Dose finding using the biased coin up-and-down design and isotonic regression

We are interested in finding a dose that has a prespecified toxicity rate in the target population. In this article, we investigate five estimators of the target dose to be used with the up-and-down biased coin design (BCD) introduced by Durham and Flournoy (1994, Statistical Decision Theory and Related Topics). These estimators are derived using maximum likelihood, weighted least squares, sample averages, and isotonic regression. A linearly interpolated isotonic regression estimate is shown to be simple to derive and to perform as well as or better than the other target dose estimators in terms of mean square error and average number of subjects needed for convergence in most scenarios studied.     

The design and analysis of breeders' trials of sugar beet (Beta vulgaris) using two-dimensional blocking structures

A method for generating two-dimensional blocking designs to fit any shape and size of experimental area is presented. The method takes an alpha design appropriate to the experimental area and imposes additional blocking perpendicular to the alpha blocks. Improvements to the design are then made by repositioning entries within the alpha blocks. Although this method of construction is less sophisticated than for other two-dimensional designs, the designs are particularly suited to large scale breeders trials where no alternative two-dimensional design may exist. The designs have been used for 3 yr in a sugar beet breeding programme, and have given improvements in efficiency over one-dimensional alpha designs.     

Construction of Resolvable Designs with Nested Treatment Structure

The construction of resolvable incomplete block and row-column designs is investigated when the treatments have a nested structure. Some theoretical results are derived for lattice designs. Efficient designs for unequal-sized treatment groups are obtained by defining a multiple objective function and carrying out a computer search using an interchange algorithm.     

Sequential designs for ordinal phase I clinical trials

Sequential designs for phase I clinical trials which incorporate maximum likelihood estimates (MLE) as data accrue are inherently problematic because of limited data for estimation early on. We address this problem for small phase I clinical trials with ordinal responses. In particular, we explore the problem of the nonexistence of the MLE of the logistic parameters under a proportional odds model with one predictor. We incorporate the probability of an undetermined MLE as a restriction, as well as ethical considerations, into a proposed sequential optimal approach, which consists of a start‐up design, a follow‐on design and a sequential dose‐finding design. Comparisons with nonparametric sequential designs are also performed based on simulation studies with parameters drawn from a real data set.     

Fractional simplex designs for interaction screening in complex mixtures

In mixture experiments, one may be interested in estimating not only main effects but also some interactions. Main effects and significant interactions in a mixture may be estimated through appropriate mixture experiments, such as simplex-centroid designs. However, for mixtures with a large number of factors, the run size for these designs becomes impractically large. A subset of a full simplex-centroid design may be used, but the problem remains regarding which factor-level settings should be selected. In this paper, we propose a solution that considers design points with either one or p individual nonzero factor-level settings. These fractional simplex designs provide a means of screening for interactions and of investigating the behavior of many-component mixtures as a whole while greatly reducing the run size compared with full simplex-centroid designs. The means of construction of the design arrays is described, and designs for < or = 31 factors are presented. Some of the proposed methodology is illustrated using generated data.     

SMR analysis of historical follow-up studies with missing death certificates

The evaluation of epidemiological follow-up studies is frequently based on a comparison of the number O of deaths observed in the cohort from a specified cause with the expected number E calculated from person years in the cohort and mortality rates from a reference population. The ratio SMR = 100 x O/E is called the standardized mortality ratio (SMR). While person years can easily be calculated from the cohort and reference rates are generally available from the national statistical offices or the World Health Organization (WHO), problems can arise with the accessibility of the causes of death of the deceased study participants. However, the information that a person has died may be available, e.g., from population registers. In this paper, a statistical model for this situation is developed to derive a maximum likelihood (ML) estimator for the true (but unknown) number O* of deaths from a specified cause, which uses the known number O of deaths from this cause and the proportion p of all known causes of death among all decreased participants. It is shown that the standardized mortality ratio SMR* based on this estimated number is just SMR* = SMR/p. Easily computable confidence limits can be obtained by dividing the usual confidence limits of the SMR by the opposite limit of the proportion p. However, the confidence level alpha has to be adjusted appropriately.     

Analysis of streptozotocin-induced incomplete chromosome elements and excess acentric fragments in Chinese hamster cells using a telomeric PNA probe

Fluorescence in situ hybridization (FISH) with a telomeric peptide nucleic acid (PNA) probe was employed to analyze the induction of incomplete chromosome elements (ICE, i.e., unjoined or “open” chromosome elements with telomeric signal at only one end) and excess acentric fragments (i.e., in excess of fragments resulting from the formation of dicentric and ring chromosomes) by the methylating agent streptozotocin (STZ) in a Chinese hamster embryo (CHE) cell line. CHE cells were treated with 0–4 mM STZ and chromosomal aberrations were analyzed in the first mitosis after treatment using the telomeric probe. Centric (incomplete chromosomes) and acentric (terminal fragments) ICE were the only unstable chromosome-type aberrations induced by STZ in CHE cells. The induction of these aberrations exhibited a curvilinear concentration–response relationship. About 40% of the metaphases present in cell cultures treated with STZ contained one or more pairs of ICE. In STZ-treated cells, ICE were always observed as pairs consisting of an incomplete chromosome and a terminal fragment. Moreover, all of the excess acentric fragments induced by STZ were of terminal type. These results indicate that chromosomal incompleteness is a very common event following exposure to STZ and suggest that all of the excess acentric fragments induced by STZ originate from terminal deletions.     

Analysis of logistic growth models

A variety of growth curves have been developed to model both unpredated, intraspecific population dynamics and more general biological growth. Most predictive models are shown to be based on variations of the classical Verhulst logistic growth equation. We review and compare several such models and analyse properties of interest for these. We also identify and detail several associated limitations and restrictions.A generalized form of the logistic growth curve is introduced which incorporates these models as special cases. Several properties of the generalized growth are also presented. We furthermore prove that the new growth form incorporates additional growth models which are markedly different from the logistic growth and its variants, at least in their mathematical representation. Finally, we give a brief outline of how the new curve could be used for curve-fitting.     

Cellular aspects of tolerance. VII. Inheritance of the resistance to tolerance induction

The half-lives of elimination ($\text{T}{}_{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}$) of ¹³¹I-RGG from the body of normal A or Balb/c animals was much longer than the $\text{T}{}_{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}$ of SJL mice. At all ages, the $\text{T}{}_{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}$ of normal hybrids (A × SJL, SJL × A, Balb/c × SJL) was similar to or longer than that of the A or Balb/c parents. Thus, in terms of the $\text{T}\text{1}\text{2}$ of normal animals, the SJL responsiveness to ¹³¹I-RGG appeared to be a recessive trait. Tolerance could be induced in newborn animals and, in terms of $\text{T}{}_{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}$, the degree of unresponsiveness at the age of 6 weeks, was the same in A, Balb/c, A × SJL, and Balb/c × SJL animals but was much shorter in SJL mice. Thus, in neonatally induced tolerance, the duration of tolerance was recessive for the SJL type. The average $\text{T}{}_{\mathrm{<mtext>built1</mtext><mtext>2</mtext>}}$ after tolerance induction in 3-week-old hybrids (A × SJL, SJL × A, Balb/c × SJL) was similar to that of the A or Balb/c parent, but by the 8th and 12th week it approached the average $\text{T}{}_{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}$ of the SJL parent. Comparing 8-week-old hybrids, the average $\text{T}{}_{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}$ was longest in A × SJL hybrids and identical in SJL × A and Balb/c × SJL mice. An examination of $\text{T}{}_{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}$ distribution in various 8- and 12-week-old crosses and backcrosses revealed a fairly large proportion of individuals with a $\text{T}{}_{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}$ which was intermediate between SJL and the other parent. There was a tendency for this number to decrease in 12 weeks as compared to 8-week-old mice. In 8-week-old mice, the number of animals with intermediate $\text{T}{}_{\mathrm{<mtext>built1</mtext><mtext>2</mtext>}}$ was smallest when SJL was the maternal animal [(SJL × A); SJL × (A × SJL); SJL × (SJL × A)]. There was no link between $\text{T}{}_{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}$ of tolerant animals and either the immunoglobulin allotype (MuAl/MuA2) or the C5 eniotype (MuB1 positive/MuB1 negative).