Bruce Turnbull - Academia.edu (original) (raw)
Papers by Bruce Turnbull
Choosing the sample size for a trial Let θ denote the effect size of a new treatment, i.e., the d... more Choosing the sample size for a trial Let θ denote the effect size of a new treatment, i.e., the difference in mean response between the new treatment and the control. Sample size is determined by: Type I error rate α, and Treatment effect size θ = ∆ at which power 1 − β is to be achieved. Dispute may arise over the choice of ∆. Should investigators use: The minimum effect of interest ∆1, or The anticipated effect size ∆2? 2 Choosing the sample size for a trial Power curves for designs with sample sizes of 500 and 1000.
Journal of Dairy Science, Aug 1, 2006
Paratuberculosis (Johne's disease) is a significant animal health problem. Evaluation of diagnost... more Paratuberculosis (Johne's disease) is a significant animal health problem. Evaluation of diagnostic tests for Johne's disease has been difficult due to lack of a gold standard test. In recent years, there has been interest in receiver operating characteristic (ROC) curve estimation without any gold standard test. Typically, either Bayesian or maximum likelihood methods are proposed. Although these methods overcome the lack of a gold standard test in ROC curve estimation, little work has been done to incorporate covariates in the analysis. In this paper, we propose a method for estimation of ROC curves based on statistical models to adjust for covariate effects when the true disease states of test animals are unknown. The covariates may be correlated with the disease process or with the diagnostic testing procedure, or both. We propose a 2-part Bayesian model: first, a logistic regression model for disease prevalence is used to fit the covariates; second, a linear model is used to fit the covariates to the distribution of test scores. We used Markov chain Monte Carlo methods to compute the posterior estimates of the sensitivities and specificities that provide the groundwork for inference concerning the diagnostic procedure's accuracy. We applied the methodology to milk ELISA scores from several dairy-cow herds for the diagnostic testing of paratuberculosis. We found that both milk yield and its interaction with age had significant effects on the disease process whereas only milk yield was significant on the testing procedure.
We consider the likelihood ratio test for a changepoint or lag of the effect of some covariates, ... more We consider the likelihood ratio test for a changepoint or lag of the effect of some covariates, e.g. treatment, in regression modelling of survival data subject to right cen-soring. Asymptotic distributions under null hypotheses are derived. Numerical examples are used to illustrate the implementation of the procedure. Finally we apply the theory to data from a large randomised cancer prevention trial.
In this paper we describe the so-called “indirect ” method of inference, originally developed fro... more In this paper we describe the so-called “indirect ” method of inference, originally developed from the econometric literature, and apply it to survival analyses of two data sets with repeated events. This method is often more convenient computationally than maximum likelihood estimation when handling such model complexities as random effects and measurement error, for example; and it can also serve as a basis for robust inference with less stringent assumptions on the data generating mechanism. The first data set concerns recurrence times of mammary tumors in rats and is modeled using a Poisson process model with covariates and frailties. The second data set involves times of recurrences of skin tumors in individual patients in a clinical trial. The methodology is applied in both parametric and semi-parametric regression analyses to accommodate random effects and covariate measurement error.
Journal of Agricultural, Biological, and Environmental Statistics, 2007
We develop a Bayesian methodology for nonparametric estimation of ROC curves used for evaluation ... more We develop a Bayesian methodology for nonparametric estimation of ROC curves used for evaluation of the accuracy of a diagnostic procedure. We consider the situation where there is no perfect reference test, i.e., no "gold standard". The method is based on a multinomial model for the joint distribution of test-positive and test-negative observations. We use a Bayesian approach which assures the natural monotonicity property of the resulting ROC curve estimate. MCMC methods are used to compute the posterior estimates of the sensitivities and specificities that provide the basis for inference concerning the accuracy of the diagnostic procedure. Because there is no gold standard, identifiability requires that the data come from at least two populations with different prevalences. No assumption is needed concerning the shape of the distributions of test values of the diseased and non-diseased in these populations. We discuss an application to an analysis of ELISA scores in the diagnostic testing of paratuberculosis (Johne's Disease) for several herds of dairy cows and compare the results to those obtained from some previously proposed methods.
Biometrics, 1990
We consider the statistical modeling and analysis of replicated multi-type point process data wit... more We consider the statistical modeling and analysis of replicated multi-type point process data with covariates. Such data arise when heterogeneous subjects experience repeated events or failures which may be of several distinct types. The underlying processes are modeled as nonhomogeneous mixed Poisson processes with random (subject) and fixed (covariate) effects. The method of maximum likelihood is used to obtain estimates and standard errors of the failure rate parameters and regression coefficients. Score tests and likelihood ratio statistics are used for covariate selection. A graphical test of goodness of fit of the selected model is based on generalized residuals. Measures for determining the influence of an individual observation on the estimated regression coefficients and on the score test statistic are developed. An application is described to a large ongoing randomized controlled clinical trial for the efficacy of nutritional supplements of selenium for the prevention of two types of skin cancer.
It is standard practice to monitor clinical trials with a view to stopping early if results are s... more It is standard practice to monitor clinical trials with a view to stopping early if results are sufficiently compelling. We explain how the properties of stopping boundaries can be calculated numerically and how to optimise boundaries to minimise expected sample size while controlling type I and II error probabilities. Our optimisation method involves the use of dynamic programming to solve Bayes decision problems with no constraint on error rates. This conversion to an unconstrained problem is equivalent to using Lagrange multipliers. Applications of these methods in clinical trial design include the derivation of optimal adaptive designs in which future group sizes are allowed to depend on previously observed responses; designs which test both for superiority and non-inferiority; and group sequential tests which allow for a delay between treatment and response.
Journal of Quality Technology
Journal of the Royal Statistical Society: Series B (Methodological)
Clinical trials (London, England), 2017
This article describes vignettes concerning interactions with Data Safety Monitoring Boards durin... more This article describes vignettes concerning interactions with Data Safety Monitoring Boards during the design and monitoring of some clinical trials with an adaptive design. Most reflect personal experiences by the author.
Communications in Statistics Theory and Methods, Jun 27, 2007
Journal of Biopharmaceutical Statistics, May 1, 2006
Statistics in Medicine, Sep 30, 1993
Http Dx Doi Org 10 1198 016214502753479220, Dec 31, 2011
Journal of the American Statistical Association, 2002
Http Dx Doi Org 10 1198 016214505000000114, 2012
Cancer Epidemiology Biomarkers Prevention, Nov 1, 2002
Choosing the sample size for a trial Let θ denote the effect size of a new treatment, i.e., the d... more Choosing the sample size for a trial Let θ denote the effect size of a new treatment, i.e., the difference in mean response between the new treatment and the control. Sample size is determined by: Type I error rate α, and Treatment effect size θ = ∆ at which power 1 − β is to be achieved. Dispute may arise over the choice of ∆. Should investigators use: The minimum effect of interest ∆1, or The anticipated effect size ∆2? 2 Choosing the sample size for a trial Power curves for designs with sample sizes of 500 and 1000.
Journal of Dairy Science, Aug 1, 2006
Paratuberculosis (Johne's disease) is a significant animal health problem. Evaluation of diagnost... more Paratuberculosis (Johne's disease) is a significant animal health problem. Evaluation of diagnostic tests for Johne's disease has been difficult due to lack of a gold standard test. In recent years, there has been interest in receiver operating characteristic (ROC) curve estimation without any gold standard test. Typically, either Bayesian or maximum likelihood methods are proposed. Although these methods overcome the lack of a gold standard test in ROC curve estimation, little work has been done to incorporate covariates in the analysis. In this paper, we propose a method for estimation of ROC curves based on statistical models to adjust for covariate effects when the true disease states of test animals are unknown. The covariates may be correlated with the disease process or with the diagnostic testing procedure, or both. We propose a 2-part Bayesian model: first, a logistic regression model for disease prevalence is used to fit the covariates; second, a linear model is used to fit the covariates to the distribution of test scores. We used Markov chain Monte Carlo methods to compute the posterior estimates of the sensitivities and specificities that provide the groundwork for inference concerning the diagnostic procedure's accuracy. We applied the methodology to milk ELISA scores from several dairy-cow herds for the diagnostic testing of paratuberculosis. We found that both milk yield and its interaction with age had significant effects on the disease process whereas only milk yield was significant on the testing procedure.
We consider the likelihood ratio test for a changepoint or lag of the effect of some covariates, ... more We consider the likelihood ratio test for a changepoint or lag of the effect of some covariates, e.g. treatment, in regression modelling of survival data subject to right cen-soring. Asymptotic distributions under null hypotheses are derived. Numerical examples are used to illustrate the implementation of the procedure. Finally we apply the theory to data from a large randomised cancer prevention trial.
In this paper we describe the so-called “indirect ” method of inference, originally developed fro... more In this paper we describe the so-called “indirect ” method of inference, originally developed from the econometric literature, and apply it to survival analyses of two data sets with repeated events. This method is often more convenient computationally than maximum likelihood estimation when handling such model complexities as random effects and measurement error, for example; and it can also serve as a basis for robust inference with less stringent assumptions on the data generating mechanism. The first data set concerns recurrence times of mammary tumors in rats and is modeled using a Poisson process model with covariates and frailties. The second data set involves times of recurrences of skin tumors in individual patients in a clinical trial. The methodology is applied in both parametric and semi-parametric regression analyses to accommodate random effects and covariate measurement error.
Journal of Agricultural, Biological, and Environmental Statistics, 2007
We develop a Bayesian methodology for nonparametric estimation of ROC curves used for evaluation ... more We develop a Bayesian methodology for nonparametric estimation of ROC curves used for evaluation of the accuracy of a diagnostic procedure. We consider the situation where there is no perfect reference test, i.e., no "gold standard". The method is based on a multinomial model for the joint distribution of test-positive and test-negative observations. We use a Bayesian approach which assures the natural monotonicity property of the resulting ROC curve estimate. MCMC methods are used to compute the posterior estimates of the sensitivities and specificities that provide the basis for inference concerning the accuracy of the diagnostic procedure. Because there is no gold standard, identifiability requires that the data come from at least two populations with different prevalences. No assumption is needed concerning the shape of the distributions of test values of the diseased and non-diseased in these populations. We discuss an application to an analysis of ELISA scores in the diagnostic testing of paratuberculosis (Johne's Disease) for several herds of dairy cows and compare the results to those obtained from some previously proposed methods.
Biometrics, 1990
We consider the statistical modeling and analysis of replicated multi-type point process data wit... more We consider the statistical modeling and analysis of replicated multi-type point process data with covariates. Such data arise when heterogeneous subjects experience repeated events or failures which may be of several distinct types. The underlying processes are modeled as nonhomogeneous mixed Poisson processes with random (subject) and fixed (covariate) effects. The method of maximum likelihood is used to obtain estimates and standard errors of the failure rate parameters and regression coefficients. Score tests and likelihood ratio statistics are used for covariate selection. A graphical test of goodness of fit of the selected model is based on generalized residuals. Measures for determining the influence of an individual observation on the estimated regression coefficients and on the score test statistic are developed. An application is described to a large ongoing randomized controlled clinical trial for the efficacy of nutritional supplements of selenium for the prevention of two types of skin cancer.
It is standard practice to monitor clinical trials with a view to stopping early if results are s... more It is standard practice to monitor clinical trials with a view to stopping early if results are sufficiently compelling. We explain how the properties of stopping boundaries can be calculated numerically and how to optimise boundaries to minimise expected sample size while controlling type I and II error probabilities. Our optimisation method involves the use of dynamic programming to solve Bayes decision problems with no constraint on error rates. This conversion to an unconstrained problem is equivalent to using Lagrange multipliers. Applications of these methods in clinical trial design include the derivation of optimal adaptive designs in which future group sizes are allowed to depend on previously observed responses; designs which test both for superiority and non-inferiority; and group sequential tests which allow for a delay between treatment and response.
Journal of Quality Technology
Journal of the Royal Statistical Society: Series B (Methodological)
Clinical trials (London, England), 2017
This article describes vignettes concerning interactions with Data Safety Monitoring Boards durin... more This article describes vignettes concerning interactions with Data Safety Monitoring Boards during the design and monitoring of some clinical trials with an adaptive design. Most reflect personal experiences by the author.
Communications in Statistics Theory and Methods, Jun 27, 2007
Journal of Biopharmaceutical Statistics, May 1, 2006
Statistics in Medicine, Sep 30, 1993
Http Dx Doi Org 10 1198 016214502753479220, Dec 31, 2011
Journal of the American Statistical Association, 2002
Http Dx Doi Org 10 1198 016214505000000114, 2012
Cancer Epidemiology Biomarkers Prevention, Nov 1, 2002