PubMed · 8969323
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J Mauskopf. 1996. Industry responsibility in interactive computer modeling.. https://pubmed.ncbi.nlm.nih.gov/8969323/
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Simulation of realistic omics data is a key input for benchmarking studies that help users obtain optimal computational pipelines. Omics data involves large numbers of measured features on each sample and these measures are generally correlated with each other. However, simulation too often ignores these correlations, perhaps due to computational and statistical hurdles of doing so. To alleviate this, we describe three approaches for generating omics-scale data with correlated measures which mimic real datasets. These approaches are all based on a Gaussian copula approach with a covariance matrix that decomposes into a diagonal part and a low-rank part. This decomposition allows for extremely efficient simulation, overcoming a hurdle for adoption of past methods. We use these approaches to demonstrate the importance of including correlation in two benchmarking applications. First, we show that variance of results from the popular DESeq2 method increases when dependence is included. Second, we demonstrate that CYCLOPS, a method for inferring circadian time of collection from transcriptomics, improves in performance when given gene-gene dependencies in some circumstances. We provide an R package, dependentsimr, that has efficient implementations of these methods and can generate dependent data with arbitrary marginal distributions, including discrete (binary, ordered categorical, Poisson, negative binomial), continuous (normal), or with an empirical distribution.
The goal of cancer immunotherapy is to boost a patient's immune response to a tumour. Yet, the design of an effective immunotherapy is complicated by various factors, including a potentially immunosuppressive tumour microenvironment, immune-modulating effects of conventional treatments and therapy-related toxicities. These complexities can be incorporated into mathematical and computational models of cancer immunotherapy that can then be used to aid in rational therapy design. In this review, we survey modelling approaches under the umbrella of the major challenges facing immunotherapy development, which encompass tumour classification, optimal treatment scheduling and combination therapy design. Although overlapping, each challenge has presented unique opportunities for modellers to make contributions using analytical and numerical analysis of model outcomes, as well as optimization algorithms. We discuss several examples of models that have grown in complexity as more biological information has become available, showcasing how model development is a dynamic process interlinked with the rapid advances in tumour-immune biology. We conclude the review with recommendations for modellers both with respect to methodology and biological direction that might help keep modellers at the forefront of cancer immunotherapy development.
We applied a mixed effects model to investigate between- and within-study variation in improvement rates of 180 schizophrenia outcome studies. The between-study variation was explained by the fixed study characteristics and an additional random study effect. Both rate difference and logit models were used. For a binary proportion outcome p(i) with sample size n(i) in the ith study, (circumflexp(i)(1-circumflexp(i))n)(-1) is the usual estimate of the within-study variance sigma(i)(2) in the logit model, where circumflexpi) is the sample mean of the binary outcome for subjects in study i. This estimate can be highly correlated with logit(circumflexp(i)). We used (macronp(i)(1-macronp)n(i))(-1) as an alternative estimate of sigma(i)(2), where macronp is the weighted mean of circumflexp(i)'s. We estimated regression coefficients (beta) of the fixed effects and the variance (tau(2)) of the random study effect using a quasi-likelihood estimating equations approach. Using the schizophrenia meta-analysis data, we demonstrated how the choice of the estimate of sigma(2)(i) affects the resulting estimates of beta and tau(2). We also conducted a simulation study to evaluate the performance of the two estimates of sigma(2)(i) in different conditions, where the conditions vary by number of studies and study size. Using the schizophrenia meta-analysis data, the estimates of beta and tau(2) were quite different when different estimates of sigma(2)(i) were used in the logit model. The simulation study showed that the estimates of beta and tau(2) were less biased, and the 95 per cent CI coverage was closer to 95 per cent when the estimate of sigma(2)(i) was (macronp(1-macronp)n(i))(-1) rather than (circumflexp(i)(1-circumflexp)n(i))(-1). Finally, we showed that a simple regression analysis is not appropriate unless tau(2) is much larger than sigma(2)(i), or a robust variance is used.