Objective method for estimating asymptotic parameters, with an application to sequence alignment

A comprehensive estimation of country-level basic reproduction numbers R0 for COVID-19: Regime regression can automatically estimate the end of the exponential phase in epidemic data

In a compartmental epidemic model, the initial exponential phase reflects a fixed interaction between an infectious agent and a susceptible population in steady state, so it determines the basic reproduction number R₀ on its own. After the exponential phase, dynamic complexities like societal responses muddy the practical interpretation of many estimated parameters. The computer program ARRP, already available from sequence alignment applications, automatically estimated the end of the exponential phase in COVID-19 and extracted the exponential growth rate r for 160 countries. By positing a gamma-distributed generation time, the exponential growth method then yielded R₀ estimates for COVID-19 in 160 countries. The use of ARRP ensured that the R₀ estimates were largely freed from any dependency outside the exponential phase. The Prem matrices quantify rates of effective contact for infectious disease. Without using any age-stratified COVID-19 data, but under strong assumptions about the homogeneity of susceptibility, infectiousness, etc., across different age-groups, the Prem contact matrices also yielded theoretical R₀ estimates for COVID-19 in 152 countries, generally in quantitative conflict with the R₀ estimates derived from the exponential growth method. An exploratory analysis manipulating only the Prem contact matrices reduced the conflict, suggesting that age-groups under 20 years did not promote the initial exponential growth of COVID-19 as much as other age-groups. The analysis therefore supports tentatively and tardily, but independently of age-stratified COVID-19 data, the low priority given to vaccinating younger age groups. It also supports the judicious reopening of schools. The exploratory analysis also supports the possibility of suspecting differences in epidemic spread among different age-groups, even before substantial amounts of age-stratified data become available.

Analyzing similarities in genome sequences

This article investigates aspects of similarity between complete sequences of mitochondrial DNA by determining the distribution of the relative frequencies of words with different lengths and the characteristics of their relevance throughout the sequences. The degree of similarity is obtained by comparing the distances between words contained within these sequences. Our results indicate that the best groupings among different species depend on the lengths of words and their respective relative frequencies. We also observed that the longer the word the more consistent the grouping between the sequences becomes. The application of our results, together with the perspective of analyzing DNA sequences belonging to a single biological species, may be important for the construction of phylogenetic trees, which are appropriate structures for understanding the evolutionary history of the species.

Empirical null estimation using zero-inflated discrete mixture distributions and its application to protein domain data

In recent mutation studies, analyses based on protein domain positions are gaining popularity over gene-centric approaches since the latter have limitations in considering the functional context that the position of the mutation provides. This presents a large-scale simultaneous inference problem, with hundreds of hypothesis tests to consider at the same time. This article aims to select significant mutation counts while controlling a given level of Type I error via False Discovery Rate (FDR) procedures. One main assumption is that the mutation counts follow a zero-inflated model in order to account for the true zeros in the count model and the excess zeros. The class of models considered is the Zero-inflated Generalized Poisson (ZIGP) distribution. Furthermore, we assumed that there exists a cut-off value such that smaller counts than this value are generated from the null distribution. We present several data-dependent methods to determine the cut-off value. We also consider a two-stage procedure based on screening process so that the number of mutations exceeding a certain value should be considered as significant mutations. Simulated and protein domain data sets are used to illustrate this procedure in estimation of the empirical null using a mixture of discrete distributions. Overall, while maintaining control of the FDR, the proposed two-stage testing procedure has superior empirical power.

New finite-size correction for local alignment score distributions

BACKGROUND

Local alignment programs often calculate the probability that a match occurred by chance. The calculation of this probability may require a "finite-size" correction to the lengths of the sequences, as an alignment that starts near the end of either sequence may run out of sequence before achieving a significant score.

FINDINGS

We present an improved finite-size correction that considers the distribution of sequence lengths rather than simply the corresponding means. This approach improves sensitivity and avoids substituting an ad hoc length for short sequences that can underestimate the significance of a match. We use a test set derived from ASTRAL to show improved ROC scores, especially for shorter sequences.

CONCLUSIONS

The new finite-size correction improves the calculation of probabilities for a local alignment. It is now used in the BLAST+ package and at the NCBI BLAST web site ( http://blast.ncbi.nlm.nih.gov).