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doi: 10.1002/bimj.4710350102pmid: N/A
John Graunt (1662) was the first to estimate the ratio y/x where y represents the total population and x the known total number of registered births in the same areas during the preceding year. About 1765 Messance (Stephan, 1948) and Moheau (1778) published very carefully prepared estimates for France based on enumeration of population in certain districts and on the count of births, deaths and marriages as reported for the whole country. The districts from which the ratio of inhabitants to birth was determined only constituted a sample. Laplace (1786) prepared similar estimates in 1802 based on a two‐stage sampling plan. Recently Hansen and Hurwitz (1943) showed that the ratio estimate (yi/ni)X of Y is unbiased where all xi's are known and the nth cluster is selected with p.p.s. More recently Hájek (1949), Lahiri (1951), Midzuno (1952) and Sen (1952) developed independently the sampling of n clusters with p.p.s to the totals of the sizes of the sample clusters S(xi). Des Raj (1954) and Sen (1952, 1953) gave unbiased estimate of the variance of the estimator which was generally non‐negative for samples with smaller probabilities. Rao and Vijayan (1977) gave an unbiased estimator which is non‐negative for samples with larger probabilities. Hájek (1949) provided an almost unbiased estimator of the variance of the estimator. The paper discusses situations where Hájek's estimator of variance should be preferred to the Rao‐Vijayan estimator and vice versa.
doi: 10.1002/bimj.4710350103pmid: N/A
The aim of this paper is to study the properties of the asymptotic variances of the maximum likelihood estimators of the parameters of the exponential mixture model with long‐term survivors for randomly censored data. In addition, we study the asymptotic relative efficiency of these estimators versus those which would be obtained with complete follow‐up. It is shown that fixed censoring at time T produces higher precision as well as higher asymptotic relative efficiency than those obtainable under uniform and uniform‐exponential censoring distributions over (0, T). The results are useful in planning the size and duration of survival experiments with long‐term survivors under random censoring schemes.
doi: 10.1002/bimj.4710350104pmid: N/A
An estimation procedure using the idea of sample coverage is proposed to estimate population size for capture‐recapture experiments in continuous time. The capture rates (intensity) are allowed to vary by time and individuals (heterogeneity). Only capture frequency history are sufficient for estimating population size while capture times and sequential orders of animals caught are irrelevant for the analysis. An example is given for illustration. The performance of the proposed estimation procedure is also investigated by simulation.
doi: 10.1002/bimj.4710350105pmid: N/A
The conventional definition of bioequivalence in terms of population means only, is criticized for lacking relevance to the individual subject. Both approaches to bioequivalence assessment proposed here for avoiding this shortcoming, focus on the probability of an event induced by the response of a randomly selected subject to two formulations of a given active agent. The first approach leads to converting the basic idea underlying the well‐known 75‐rule into an exact statistical procedure. The second approach is of a parametric nature. It reduces bioequivalence assessment to testing against the alternative hypothesis that the standardized expected value of a Gaussian distribution is contained in a short interval around zero. For this problem, an exact optimal solution is provided as well.
doi: 10.1002/bimj.4710350106pmid: N/A
A method used by various researchers for estimation of incidence from prevalence data of a stable population for irreversible stable diseases has been validated. For this purpose a followup data was generated by life table distribution techniques with known mortality and incidence rates. The results show that the method as such cannot be used to estimate the true incidence from prevalence data of a crossectional study from stable population. The remote situation where the method will work has been discussed. A method has also been presented for situations where the known method fails i.e. duration of irreversible disease is less than the age of effected persons in a stable population.
doi: 10.1002/bimj.4710350107pmid: N/A
The precision of a treatment contrast, as conventionally estimated in Zelen's Single‐Consent Design, is shown under randomization theory to be positively biased. The magnitude of this bias is demonstrated and a new statistic is derived which is a consistent estimator of the precision. Confidence interval estimation for the treatment contrast is also presented.
doi: 10.1002/bimj.4710350108pmid: N/A
There may be experiments where due to misadventure or logistic or ethical reasons final measurements on all experimental units cannot be obtained. If at least 50% of the final measurements have been taken estimates of the lower quantiles and the median can be obtained. For such curtailed experiments it is shown how quantiles, above those that can be estimated directly from the data set, can be estimated indirectly by exploiting a property of symmetric distributions. The performance of the indirect quantile estimator is compared with that of the direct quantile estimator and conditions for the indirect estimator to have smaller variance than the direct estimator are presented. It is also shown how the indirect estimator may be pooled with the direct estimator to obtain an improved estimate of the upper quantiles. When it cannot be assumed that the data come from a symmetric distribution transformations to symmetry may be performed and the indirect estimation technique used on the transformed data; back transformations then yield the estimates of the upper quantiles.
Dash, S. P.; Bourghawi, Suad M.; El‐Amaari, Ali
doi: 10.1002/bimj.4710350109pmid: N/A
The first two randomization moments of W = Tt.S.S./(Tt.S.S. + Error S.S.) are derived in case of (a) a completely randomized design with one observation missing using (I) Yates method of fitting constants and (II) the available observations only and in case of (b) a randomized block design in which one treatment is tested twice by mistake in a block and another treatment is not tested at all in that block using (I) all the available observations and (II) the data after deleting the observation due to the treatment tested by mistake in place of another treatment in a block. It is concluded that in each of the two cases for a completely randomized design, the F‐test is unbiased whereas in each of the two cases for a randomized block design the F‐test is in general not unbiased. However, if one treatment is tested twice by mistake in randomly chosen plots of some block, the F‐test is unbiased in both cases for a randomized block design. For a completely randomized design the F‐test is found to be a good approximation to the corresponding randomized test if N ≧ 80 in case (I) whereas in case (II) this approximation is of the same accuracy as that of case (I) if N ≧ 90. For a randomized block design it is seen that in case (I), the F‐test provides a good approximation to the corresponding randomization test if v≧r≧7 and in case (II) this approximation is of the same accuracy if r≧6 and r(v‐1)≧45. The analysis of several uniformity trial data shows that for values of “N” in the neighbourhood of 50 the agreement of the first two moments of “W” under the randomization theory and normal theory are reasonably close in all the four cases considered.
doi: 10.1002/bimj.4710350110pmid: N/A
A review is provided of the several bivariate generalisations of quantal response analysis that have appeared in the biometric and econometric literatures. There are three main types: (i) where a binary outcome is the result of two stimulants, and thus the bivariate distribution of the thresholds for response is relevant; (ii) where three or more alternative outcomes may arise from a single stimulant; and (iii) where the response itself is bivariate (i.e., two types of response may simultaneously be observed).
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