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.

Genome scan for teratogen-induced clefting susceptibility loci in the mouse: Evidence of both allelic and locus heterogeneity distinguishing cleft lip and cleft palate

Nonsyndromic clefting of the lip and palate in humans has a highly complex etiology, with both multiple genetic loci and exposure to teratogens influencing susceptibility. Previous studies using mouse models have examined only very small portions of the genome. Here we report the findings of a genome-wide search for susceptibility genes for teratogen-induced clefting in the AXB and BXA set of recombinant inbred mouse strains. We compare results obtained using phenytoin (which induces cleft lip) and 6-aminonicotinamide (which induces cleft palate). We use a new statistical approach based on logistic regression suitable for these categorical data to identify several chromosomal regions as possible locations of clefting susceptibility loci, and we review candidate genes located within each region. Because cleft lip and cleft palate do not frequently co-aggregate in human families and because these structures arise semi-independently during development, these disorders are usually considered to be distinct in etiology. Our data, however, implicate several of the same chromosomal regions for both forms of clefting when teratogen-induced. Furthermore, different parental strain alleles are usually associated with clefting of the lip versus that of the palate (i.e., allelic heterogeneity). Because several other chromosomal regions are associated with only one form of clefting, locus heterogeneity also appears to be involved. Our findings in this mouse model suggest several priority areas for evaluation in human epidemiological studies.