Optimal generalized truncated sequential Monte Carlo test

circGPA: circRNA functional annotation based on probability-generating functions

Recent research has already shown that circular RNAs (circRNAs) are functional in gene expression regulation and potentially related to diseases. Due to their stability, circRNAs can also be used as biomarkers for diagnosis. However, the function of most circRNAs remains unknown, and it is expensive and time-consuming to discover it through biological experiments. In this paper, we predict circRNA annotations from the knowledge of their interaction with miRNAs and subsequent miRNA-mRNA interactions. First, we construct an interaction network for a target circRNA and secondly spread the information from the network nodes with the known function to the root circRNA node. This idea itself is not new; our main contribution lies in proposing an efficient and exact deterministic procedure based on the principle of probability-generating functions to calculate the p-value of association test between a circRNA and an annotation term. We show that our publicly available algorithm is both more effective and efficient than the commonly used Monte-Carlo sampling approach that may suffer from difficult quantification of sampling convergence and subsequent sampling inefficiency. We experimentally demonstrate that the new approach is two orders of magnitude faster than the Monte-Carlo sampling, which makes summary annotation of large circRNA files feasible; this includes their reannotation after periodical interaction network updates, for example. We provide a summary annotation of a current circRNA database as one of our outputs. The proposed algorithm could be generalized towards other types of RNA in way that is straightforward.

A simple method for implementing Monte Carlo tests

We consider a statistical test whose p value can only be approximated using Monte Carlo simulations. We are interested in deciding whether the p value for an observed data set lies above or below a given threshold such as 5%. We want to ensure that the resampling risk, the probability of the (Monte Carlo) decision being different from the true decision, is uniformly bounded. This article introduces a simple open-ended method with this property, the confidence sequence method (CSM). We compare our approach to another algorithm, SIMCTEST, which also guarantees an (asymptotic) uniform bound on the resampling risk, as well as to other Monte Carlo procedures without a uniform bound. CSM is free of tuning parameters and conservative. It has the same theoretical guarantee as SIMCTEST and, in many settings, similar stopping boundaries. As it is much simpler than other methods, CSM is a useful method for practical applications.

Composite sequential Monte Carlo test for post-market vaccine safety surveillance

Group sequential hypothesis testing is now widely used to analyze prospective data. If Monte Carlo simulation is used to construct the signaling threshold, the challenge is how to manage the type I error probability for each one of the multiple tests without losing control on the overall significance level. This paper introduces a valid method for a true management of the alpha spending at each one of a sequence of Monte Carlo tests. The method also enables the use of a sequential simulation strategy for each Monte Carlo test, which is useful for saving computational execution time. Thus, the proposed procedure allows for sequential Monte Carlo test in sequential analysis, and this is the reason that it is called 'composite sequential' test. An upper bound for the potential power losses from the proposed method is deduced. The composite sequential design is illustrated through an application for post-market vaccine safety surveillance data.