Generalized linear mixed models have been widely used in the analysis of correlated binary data arisen in many research areas. Maximum likelihood fitting of these models remains to be a challenge because of the complexity of the likelihood function. Current approaches are primarily to either approximate the likelihood or use a sampling method to find the exact likelihood solution. The former results in biased estimates, and the latter uses Monte Carlo EM (MCEM) methods with a Markov chain Monte Carlo algorithm in each E-step, leading to problems of convergence and slow convergence. This paper develops a new MCEM algorithm to maximize the likelihood for generalized linear mixed probit-normal models for correlated binary data. At each E-step, utilizing the inverse Bayes formula, we propose a direct importance sampling approach (i.e. weighted Monte Carlo integration) to numerically evaluate the first- and the second-order moments of a truncated multivariate normal distribution, thus eliminating problems of convergence and slow convergence. To monitor the convergence of the proposed MCEM, we again employ importance sampling to directly calculate the log-likelihood values and then to plot the difference of the consecutive log-likelihood values against the MCEM iteration. Two real data sets from the children's wheeze study and a three-period crossover trial are analyzed to illustrate the proposed method and for comparison with existing methods. The results show that the new MCEM algorithm outperformed that of McCulloch [McCulloch, C.E., 1994, Maximum likelihood variance components estimation for binary data. Journal of the American Statistical Association, 89, 330–335.] substantially.
Mutations in the gene ankyrin repeat domain containing 11 (ANKRD11/ANCO1) play a role in neurodegenerative disorders, and its loss of heterozygosity and low expression are seen in some cancers. Here, we show that low ANCO1 mRNA and protein expression levels are prognostic markers for poor clinical outcomes in breast cancer and that loss of nuclear ANCO1 protein expression predicts lower overall survival of patients with triple-negative breast cancer (TNBC). Knockdown of ANCO1 in early-stage TNBC cells led to aneuploidy, cellular senescence, and enhanced invasion in a 3D matrix. The presence of a subpopulation of ANCO1-depleted cells enabled invasion of the overall cell population in vitro and they converted more rapidly to invasive lesions in a xenograft mouse model. In ANCO1-depleted cells, ChIP-seq analysis showed a global increase in H3K27Ac signals that were enriched for AP-1, TEAD, STAT3, and NFκB motifs. ANCO1-regulated H3K27Ac peaks had a significantly higher overlap with known breast cancer enhancers compared to ANCO1-independent ones. H3K27Ac engagement was associated with transcriptional activation of genes in the PI3K-AKT, epithelial–mesenchymal transition (EMT), and senescence pathways. In conclusion, ANCO1 has hallmarks of a tumor suppressor whose loss of expression activates breast-cancer-specific enhancers and oncogenic pathways that can accelerate the early-stage progression of breast cancer.
1 April 2011 in Computational Statistics & Data Analysis