# Louisiana ASA Chapter

## Fall 2018 Meeting

Friday, 9 November 2018

Patrick F. Taylor (PFT) room 1236

Louisiana State University

Baton Rouge, Louisiana

Last updated 27 October 2018. **Note: major changes on 27 October**. Any late changes to the schedule or other information on this page will be noted here.

## Maps

- Here is a simple LSU Campus map with Patrick F. Taylor Hall indcated (pdf)
- Here is a detailed LSU Campus map with Patrick F. Taylor Hall indcated (pdf)

## Schedule

Time | Title and Speaker |
---|---|

9:30-10:00 |
Reception |

10:00-11:00 |
Keynote AddressGeneralized Fiducial Inference: A ReviewJan Hannig Department of Statistics and Operations Research University of North Carolina Chapel Hill, North Carolina |

11:00-11:30 |
Discussion |

11:30-12:00 |
Highest posterior mass prediction intervals for binomial and poisson distributionsShanshan Lv Mathematics Department University of Louisiana at Lafayette Lafayette, Louisiana |

12:00-1:30 |
Lunch |

1:30-2:00 |
Generalizing Multistage Partition Procedures for Two-parameter Exponential PopulationsRui Wang Department of Mathematics University of New Orleans New Orleans, Louisiana |

2:00-2:30 |
Subgroup-specific dose finding in phase I clinical trials based on time to toxicity allowing adaptive subgroup combinationAndrew G. Chapple LSU Health New Orleans New Orleans, Louisiana |

2:30-2:45 |
Break |

2:45-3:30 |
ANOVA SSs and Proportional Subclass NumbersLynn Roy LaMotte LSU Health New Orleans New Orleans, Louisiana |

3:30-4:00 |
Confidence intervals for the mean and a percentile based on zero-inflated lognormal dataMd Sazib Hasan Mathematics Department University of Louisiana at Lafayette Lafayette, Louisiana |

## Titles and Abstracts

### Keynote Address

**Generalized Fiducial Inference: A Review**

Jan Hannig

Department of Statistics and Operations Research

University of North Carolina

Chapel Hill, North Carolina

R. A. Fisher, the father of modern statistics, developed the idea of fiducial inference during the first half of the 20th century. While his proposal led to interesting methods for quantifying uncertainty, other prominent statisticians of the time did not accept Fisher's approach as it became apparent that some of Fisher's bold claims about the properties of fiducial distribution did not hold up for multi-parameter problems. Beginning around the year 2000, the authors and collaborators started to re-investigate the idea of fiducial inference and discovered that Fisher's approach, when properly generalized, would open doors to solve many important and difficult inference problems. They termed their generalization of Fisher's idea as generalized fiducial inference (GFI). The main idea of GFI is to carefully transfer randomness from the data to the parameter space using an inverse of a data generating equation without the use of Bayes theorem. The resulting generalized fiducial distribution (GFD) can then be used for inference. After more than a decade of investigations, the authors and collaborators have developed a unifying theory for GFI, and provided GFI solutions to many challenging practical problems in different fields of science and industry. Overall, they have demonstrated that GFI is a valid, useful, and promising approach for conducting statistical inference. In this talk we latest developments and some successful applications of generalized fiducial inference.

This is joint work with T. C.M Lee (UC Davis), H. Iyer (NIST), Randy Lai (U of Maine), J. Williams (UNC), Y. Cui (U Pennsylvania).

**Highest posterior mass prediction intervals for binomial and poisson distributions**

Shanshan Lv

Mathematics Department

University of Louisiana at Lafayette

Lafayette, Louisiana

The problems of constructing prediction intervals(PIs) for the binomial and Poisson distributions are considered. New highest posterior mass (HPM) PIs based on fiducial approach are proposed. Other fiducial PIs, an exact PI and approximate PIs are reviewed and compared with the HPM-PIs. Exact coverage studies and expected widths of prediction intervals show that the new prediction intervals are less conservative than other fiducial PIs and comparable with the approximate one based on the joint sampling approach for the binomial case. For the Poisson case, the HPM-PIs are better than the other PIs in terms of coverage probabilities and precision. The methods are illustrated using some practical examples.

**Generalizing Multistage Partition Procedures for Two-parameter Exponential Populations**

Rui Wang

Department of Mathematics

University of New Orleans

New Orleans, Louisiana

ANOVA analysis is a classic tool for multiple comparisons and has been widely used in numerous disciplines due to its simplicity and convenience. The ANOVA procedure is designed to test if a number of populations are all different. This is followed by usual multiple comparison tests to rank the populations. However, the probability of selecting the best population via ANOVA procedure does not guarantee the probability to be larger than some desired pre-specified level. This lack of desirability of the ANOVA procedure was overcome by researchers in early 1950's by designing experiments with the goal of selecting the best population. In this talk, a single-stage procedure is introduced to partition k treatments into "good" and "bad" groups with respect to a control population assuming some key parameters are known. Also, the proposed partition procedure is generalized for the case when the parameters are unknown and a purely-sequential procedure and a two-stage procedure are derived. Theoretical asymptotic properties, such as first order and second order properties, of the proposed procedures are derived to document the efficiency of the proposed procedures. These theoretical properties are studied via Monte Carlo simulations to document the performance of the procedures for small and moderate sample sizes.

**Subgroup-specific dose finding in phase I clinical trials based on time to toxicity allowing adaptive subgroup combination**

Andrew G. Chapple

LSU Health New Orleans

New Orleans, Louisiana

A Bayesian design is presented that does precision dose finding based on time to toxicity in a phase I clinical trial with two or more patient subgroups. The design, called Sub-TITE, makes sequentially adaptive subgroup-specific decisions while possibly combining subgroups that have similar estimated dose-toxicity curves. Decisions are based on posterior quantities computed under a logistic regression model for the probability of toxicity within a fixed follow-up period, as a function of dose and subgroup. Similarly to the time-to-event continual reassessment method (TITE-CRM, Cheung and Chappell), the Sub-TITE design downweights each patient's likelihood contribution using a function of follow-up time. Spike-and-slab priors are assumed for subgroup parameters, with latent subgroup combination variables included in the logistic model to allow different subgroups to be combined for dose finding if they are homogeneous. This framework can be used in trials where clinicians have identified patient subgroups but are not certain whether they will have different dose-toxicity curves. A simulation study shows that, when the dose-toxicity curves differ between all subgroups, Sub-TITE has superior performance compared with applying the TITE-CRM while ignoring subgroups and has slightly better performance than applying the TITE-CRM separately within subgroups or using the two-group maximum likelihood approach of Salter et al that borrows strength among the two groups. When two or more subgroups are truly homogeneous but differ from other subgroups, the Sub-TITE design is substantially superior to either ignoring subgroups, running separate trials within all subgroups, or the maximum likelihood approach of Salter et al. Practical guidelines and computer software are provided to facilitate application.

**ANOVA SSs and Proportional Subclass Numbers**

Lynn Roy LaMotte

LSU Health New Orleans

New Orleans, Louisiana

Soon after Fisher introduced analysis of variance for effects of two factors, it was clear that "the addition law'' didn't work in unbalanced models unless the cell sample sizes had the "proportional subclass numbers'' property (psn), that $n_{ij} = n_{i\cdot}n_{\cdot j}/n_{\cdot\cdot}$. If not, then $SS_{AB}$, computed as Fisher described, was not a true SS in the usual sense, and it could take negative values. This led to the continuing ambivalence about the appropriate SSs for testing factor main effects in unbalanced models without psn. Consistently, though, textbooks have taught that there is no problem in models having psn: psn is the same as balanced.

In this talk I'll note that this is not true. In unbalanced models that don't have psn, the classical ANOVA SSs test hypotheses that are unrelated to the ANOVA definition of main effects. $SS_{AB}$ tests the right hypothesis iff the model has psn. $SS_A$ tests the right hypothesis iff $n_{ij} = n_{i\cdot}/b$, an additional requirement beyond psn.

The process of examining these properties reveals relations among Types I, II, III, and marginal-means (MM) SSs. For example, the Type II noncentrality parameter for A main effects can be 0 even though there are differences (arbitrarily great) among the A marginal means. Type III SSs, on the other hand, always test at least the estimable part of the corresponding effect contrasts, and MM SSs test exactly the estimable part.

**Confidence intervals for the mean and a percentile based on zero-inflated lognormal data**

Md Sazib Hasan

Mathematics Department

University of Louisiana at Lafayette

Lafayette, Louisiana

The problems of estimating the mean and an upper percentile of a lognormal population with nonnegative values are considered. For estimating the mean of a such population based on data that include zeros, a simple confidence interval (CI) that is obtained by modifying Tian's [Inferences on the mean of zero-inflated lognormal data: the generalized variable approach. Stat Med. 2005;24:3223-3232] generalized CI, is proposed. A fiducial upper confidence limit (UCL) and a closed-form approximate UCL for an upper percentile are developed. Our simulation studies indicate that the proposed methods are very satisfactory in terms of coverage probability and precision, and better than existing methods for maintaining balanced tail error rates. The proposed CI and the UCL are simple and easy to calculate. All the methods considered are illustrated using samples of data involving airborne chlorine concentrations and data on diagnostic test costs.

### 2018 Chapter Officers

#### President:

Sungsu Kim

Mathematics Department

University of Louisiana at Lafayette

Box 43568

Lafayette, LA 70504-3568

sungsu@louisiana.edu

#### Vice President:

Lee McDaniel

Biostatistics Section

LSUHSC School of Public Health

2020 Gravier Street, 3rd Floor

New Orleans, LA 70112

lmcda4@lsuhsc.edu

#### Secretary/Treasurer:

BeiBei Guo

Department of Experimental Statistics

Room 61 Martin D. Woodin Hall

Louisiana State University

Baton Rouge, LA 70803-5606

beibeiguo@lsu.edu

#### Chapter Representative:

James Calvin Berry

Mathematics Department

University of Louisiana at Lafayette

Box 43568

Lafayette, LA 70504-3568

cberry@louisiana.edu

If you have any suggestions regarding the chapter such as: proposals for activities, potential speakers, or the like, please send them to the president.