Three-point appraisal of genetic linkage maps.

This paper develops a simple diagnostic for the investigation of uncertainty within genetic linkage maps using a Bayesian procedure. The method requires only the genotyping data and the proposed genetic map, and calculates the posterior probability for the possible orders of any set of three markers, accounting for the presence of genotyping error (mistyping) and for missing genotype data. The method uses a Bayesian approach to give insight into conflicts between the order in the proposed map and the genotype scores. The method can also be used to assess the accuracy of a genetic map at different genomic scales and to assess alternative potential marker orders. Simulation and two case studies were used to illustrate the method. In the first case study, the diagnostic revealed conflicts in map ordering for short inter-marker distances that were resolved at a distance of 8-12 cM, except for a set of markers at the end of the linkage group. In the second case study, the ordering did not resolve as distances increase, which could be attributed to regions of the map where many individuals were untyped.

Estimating the incidence of an epidemic when it is first discovered and the design of early detection monitoring.

The early detection of an invading epidemic is crucial for successful disease control. Although models have been used extensively to test control strategies following the first detection of an epidemic, few studies have addressed the issue of how to achieve early detection in the first place. Moreover, sampling theory has made great progress in understanding how to estimate the incidence or spatial distribution of an epidemic but how to sample for early detection has been largely ignored. Using a simple epidemic model we demonstrate a method to calculate the incidence of an epidemic when it is discovered for the first time (given a monitoring programme taking samples at regular intervals). We use the method to explore how the intensity and frequency of sampling influences early detection. In particular, we find that for epidemics characterised by high population growth rates it is most effective to spread sampling resources evenly in time. In addition we derive a useful approximation to our method which results in a simple equation capturing the relation between monitoring and epidemic dynamics. Not only does this provide valuable new insight but it provides a simple rule of thumb for the design of monitoring programmes in practice.

Statistical information characterization of conserved non-coding elements in vertebrates.

Recently, a set of highly conserved non-coding elements (CNEs) has been derived from a comparison between the genomes of the puffer fish, Takifugu or Fugu rubripes, and man. In order to facilitate the identification of these conserved elements in silico, we characterize them by a number of statistical features. We found a pronounced information pattern around CNE borders; although the CNEs themselves are AT rich and have high entropy (complexity), they are flanked by GC-rich regions of low entropy (complexity). We also identified the most abundant motifs within and around of CNEs, and identified those that group around their borders. Like in human promoter regions, the TBP, NF-Y and some other binding motifs are clustered around CNE boundaries, which may suggest a possible transcription regulatory function of CNEs.

Evidence for interrupted bone resorption in human iliac cancellous bone.

Bone resorption and formation are coupled both in time and space and may occur simultaneously in the same remodeling unit. A number of studies have shown that the formative phase of the remodeling sequence may undergo temporary interruptions prior to completion and it is possible that bone resorption may be subject to similar interruptions. We have investigated this hypothesis by studying the distribution of eroded depth in resorption cavities in human cancellous bone. Eroded depth was assessed in iliac crest cancellous bone from 41 normal healthy subjects using a cubic spline curve fitting technique. The distribution of mean eroded depths was skewed to the right. Comparison of the observed distribution with an expected distribution, which was calculated from previously published data and assumes resorption begins rapidly and slows as it approaches completion, showed a significantly greater proportion of shallower cavities than expected (p<0001). Similarly, comparison of observed and uniform distributions, which assumes a constant rate of resorption throughout the erosion period, also showed a significantly greater proportion of smaller cavities (p<0.01). In subjects aged less than 39 years, there were fewer small cavities than in those aged 40-59 years. In addition, there was some evidence that females of 40-59 years had a proportionately greater number of smaller cavities than males; however, there were no differences in other age groups. Our results demonstrate a significantly greater proportion of smaller resorption cavities than would be expected from current models of bone remodeling and are consistent with the hypothesis that resorption undergoes temporary interruptions and/or permanent arrest during the process of bone remodeling.

The variation among transplant center results in the United Kingdom and Ireland from 1977 to 1981.

An analysis of pooled data from transplants performed between 1977 and 1981 in 29 centers throughout the United Kingdom and Ireland revealed that the pattern of loss varied according to cause and postoperative time. Loss from rejection was characterized by a bimodal pattern in which early (0-25 days) and late (26-100 days) peaks of rejection were distinguishable. Rejected second transplants exhibited this phenomenon more than first transplants, and the loss was proportionately greater during the early period, suggesting that prior sensitization played an important role. Graft loss from technical causes and recipient death showed distinctly different patterns of loss. These findings suggested that, when possible, transplant survival statistics should be analyzed separately according to postoperative time and cause of loss. In applying these preliminary observations of the pooled data to a comparative study of the results in the different centers it was noted that such comparisons could be substantially affected by random variability in estimates of actuarial survival rates. Therefore, a simple method of ranking was developed in which centers were allocated to high or low survivorship categories, or to an indeterminate category when the standard error in estimated actuarial survival was relatively large. Whereas the variation in loss rate from death with a functioning transplant (DWFT) was found to be indistinguishable from random variability, both nonimmunological failure (NIF) and immunological failure (IF) of the graft were found to be legitimate bases for ranking. Furthermore, center ranking based on IF at 0-25 days failed to exhibit a significant relationship with IF at 26-100 days, which could indicate important center differences associated with antirejection treatments during these two periods. These results showed that, ideally, time-cause parameters should be analyzed separately when comparing transplant survival statistics in different centers.

Renal transplant rejection. Transient immunodominance of HLA mismatches.

Many studies have shown long-term benefits of HLA matching in kidney transplantation. By examining rates of graft loss within consecutive posttransplant intervals, using data from the UK Transplant Service, we show that the long-term benefits of HLA matching are due to reduction of the graft failure rate within five months of transplantation. After 5-months, HLA-A,B,DR matching appears to have little impact on graft loss. We suggest that graft losses after 5 months may be attributable to non-HLA targets.

Analyzing transplant survival data.

Stratified proportional hazards regression is described as a method of estimating multifactorially preoperative factor effects on graft survival--and, at the same time, making due allowances for unknown transplant-center-specific influences. The multifactorial aspect of the method overcomes the biases inherent in analyzing transplant survival data one factor at a time, and stratification allows the data from many centers to be used simultaneously without the dangers associated with simple pooling of data from many sources. The proportionality and regression assumptions implicit in the method enable the data to be used efficiently, but must be validated on the data. Methods by which these assumptions may be relaxed are described--in particular, the stratified piece-wise proportional hazards regression method.

Predicting match grade and waiting time to kidney transplantation.

We show how to estimate expected waiting time to transplantation and match grade potential for each patient awaiting kidney transplantation on a multicenter waiting list. We predict that some easily well-matched patients may be unlikely to receive a well-matched graft through accepting an earlier offer of a poorly matched kidney. Other patients, who are difficult to match, may be unlikely to receive even a poorly matched kidney within a reasonable time.

Immunogenetic and clinical factors affecting renal transplantation. A rigorous analysis of data recorded by the UK Transplant Service.

A total of 3653 first cadaver kidney transplants in nondiabetic recipients over 15 years of age, performed in 30 transplant centers throughout the United Kingdom between 1978 and 1983, were analyzed to discover which of many recorded recipient, donor, surgical, and tissue-matching variables were important for graft survival, and in which postoperative period they exerted their maximum influence. A considerable effort was invested in checking the validity of the data and the appropriateness of the statistical methods. The duration of dialysis prior to transplantation was associated with a substantially reduced risk of graft failure, particularly at later postoperative times. Good HLA-B locus matching was also found to enhance graft survival--but, by contrast, HLA-A locus matching showed no significant effect on survival. Recipient age over 45 years, high serum reactivity, and grafts with anoxia time (the interval between circulatory arrest and perfusion with ice) exceeding 10 min were found to be associated with poor graft survival. Trends in survival were identified across calendar years of transplant, such that early graft failure (0-15 days) had increased in recent years, whereas later graft failure (greater than 15 days) had declined.

Substantial benefits of tissue matching in renal transplantation.

The purpose of this study was to perform a rigorous statistical analysis of the benefits of HLA-A,B and DR matching in renal transplantation. Graft survival in 2282 first cadaver kidney transplants, recorded and followed up by the United Kingdom Transplant Service (UKTS), was analyzed using the piecewise proportional hazards regression method. The results show that substantial improvements in graft survival are obtained when there is DR compatibility and at most one A or B mismatch, but that there is little advantage in tissue matching unless this degree of matching can be attained. So far, few graft recipients have benefited substantially through tissue matching (24% of kidneys exchanged through UKTS in 1984). This is partly attributable to unresolved technical problems in DR typing. However simulations show that under ideal conditions, with a pool of 3000 patients awaiting transplantation, considerable improvements in graft survival can be obtained in over 60% of recipients.

AIDS: the statistical basis for public health.

The backcalculation method has been extensively used in AIDS modelling and forecasting. Knowledge of reported AIDS cases, information on the time between HIV infection and onset of AIDS, and assumptions on the rate at which infections occurs, can be used to reconstruct the past history of the HIV epidemic, as well as to provide short term predictions of AIDS incidence. Uncertainty in the three components of the backcalculation method and the increasingly available information on HIV prevalence must be taken into account in order to provide realistic projections. In this paper we discuss ways of acknowledging uncertainty and suggest a Bayesian formulation of the backcalculation idea as a means of combining into a single model both random and systematic variation as well as prior information.

Conditional independence models for epidemiological studies with covariate measurement error.

We construct a unifying representation of the structure of measurement error problems with particular reference to situations commonly encountered in epidemiological studies, and outline how estimation of the parameters of interest can be carried out in a Bayesian framework using Gibbs sampling. We show how this approach can be implemented for designs involving continuous measurement errors assessed through a validation substudy, and discuss our results on simulated data.

A Bayesian approach to measurement error problems in epidemiology using conditional independence models.

Risk factors used in epidemiology are often measured with error which can seriously affect the assessment of the relation between risk factors and disease outcome. In this paper, a Bayesian perspective on measurement error problems in epidemiology is taken and it is shown how the information available in this setting can be structured in terms of conditional independence models. The modeling of common designs used in the presence of measurement error (validation group, repeated measures, ancillary data) is described. The authors indicate how Bayesian estimation can be carried out in these settings using Gibbs sampling, a sampling technique which is being increasingly referred to in statistical and biomedical applications. The method is illustrated by analyzing a design with two measuring instruments and no validation group.

Analysis of disease risks using ancillary risk factors, with application to job-exposure matrices.

Epidemiological studies of disease can make use of ancillary risk-factors, acquired from individuals outside the disease study. For example, several disease studies might use the same job-exposure matrix to quantify risks due to occupational exposure to industrial agents. We construct a graphical model to combine a logistic regression disease model with models for the ancillary data and the risk-factor distribution in the population. We estimate the graphical model using Gibbs sampling, and in simulations compare it with methods of direct substitution into logistic regression.

Matchability in kidney transplantation.

The matchability of a patient awaiting kidney transplantation is his propensity for being 'well-matched'. We present two methods for estimating matchability. It is commonly supposed that phenotype frequency is a good predictor of matchability. We show a correlation of only 0.3 between matchability and phenotype frequency using the definition of 'well-matched' used by the UK Transplant Service. We also show that ABO type and HLA homozygocity can affect matchability.