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.

Incomplete embryonic lethality and fatal neonatal hemorrhage caused by prothrombin deficiency in mice

Deficiency of blood coagulation factor V or tissue factor causes the death of mouse embryos by 10.5 days of gestation, suggesting that part of the blood coagulation system is necessary for development. This function is proposed to require either generation of the serine protease thrombin and cell signaling through protease-activated receptors or an activity of tissue factor that is distinct from blood clotting. We find that murine deficiency of prothrombin clotting factor 2 (Cf2) was associated with the death of approximately 50% of Cf2−/− embryos by embryonic day 10.5 (E10.5), and surviving embryos had characteristic defects in yolk sac vasculature. Most of the remaining Cf2−/− embryos died by E15.5, but those surviving to E18.5 appeared normal. The rare Cf2−/− neonates died of hemorrhage on the first postnatal day. These studies suggest that a part of the blood coagulation system is adapted to perform a developmental function. Other mouse models show that the absence of platelets or of fibrinogen does not cause fetal wastage. Therefore, the role of thrombin in development may be independent of its effects on blood coagulation and instead may involve signal transduction on cells other than platelets.

Incomplete penetrance of familial retinoblastoma linked to germ-line mutations that result in partial loss of RB function

To study the molecular basis for the clinical phenotype of incomplete penetrance of familial retinoblastoma, we have examined the functional properties of three RB mutations identified in the germ line of five different families with low penetrance. RB mutants isolated from common adult cancers and from classic familial retinoblastoma (designated as classic RB mutations) are unstable and generally do not localize to the nucleus, do not undergo cyclin-dependent kinase (cdk)-mediated hyperphosphorylation, show absent protein “pocket” binding activity, and do not suppress colony growth of RB(−) cells. In contrast, two low-penetrant alleles (661W and “deletion of codon 480”) retained the ability to localize to the nucleus, showed normal cdk-mediated hyperphosphorylation in vivo, exhibited a binding pattern to simian virus 40 large T antigen using a quantitative yeast two-hybrid assay that was intermediate between classic mutants (null) and wild-type RB, and had absent E2F1 binding in vitro. A third, low-penetrant allele, “deletion of RB exon 4,” showed minimal hyperphosphorylation in vivo but demonstrated detectable E2F1 binding in vitro. In addition, each low-penetrant RB mutant retained the ability to suppress colony growth of RB(−) tumor cells. These findings suggest two categories of mutant, low-penetrant RB alleles. Class 1 alleles correspond to promoter mutations, which are believed to result in reduced or deregulated levels of wild-type RB protein, whereas class 2 alleles result in mutant proteins that retain partial activity. Characterization of the different subtypes of class 2 low-penetrant genes may help to define more precisely functional domains within the RB product required for tumor suppression.

A resistant genetic background leading to incomplete penetrance of intestinal neoplasia and reduced loss of heterozygosity in ApcMin/+ mice

Previous studies of Min/+ (multiple intestinal neoplasia) mice on a sensitive genetic background, C57BL/6 (B6), showed that adenomas have lost heterozygosity for the germ-line ApcMin mutation in the Apc (adenomatous polyposis coli) gene. We now report that on a strongly resistant genetic background, AKR/J (AKR), Min-induced adenoma multiplicity is reduced by about two orders of magnitude compared with that observed on the B6 background. Somatic treatment with a strong mutagen increases tumor number in AKR Min/+ mice in an age-dependent manner, similar to results previously reported for B6 Min/+ mice. Immunohistochemical analyses indicate that Apc expression is suppressed in all intestinal tumors from both untreated and treated AKR Min/+ mice. However, the mechanism of Apc inactivation in AKR Min/+ mice often differs from that observed for B6 Min/+ mice. Although loss of heterozygosity is observed in some tumors, a significant percentage of tumors showed neither loss of heterozygosity nor Apc truncation mutations. These results extend our understanding of the effects of genetic background on Min-induced tumorigenesis in several ways. First, the AKR strain carries modifiers of Min in addition to Mom1. This combination of AKR modifiers can almost completely suppress spontaneous intestinal tumorigenesis associated with the Min mutation. Second, even on such a highly resistant genetic background, tumor formation continues to involve an absence of Apc function. The means by which Apc function is inactivated is affected by genetic background. Possible scenarios are discussed.