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Statistical issues in the analysis of disease mapping data.

In this paper we discuss a number of issues that are pertinent to the analysis of disease mapping data. As an illustrative example we consider the mapping of larynx cancer across electoral wards in the North West Thames region of the U.K. Bayesian hierarchical models are now frequently employed to carry out such mapping. In a typical situation, a three-stage hierarchical model is specified in which the data are modelled as a function of area-specific relative risks at stage one; the collection of relative risks across the study region are modelled at stage two; and at stage three prior distributions are assigned to parameters of the stage two distribution. Such models allow area-specific disease relative risks to be 'smoothed' towards global and/or local mean levels across the study region. However, these models contain many structural and functional assumptions at different levels of the hierarchy; we aim to discuss some of these assumptions and illustrate their sensitivity. When relative risks are the endpoint of interest, it is common practice to assume that, for each of the age-sex strata of a particular area, there is a common multiplier (the relative risk) acting upon each of the stratum-specific risks in that area; we will examine this proportionality assumption. We also consider the choices of models and priors at stages two and three of the hierarchy, the effect of outlying areas, and an assessment of the level of smoothing that is being carried out. For inference, we concentrate on the description of the spatial variability in relative risks and on the association between the relative risks of larynx cancer and an area-level measure of socio-economic status.

Age Factors↗

PubMed1996

Improved designs for dose escalation studies using pharmacokinetic measurements.

We describe a method for incorporating pharmacokinetic (PK) data into dose escalation clinical trial designs. Doing so can improve the efficiency and accuracy of these studies. The method proposed uses a parametric dose response function that models the probability of response in each person with two effects: the dose of drug administered and an ancillary pharmacokinetic measurements. After treatment and observation of each subject (or group of subjects) for response, one calculates the dose to be administered to the next individual (or group) to yield the target probability of response from the current best estimate of the dose-response curve. This procedure is a variant of the continual reassessment method (CRM). Statistical simulations employing a logistic dose-response model (that is, we model the logit of the response probability as a linear combination of predictors), dose of drug, and the area under the time-concentration curve (AUC) demonstrate that the addition of pharmacokinetic information to the CRM is a practical and useful way to improve both dose-response modelling and the design of dose escalation studies.

Area Under Curve↗

PubMed2004

Analysis of the molecular evolutionary history of the ascorbate peroxidase gene family: inferences from the rice genome.

Ascorbate peroxidase (APx) is a class I peroxidase that catalyzes the conversion of H(2)O(2) to H(2)O and O(2) using ascorbate as the specific electron donor. This enzyme has a key function in scavenging reactive oxygen species (ROS) and the protection against toxic effects of ROS in higher plants, algae, and Euglena. Here we report the identification of an APx multigene family in rice and propose a molecular evolutionary relationship between the diverse APx isoforms. In rice, the APx gene family has eight members, which encode two cytosolic, two putative peroxisomal, and four chloroplastic isoforms, respectively. Phylogenetic analyses were conducted using all APx protein sequences available in the NCBI databases. The results indicate that the different APx isoforms arose by a complex evolutionary process involving several gene duplications. The structural organization of APx genes also reflects this process and provides evidence for a close relationship among proteins located in the same subcellular compartment. A molecular evolutionary pathway, in which cytosolic and peroxisomal isoforms diverged early from chloroplastic ones, is proposed.

Amino Acid Sequence↗

PubMed1999

Segregation analysis of body mass index in a large sample selected for obesity: the Swedish Obese Subjects study.

OBJECTIVE: To investigate a major gene hypothesis for body mass index (BMI) in a large sample of probands (n = 2580, ages 37-57 years) who were selected for obesity (BMI> or =34 kg/m2 for males and > or =38 kg/m2 for females), along with their spouses and first-degree relatives (n = 11,204 family members). The probands were recruited as part of an intervention trial assessing whether mortality and morbidity were improved after surgical intervention for obesity as part of the Swedish Obese Subjects (SOS) study. METHODS AND PROCEDURES: The current analyses were based on BMI measures obtained before intervention. Segregation analysis was carried out using the mixed model implementation in PAP (Pedigree Analysis Package), which allowed for ascertainment correction and for genotype-dependent effects of covariates (sex and age) in both the major gene component and the multifactorial (i.e., polygenic and familial environment) component. RESULTS: Both a major effect and a multifactorial effect were significant. The percentage of the total variance accounted for by the multifactorial effect was 17%-24% (increasing as a function of age), and by the major effect, 8%-34% (decreasing as a function of age). Although tests on the transmission probabilities (taus) were not compatible with Mendelian expectations of 1, 1/2, and 0, the equal taus model was rejected (i.e., the effect is transmitted in families) and the point estimates (0.96, 0.60, and 0.17) compared favorably to Mendelian expectations. The major effect was transmitted in a codominant fashion, consistent with a gene-environment interaction. DISCUSSION: These results suggest both multifactorial and major effect etiologies for BMI in these families of extremely obese probands. Before 20 years of age, the major effect dominates the BMI expression, but after age 20, multifactorial effects account for the most variance. Although the major effect is transmitted in these families, the pattern does not appear to be consistent with a simple Mendelian trait. The possibility of additional major loci (i.e., epistasis) and gene by environment interactions may explain these findings.

Adult↗

PubMed2003

Patterns of variation within self-incompatibility loci.

Diverse self-incompatibility (SI) mechanisms permit flowering plants to inhibit fertilization by pollen that express specificities in common with the pistil. Characteristic of at least two model systems is greatly reduced recombination across large genomic tracts surrounding the S-locus, which regulates SI. In three angiosperm families, including the Solanaceae, the gene that controls the expression of gametophytic SI in the pistil encodes a ribonuclease (S-RNase). The gene that controls pollen SI expression is currently unknown, although several candidates have recently been proposed. Although each candidate shows a high level of polymorphism and complete allelic disequilibrium with the S-RNase gene, such properties may merely reflect tight linkage to the S-locus, irrespective of any functional role in SI. We analyzed the magnitude and nature of nucleotide variation, with the objective of distinguishing likely candidates for regulators of SI from other genes embedded in the S-locus region. We studied the S-RNase gene of the Solanaceae and 48A, a candidate for the pollen gene in this system, and we also conducted a parallel analysis of the regulators of sporophytic SI in Brassica, a system in which both the pistil and pollen genes are known. Although the pattern of variation shown by the pollen gene of the Brassica system is consistent with its role as a determinant of pollen specificity, that of 48A departs from expectation. Our analysis further suggests that recombination between 48A and S-RNase may have occurred during the interval spanned by the gene genealogy, another indication that 48A may not regulate SI expression in pollen.

3' Untranslated Regions↗

PubMed2004

Residual analysis in linear regression models with an interval-censored covariate.

Residual analysis is a useful class of techniques for the evaluation of the goodness of a fitted model. Checking the underlying assumptions is important since most linear regression estimators require a correctly specified regression function and independent and identically distributed errors to be consistent. For uncensored data, the examination of the residuals of the fitted model is a standard tool for checking whether or not the underlying model assumptions hold. Such analysis has not been widely developed for censored data. Hillis (Statistics in Medicine 1995; 14:2023-2036) developed a residual plot for model checking when the response variable of a linear model is right-censored, and Gomez et al. (Statistics in Medicine 2003; 22:409-425) proposed residuals in models with interval-censored covariates. In this paper, we propose a new definition of residuals for linear models that incorporate interval-censored covariates. This definition can be also applied when the response variable is interval-censored. These new residuals are shown to perform better in model checking than other types of residuals in this context. We illustrate them with a data set from an AIDS clinical trial study.

Anti-HIV Agents↗

PubMed1994

Noise properties of the EM algorithm: II. Monte Carlo simulations.

In an earlier paper we derived a theoretical formulation for estimating the statistical properties of images reconstructed using the iterative ML-EM algorithm. To gain insight into this complex problem, two levels of approximation were considered in the theory. These techniques revealed the dependence of the variance and covariance of the reconstructed image noise on the source distribution, imaging system transfer function, and iteration number. In this paper a Monte Carlo approach was taken to study the noise properties of the ML-EM algorithm and to test the predictions of the theory. The study also served to evaluate the approximations used in the theory. Simulated data from phantoms were used in the Monte Carlo experiments. The ML-EM statistical properties were calculated from sample averages of a large number of images with different noise realizations. The agreement between the more exact form of the theoretical formulation and the Monte Carlo formulation was better than 10% in most cases examined, and for many situations the agreement was within the expected error of the Monte Carlo experiments. Results from the studies provide valuable information about the noise characteristics of ML-EM reconstructed images. Furthermore, the studies demonstrate the power of the theoretical and Monte Carlo approaches for investigating noise properties of statistical reconstruction algorithms.

Algorithms↗

PubMed2004

Genome-wide patterns of nucleotide substitution reveal stringent functional constraints on the protein sequences of thermophiles.

To test the hypothesis that the proteins of thermophilic prokaryotes are subject to unusually stringent functional constraints, we estimated the numbers of synonymous and nonsynonymous nucleotide substitutions per site between 17,957 pairs of orthologous genes from 22 pairs of closely related species of Archaea and Bacteria. The average ratio of nonsynonymous to synonymous substitutions was significantly lower in thermophiles than in nonthermophiles, and this effect was observed in both Archaea and Bacteria. There was no evidence that this difference could be explained by factors such as nucleotide content bias. Rather, the results support the hypothesis that proteins of thermophiles are subject to unusually strong purifying selection, leading to a reduced overall level of amino acid evolution per mutational event. The results show that genome-wide patterns of sequence evolution can be influenced by natural selection exerted by a species' environment and shed light on a previous observation that relatively few of the mutations arising in a thermophilic archaeon were nucleotide substitutions in contrast to indels.

Adaptation, Biological↗

PubMed2004

Operon prediction by comparative genomics: an application to the Synechococcus sp. WH8102 genome.

We present a computational method for operon prediction based on a comparative genomics approach. A group of consecutive genes is considered as a candidate operon if both their gene sequences and functions are conserved across several phylogenetically related genomes. In addition, various supporting data for operons are also collected through the application of public domain computer programs, and used in our prediction method. These include the prediction of conserved gene functions, promoter motifs and terminators. An apparent advantage of our approach over other operon prediction methods is that it does not require many experimental data (such as gene expression data and pathway data) as input. This feature makes it applicable to many newly sequenced genomes that do not have extensive experimental information. In order to validate our prediction, we have tested the method on Escherichia coli K12, in which operon structures have been extensively studied, through a comparative analysis against Haemophilus influenzae Rd and Salmonella typhimurium LT2. Our method successfully predicted most of the 237 known operons. After this initial validation, we then applied the method to a newly sequenced and annotated microbial genome, Synechococcus sp. WH8102, through a comparative genome analysis with two other cyanobacterial genomes, Prochlorococcus marinus sp. MED4 and P.marinus sp. MIT9313. Our results are consistent with previously reported results and statistics on operons in the literature.

ATP-Binding Cassette Transporters↗

PubMed2004

A parametric model for detecting hormetic effects in developmental toxicity studies.

Hormetic effects have been observed at low exposure levels based on the dose-response pattern of data from developmental toxicity studies. This indicates that there might actually be a reduced risk of exhibiting toxic effects at low exposure levels. Hormesis implies the existence of a threshold dose level and there are dose-response models that include parameters that account for the threshold. We propose a function that introduces a parameter to account for hormesis. This function is a subset of the set of all functions that could represent a hormetic dose-response relationship at low exposure levels to toxic agents. We characterize the overall dose-response relationship with a piecewise function that consists of a hormetic u-shape curve at low dose levels and a logistic curve at high dose levels. We apply our model to a data set from an experiment conducted at the National Toxicology Program (NTP). We also use the beta-binomial distribution to model the litter response data. It can be seen by observing the structure of these data that current experimental designs for developmental studies employ a limited number of dose groups. These designs may not be satisfactory when the goal is to illustrate the existence of hormesis. In particular, increasing the number of low-level doses improves the power for detecting hormetic effects. Therefore, we also provide the results of simulations that were done to characterize the power of current designs in detecting hormesis and to demonstrate how this power can be improved upon by altering these designs with the addition of only a few low exposure levels.

Animals↗

PubMed2003

Estimating mean hospital cost as a function of length of stay and patient characteristics.

Statistical models have been used to assess the influence of clinical and demographic factors on hospital charge and length of stay (LOS). Hospital costs constitute a significant proportion of overall expenditure in health care. With escalating costs, knowing the correlates of LOS and in-hospital cost is important for decisions on allocating resources. However, hospital charge and LOS are correlated. We describe two regression models that permit estimation of mean charges as a function of patient hospital stay and adjust for the influence of patient characteristics and treatment procedures on LOS and charge. In the first model, the mean charge over a specified duration is a weighted average of the expected cumulative charge, with weighting determined by the distribution of LOS. The second model for LOS and charge explicitly accounts for their correlation and yields estimates of the average charge per average LOS. The methods are applied to assess mean charges and mean charge per day by cardiac procedure in a cohort of patients hospitalized for acute myocardial infarction, while adjusting for the impact of patient demographic and clinical factors on LOS and charge. For relatively short hospital stays, and when only total hospital charges are available, these models provide a flexible approach to estimating summary measures on resource use while controlling for the effects of covariates on LOS and charge.

Aged↗

PubMed2006

Fat-tailed gene flow in the dioecious canopy tree species Fraxinus mandshurica var. japonica revealed by microsatellites.

Pollen flow, seed dispersal and individual reproductive success can be simultaneously estimated from the genotypes of adults and offspring using stochastic models. Using four polymorphic microsatellite loci, gene flow of the wind-pollinated and wind-seed-dispersed dioecious tree species, Fraxinus mandshurica var. japonica, was quantified in a riparian forest, in northern Japan. In a 10.5-ha plot, 74 female adults, 76 male adults and 292 current-year seedlings were mapped and genotyped, together with 200 seeds. To estimate dispersal kernels of pollen and seeds, we applied normal, exponential power, Weibull, bivariate t-distribution kernels, and two-component models consisting of two normal distribution functions, one with a small and one with a large variance. A two-component pollen flow model with a small contribution (26.1%) from short-distance dispersal (sigma = 7.2 m), and the rest from long-distance flow (sigma = 209.9 m), was chosen for the best-fitting model. The average distance that integrated pollen flows inside and outside the study plot was estimated to be 196.8 m. Tree size and flowering intensity affected reproduction, and there appeared to be critical values that distinguished reproductively successful and unsuccessful adults. In contrast, the gene flow model that estimated both pollen and seed dispersal from established seedlings resulted in extensive seed dispersal, and the expected spatial genetic structures did not satisfactorily fit with the observations, even for the selected model. Our results advanced small-scale individual-based parentage analysis for quantifying fat-tailed gene flow in wind-mediated species, but also clarified its limitations and suggested future possibilities for gene flow studies.

Alleles↗

PubMed2004

A common ABCC2 promoter polymorphism is not a determinant of the risk of spina bifida.

BACKGROUND: There is compelling evidence that the risk of spina bifida, a malformation of the caudal neural tube, is associated with maternal and/or embryonic disturbances in folate/homocysteine metabolism. Hence, functional variants of genes that influence folate/homocysteine metabolism constitute a biologically plausible group of candidate risk factors for spina bifida and other neural tube defects. One such candidate is ABCC2, the gene encoding ABCC2, (a.k.a. canalicular multispecific organic anion transporter [cMOAT], multidrug resistance related protein 2 [MRP2]), a member of the ABC transporter family that effluxes natural folates and anti-folate drugs such as methotrexate. METHODS: The association between the risk of spina bifida and both the maternal and embryonic ABCC2 C(-24)T genotype was evaluated by using the transmission disequilibrium test and log-linear modeling. RESULTS: These analyses provided no evidence that the risk of spina bifida was significantly related to either the maternal or embryonic ABCC2 C(-24)T genotype. CONCLUSIONS: The results of the present analyses suggest that the C(-24)T variant of the ABCC2 gene is not a major determinant of spina bifida risk.

ATP-Binding Cassette Transporters↗

PubMed2004

Analysis of EphA4 in the lesser spotted catshark identifies a primitive gnathostome expression pattern and reveals co-option during evolution of shark-specific morphology.

The Eph family is the largest known group of structurally related receptor tyrosine kinases (RTKs). Each Eph receptor has a specific Ephrin ligand, and these function to define spatial boundaries during development. Analyses of EphA4 in mouse, chick, frog and zebrafish embryos have implicated this gene in a number of developmental processes, including maintenance of segmental boundaries, axon guidance, limb development, neural crest migration and patterning of the ear. In order to determine which components of EphA4 function may be primitive for gnathostomes, we cloned EphA4 from the lesser spotted catshark ( Scyliorhinus canicula) and examined its expression pattern during shark embryonic development. Consistent with the patterns reported for bony fish and tetrapods, we observed segmental expression of EphA4 in the developing hindbrain and later in the pharyngeal arches of shark embryos. EphA4 was also detected during sensory organogenesis, in the developing ear, eye, nasal pits and lateral line. A dynamic pattern of EphA4expression occurs during shark fin development, suggesting an early role in outgrowth and patterning of the fin buds and a later role in tissue differentiation. We also observed several novel domains of EphA4expression that have not been reported in other vertebrates, including external gill buds, dermal denticles, median fins and claspers. While some of these domains may reflect co-option of EphA4expression to novel sites for development of shark-specific characters, others are more likely to be ancestral patterns of expression that were lost in other vertebrate lineages.

Amino Acid Sequence↗

PubMed2006

Bayesian dose-finding in phase I/II clinical trials using toxicity and efficacy odds ratios.

A Bayesian adaptive design is proposed for dose-finding in phase I/II clinical trials to incorporate the bivariate outcomes, toxicity and efficacy, of a new treatment. Without specifying any parametric functional form for the drug dose-response curve, we jointly model the bivariate binary data to account for the correlation between toxicity and efficacy. After observing all the responses of each cohort of patients, the dosage for the next cohort is escalated, deescalated, or unchanged according to the proposed odds ratio criteria constructed from the posterior toxicity and efficacy probabilities. A novel class of prior distributions is proposed through logit transformations which implicitly imposes a monotonic constraint on dose toxicity probabilities and correlates the probabilities of the bivariate outcomes. We conduct simulation studies to evaluate the operating characteristics of the proposed method. Under various scenarios, the new Bayesian design based on the toxicity-efficacy odds ratio trade-offs exhibits good properties and treats most patients at the desirable dose levels. The method is illustrated with a real trial design for a breast medical oncology study.

Antineoplastic Combined Chemotherapy Protocols↗

PubMed1998

Treatment of adolescent depression: frequency of services and impact on functioning in young adulthood.

In this report, we (a) present descriptive information about the extent and the kinds of treatments being provided to depressed adolescents; (b) identify the factors that are related to treatment utilization; and (c) examine whether the provision of treatment during adolescence reduced the risk for the occurrence of depression during young adulthood (19-24 years). The sample consisted of 1,507 randomly selected high school students who were diagnostically assessed on two occasions with an interval of approximately one year; 627 were assessed a third time when they reached the age of 24. The findings may be summarized as follows: 60.7% of those with major depressive disorder were provided with treatment. The modal treatment was outpatient, individual psychotherapy administered by a mental health provider. Inpatient treatment and medications were rare. Factors found to be related to treatment utilization were the severity of the depression, the existence of a comorbid nonaffective disorder, the number of previous episodes of depression, history of suicide attempt, academic problems, lack of intact family, and female gender. Unexpectedly, those who had received treatment were not less likely to relapse into another episode of depression during young adulthood.

Adolescent↗

PubMed2005

Positive and negative selection on mammalian Y chromosomes.

Y chromosomes are genetically degenerate in most organisms studied. The loss of genes from Y chromosomes is thought to be due to the inefficiency of purifying selection in nonrecombining regions, which leads to the accumulation of deleterious mutations via the processes of hitchhiking, background selection, and Muller's ratchet. As the severity of these processes depends on the number of functional genes linked together on the nonrecombining Y, it is not clear whether these processes are still at work on the old, gene-poor mammalian Y chromosomes. If purifying selection is indeed less efficient in the Y-linked, compared to the X-linked genes, deleterious nonsynonymous substitutions are expected to accumulate faster on the Y chromosome. However, positive selection on Y-linked genes could also increase the rate of amino acid-changing substitutions. Thus, the previous reports of an elevated nonsynonymous substitution rate in Y-linked genes are still open to interpretation. Here, we report evidence for positive selection in two out of three studied mammalian Y-linked genes, suggesting that adaptive Darwinian evolution may be common on mammalian Y chromosomes. Taking positive selection into account, we demonstrate that purifying selection is less efficient in mammalian Y-linked genes compared to their X-linked homologues, suggesting that these genes continue to degenerate.

Animals↗

PubMed2006

Thyroid hormone metabolism and peroxidase function in two non-chordate animals.

In mammals, thyroid hormone (TH) signaling is essential for metabolic control, differentiation and homeostasis. These hormones are also involved in the regulation of metamorphosis in amphibians and lampreys and a role in basal chordates has been suggested. Increasing evidence supports TH-related function not only in basal chordates such as urochordates and cephalochordates but also in other invertebrate groups. However, the regulatory mechanisms underlying TH function including the mechanisms of endogenous synthesis of hormones in these groups are essentially unknown. Our data provide evidence for endogenous TH synthesis in the sea hare Aplysia californica and the sea urchin Lytechinus variegatus based on thin layer chromatography. Pharmacological experiments show that these hormones accelerate development to metamorphosis and specifically affect the formation of juvenile skeletal structures in the sea urchin. Furthermore, we identified two new peroxidase genes (LvTPO from L. variegatus and AcaTPO from A. californica) showing high sequence similarity with peroxidasin and thyroid peroxidases (the critical TH synthesis enzymes found in all vertebrates). Spatial and temporal expression patterns of these transcripts suggest a role of LvTPO and AcaTPO in a variety of processes such as development to metamorphosis and the regulation of the animal's energetics. We discuss our new findings in the context of evolution of TH synthesis and TH signaling in non-chordate animals.

Animals↗