Dosing algorithm to target a predefined AUC in patients with primary central nervous system lymphoma receiving high dose methotrexate

There is no consensus regarding optimal dosing of high dose methotrexate (HDMTX) in patients with primary CNS lymphoma. Our aim was to develop a convenient dosing algorithm to target AUC(MTX) in the range between 1000 and 1100 µmol l(-1) h.

Randomised trial of a clinical dosing algorithm to start anticoagulation with phenprocoumon

Prospective validation of two algorithms for the initiation of phenprocoumon treatment.

Squared Extrapolation Methods (SQUAREM): A New Class of Simple and Efficient Numerical Schemes for Accelerating the Convergence of the EM Algorithm

We derive a new class of iterative schemes for accelerating the convergence of the EM algorithm, by exploiting the connection between fixed point iterations and extrapolation methods. First, we present a general formulation of one-step iterative schemes, which are obtained by cycling with the extrapolation methods. We, then square the one-step schemes to obtain the new class of methods, which we call SQUAREM. Squaring a one-step iterative scheme is simply applying it twice within each cycle of the extrapolation method. Here we focus on the first order or rank-one extrapolation methods for two reasons, (1) simplicity, and (2) computational efficiency. In particular, we study two first order extrapolation methods, the reduced rank extrapolation (RRE1) and minimal polynomial extrapolation (MPE1). The convergence of the new schemes, both one-step and squared, is non-monotonic with respect to the residual norm. The first order one-step and SQUAREM schemes are linearly convergent, like the EM algorithm but they have a faster rate of convergence. We demonstrate, through five different examples, the effectiveness of the first order SQUAREM schemes, SqRRE1 and SqMPE1, in accelerating the EM algorithm. The SQUAREM schemes are also shown to be vastly superior to their one-step counterparts, RRE1 and MPE1, in terms of computational efficiency. The proposed extrapolation schemes can fail due to the numerical problems of stagnation and near breakdown. We have developed a new hybrid iterative scheme that combines the RRE1 and MPE1 schemes in such a manner that it overcomes both stagnation and near breakdown. The squared first order hybrid scheme, SqHyb1, emerges as the iterative scheme of choice based on our numerical experiments. It combines the fast convergence of the SqMPE1, while avoiding near breakdowns, with the stability of SqRRE1, while avoiding stagnations. The SQUAREM methods can be incorporated very easily into an existing EM algorithm. They only require the basic EM step for their implementation and do not require any other auxiliary quantities such as the complete data log likelihood, and its gradient or hessian. They are an attractive option in problems with a very large number of parameters, and in problems where the statistical model is complex, the EM algorithm is slow and each EM step is computationally demanding.

A Faster Circular Binary Segmentation Algorithm for the Analysis of Array CGH Data

Motivation: Array CGH technologies enable the simultaneous measurement of DNA copy number for thousands of sites on a genome. We developed the circular binary segmentation (CBS) algorithm to divide the genome into regions of equal copy number (Olshen {\it et~al}, 2004). The algorithm tests for change-points using a maximal $t$-statistic with a permutation reference distribution to obtain the corresponding $p$-value. The number of computations required for the maximal test statistic is $O(N^2),$ where $N$ is the number of markers. This makes the full permutation approach computationally prohibitive for the newer arrays that contain tens of thousands markers and highlights the need for a faster. algorithm. Results: We present a hybrid approach to obtain the $p$-value of the test statistic in linear time. We also introduce a rule for stopping early when there is strong evidence for the presence of a change. We show through simulations that the hybrid approach provides a substantial gain in speed with only a negligible loss in accuracy and that the stopping rule further increases speed. We also present the analysis of array CGH data from a breast cancer cell line to show the impact of the new approaches on the analysis of real data. Availability: An R (R Development Core Team, 2006) version of the CBS algorithm has been implemented in the ``DNAcopy'' package of the Bioconductor project (Gentleman {\it et~al}, 2004). The proposed hybrid method for the $p$-value is available in version 1.2.1 or higher and the stopping rule for declaring a change early is available in version 1.5.1 or higher.

[Acute lower gastrointestinal bleeding--an evidence-based algorithm for diagnosis and treatment]

Novel means to locate and treat lower gastrointestinal bleeding (lGB) allow to reduce the rate of required surgical interventions and help to limit the extend of resection. The risk stratification of patients with lGB is the primary step of our recommended treatment algorithm. Accordingly, risk stratifying instruments, which are only partly validated up to now, are gaining significance in lGB. Whereas, gastro-duodenoscopy and colonoscopy prior to angiography or scintigraphy are established diagnostic tools, capsule enteroscopy offers a novel approach to hemodynamic stable patients with lGB that are difficult to localize. With its every increasing sensitivity, Angio-Computer Tomography is likely to replace scintigraphy and diagnostic angiography in the very near future. In addition, recent advances in superselective microembolisation have been shown to have the potential rendering surgical interventions in a majority of patients with acute lGB unnecessary. The extend of required surgical resection is largely dependent on the success to localize the bleeding source of prior diagnostics. Only if the source is identified, a limited segmental resection should be performed. Should surgery be required, we suggest to maintain the effort to localize the bleeding, either by prior laparoscopy and/or by intraoperative entero-colonoscopy. Eventually, if the source of bleeding remains unclear total colectomy with ileorectal anastomosis represents the procedure of choice in patients with acute lGB.

Bayesian Hidden Markov Modeling of Array CGH Data

Genomic alterations have been linked to the development and progression of cancer. The technique of Comparative Genomic Hybridization (CGH) yields data consisting of fluorescence intensity ratios of test and reference DNA samples. The intensity ratios provide information about the number of copies in DNA. Practical issues such as the contamination of tumor cells in tissue specimens and normalization errors necessitate the use of statistics for learning about the genomic alterations from array-CGH data. As increasing amounts of array CGH data become available, there is a growing need for automated algorithms for characterizing genomic profiles. Specifically, there is a need for algorithms that can identify gains and losses in the number of copies based on statistical considerations, rather than merely detect trends in the data. We adopt a Bayesian approach, relying on the hidden Markov model to account for the inherent dependence in the intensity ratios. Posterior inferences are made about gains and losses in copy number. Localized amplifications (associated with oncogene mutations) and deletions (associated with mutations of tumor suppressors) are identified using posterior probabilities. Global trends such as extended regions of altered copy number are detected. Since the posterior distribution is analytically intractable, we implement a Metropolis-within-Gibbs algorithm for efficient simulation-based inference. Publicly available data on pancreatic adenocarcinoma, glioblastoma multiforme and breast cancer are analyzed, and comparisons are made with some widely-used algorithms to illustrate the reliability and success of the technique.