normal scores signed rank statistic.
Abstract: SUMMARY Exact and approximate inference based on the marginal likelihood which results from the signed ranks of the within pair differences of independent matched pairs is con- sidered. Inference is made using Bayesian ideas. A quickly computed approximate analysis is introduced and this is shown to be extremely good when the within pair differences are assumed to have a normal distribution. Numerical comparisons are also made when the differences have a logistic distribution, but for this case the approxi- mation is not as good. The approximations involve the Wilcoxon signed rank statistic and the half-normal scores signed rank statistic. The approximation is extended to consider regression models for matched pairs data. An application is given illustrating the ideas. In this paper we consider exact and approximate inference based on the marginal rank-sign likelihood which results from independent matched pairs data. It is assumed that the within pair differences are independent and symmetrically distributed. Inference is made using Bayesian ideas. Suppose that D1, . ., 1Dn are observable differences which result from a matched pairs experiment and that it is possible to transform the Dj 's, giving Yj = sign (Dj) h (IDj 1), where h(.) is an unknown increasing and differentiable function on (0, oo) and h(O) = 0. It is assumed that the Y1's are independent and symmetrically distribtuted about 0 with a known density. Under such circumstances the signs of the Dj's and the ranks of the absolute values of the Dj's remain invariant under the transformation, and these are given by the signs and ranks of the Y1's. In non- parametric statistics inference can be made for 0 using the signs of the differences-the sign-test- and also by utilizing between pair comparisons, the ranks of the absolute differences, giving the signed rank test of Wilcoxon or the half-normal scores test. Lehmann (1975, Chapter 5) gives an-account of non-parametric tests based on signed ranks using matched pairs data. In this paper we consider the marginal likelihood, p(r, s I 0), of the Dj's based on their signs, s, and the ranks r, of their absolute values. The idea of a marginal rank likelihood was proposed by Kalbfleisch and Prentice (1973) and the likelihood p(r, s I 0), for matched pairs data, was considered by Woolson and Lachenbruch (1980), who developed test statistics for the hypothesis H: 0 = 0 with censored data. We use the marginal likelihood, p(r, s I 0), to make inferences about 0 from a Bayesian point of view. In particular, when the prior density for 0 is chosen to be locally uniform, the posterior density of 0 is given by the standardized likelihood