A three-stage clinical trial design for rare disorders.

Many clinical trials of uncommon diseases are underpowered because of the difficulty of recruiting adequate numbers of subjects. We propose a clinical trial design with improved statistical power compared to the traditional randomized trial for use in clinical trials of rare diseases. The three-stage clinical trial design consists of an initial randomized placebo-controlled stage, a randomized withdrawal stage for subjects who responded, and a third randomized stage for placebo non-responders who subsequently respond to treatment. Test level and power were assessed by computer-intensive exact calculations. The three-stage clinical trial design was found to be consistently superior to the traditional randomized trial design in all cases examined, with sample sizes typically reduced by 20 per cent to 30 per cent while maintaining comparable power. When a treatment clearly superior to placebo was considered, our design reached a power of 75 per cent with a sample of 21 patients compared with the 52 needed to attain this power when only a randomized controlled trial was used. In situations where patient numbers are limited, a three-stage clinical trial design may be a more powerful design than the traditional randomized trial for detecting clinical benefits.

Modeling the feasibility of whole genome shotgun sequencing using a pairwise end strategy.

In pairwise end sequencing, sequences are determined from both ends of random subclones derived from a DNA target. Sufficiently similar overlapping end sequences are identified and grouped into contigs. When a clone's paired end sequences fall in different contigs, the contigs are connected together to form scaffolds. Increasingly, the goals of pairwise strategies are large and highly repetitive genomic targets. Here, we consider large-scale pairwise strategies that employ mixtures of subclone sizes. We explore the properties of scaffold formation within a hybrid theory/simulation mathematical model of a genomic target that contains many repeat families. Using this model, we evaluate problems that may arise, such as falsely linked end sequences (due either to random matches or to homologous repeats) and scaffolds that terminate without extending the full length of the target. We illustrate our model with an exploration of a strategy for sequencing the human genome. Our results show that, for a strategy that generates 10-fold sequence coverage derived from the ends of clones ranging in length from 2 to 150 kb, using an appropriate rule for detecting overlaps, we expect few false links while obtaining a single scaffold extending the length of each chromosome.

Parking strategies for genome sequencing.

The parking strategy is an iterative approach to DNA sequencing. Each iteration consists of sequencing a novel portion of target DNA that does not overlap any previously sequenced region. Subject to the constraint of no overlap, each new region is chosen randomly. A parking strategy is often ideal in the early stages of a project for rapidly generating unique data. As a project progresses, parking becomes progressively more expensive and eventually prohibitive. We present a mathematical model with a generalization to allow for overlaps. This model predicts multiple parameters, including progress, costs, and the distribution of gap sizes left by a parking strategy. The highly fragmented nature of the gaps left after an initial parking strategy may make it difficult to finish a project efficiently. Therefore, in addition to our parking model, we model gap closing by walking. Our gap-closing model is generalizable to many other strategies. Our discussion includes modified parking strategies and hybrids with other strategies. A hybrid parking strategy has been employed for portions of the Human Genome Project.

Testing for differentially-expressed genes by maximum-likelihood analysis of microarray data.

Although two-color fluorescent DNA microarrays are now standard equipment in many molecular biology laboratories, methods for identifying differentially expressed genes in microarray data are still evolving. Here, we report a refined test for differentially expressed genes which does not rely on gene expression ratios but directly compares a series of repeated measurements of the two dye intensities for each gene. This test uses a statistical model to describe multiplicative and additive errors influencing an array experiment, where model parameters are estimated from observed intensities for all genes using the method of maximum likelihood. A generalized likelihood ratio test is performed for each gene to determine whether, under the model, these intensities are significantly different. We use this method to identify significant differences in gene expression among yeast cells growing in galactose-stimulating versus non-stimulating conditions and compare our results with current approaches for identifying differentially-expressed genes. The effect of sample size on parameter optimization is also explored, as is the use of the error model to compare the within- and between-slide intensity variation intrinsic to an array experiment.

Analysis of sequence-tagged-connector strategies for DNA sequencing.

The BAC-end sequencing, or sequence-tagged-connector (STC), approach to genome sequencing involves sequencing the ends of BAC inserts to scatter sequence tags (STCs) randomly across the genome. Once any BAC or other large segment of DNA is sequenced to completion by conventional shotgun approaches, these STC tags can be used to identify a minimum tiling path of BAC clones overlapping the nucleation sequence for sequence extension. Here, we explore the properties of STC-sequencing strategies within a mathematical model of a random target with homologous repeats and imperfect sequencing technology to understand the consequences of varying various parameters on the incidence of problem clones and the cost of the sequencing project. Problem clones are defined as clones for which either (A) there is no identifiable overlapping STC to extend the sequence in a particular direction or (B) the identified STC with minimum overlap comes from a nonoverlapping clone, either owing to random false matches or repeat-family homology. Based on the minimum overlap, we estimate the number of clones to be entirely sequenced and, then, using cost estimates, identify the decision rule (the degree of sequence similarity required before a match is declared between an STC and a clone) to minimize overall sequencing cost. A method to optimize the overlap decision rule is highly desirable, because both the total cost and the number of problem clones are shown to be highly sensitive to this choice. For a target of 3 Gb containing approximately 800 Mb of repeats with 85%-90% identity, we expect <10 problem clones with 15 times coverage by 150-kb clones. We derive the optimal redundancy and insert sizes of clone libraries for sequencing genomes of various sizes, from microbial to human. We estimate that establishing the resource of STCs as a means of identifying minimally overlapping clones represents only 1%-3% of the total cost of sequencing the human genome, and, up to a point of diminishing returns, a larger STC resource is associated with a smaller total sequencing cost.

Optimization of restriction fragment DNA mapping.

Consider a mapping project in which overlap of clonal segments is inferred from complete multiple restriction digests. The fragment sizes of the clones are measured with some error, potentially leading to a map with erroneous links. The number of errors in the map depends on the number and types of enzymes used to characterize the clones. The most critical parameter is the decision rule k, or the criterion for declaring clone overlap. Small changes in k may cause an order of magnitude change in the amount of work it takes to build a map of given completion. We observe that the cost of an optimal mapping strategy is approximately proportional to the target size. While this finding is encouraging, considerable effort is nonetheless required: for large-scale sequencing projects with up-front mapping, mapping will be a non-negligible fraction of the total sequencing cost.

Expectation and variance of true and false fragment matches in DNA restriction mapping.

Consider a DNA mapping project in which overlap of clones is inferred from multiple complete restriction enzyme digests. Each enzyme cuts each clone randomly into fragments whose lengths are determined with some error. Clones that share fragments with matching lengths could contain a region of overlap. However, common fragment lengths may be due to random coincidence leading to a false overlap declaration. Although the probability of false fragment matching is small, a mapping project involves a large number of clone comparisons. Consequently, erroneous fragment matches can be a serious problem. We use a geometrical probability approach to develop exact integral formulas and first-order approximations for the expected number and variance of classes of fragment pairs that will be identified falsely as matching. We also find exact formulas for the expected value, and variance of the number of true fragment matches. These formulas are useful in comparing different mapping strategies.

Robust and least-squares orthogonal mapping: methods for the study of cephalofacial form and growth.

A method is presented for the description and analysis of cephalofacial form and growth using two-dimensional coordinate data. The procedure permits the identification of shape differences at specific cephalofacial coordinate locations without reliance upon conventional cephalometric landmarks. The resulting size-standardized coordinates can be analyzed by statistical methods for further data exploration. Two methods of shape transformation--least-squares and robust fitting--are described and compared. An example of the utility of the technique for cephalofacial growth studies is provided.

A robust comparison of biological shapes.

Localized differences in the form of two related animal skeletons are more effectively determined when resistant fitting techniques are used rather than at least squares. The repeated median resistant fitting algorithm is introduced. The methods are tested by comparing hominid skulls with those of the least squares fit, in that the differences are more readily identified and agree more closely with the structural differences perceived on biological grounds.