BLUE, BLUP and the Kalman filter: some new results

In this contribution, we extend ‘Kalman-filter’ theory by introducing a new BLUE–BLUP recursion of the partitioned measurement and dynamic models. Instead of working with known state-vector means, we relax the model and assume these means to be unknown. The recursive BLUP is derived from first principles, in which a prominent role is played by the model’s misclosures. As a consequence of the mean state-vector relaxing assumption, the recursion does away with the usual need of having to specify the initial state-vector variance matrix. Next to the recursive BLUP, we introduce, for the same model, the recursive BLUE. This extension is another consequence of assuming the state-vector means unknown. In the standard Kalman filter set-up with known state-vector means, such difference between estimation and prediction does not occur. It is shown how the two intertwined recursions can be combined into one general BLUE–BLUP recursion, the outputs of which produce for every epoch, in parallel, the BLUP for the random state-vector and the BLUE for the mean of the state-vector

Performance of mitochondrial DNA mutations detecting early stage cancer

<p>Abstract</p> <p>Background</p> <p>Mutations in the mitochondrial genome (mtgenome) have been associated with cancer and many other disorders. These mutations can be point mutations or deletions, or admixtures (heteroplasmy). The detection of mtDNA mutations in body fluids using resequencing microarrays, which are more sensitive than other sequencing methods, could provide a strategy to measure mutation loads in remote anatomical sites.</p> <p>Methods</p> <p>We determined the mtDNA mutation load in the entire mitochondrial genome of 26 individuals with different early stage cancers (lung, bladder, kidney) and 12 heavy smokers without cancer. MtDNA was sequenced from three matched specimens (blood, tumor and body fluid) from each cancer patient and two matched specimens (blood and sputum) from smokers without cancer. The inherited wildtype sequence in the blood was compared to the sequences present in the tumor and body fluid, detected using the Affymetrix Genechip^®Human Mitochondrial Resequencing Array 1.0 and supplemented by capillary sequencing for noncoding region.</p> <p>Results</p> <p>Using this high-throughput method, 75% of the tumors were found to contain mtDNA mutations, higher than in our previous studies, and 36% of the body fluids from these cancer patients contained mtDNA mutations. Most of the mutations detected were heteroplasmic. A statistically significantly higher heteroplasmy rate occurred in tumor specimens when compared to both body fluid of cancer patients and sputum of controls, and in patient blood compared to blood of controls. Only 2 of the 12 sputum specimens from heavy smokers without cancer (17%) contained mtDNA mutations. Although patient mutations were spread throughout the mtDNA genome in the lung, bladder and kidney series, a statistically significant elevation of tRNA and ND complex mutations was detected in tumors.</p> <p>Conclusion</p> <p>Our findings indicate comprehensive mtDNA resequencing can be a high-throughput tool for detecting mutations in clinical samples with potential applications for cancer detection, but it is unclear the biological relevance of these detected mitochondrial mutations. Whether the detection of tumor-specific mtDNA mutations in body fluidsy this method will be useful for diagnosis and monitoring applications requires further investigation.</p