# Michael Fay

#### asht

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Gives some hypothesis test functions (sign test, median and other quantile tests, Wilcoxon signed rank test, coefficient of variation test, test of normal variance, test on weighted sums of Poisson [see Fay and Kim <doi:10.1002/bimj.201600111>], sample size for t-tests with different variances and non-equal n per arm, Behrens-Fisher test, nonparametric ABC intervals, Wilcoxon-Mann-Whitney test [with effect estimates and confidence intervals, see Fay and Malinovsky <doi:10.1002/sim.7890>], two-sample melding tests [see Fay, Proschan, and Brittain <doi:10.1111/biom.12231>], one-way ANOVA allowing var.equal=FALSE [see Brown and Forsythe, 1974, Biometrics]), prevalence confidence intervals that adjust for sensitivity and specificity [see Lang and Reiczigel, 2014 <doi:10.1016/j.prevetmed.2013.09.015>]). The focus is on hypothesis tests that have compatible confidence intervals, but some functions only have confidence intervals (e.g., prevSeSp).

#### binseqtest

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For a series of binary responses, create stopping boundary with exact results after stopping, allowing updating for missing assessments.

#### bpcp

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Calculates nonparametric pointwise confidence intervals for the survival distribution for right censored data, and for medians [Fay and Brittain <doi:10.1002/sim.6905>]. Has two-sample tests for dissimilarity (e.g., difference, ratio or odds ratio) in survival at a fixed time, and differences in medians [Fay, Proschan, and Brittain <doi:10.1111/biom.12231>]. Especially important for latter parts of the survival curve, small sample sizes or heavily censored data. Includes mid-p options.

#### choplump

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Choplump Tests are Permutation Tests for Comparing Two Groups with Some Positive but Many Zero Responses

#### exact2x2

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Calculates conditional exact tests (Fisher's exact test, Blaker's exact test, or exact McNemar's test) and unconditional exact tests (including score-based tests on differences in proportions, ratios of proportions, and odds ratios, and Boshcloo's test) with appropriate matching confidence intervals, and provides power and sample size calculations. Gives melded confidence intervals for the binomial case (Fay, et al, 2015, <DOI:10.1111/biom.12231>). Gives boundary-optimized rejection region test (Gabriel, et al, 2018, <DOI:10.1002/sim.7579>), an unconditional exact test for the situation where the controls are all expected to fail.

#### exactci

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Calculates exact tests and confidence intervals for one-sample binomial and one- or two-sample Poisson cases.

#### hbim

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Calculate expected relative risk and proportion protected assuming normally distributed log10 transformed antibody dose for several component vaccine. Uses Hill models for each component which are combined under Bliss independence.

#### interval

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Functions to fit nonparametric survival curves, plot them, and perform logrank or Wilcoxon type tests.

#### MChtest

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Performs Monte Carlo hypothesis tests, allowing a couple of different sequential stopping boundaries. For example, a truncated sequential probability ratio test boundary (Fay, Kim and Hachey, 2007 <DOI:10.1198/106186007X257025>) and a boundary proposed by Besag and Clifford, 1991 <DOI:10.1093/biomet/78.2.301>. Gives valid p-values and confidence intervals on p-values.

#### nivm

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Noninferiority tests for difference in failure rates at a prespecified control rate or prespecified time.

#### perm

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Perform Exact or Asymptotic permutation tests

#### rateratio.test

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A function which performs exact rate ratio tests and returns an object of class htest.

#### saws

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Tests coefficients with sandwich estimator of variance and with small samples. Regression types supported are gee, linear regression, and conditional logistic regression.

#### ssanv

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A set of functions to calculate sample size for two-sample difference in means tests. Does adjustments for either nonadherence or variability that comes from using data to estimate parameters.

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Estimate model parameters to determine whether two compounds have synergy, antagonism, or Loewe's Additivity.

#### testassay

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A common way of validating a biological assay for is through a procedure, where m levels of an analyte are measured with n replicates at each level, and if all m estimates of the coefficient of variation (CV) are less than some prespecified level, then the assay is declared validated for precision within the range of the m analyte levels. Two limitations of this procedure are: there is no clear statistical statement of precision upon passing, and it is unclear how to modify the procedure for assays with constant standard deviation. We provide tools to convert such a procedure into a set of m hypothesis tests. This reframing motivates the m:n:q procedure, which upon completion delivers a 100q% upper confidence limit on the CV. Additionally, for a post-validation assay output of y, the method gives an effective standard deviation interval'' of log(y) plus or minus r, which is a 68% confidence interval on log(mu), where mu is the expected value of the assay output for that sample. Further, the m:n:q procedure can be straightforwardly applied to constant standard deviation assays. We illustrate these tools by applying them to a growth inhibition assay. This is an implementation of the methods described in Fay, Sachs, and Miura (2018) <doi:10.1002/sim.7528>.