Bias-Corrected GEE for Cluster Randomized Trials

Population-averaged models have been increasingly used in the design and analysis of cluster randomized trials (CRTs). To facilitate the applications of population-averaged models in CRTs, the package implements the generalized estimating equations (GEE) and matrix-adjusted estimating equations (MAEE) approaches to jointly estimate the marginal mean models correlation models both for general CRTs and stepped wedge CRTs. Despite the general GEE/MAEE approach, the package also implements a fast cluster-period GEE method by Li et al. (2022) specifically for stepped wedge CRTs with large and variable cluster-period sizes and gives a simple and efficient estimating equations approach based on the cluster-period means to estimate the intervention effects as well as correlation parameters. In addition, the package also provides functions for generating correlated binary data with specific mean vector and correlation matrix based on the multivariate probit method in Emrich and Piedmonte (1991) or the conditional linear family method in Qaqish (2003) .

Replicability Analysis for Multiple Studies of High Dimension

Estimation of Bayes and local Bayes false discovery rates for replicability analysis (Heller & Yekutieli, 2014 ; Heller at al., 2015 ).

Perform Set Operations on Vectors, Automatically Generating All n-Wise Comparisons, and Create Markdown Output

Automates set operations (i.e., comparisons of overlap) between multiple vectors. It also contains a function for automating reporting in 'RMarkdown', by generating markdown output for easy analysis, as well as an 'RMarkdown' template for use with 'RStudio'.

Interactive Graphics Functions for the 'spatstat' Package

Extension to the 'spatstat' package, containing interactive graphics capabilities.

Utility Functions for 'spatstat'

Contains utility functions for the 'spatstat' family of packages which may also be useful for other purposes.

The Self-Controlled Case Series Method

Various self-controlled case series models used to investigate associations between time-varying exposures such as vaccines or other drugs or non drug exposures and an adverse event can be fitted. Detailed information on the self-controlled case series method and its extensions with more examples can be found in Farrington, P., Whitaker, H., and Ghebremichael Weldeselassie, Y. (2018, ISBN: 978-1-4987-8159-6. Self-controlled Case Series studies: A modelling Guide with R. Boca Raton: Chapman & Hall/CRC Press) and < https://sccs-studies.info/index.html>.

Visualization and Analysis of Statistical Measures of Confidence

Enables: (1) plotting two-dimensional confidence regions, (2) coverage analysis of confidence region simulations, (3) calculating confidence intervals and the associated actual coverage for binomial proportions, (4) calculating the support values and the probability mass function of the Kaplan-Meier product-limit estimator, and (5) plotting the actual coverage function associated with a confidence interval for the survivor function from a randomly right-censored data set. Each is given in greater detail next. (1) Plots the two-dimensional confidence region for probability distribution parameters (supported distribution suffixes: cauchy, gamma, invgauss, logis, llogis, lnorm, norm, unif, weibull) corresponding to a user-given complete or right-censored dataset and level of significance. The crplot() algorithm plots more points in areas of greater curvature to ensure a smooth appearance throughout the confidence region boundary. An alternative heuristic plots a specified number of points at roughly uniform intervals along its boundary. Both heuristics build upon the radial profile log-likelihood ratio technique for plotting confidence regions given by Jaeger (2016) , and are detailed in a publication by Weld et al. (2019) . (2) Performs confidence region coverage simulations for a random sample drawn from a user- specified parametric population distribution, or for a user-specified dataset and point of interest with coversim(). (3) Calculates confidence interval bounds for a binomial proportion with binomTest(), calculates the actual coverage with binomTestCoverage(), and plots the actual coverage with binomTestCoveragePlot(). Calculates confidence interval bounds for the binomial proportion using an ensemble of constituent confidence intervals with binomTestEnsemble(). Calculates confidence interval bounds for the binomial proportion using a complete enumeration of all possible transitions from one actual coverage acceptance curve to another which minimizes the root mean square error for n <= 15 and follows the transitions for well-known confidence intervals for n > 15 using binomTestMSE(). (4) The km.support() function calculates the support values of the Kaplan-Meier product-limit estimator for a given sample size n using an induction algorithm described in Qin et al. (2023) . The km.outcomes() function generates a matrix containing all possible outcomes (all possible sequences of failure times and right-censoring times) of the value of the Kaplan-Meier product-limit estimator for a particular sample size n. The km.pmf() function generates the probability mass function for the support values of the Kaplan-Meier product-limit estimator for a particular sample size n, probability of observing a failure h at the time of interest expressed as the cumulative probability percentile associated with X = min(T, C), where T is the failure time and C is the censoring time under a random-censoring scheme. The km.surv() function generates multiple probability mass functions of the Kaplan-Meier product-limit estimator for the same arguments as those given for km.pmf(). (5) The km.coverage() function plots the actual coverage function associated with a confidence interval for the survivor function from a randomly right-censored data set for one or more of the following confidence intervals: Greenwood, log-minus-log, Peto, arcsine, and exponential Greenwood. The actual coverage function is plotted for a small number of items on test, stated coverage, failure rate, and censoring rate. The km.coverage() function can print an optional table containing all possible failure/censoring orderings, along with their contribution to the actual coverage function.

Pipeline for Topological Data Analysis

A comprehensive toolset for any useR conducting topological data analysis, specifically via the calculation of persistent homology in a Vietoris-Rips complex. The tools this package currently provides can be conveniently split into three main sections: (1) calculating persistent homology; (2) conducting statistical inference on persistent homology calculations; (3) visualizing persistent homology and statistical inference. The published form of TDAstats can be found in Wadhwa et al. (2018) . For a general background on computing persistent homology for topological data analysis, see Otter et al. (2017) . To learn more about how the permutation test is used for nonparametric statistical inference in topological data analysis, read Robinson & Turner (2017) . To learn more about how TDAstats calculates persistent homology, you can visit the GitHub repository for Ripser, the software that works behind the scenes at < https://github.com/Ripser/ripser>. This package has been published as Wadhwa et al. (2018) .

Identify Distributions that Match Reported Sample Parameters (SPRITE)

The SPRITE algorithm creates possible distributions of discrete responses based on reported sample parameters, such as mean, standard deviation and range (Heathers et al., 2018, ). This package implements it, drawing heavily on the code for Nick Brown's 'rSPRITE' Shiny app < https://shiny.ieis.tue.nl/sprite/>. In addition, it supports the modeling of distributions based on multi-item (Likert-type) scales and the use of restrictions on the frequency of particular responses.

Poly-Omic Prediction of Complex TRaits

It provides functions to generate a correlation matrix from a genetic dataset and to use this matrix to predict the phenotype of an individual by using the phenotypes of the remaining individuals through kriging. Kriging is a geostatistical method for optimal prediction or best unbiased linear prediction. It consists of predicting the value of a variable at an unobserved location as a weighted sum of the variable at observed locations. Intuitively, it works as a reverse linear regression: instead of computing correlation (univariate regression coefficients are simply scaled correlation) between a dependent variable Y and independent variables X, it uses known correlation between X and Y to predict Y.