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1.  Biometrika 
The Eugenics Review  1935;26(4):310-311.
PMCID: PMC2985393  PMID: 21260154
2.  Variable Selection in the Cox Regression Model with Covariates Missing at Random 
Biometrics  2009;66(1):97-104.
We consider variable selection in the Cox regression model (Cox, 1975, Biometrika 362, 269–276) with covariates missing at random. We investigate the smoothly clipped absolute deviation penalty and adaptive least absolute shrinkage and selection operator (LASSO) penalty, and propose a unified model selection and estimation procedure. A computationally attractive algorithm is developed, which simultaneously optimizes the penalized likelihood function and penalty parameters. We also optimize a model selection criterion, called the ICQ statistic (Ibrahim, Zhu, and Tang, 2008, Journal of the American Statistical Association 103, 1648–1658), to estimate the penalty parameters and show that it consistently selects all important covariates. Simulations are performed to evaluate the finite sample performance of the penalty estimates. Also, two lung cancer data sets are analyzed to demonstrate the proposed methodology.
PMCID: PMC3303197  PMID: 19459831
ALASSO; Missing data; Partial likelihood; Penalized likelihood; Proportional hazards model; SCAD; Variable selection
3.  Association analyses of clustered competing risks data via cross hazard ratio 
Bandeen-Roche and Liang (2002, Modelling multivariate failure time associations in the presence of a competing risk. Biometrika 89, 299–314.) tailored Oakes (1989, Bivariate survival models induced by frailties. Journal of the American Statistical Association 84, 487–493.)'s conditional hazard ratio to evaluate cause-specific associations in bivariate competing risks data. In many population-based family studies, one observes complex multivariate competing risks data, where the family sizes may be  > 2, certain marginals may be exchangeable, and there may be multiple correlated relative pairs having a given pairwise association. Methods for bivariate competing risks data are inadequate in these settings. We show that the rank correlation estimator of Bandeen-Roche and Liang (2002) extends naturally to general clustered family structures. Consistency, asymptotic normality, and variance estimation are easily obtained with U-statistic theories. A natural by-product is an easily implemented test for constancy of the association over different time regions. In the Cache County Study on Memory in Aging, familial associations in dementia onset are of interest, accounting for death prior to dementia. The proposed methods using all available data suggest attenuation in dementia associations at later ages, which had been somewhat obscured in earlier analyses.
PMCID: PMC2800162  PMID: 19826137
Cause-specific hazard ratio; Concordance estimator; Dependent censoring; Exchangeable clustered data; Time-varying association
4.  On a Closed-Form Doubly Robust Estimator of the Adjusted Odds Ratio for a Binary Exposure 
American Journal of Epidemiology  2013;177(11):1314-1316.
Epidemiologic studies often aim to estimate the odds ratio for the association between a binary exposure and a binary disease outcome. Because confounding bias is of serious concern in observational studies, investigators typically estimate the adjusted odds ratio in a multivariate logistic regression which conditions on a large number of potential confounders. It is well known that modeling error in specification of the confounders can lead to substantial bias in the adjusted odds ratio for exposure. As a remedy, Tchetgen Tchetgen et al. (Biometrika. 2010;97(1):171–180) recently developed so-called doubly robust estimators of an adjusted odds ratio by carefully combining standard logistic regression with reverse regression analysis, in which exposure is the dependent variable and both the outcome and the confounders are the independent variables. Double robustness implies that only one of the 2 modeling strategies needs to be correct in order to make valid inferences about the odds ratio parameter. In this paper, I aim to introduce this recent methodology into the epidemiologic literature by presenting a simple closed-form doubly robust estimator of the adjusted odds ratio for a binary exposure. A SAS macro (SAS Institute Inc., Cary, North Carolina) is given in an online appendix to facilitate use of the approach in routine epidemiologic practice, and a simulated data example is also provided for the purpose of illustration.
PMCID: PMC3664333  PMID: 23558352
case-control sampling; doubly robust estimator; logistic regression; odds ratio; SAS macro
5.  Handling Missing Data in Randomized Experiments with Noncompliance 
Treatment noncompliance and missing outcomes at posttreatment assessments are common problems in field experiments in naturalistic settings. Although the two complications often occur simultaneously, statistical methods that address both complications have not been routinely considered in data analysis practice in the prevention research field. This paper shows that identification and estimation of causal treatment effects considering both noncompliance and missing outcomes can be relatively easily conducted under various missing data assumptions. We review a few assumptions on missing data in the presence of noncompliance, including the latent ignorability proposed by Frangakis and Rubin (Biometrika 86:365–379, 1999), and show how these assumptions can be used in the parametric complier average causal effect (CACE) estimation framework. As an easy way of sensitivity analysis, we propose the use of alternative missing data assumptions, which will provide a range of causal effect estimates. In this way, we are less likely to settle with a possibly biased causal effect estimate based on a single assumption. We demonstrate how alternative missing data assumptions affect identification of causal effects, focusing on the CACE. The data from the Johns Hopkins School Intervention Study (Ialongo et al., Am J Community Psychol 27:599–642, 1999) will be used as an example.
PMCID: PMC2912956  PMID: 20379779
Causal inference; Complier average causal effect; Latent ignorability; Missing at random; Missing data; Noncompliance
6.  A Solution to Separation and Multicollinearity in Multiple Logistic Regression 
Journal of data science : JDS  2008;6(4):515-531.
In dementia screening tests, item selection for shortening an existing screening test can be achieved using multiple logistic regression. However, maximum likelihood estimates for such logistic regression models often experience serious bias or even non-existence because of separation and multicollinearity problems resulting from a large number of highly correlated items. Firth (1993, Biometrika, 80(1), 27–38) proposed a penalized likelihood estimator for generalized linear models and it was shown to reduce bias and the non-existence problems. The ridge regression has been used in logistic regression to stabilize the estimates in cases of multicollinearity. However, neither solves the problems for each other. In this paper, we propose a double penalized maximum likelihood estimator combining Firth’s penalized likelihood equation with a ridge parameter. We present a simulation study evaluating the empirical performance of the double penalized likelihood estimator in small to moderate sample sizes. We demonstrate the proposed approach using a current screening data from a community-based dementia study.
PMCID: PMC2849171  PMID: 20376286
Logistic regression; maximum likelihood; penalized maximum likelihood; ridge regression; item selection
7.  Empirical likelihood analysis of the Buckley–James estimator 
Journal of multivariate analysis  2008;99(4):649-664.
The censored linear regression model, also referred to as the accelerated failure time (AFT) model when the logarithm of the survival time is used as the response variable, is widely seen as an alternative to the popular Cox model when the assumption of proportional hazards is questionable. Buckley and James [Linear regression with censored data, Biometrika 66 (1979) 429−436] extended the least squares estimator to the semiparametric censored linear regression model in which the error distribution is completely unspecified. The Buckley–James estimator performs well in many simulation studies and examples. The direct interpretation of the AFT model is also more attractive than the Cox model, as Cox has pointed out, in practical situations. However, the application of the Buckley–James estimation was limited in practice mainly due to its illusive variance. In this paper, we use the empirical likelihood method to derive a new test and confidence interval based on the Buckley–James estimator of the regression coefficient. A standard chi-square distribution is used to calculate the P-value and the confidence interval. The proposed empirical likelihood method does not involve variance estimation. It also shows much better small sample performance than some existing methods in our simulation studies.
PMCID: PMC2583435  PMID: 19018294
Censored data; Wilks theorem; Accelerated failure time model; Linear regression model
8.  British Medical Journal 
British Medical Journal  1910;2(2609):2035-2036.
PMCID: PMC2336486
9.  The Statistician and Medical Research 
British Medical Journal  1948;2(4574):467-468.
PMCID: PMC2091903  PMID: 18881275
10.  Prevalence of Erectile and Ejaculatory Difficulties among Men in Croatia 
Croatian medical journal  2006;47(1):114-124.
To determine the prevalence and risk factors of erectile difficulties and rapid ejaculation in men in Croatia.
We surveyed 615 of 888 contacted men aged 35-84 years. The mean age of participants was 54 ± 12 years. College-educated respondents and the respondents from large cities were slightly overrepresented in the sample. Structured face-to-face interviews were conducted in June and July 2004 by 63 trained interviewers. The questionnaire used in interviews was created for commercial purposes and had not been validated before.
Out of 615 men who were sexually active in the preceding month and gave the valid answers to the questions on erectile difficulties and rapid ejaculation, 130 suffered from erectile or ejaculatory difficulties. Men who had been sexually active the month before the interview and gave the valid answers to the questions on sexual difficulties reported having erectile difficulties more often (77 out of 615) than rapid ejaculation (57 out of 601). Additional 26.8% (165 out of 615) and 26.3% (158 out of 601) men were classified as being at risk for erectile difficulties and rapid ejaculation, respectively. The prevalence of erectile difficulties varied from 5.8% in the 35-39 age group to 30% in the 70-79 age group. The association between age and rapid ejaculation was curvilinear, ie, U-shaped. Rates of rapid ejaculation were highest in the youngest (15.7%) and the oldest (12.5%) age groups. Older age (odds ratios [OR], 6.2-10.3), overweight (OR, 3.3-4.2), alcohol (OR, 0.3-0.4), intense physical activity (OR, 0.3), traditional attitudes about sexuality (OR, 2.8), and discussing sex with one’s partner (OR, 0.1-0.3) were associated with erectile difficulties. Education (OR, 0.1-0.3), being overweight (OR, 22.0) or obese (OR, 20.1), alcohol consumption (OR, 0.2-0.3), stress and anxiety (OR, 10.8-12.5), holding traditional attitudes (OR, 2.8) and moderate physical activity (OR, 0.1) were factors associated with rapid ejaculation.
The prevalence of erectile difficulties was higher than the prevalence of rapid ejaculation in men in Croatia. The odds of having these sexual difficulties increased with older age, overweight, traditional attitudes toward sex, and higher level of stress and anxiety.
PMCID: PMC2080357  PMID: 16489704
British Medical Journal  1908;2(2482):228-229.
PMCID: PMC2437068
12.  The eugenics review 
The Eugenics Review  1936;28(2):165.
PMCID: PMC2985587  PMID: 21260220
14.  Statistics in Medicine 
British Medical Journal  1950;1(4644):68-69.
PMCID: PMC2036382  PMID: 20787727
15.  Sir Thomas Browne's Skull 
PMCID: PMC2311878  PMID: 19310461
16.  The scope of eugenics 
The Eugenics Review  1936;28(1):84.
PMCID: PMC2985542  PMID: 21260203
17.  Karl Pearson 
British Medical Journal  1940;1(4136):617.
PMCID: PMC2177038

Results 1-17 (17)