A key difference between using blockchains to store data and centrally controlled databases is that transactions are accepted to a blockchain via a consensus mechanism, and not by a controlling central party. Hence, once a user has issued a transaction, she cannot be certain if it will be accepted. Moreover, a yet unaccepted transaction cannot be retracted by the user, and may (or may not) be appended to the blockchain at any point in the future. This causes difficulties as the user may wish to formulate new transactions based on the knowledge of which previous transactions will be accepted. Yet this knowledge is inherently uncertain. We introduce a formal abstraction for blockchains as a data storage layer that underlies a database. The main issue that we tackle is the need to reason about possible worlds, due to the uncertainty in transaction appending. In particular, we consider the theoretical complexity of determining whether it is possible for a denial constraint to be contradicted, given the current state of the blockchain, pending transactions, and integrity constraints on blockchain data. We then present practical algorithms for this problem that work well in practice.

BACKGROUND: Gene expression profiling (GEP) via microarray analysis is a widely used tool for assessing risk and other patient diagnostics in clinical settings. However, non-biological factors such as systematic changes in sample preparation, differences in scanners, and other potential batch effects are often unavoidable in long-term studies and meta-analysis. In order to reduce the impact of batch effects on microarray data, Johnson, Rabinovic, and Li developed ComBat for use when combining batches of gene expression microarray data. We propose a modification to ComBat that centers data to the location and scale of a pre-determined, 'gold-standard' batch. This modified ComBat (M-Combat) is designed specifically in the context of meta-analysis and batch effect adjustment for use with predictive models that are validated and fixed on historical data from a 'gold-standard' batch. RESULTS: We combined data from MIRT across two batches ('Old' and 'New' Kit sample preparation) as well as external data sets from the HOVON-65/GMMG-HD4 and MRC-IX trials into a combined set, first without transformation and then with both ComBat and M-ComBat transformations. Fixed and validated gene risk signatures developed at MIRT on the Old Kit standard (GEP5, GEP70, and GEP80 risk scores) were compared across these combined data sets. Both ComBat and M-ComBat eliminated all of the differences among probes caused by systematic batch effects (over 98% of all untransformed probes were significantly different by ANOVA with 0.01 q-value threshold reduced to zero significant probes with ComBat and M-ComBat). The agreement in mean and distribution of risk scores, as well as the proportion of high-risk subjects identified, coincided with the 'gold-standard' batch more with M-ComBat than with ComBat. The performance of risk scores improved overall using either ComBat or M-Combat; however, using M-ComBat and the original, optimal risk cutoffs allowed for greater ability in our study to identify smaller cohorts of high-risk subjects. CONCLUSION: M-ComBat is a practical modification to an accepted method that offers greater power to control the location and scale of batch-effect adjusted data. M-ComBat allows for historical models to function as intended on future samples despite known, often unavoidable systematic changes to gene expression data.