Category: Biostatistics

Dropout is a statistical problem which occurs when an experimental unit that one is taking serial measurements from becomes unavailable for further measurements, prior to the end of the study. One common instance of dropout is found in tumor growth experiments performed on animal subjects: some animals are sacrificed when they are in too much pain, or bad condition. Unlike traditional missing data problems in time series data, this issue poses unique statistical problems due to the fact that the resultant dropout process results in a monotonic missingness pattern: if we observe missingness at a time t, then we necessarily have missingness at all timepoints t* >t. We introduce a novel method for imputation of tumor volume counterfactuals: we build a multivariate growth curve with random effects as inspired by Heitjan, et al (1993), and apply Bayesian methods in order to acquire a random sample for each parameter, in concordence with the literature on multiple imputation. One can then leverage conditional distribution theory to acquire a complete dataset from each of the random posterior samples. We additionally supply an R package for ease of execution of our method.

The Fourier Coefficients (FC) of a genomic sequence can be calculated according to a method proposed earlier this decade by Yin et al. Here we are concerned with the efficacy of these coefficients in capturing useful information about viral sequences. The FCs are rapidly computable and comparable which allows for speedy real-time numerical analyses of sequences. In this work we investigate using the FCs as summaries of SARS-CoV-2 sequences by applying regional classification procedures, and graphical examination. Specifically we extract geographic submission location from sequences submitted to the GISAID Initiative, and attempt to use the FCs to classify these sequences in addition to displaying them visually utilizing dimensionality reduction. We show that the FCs may serve as useful numerical summaries for sequences which allow manipulation, identification, and differentiation via classical mathematical and statistical methods not readily applicable to character strings. Further we argue that subsets of the FCs may be usable for the same purposes, indicating a reduction in storage requirements. We conclude by offering extensions of the research, and potential future directions for subsequent analyses and further theoretical development of techniques specific to the FCs and suggesting different kinds of series transforms for discretely indexed signals like genomes.

A fare splitting algorithm that is guaranteed to remove all redundant transactions is proposed. We proved the equivalence of the non-existence of redundant transactions and the minimization of the total transaction amount in the system. We also showed that although the resulting transaction amount is unique, the final transaction graph is not. By selecting a basic feasible solution, however, we can achieve a sparse solution.