Design and analysis for three level hierarchical structures with count response

In numerous intervention studies and education field trials, random assignment to treatment occurs in clusters rather than at the level of observation. This departure of random assignment of units may be due to logistics, political feasibility, or ecological validity. Data within the same cluster or grouping are often correlated. Application of traditional regression techniques, which assume independence between observations, to clustered data produce consistent parameter estimates. However such estimators are often inefficient as compared to methods which incorporate the clustered nature of the data into the estimation procedure (Neuhaus 1993).1 Multilevel models, also known as random effects or random components models, can be used to account for the clustering of data by estimating higher level, or group, as well as lower level, or individual variation. Designing a study, in which the unit of observation is nested within higher level groupings, requires the determination of sample sizes at each level. This study investigates the design and analysis of various sampling strategies for a 3-level repeated measures design on the parameter estimates when the outcome variable of interest follows a Poisson distribution. ^ Results study suggest that second order PQL estimation produces the least biased estimates in the 3-level multilevel Poisson model followed by first order PQL and then second and first order MQL. The MQL estimates of both fixed and random parameters are generally satisfactory when the level 2 and level 3 variation is less than 0.10. However, as the higher level error variance increases, the MQL estimates become increasingly biased. If convergence of the estimation algorithm is not obtained by PQL procedure and higher level error variance is large, the estimates may be significantly biased. In this case bias correction techniques such as bootstrapping should be considered as an alternative procedure. For larger sample sizes, those structures with 20 or more units sampled at levels with normally distributed random errors produced more stable estimates with less sampling variance than structures with an increased number of level 1 units. For small sample sizes, sampling fewer units at the level with Poisson variation produces less sampling variation, however this criterion is no longer important when sample sizes are large. ^ 1Neuhaus J (1993). “Estimation efficiency and Tests of Covariate Effects with Clustered Binary Data”. Biometrics , 49, 989–996^

Evaluation of the causal pathways through which subjective norms influence mammography intention and stage of change in a national sample of women veterans

Few studies have investigated causal pathways linking psychosocial factors to each other and to screening mammography. Conflicting hypotheses exist in the theoretic literature regarding the role and importance of subjective norms, a person's perceived social pressure to perform the behavior and his/her motivation to comply. The Theory of Reasoned Action (TRA) hypothesizes that subjective norms directly affect intention; while the Transtheoretical Model (TTM) hypothesizes that attitudes mediate the influence of subjective norms on stage of change. No one has examined which hypothesis best predicts the effect of subjective norms on mammography intention and stage of change. Two statistical methods are available for testing mediation, sequential regression analysis (SRA) and latent variable structural equation modeling (LVSEM); however, software to apply LVSEM to dichotomous variables like intention has only recently become available. No one has compared the methods to determine whether or not they yield similar results for dichotomous variables. ^ Study objectives were to: (1) determine whether the effect of subjective norms on mammography intention and stage of change are mediated by pros and cons; and (2) compare mediation results from the SRA and LVSEM approaches when the outcome is dichotomous. We conducted a secondary analysis of data from a national sample of women veterans enrolled in Project H.O.M.E. (H&barbelow;ealthy O&barbelow;utlook on the M&barbelow;ammography E&barbelow;xperience), a behavioral intervention trial. ^ Results showed that the TTM model described the causal pathways better than the TRA one; however, we found support for only one of the TTM causal mechanisms. Cons was the sole mediator. The mediated effect of subjective norms on intention and stage of change by cons was very small. These findings suggest that interventionists focus their efforts on reducing negative attitudes toward mammography when resources are limited. ^ Both the SRA and LVSEM methods provided evidence for complete mediation, and the direction, magnitude, and standard errors of the parameter estimates were very similar. Because SRA parameter estimates were not biased toward the null, we can probably assume negligible measurement error in the independent and mediator variables. Simulation studies are needed to further our understanding of how these two methods perform under different data conditions. ^

Effect of maternal weight status on the relationship between prenatal smoking and infant birth weight

The purpose of this study was to assess the effect of maternal pre-pregnancy weight status on the relationship between prenatal smoking and infant birth weight (IBW). Prenatal cigarette smoking and maternal weight exert opposing effects on IBW; smoking decreases birth weight while maternal pre-pregnancy weight is positively correlated with birth weight. As such, mutual effect modification may be sufficiently significant to alter the independent effects of these two birth weight correlates. Finding of such an effect has implications of prenatal smoking cessation education. Perception of risk is an important determinant of smoking cessation, and reduced or low birth weight (LBW) as a smoking-associated risk predominates prenatal smoking counseling and education. In a population such as the US, where obesity is becoming epidemic, particularly among minority and low-income groups, perception of risk may be lowered should increased maternal size attenuate the effect of smoking. Previous studies have not found a significant interaction effect of prenatal smoking and maternal pre-pregnancy weight on IBW; however, use of self-reported smoking status may have biased findings. Reliability of self-reported smoking status reported in the literature is variable, with deception rates ranging from a low of 5% to as high as 16%. This study, using data from a prenatal smoking cessation project, in which smoking status was validated by saliva cotinine, was an opportunity to assess effect modification of smoking and maternal weight using biochemically determined smoking status in lieu of self report. Stratified by saliva cotinine, 151 women from a prenatal smoking cessation cohort, who were 18 years and older and had full-term, singleton births, were included in this study. The effect of smoking in terms of mean birth weight across three levels of maternal pre-pregnancy weight was assessed by general linear modeling procedures, adjusting for other known correlates of IBW. Effect modification was marginally significant, p = .104, but only with control for differential effects among racial/ethnic groups. A smaller than planned sample of nonsmokers, or women who quit smoking during the pregnancy, prohibited rejection of the null hypothesis of no difference in the effect of smoking across levels of pre-pregnancy weight. ^

Bayesian joint modeling of longitudinal and survival data

The joint modeling of longitudinal and survival data is a new approach to many applications such as HIV, cancer vaccine trials and quality of life studies. There are recent developments of the methodologies with respect to each of the components of the joint model as well as statistical processes that link them together. Among these, second order polynomial random effect models and linear mixed effects models are the most commonly used for the longitudinal trajectory function. In this study, we first relax the parametric constraints for polynomial random effect models by using Dirichlet process priors, then three longitudinal markers rather than only one marker are considered in one joint model. Second, we use a linear mixed effect model for the longitudinal process in a joint model analyzing the three markers. In this research these methods were applied to the Primary Biliary Cirrhosis sequential data, which were collected from a clinical trial of primary biliary cirrhosis (PBC) of the liver. This trial was conducted between 1974 and 1984 at the Mayo Clinic. The effects of three longitudinal markers (1) Total Serum Bilirubin, (2) Serum Albumin and (3) Serum Glutamic-Oxaloacetic transaminase (SGOT) on patients' survival were investigated. Proportion of treatment effect will also be studied using the proposed joint modeling approaches. ^ Based on the results, we conclude that the proposed modeling approaches yield better fit to the data and give less biased parameter estimates for these trajectory functions than previous methods. Model fit is also improved after considering three longitudinal markers instead of one marker only. The results from analysis of proportion of treatment effects from these joint models indicate same conclusion as that from the final model of Fleming and Harrington (1991), which is Bilirubin and Albumin together has stronger impact in predicting patients' survival and as a surrogate endpoints for treatment. ^

Outcome-based adaptive randomization for binary data in clinical trials---Compare and contrast

Monte Carlo simulation has been conducted to investigate parameter estimation and hypothesis testing in some well known adaptive randomization procedures. The four urn models studied are Randomized Play-the-Winner (RPW), Randomized Pôlya Urn (RPU), Birth and Death Urn with Immigration (BDUI), and Drop-the-Loses Urn (DL). Two sequential estimation methods, the sequential maximum likelihood estimation (SMLE) and the doubly adaptive biased coin design (DABC), are simulated at three optimal allocation targets that minimize the expected number of failures under the assumption of constant variance of simple difference (RSIHR), relative risk (ORR), and odds ratio (OOR) respectively. Log likelihood ratio test and three Wald-type tests (simple difference, log of relative risk, log of odds ratio) are compared in different adaptive procedures. ^ Simulation results indicates that although RPW is slightly better in assigning more patients to the superior treatment, the DL method is considerably less variable and the test statistics have better normality. When compared with SMLE, DABC has slightly higher overall response rate with lower variance, but has larger bias and variance in parameter estimation. Additionally, the test statistics in SMLE have better normality and lower type I error rate, and the power of hypothesis testing is more comparable with the equal randomization. Usually, RSIHR has the highest power among the 3 optimal allocation ratios. However, the ORR allocation has better power and lower type I error rate when the log of relative risk is the test statistics. The number of expected failures in ORR is smaller than RSIHR. It is also shown that the simple difference of response rates has the worst normality among all 4 test statistics. The power of hypothesis test is always inflated when simple difference is used. On the other hand, the normality of the log likelihood ratio test statistics is robust against the change of adaptive randomization procedures. ^

News media coverage of policies surrounding the HPV vaccine before and after Texas Governor Rick Perry's executive order, February 2006-February 2008

Objective. In June 2006, the first vaccine for human papillomavirus (HPV) was approved by the FDA and shortly after approval, the Advisory Committee on Immunization Practices (ACIP) voted to recommend the HPV vaccine for young girls. As a result of ACIP recommendations, state legislators introduced bills to mandate the vaccine. Policies related to public health issues, such as vaccination mandates, are often influenced by news coverage of these issues. News media, particularly in times of controversies, reinforce specific messages and plays an essential role in framing issues for the public. The objective of this study is to examine the quality, content, and scope of policies for the HPV vaccine before and after Texas Governor Rick Perry issued an executive order mandating the vaccine for middle school girls.^ Methods. The Lexis-Nexis database was used to identify 335 articles on HPV vaccination mandate policies that were published in U.S. newspapers from February 1, 2006 to February 2, 2008. The coding instrument captured information about article type, main news story concern, general information about HPV, HPV vaccine mandate policies, arguments for and against HPV vaccination mandates, arguments for and against the HPV vaccine, and sources of information.^ Results. Most news articles (82.4%) occurred after Governor Rick Perry issued an executive order mandating the HPV vaccine. Most articles mentioned that HPV is sexually transmitted (90.7%) and linked HPV infection to cervical cancer (96.1%). Only 63.9% of the articles reported that the HPV vaccine protects against types of HPV that cause cervical cancer and 18.8% of the articles reported that the vaccine protects against genital warts. Only 18.2% of the news articles presented a balanced argument regarding mandatory HPV vaccinations, and only 39.4% of the news articles presented a balanced argument for the HPV vaccine.^ Conclusions. Our study revealed that news coverage regarding mandating the HPV vaccine and issues related to the vaccine itself is biased, unbalanced, and incomplete. Since the public pays a great deal of attention to health in the media, it is essential that news stories are balanced, complete, and accurate. In order to ensure that future vaccination mandates are not covered in the same way the HPV vaccination was, public health officials, health care providers and scientists should work effectively with the media to ensure that balanced information is provided.^

Selection bias and the cross-validation of regression models for prediction

Strategies are compared for the development of a linear regression model with stochastic (multivariate normal) regressor variables and the subsequent assessment of its predictive ability. Bias and mean squared error of four estimators of predictive performance are evaluated in simulated samples of 32 population correlation matrices. Models including all of the available predictors are compared with those obtained using selected subsets. The subset selection procedures investigated include two stopping rules, C$\sb{\rm p}$ and S$\sb{\rm p}$, each combined with an 'all possible subsets' or 'forward selection' of variables. The estimators of performance utilized include parametric (MSEP$\sb{\rm m}$) and non-parametric (PRESS) assessments in the entire sample, and two data splitting estimates restricted to a random or balanced (Snee's DUPLEX) 'validation' half sample. The simulations were performed as a designed experiment, with population correlation matrices representing a broad range of data structures.^ The techniques examined for subset selection do not generally result in improved predictions relative to the full model. Approaches using 'forward selection' result in slightly smaller prediction errors and less biased estimators of predictive accuracy than 'all possible subsets' approaches but no differences are detected between the performances of C$\sb{\rm p}$ and S$\sb{\rm p}$. In every case, prediction errors of models obtained by subset selection in either of the half splits exceed those obtained using all predictors and the entire sample.^ Only the random split estimator is conditionally (on $\\beta$) unbiased, however MSEP$\sb{\rm m}$ is unbiased on average and PRESS is nearly so in unselected (fixed form) models. When subset selection techniques are used, MSEP$\sb{\rm m}$ and PRESS always underestimate prediction errors, by as much as 27 percent (on average) in small samples. Despite their bias, the mean squared errors (MSE) of these estimators are at least 30 percent less than that of the unbiased random split estimator. The DUPLEX split estimator suffers from large MSE as well as bias, and seems of little value within the context of stochastic regressor variables.^ To maximize predictive accuracy while retaining a reliable estimate of that accuracy, it is recommended that the entire sample be used for model development, and a leave-one-out statistic (e.g. PRESS) be used for assessment. ^

Information bias and lifetime mortality risks of radiation-induced cancer

Additive and multiplicative models of relative risk were used to measure the effect of cancer misclassification and DS86 random errors on lifetime risk projections in the Life Span Study (LSS) of Hiroshima and Nagasaki atomic bomb survivors. The true number of cancer deaths in each stratum of the cancer mortality cross-classification was estimated using sufficient statistics from the EM algorithm. Average survivor doses in the strata were corrected for DS86 random error ($\sigma$ = 0.45) by use of reduction factors. Poisson regression was used to model the corrected and uncorrected mortality rates with covariates for age at-time-of-bombing, age at-time-of-death and gender. Excess risks were in good agreement with risks in RERF Report 11 (Part 2) and the BEIR-V report. Bias due to DS86 random error typically ranged from $-$15% to $-$30% for both sexes, and all sites and models. The total bias, including diagnostic misclassification, of excess risk of nonleukemia for exposure to 1 Sv from age 18 to 65 under the non-constant relative projection model was $-$37.1% for males and $-$23.3% for females. Total excess risks of leukemia under the relative projection model were biased $-$27.1% for males and $-$43.4% for females. Thus, nonleukemia risks for 1 Sv from ages 18 to 85 (DRREF = 2) increased from 1.91%/Sv to 2.68%/Sv among males and from 3.23%/Sv to 4.02%/Sv among females. Leukemia excess risks increased from 0.87%/Sv to 1.10%/Sv among males and from 0.73%/Sv to 1.04%/Sv among females. Bias was dependent on the gender, site, correction method, exposure profile and projection model considered. Future studies that use LSS data for U.S. nuclear workers may be downwardly biased if lifetime risk projections are not adjusted for random and systematic errors. (Supported by U.S. NRC Grant NRC-04-091-02.) ^

The success of worksite nutrition and physical activity interventions with environmental modifications A systematic review

Background: As obesity increases among U.S. workers, employers are implementing programs to increase physical activity and improve diets. Although programs to address individual determinants of obesity have been evaluated, less is known about the effects of workplace programs that change environmental factors, because most reviews have not isolated environmental programs; the one that did was published in 2005. ^ Objective: To update the 2005 review to determine the effectiveness of workplace environmental interventions. ^ Methods: The Medline database was searched for published English language reports (2003-2011) of randomized controlled (RCTs) or quasi-experimental trials (NRCTs) that evaluated strategies to modify physical activity opportunities or food services, targeting employees at least 18 years, not including retirees and that provided data for at least one physical activity, dietary, or health risk indicator. Three coders independently extracted study characteristics and scored the quality of study methods. Program effectiveness was determined using the 2005 review's best evidence approach. ^ Results: Seven studies represented in nine reports met eligibility criteria; three focused on diet and the remainder targeted diet and physical activity interventions. All but one study received a high quality score for internal validity. The evidence for the effectiveness of workplace environmental interventions was at best, inconclusive for diet and physical activity and limited for health risk indicators. The outcome constructs were inconsistent across the studies. ^ Conclusions: Limitations in the methods of the 2005 review made it challenging to draw conclusions about findings for this review that include: variation in outcome measures, reliance on distal measures without proximal behavior change measures, no distinction between changes at the workplace versus outside the workplace, and inappropriate analyses of cluster designs that biased findings toward statistical significance. The best evidence approach relied on vote-counting, using statistical significance alone rather than effect size and confidence intervals. Future research should address these limitations and use more rigorous methods; systematic reviews should use methods of meta-analysis to summarize study findings. These recommendations will help employers to better understand how environmental modifications in the workplace can support their efforts to combat the effects of obesity among employees.^

Data quality in trauma transfusion studies and the impact of missing data on predicting massive transfusion

Maximizing data quality may be especially difficult in trauma-related clinical research. Strategies are needed to improve data quality and assess the impact of data quality on clinical predictive models. This study had two objectives. The first was to compare missing data between two multi-center trauma transfusion studies: a retrospective study (RS) using medical chart data with minimal data quality review and the PRospective Observational Multi-center Major Trauma Transfusion (PROMMTT) study with standardized quality assurance. The second objective was to assess the impact of missing data on clinical prediction algorithms by evaluating blood transfusion prediction models using PROMMTT data. RS (2005-06) and PROMMTT (2009-10) investigated trauma patients receiving ≥ 1 unit of red blood cells (RBC) from ten Level I trauma centers. Missing data were compared for 33 variables collected in both studies using mixed effects logistic regression (including random intercepts for study site). Massive transfusion (MT) patients received ≥ 10 RBC units within 24h of admission. Correct classification percentages for three MT prediction models were evaluated using complete case analysis and multiple imputation based on the multivariate normal distribution. A sensitivity analysis for missing data was conducted to estimate the upper and lower bounds of correct classification using assumptions about missing data under best and worst case scenarios. Most variables (17/33=52%) had <1% missing data in RS and PROMMTT. Of the remaining variables, 50% demonstrated less missingness in PROMMTT, 25% had less missingness in RS, and 25% were similar between studies. Missing percentages for MT prediction variables in PROMMTT ranged from 2.2% (heart rate) to 45% (respiratory rate). For variables missing >1%, study site was associated with missingness (all p≤0.021). Survival time predicted missingness for 50% of RS and 60% of PROMMTT variables. MT models complete case proportions ranged from 41% to 88%. Complete case analysis and multiple imputation demonstrated similar correct classification results. Sensitivity analysis upper-lower bound ranges for the three MT models were 59-63%, 36-46%, and 46-58%. Prospective collection of ten-fold more variables with data quality assurance reduced overall missing data. Study site and patient survival were associated with missingness, suggesting that data were not missing completely at random, and complete case analysis may lead to biased results. Evaluating clinical prediction model accuracy may be misleading in the presence of missing data, especially with many predictor variables. The proposed sensitivity analysis estimating correct classification under upper (best case scenario)/lower (worst case scenario) bounds may be more informative than multiple imputation, which provided results similar to complete case analysis.^

Instrumental variable method for the causal relationship between soluble receptor for advanced glycation end-products (sRAGE) and risk of pancreatic cancer

This thesis project is motivated by the potential problem of using observational data to draw inferences about a causal relationship in observational epidemiology research when controlled randomization is not applicable. Instrumental variable (IV) method is one of the statistical tools to overcome this problem. Mendelian randomization study uses genetic variants as IVs in genetic association study. In this thesis, the IV method, as well as standard logistic and linear regression models, is used to investigate the causal association between risk of pancreatic cancer and the circulating levels of soluble receptor for advanced glycation end-products (sRAGE). Higher levels of serum sRAGE were found to be associated with a lower risk of pancreatic cancer in a previous observational study (255 cases and 485 controls). However, such a novel association may be biased by unknown confounding factors. In a case-control study, we aimed to use the IV approach to confirm or refute this observation in a subset of study subjects for whom the genotyping data were available (178 cases and 177 controls). Two-stage IV method using generalized method of moments-structural mean models (GMM-SMM) was conducted and the relative risk (RR) was calculated. In the first stage analysis, we found that the single nucleotide polymorphism (SNP) rs2070600 of the receptor for advanced glycation end-products (AGER) gene meets all three general assumptions for a genetic IV in examining the causal association between sRAGE and risk of pancreatic cancer. The variant allele of SNP rs2070600 of the AGER gene was associated with lower levels of sRAGE, and it was neither associated with risk of pancreatic cancer, nor with the confounding factors. It was a potential strong IV (F statistic = 29.2). However, in the second stage analysis, the GMM-SMM model failed to converge due to non- concaveness probably because of the small sample size. Therefore, the IV analysis could not support the causality of the association between serum sRAGE levels and risk of pancreatic cancer. Nevertheless, these analyses suggest that rs2070600 was a potentially good genetic IV for testing the causality between the risk of pancreatic cancer and sRAGE levels. A larger sample size is required to conduct a credible IV analysis.^