Prediction in dynamic models with time-dependent conditional variances

This paper considers forecasting the conditional mean and variance from a single-equation dynamic model with autocorrelated disturbances following an ARMA process, and innovations with time-dependent conditional heteroskedasticity as represented by a linear GARCH process. Expressions for the minimum MSE predictor and the conditional MSE are presented. We also derive the formula for all the theoretical moments of the prediction error distribution from a general dynamic model with GARCH(1, 1) innovations. These results are then used in the construction of ex ante prediction confidence intervals by means of the Cornish-Fisher asymptotic expansion. An empirical example relating to the uncertainty of the expected depreciation of foreign exchange rates illustrates the usefulness of the results. © 1992.

Dynamics of Delta/Notch signaling on endomesoderm segregation in the sea urchin embryo.

Endomesoderm is the common progenitor of endoderm and mesoderm early in the development of many animals. In the sea urchin embryo, the Delta/Notch pathway is necessary for the diversification of this tissue, as are two early transcription factors, Gcm and FoxA, which are expressed in mesoderm and endoderm, respectively. Here, we provide a detailed lineage analysis of the cleavages leading to endomesoderm segregation, and examine the expression patterns and the regulatory relationships of three known regulators of this cell fate dichotomy in the context of the lineages. We observed that endomesoderm segregation first occurs at hatched blastula stage. Prior to this stage, Gcm and FoxA are co-expressed in the same cells, whereas at hatching these genes are detected in two distinct cell populations. Gcm remains expressed in the most vegetal endomesoderm descendant cells, while FoxA is downregulated in those cells and activated in the above neighboring cells. Initially, Delta is expressed exclusively in the micromeres, where it is necessary for the most vegetal endomesoderm cell descendants to express Gcm and become mesoderm. Our experiments show a requirement for a continuous Delta input for more than two cleavages (or about 2.5 hours) before Gcm expression continues in those cells independently of further Delta input. Thus, this study provides new insights into the timing mechanisms and the molecular dynamics of endomesoderm segregation during sea urchin embryogenesis and into the mode of action of the Delta/Notch pathway in mediating mesoderm fate.

An integrated approach to the prediction of chemotherapeutic response in patients with breast cancer.

BACKGROUND: A major challenge in oncology is the selection of the most effective chemotherapeutic agents for individual patients, while the administration of ineffective chemotherapy increases mortality and decreases quality of life in cancer patients. This emphasizes the need to evaluate every patient's probability of responding to each chemotherapeutic agent and limiting the agents used to those most likely to be effective. METHODS AND RESULTS: Using gene expression data on the NCI-60 and corresponding drug sensitivity, mRNA and microRNA profiles were developed representing sensitivity to individual chemotherapeutic agents. The mRNA signatures were tested in an independent cohort of 133 breast cancer patients treated with the TFAC (paclitaxel, 5-fluorouracil, adriamycin, and cyclophosphamide) chemotherapy regimen. To further dissect the biology of resistance, we applied signatures of oncogenic pathway activation and performed hierarchical clustering. We then used mRNA signatures of chemotherapy sensitivity to identify alternative therapeutics for patients resistant to TFAC. Profiles from mRNA and microRNA expression data represent distinct biologic mechanisms of resistance to common cytotoxic agents. The individual mRNA signatures were validated in an independent dataset of breast tumors (P = 0.002, NPV = 82%). When the accuracy of the signatures was analyzed based on molecular variables, the predictive ability was found to be greater in basal-like than non basal-like patients (P = 0.03 and P = 0.06). Samples from patients with co-activated Myc and E2F represented the cohort with the lowest percentage (8%) of responders. Using mRNA signatures of sensitivity to other cytotoxic agents, we predict that TFAC non-responders are more likely to be sensitive to docetaxel (P = 0.04), representing a viable alternative therapy. CONCLUSIONS: Our results suggest that the optimal strategy for chemotherapy sensitivity prediction integrates molecular variables such as ER and HER2 status with corresponding microRNA and mRNA expression profiles. Importantly, we also present evidence to support the concept that analysis of molecular variables can present a rational strategy to identifying alternative therapeutic opportunities.