A stochastic approximation algorithm with Markov chain Monte-Carlo method for incomplete data estimation problems

We propose a general procedure for solving incomplete data estimation problems. The procedure can be used to find the maximum likelihood estimate or to solve estimating equations in difficult cases such as estimation with the censored or truncated regression model, the nonlinear structural measurement error model, and the random effects model. The procedure is based on the general principle of stochastic approximation and the Markov chain Monte-Carlo method. Applying the theory on adaptive algorithms, we derive conditions under which the proposed procedure converges. Simulation studies also indicate that the proposed procedure consistently converges to the maximum likelihood estimate for the structural measurement error logistic regression model.

Identification of inflections in T-cell counts among HIV-1-infected individuals and relationship with progression to clinical AIDS

Studies of circulating T (CD3+) lymphocytes have shown that on a population basis T-cell numbers remain stable for many years after HIV-1 infection (blind T-cell homeostasis), but decline rapidly beginning approximately 1.5–2.5 years before the onset of clinical AIDS. We derived a general method for defining the loss of homeostasis on the individual level and for determining the prevalence of homeostasis loss according to HIV status and the occurrence of AIDS in more than 5,000 men enrolled in the Multicenter AIDS Cohort Study. We used a segmented regression model for log10 CD3+ cell counts that included separate T-cell trajectories before and after a time (the T-cell inflection point) where the loss of T-cell homeostasis was most likely to have occurred. The average slope of CD3+ lymphocyte counts before the inflection point was close to zero for HIV− and HIV+ men, consistent with blind T-cell homeostasis. After the inflection point, the HIV+ individuals who developed AIDS generally showed a dramatic decline in CD3+ cell counts relative to HIV− men and HIV+ men not developing AIDS. A CD3+ cell decline of greater than 10 percent per year was present in 77% of HIV+ men developing AIDS but in only 23% of HIV+ men with no onset of AIDS. Our findings at the individual level support the blind T-cell homeostasis hypothesis and provide strong evidence that the loss of homeostasis is an important mechanism in the pathogenesis of the severe immunodeficiency that characterizes the late stages of HIV infection.

Trials of the beta model for complex inheritance.

Theoretical advantages of nonparametric logarithm of odds to map polygenic diseases are supported by tests of the beta model that depends on a single logistic parameter and is the only model under which paternal and maternal transmissions to sibs of specified phenotypes are independent. Although it does not precisely describe recurrence risks in monozygous twins, the beta model has greater power to detect family resemblance or linkage than the more general delta model which describes the probability of 0, 1, or 2 alleles identical by descent (ibd) with two parameters. Available data on ibd in sibs are consistent with the beta model, but not with the equally parsimonious but less powerful gamma model that assumes a fixed probability of 1/2 for 1 allele ibd. Additivity of loci on the liability scale is not disproven. A simple equivalence extends the beta model to multipoint analysis.

A general additive distance with time-reversibility and rate variation among nucleotide sites.

As additivity is a very useful property for a distance measure, a general additive distance is proposed under the stationary time-reversible (SR) model of nucleotide substitution or, more generally, under the stationary, time-reversible, and rate variable (SRV) model, which allows rate variation among nucleotide sites. A method for estimating the mean distance and the sampling variance is developed. In addition, a method is developed for estimating the variance-covariance matrix of distances, which is useful for the statistical test of phylogenies and molecular clocks. Computer simulation shows (i) if the sequences are longer than, say, 1000 bp, the SR method is preferable to simpler methods; (ii) the SR method is robust against deviations from time-reversibility; (iii) when the rate varies among sites, the SRV method is much better than the SR method because the distance is seriously underestimated by the SR method; and (iv) our method for estimating the sampling variance is accurate for sequences longer than 500 bp. Finally, a test is constructed for testing whether DNA evolution follows a general Markovian model.