Unsupervised discovery of ancestry-informative markers and genetic admixture proportions in biobank-scale datasets.

Admixture estimation plays a crucial role in ancestry inference and genome-wide association studies (GWASs). Computer programs such as ADMIXTURE and STRUCTURE are commonly employed to estimate the admixture proportions of sample individuals. However, these programs can be overwhelmed by the computational burdens imposed by the 105 to 106 samples and millions of markers commonly found in modern biobanks. An attractive strategy is to run these programs on a set of ancestry-informative SNP markers (AIMs) that exhibit substantially different frequencies across populations. Unfortunately, existing methods for identifying AIMs require knowing ancestry labels for a subset of the sample. This supervised learning approach creates a chicken and the egg scenario. In this paper, we present an unsupervised, scalable framework that seamlessly carries out AIM selection and likelihood-based estimation of admixture proportions. Our simulated and real data examples show that this approach is scalable to modern biobank datasets. OpenADMIXTURE, our Julia implementation of the method, is open source and available for free.

A multivariate Bernoulli model to predict DNaseI hypersensitivity status from haplotype data.

MOTIVATION: Haplotype models enjoy a wide range of applications in population inference and disease gene discovery. The hidden Markov models traditionally used for haplotypes are hindered by the dubious assumption that dependencies occur only between consecutive pairs of variants. In this article, we apply the multivariate Bernoulli (MVB) distribution to model haplotype data. The MVB distribution relies on interactions among all sets of variants, thus allowing for the detection and exploitation of long-range and higher-order interactions. We discuss penalized estimation and present an efficient algorithm for fitting sparse versions of the MVB distribution to haplotype data. Finally, we showcase the benefits of the MVB model in predicting DNaseI hypersensitivity (DH) status--an epigenetic mark describing chromatin accessibility--from population-scale haplotype data. RESULTS: We fit the MVB model to real data from 59 individuals on whom both haplotypes and DH status in lymphoblastoid cell lines are publicly available. The model allows prediction of DH status from genetic data (prediction R2=0.12 in cross-validations). Comparisons of prediction under the MVB model with prediction under linear regression (best linear unbiased prediction) and logistic regression demonstrate that the MVB model achieves about 10% higher prediction R2 than the two competing methods in empirical data. AVAILABILITY AND IMPLEMENTATION: Software implementing the method described can be downloaded at http://bogdan.bioinformatics.ucla.edu/software/. CONTACT: shihuwenbo@ucla.edu or pasaniuc@ucla.edu.

Extinction models for cancer stem cell therapy.

Cells with stem cell-like properties are now viewed as initiating and sustaining many cancers. This suggests that cancer can be cured by driving these cancer stem cells to extinction. The problem with this strategy is that ordinary stem cells are apt to be killed in the process. This paper sets bounds on the killing differential (difference between death rates of cancer stem cells and normal stem cells) that must exist for the survival of an adequate number of normal stem cells. Our main tools are birth-death Markov chains in continuous time. In this framework, we investigate the extinction times of cancer stem cells and normal stem cells. Application of extreme value theory from mathematical statistics yields an accurate asymptotic distribution and corresponding moments for both extinction times. We compare these distributions for the two cell populations as a function of the killing rates. Perhaps a more telling comparison involves the number of normal stem cells NH at the extinction time of the cancer stem cells. Conditioning on the asymptotic time to extinction of the cancer stem cells allows us to calculate the asymptotic mean and variance of NH. The full distribution of NH can be retrieved by the finite Fourier transform and, in some parameter regimes, by an eigenfunction expansion. Finally, we discuss the impact of quiescence (the resting state) on stem cell dynamics. Quiescence can act as a sanctuary for cancer stem cells and imperils the proposed therapy. We approach the complication of quiescence via multitype branching process models and stochastic simulation. Improvements to the τ-leaping method of stochastic simulation make it a versatile tool in this context. We conclude that the proposed therapy must target quiescent cancer stem cells as well as actively dividing cancer stem cells. The current cancer models demonstrate the virtue of attacking the same quantitative questions from a variety of modeling, mathematical, and computational perspectives.

On the Bumpy Road to the Dominant Mode.

Maximum likelihood estimation in many classical statistical problems is beset by multimodality. This article explores several variations of deterministic annealing that tend to avoid inferior modes and find the dominant mode. In Bayesian settings, annealing can be tailored to find the dominant mode of the log posterior. Our annealing algorithms involve essentially trivial changes to existing optimization algorithms built on block relaxation or the EM or MM principle. Our examples include estimation with the multivariate t distribution, Gaussian mixture models, latent class analysis, factor analysis, multidimensional scaling and a one-way random effects model. In the numerical examples explored, the proposed annealing strategies significantly improve the chances for locating the global maximum.

Accurate stochastic simulation via the step anticipation tau-leaping (SAL) algorithm.

Stochastic simulation methods are important in modeling chemical reactions, and biological and physical stochastic processes describable as continuous-time discrete-state Markov chains with a finite number of reactant species and reactions. The current algorithm of choice, tau-leaping, achieves fast and accurate stochastic simulation by taking large time steps that leap over individual reactions. During a leap interval (t, t + tau) in tau-leaping, each reaction channel operates as a Poisson process with a constant intensity. We modify tau-leaping to allow linear and quadratic changes in reaction intensities. Because our version of tau-leaping accurately anticipates how intensities change over time, we propose calling it the step anticipation tau-leaping (SAL) algorithm. We apply SAL to four examples: Kendall's process, a two-type branching process, Ehrenfest's model of diffusion, and Michaelis-Menten enzyme kinetics. In each case, SAL is more accurate than ordinary tau-leaping. The degree of improvement varies with the situation. Near stochastic equilibrium, reaction intensities are roughly constant, and SAL and ordinary tau-leaping perform about equally well.

Differential destruction of stem cells: implications for targeted cancer stem cell therapy.

Cancer stem cells represent a novel therapeutic target. The major challenge in targeting leukemic stem cells (LSC) is finding therapies that largely spare normal hematopoietic stem cells (HSC) while eradicating quiescent LSCs. We present a mathematical model to predict how selective a therapy must be to ensure that enough HSCs survive when LSCs have been eradicated. Stem cell population size is modeled as a birth-death process. This permits comparison of LSC and HSC eradication times under therapy and calculation of the number of HSCs at the time of LSC eradication for varied initial population sizes and stem cell death rates. We further investigate the effects of LSC quiescence and resistance mutations on our predictions. From a clinical point of view, our models suggest criteria by which cancer stem cell therapy safety can be assessed. We anticipate that in conjunction with experimental observation of cancer stem cell killing rates, our results will be useful in screening targeted therapies for both hematologic and solid tumor malignancies.

Palmar hyperhidrosis: evidence of genetic transmission.

BACKGROUND: Primary palmar hyperhidrosis is a condition marked by excessive perspiration and is reported to have an incidence of 1% in the Western population. It is a potentially disabling disorder that interferes with social, psychological, and professional activities. Over the past several years, several investigators have reported a positive family history in their patients treated for hyperhidrosis. To date, the cause is unknown; furthermore, epidemiologic data are scarce and inadequate. METHODS: To characterize the genetic contribution to hyperhidrosis, we conducted a prospective study of 58 consecutive patients with palmar, plantar, or axillary hyperhidrosis treated with thoracoscopic sympathectomy from September 1993 to July 1999. Forty-nine of the 58 probands volunteered family history data for these analyses (84% response rate). A standardized questionnaire was administered during the postoperative visit or by phone interview, and a detailed family history was obtained. The same questionnaire was also administered to a set of 20 control patients. The familial aggregation of hyperhidrosis has been quantified by estimating the recurrence risks to the offspring, parents, siblings, aunts, uncles, and cousins of 49 probands and 20 controls. We estimated the penetrance by use of a genetic analysis program. RESULTS: Thirty-two of 49 (65%) reported a positive family history in our hyperhidrosis group, and 0% reported a positive family history in our control group. A recurrence risk of 0.28 in the offspring of probands compared with frequency of 0.01 in the general population provides strong evidence for vertical transmission of this disorder in pedigrees and is further supported by the 0.14 risk to the parents of the probands. The results indicate that the disease allele is present in about 5% of the population and that one or two copies of the allele will result in hyperhidrosis 25% of the time, whereas the normal allele will result in hyperhidrosis less than 1% of the time. CONCLUSIONS: We conclude that primary palmar hyperhidrosis is a hereditary disorder, with variable penetrance and no proof of sex-linked transmission. However, this does not exclude other possible causes, and we anticipate that genetic confirmation of this disorder may lead to earlier diagnoses and advances in medical and psychosocial interventions.