TLDR: Begin with N of 10, increase by 10 until p __ 0.05 or max N reached. This design has inflated type-I error. Lower p-value threshold needed to ensure specified type-I error rate. The number of interim analyses and max N affect the type-I error rate. Threshold can be identified using simulation. A recent ... [Read more...]

I had an opportunity recently to design a Bayesian adaptive trial with several interim analyses that allow for early stopping due to efficacy or futility. The code below implements the one-arm trial described in the great introductory article by Ben Saville et al. Three of the coauthors are current or ... [Read more...]

The code below gives a simple implementation of the Metropolis and Metropolis-in-Gibbs sampling algorithms, which are useful for sampling probability densities for which the normalizing constant is difficult to calculate, are irregular, or have high dimension (Metropolis-in-Gibbs). ## Metropolis sampling ## x - current value of Markov chain (numeric vector) ## targ - ... [Read more...]

After an embarrassing teleconference in which I presented a series of percentages that did not sum to 100 (as they should have), I found some R code on stackoverflow.com to help me to avoid this in the future. In general, the sum of rounded numbers (e.g., using the base::... [Read more...]

The bit of R code below illustrates the principal curves methods as described in The Elements of Statistical Learning, by Hastie, Tibshirani, and Friedman (Ch. 14; the book is freely available from the authors' website). Specifically, the code generates some bivariate data that have a nonlinear association, initializes the principal curve ... [Read more...]

I'm recently returned from the 2015 Rocky Mountain Bioinformatics Conference, where I presented the above poster. This is work with a colleague, Rick Gray, at the FDA. He and I collaborate on our NIH award "Optimal Design of Challenge-Response Experiments in Cardiac Electrophysiology" (HL118392) The (original) poster abstract is below, but ... [Read more...]

I am often asked about the number of subjects needed to study a binary outcome, which usually leads to a discussion of confidence intervals for binary proportions, and the associated precision. Sometimes the precision is quantified as the width or half-width of a 95% confidence interval. For proportions, I like the ... [Read more...]

This post follows from a previous post (2798), in which the delta method was used to create an approximate pointwise 95% confidence band for a Gaussian density estimate. Note that the quality of this estimate was not assessed (e.g., whether the band has the correct pointwise coverage). Here we extend that ... [Read more...]

During one of our Department's weekly biostatistics "clinics", a visitor was interested in creating confidence bands for a Gaussian density estimate (or a Gaussian mixture density estimate). The mean, variance, and two "nuisance" parameters, were simultaneously estimated using least-squares. Thus, the approximate sampling variance-covariance matrix (4x4) was readily available. The ... [Read more...]

Statisticians often need to integrate some function with respect to the multivariate normal (Gaussian) distribution, for example, to compute the standard error of a statistic, or the likelihood function in of a mixed effects model. In many (most?) useful cases, these integrals are intractable, and must be approximated using computational ... [Read more...]

The code snippet below creates the above graphic: ## radially symmetric kernel (Gussian kernel) RadSym [Read more...]

There is a nice package and paper about this here: http://www.jstatsoft.org/v57/i05/paper. However, the associated code is complex and uses lattice. Here's a brief recipe using base graphics that implements the above figure: set.seed(40) x [Read more...]

The R script below illustrates the nested versus non-nested (crossed) random effects functionality in the R packates lme4 and nlme. Note that crossed random effects are difficult to specify in the nlme framework. Thus, I've included a back-of-the-envelope (literally a scanned image of my scribble) interpretation of the 'trick' to ... [Read more...]

Consider planning a clinicial trial where patients are randomized in permuted blocks of size four to either a 'control' or 'treatment' group. The outcome is measured on an 11-point ordinal scale (e.g., the numerical rating scale for pain). It may be reasonable to evaluate the results of this trial ... [Read more...]

This post builds on a previous post, but can be read and understood independently. As part of my course on statistical learning, we created 3D graphics to foster a more intuitive understanding of the various methods that are used to relax the assumption of linearity (in the predictors) in regression ... [Read more...]

This semester I'm teaching from Hastie, Tibshirani, and Friedman's book, The Elements of Statistical Learning, 2nd Edition. The authors provide a Mixture Simulation data set that has two continuous predictors and a binary outcome. This data is used to demonstrate classification procedures by plotting classification boundaries in the two predictors. ... [Read more...]

... using the new R package sas7bdat.parso. The software company GGASoftware has extended the work of myself and others on the sas7bdat R package by developing a Java library called Parso, which also reads sas7bdat files. They have worked out most of the remaining kinks. For example, ... [Read more...]

This post builds on my last: Alternatives to model diagnostics for statistical inference?, where I had claimed that we could make quality inferences about the best linear approximation to a quadratic relationship. The R code below implements such a scenario, to establish a framework for discussion. I have inserted comments ... [Read more...]

Consider the problem of making statistical inferences, as opposed to predictions. The product of statistical inference is a probabilistic statement about a population quantity, for example a 100(1-)% confidence interval for a population median. In this context, the principal reason for diagnostics is to comfort ourselves about the quality of ... [Read more...]

I received an email recently with a question about using R in the common gateway interface (CGI) framework to create and pass image data to the web browser. I posted to stackoverflow about this some time ago, but had forgotten the details. The trouble is that R's graphics devices only ... [Read more...]