Juanjuan Fan

Interaction Trees with Censored Survival Data

We propose an interaction tree (IT) procedure to optimize the subgroup analysis in comparative studies that involve censored survival times. The proposed method recursively partitions the data into two subsets that show the greatest interaction with the treatment, which results in a number of objectively defined subgroups: in some of them the treatment effect is prominent while in others the treatment may have a negligible or even negative effect. The resultant tree structure can be used to explore the overall interaction between treatment and other covariates and help identify and describe possible target populations on which an experimental treatment demonstrates desired efficacy. We follow the standard CART (Breiman, et al., 1984) methodology to develop the interaction tree structure. Variable importance information is extracted via random forests of interaction trees. Both simulated experiments and an analysis of the primary billiary cirrhosis (PBC) data are provided for evaluation and illustration of the proposed procedure.

Maximum Likelihood Regression Trees

We propose a method of constructing regression trees within the framework of maximum likelihood. It inherits the backward fitting idea of classification and regression trees (CART) but has more rigorous justification. Simulation studies show that it provides more accurate tree model selection compared to CART. The analysis of a baseball dataset is given as an illustration.

Visual field quality control in the Ocular Hypertension Treatment Study (OHTS).

ObjectiveTo report the impact of visual field quality control (QC) procedures on the rates of visual field unreliability, test parameter errors, and visual field defects attributed to testing artifacts in the Ocular Hypertension Treatment Study (OHTS). MethodsOHTS technicians were certified for perimetry and were required to submit 2 sets of visual fields that met study criteria before testing study participants. The OHTS Visual Field Reading Center (VFRC) evaluated 46,777 visual fields completed by 1618 OHTS participants between February 1994 and December 2003. Visual field QC errors, rates of unreliability, and defects attributed to testing artifacts were assessed. The OHTS QC system addressed 3 areas of clinic performance: (1) test parameter errors, (2) patient data errors, and (3) shipment errors. A visual field was classified as unreliable if any of the reliability indices exceeded the 33% limit. Clinical sites were immediately contacted by the VFRC via fax, e-mail, and/or phone and instructed on how to prevent further testing errors on fields with defects attributed to testing artifacts. Main Outcome MeasuresQC errors (test parameter errors) and unreliability rates. ResultsA total of 2.4% (1136/ 46,777) of the visual fields were unreliable and 0.23% (107/46,777) had incorrect test parameters. Visual field defects attributed to testing artifacts occurred in approximately 1% (483/46,777) of the visual fields. ConclusionsPrompt transmission of visual fields to the VFRC for ongoing and intensive QC monitoring and rapid feedback to technicians helps to reduce the frequency of unreliable visual fields and incorrect testing parameters. Visual field defects attributed to testing artifacts were infrequent in the OHTS.

An automated (Markov chain) Monte Carlo EM algorithm

We present an automated Monte Carlo EM (MCEM) algorithm which efficiently assesses Monte Carlo error in the presence of dependent Monte Carlo, particularly Markov chain Monte Carlo, E-step samples and chooses an appropriate Monte Carlo sample size to minimize this Monte Carlo error with respect to progressive EM step estimates. Monte Carlo error is gauged though an application of the central limit theorem during renewal periods of the MCMC sampler used in the E-step. The resulting normal approximation allows us to construct a rigorous and adaptive rule for updating the Monte Carlo sample size each iteration of the MCEM algorithm. We illustrate our automated routine and compare the performance with competing MCEM algorithms in an analysis of a data set fit by a generalized linear mixed model. †Supported by National Science Foundation/Environmental Protection Agency Grant DMS-99-78321 ‡E-mail: jjfan@sciences.sdsu.edu

A class of weighted dependence measures for bivariate failure time data

This paper considers a class of summary measures of the dependence between a pair of failure time variables over a finite follow‐up region. The class consists of measures that are weighted averages of local dependence measures, and includes the cross‐ratio‐measure and finite region version of Kendalls τ; recently proposed by the authors. Two new special cases are identified that can avoid the need to estimate the bivariate survivor function and that admit explicit variance estimators. Nonparametric estimators of such dependence measures are proposed and are shown to be consistent and asymptotically normal with variances that can be consistently estimated. Properties of selected estimators are evaluated in a simulation study, and the method is illustrated through an analysis of Australian Twin Study data.

Trees for Correlated Survival Data by Goodness of Split, With Applications to Tooth Prognosis

In this article the regression tree method is extended to correlated survival data and applied to the problem of developing objective prognostic classification rules in periodontal research. The robust logrank statistic is used as the splitting statistic to measure the between-node difference in survival, while adjusting for correlation among failure times from the same patient. The partition-based survival function estimator is shown to converge to the true conditional survival function. Tooth loss data from 100 periodontal patients (2,509 teeth) was analyzed using the proposed method. The goal is to assign each tooth to one of the five prognosis categories (good, fair, poor, questionable, or hopeless). After the best-sized tree was identified, an amalgamation procedure was used to form five prognostic groups. The prognostic rules established here may be used by periodontists, general dentists, and insurance companies in devising appropriate treatment plans for periodontal patients.

A general test of association for complex diseases with variable age of onset.

Analysis of age of onset is a key factor in linkage and association studies of some complex genetic traits. Recent methodological developments are mainly concentrated on binary or quantitative traits, in which age of onset information is ignored. We propose a linkage disequilibrium‐based Cox model and a robust score test for testing association between a marker and a disease with variable age of onset. The proposed model is semi‐parametric, with an unspecified baseline hazard function. Simulation results indicate that the proposed methods have correct error rates and good statistical power, even in the presence of population admixture. This approach offers a solution to the problem of testing for marker associations when there is a variable age of onset. Genet. Epidemiol. 19(Suppl 1):S43–S49, 2000.

Development of prognostic indicators using classification and regression trees for survival

The development of an accurate prognosis is an integral component of treatment planning in the practice of periodontics. Prior work has evaluated the validity of using various clinical measured parameters for assigning periodontal prognosis as well as for predicting tooth survival and change in clinical conditions over time. We critically review the application of multivariate Classification And Regression Trees (CART) for survival in developing evidence-based periodontal prognostic indicators. We focus attention on two distinct methods of multivariate CART for survival: the marginal goodness-of-fit approach, and the multivariate exponential approach. A number of common clinical measures have been found to be significantly associated with tooth loss from periodontal disease, including furcation involvement, probing depth, mobility, crown-to-root ratio, and oral hygiene. However, the inter-relationships among these measures, as well as the relevance of other clinical measures to tooth loss from periodontal disease (such as bruxism, family history of periodontal disease, and overall bone loss), remain less clear. While inferences drawn from any single current study are necessarily limited, the application of new approaches in epidemiologic analyses to periodontal prognosis, such as CART for survival, should yield important insights into our understanding, and treatment, of periodontal diseases.

Multivariate exponential survival trees and their application to tooth prognosis

This paper is concerned with developing rules for assignment of tooth prognosis based on actual tooth loss in the VA Dental Longitudinal Study. It is also of interest to rank the relative importance of various clinical factors for tooth loss. A multivariate survival tree procedure is proposed. The procedure is built on a parametric exponential frailty model, which leads to greater computational efficiency. We adopted the goodness-of-split pruning algorithm of LeBlanc and Crowley (1993) to determine the best tree size. In addition, the variable importance method is extended to trees grown by goodness-of-fit using an algorithm similar to the random forest procedure in Breiman (2001). Simulation studies for assessing the proposed tree and variable importance methods are presented. To limit the final number of meaningful prognostic groups, an amalgamation algorithm is employed to merge terminal nodes that are homogenous in tooth survival. The resulting prognosis rules and variable importance rankings seem to offer simple yet clear and insightful interpretations.

Differences in gene expression in muscle-invasive bladder cancer: A comparison of Italian and American patients

Objective: To seek differences in gene expression in the primary muscle–invasive bladder cancers of two cohorts of patients having different survival rates. An Italian group treated by transurethral resection of the bladder tumor (TURBT) and neo–adjuvant chemotherapy using methotrexate, vinblastine, adriamycin and cisplatin (M–VAC) followed by TURBT, partial cystectomy or radical cystectomy (75% 3–year survival) was compared to an American cohort treated by radical cystectomy (51% 3–year survival). Methods: Immunohistochemistry was used to examine the protein expression levels of three genes that act at the G1/S cell cycle checkpoint, p53, p21/waf–1/cip1 (a downstream effector gene in the p53 pathway) and Rb, plus a major inhibitor of apoptosis, Bcl–2. Results: For the bladder cancers of the Italian patient cohort, there was a significantly higher rate of p53 immunopositivity (93 vs. 63%, p = 0.002) and a significantly lower rate of Rb loss (25 vs. 54%, p = 0.009). In bivariate analysis, 72% of Italian tumors were immunopositive for both p53 and p21 (p53+/p21+) vs. 49% for the American tumors. The subset of Italian patients with p53+/p21+ tumors were more frequently disease–free (stage pT0) following chemotherapy and were less likely to fail therapy than those with p53+/p21– tumors (p = 0.0357). Loss of Rb staining was associated with a decreased 5–year survival in the Italian, but not in the American patients. Conclusions: (1) Significant differences in the expression of the p53, p21 and Rb genes were found between the 2 groups of patients. (2) Italian patients with p53+/p21+ tumors had significantly lower recurrence rates after TURBT and chemotherapy than those having p53+/p21– tumors. (3) Absence of p21 immunopositivity in the Italian tumors may identify alterations in the p53 pathway that predict poor outcome.