Effect of nonnormal random components on level and power in group-randomized trials

The use of group-randomized trials is particularly widespread in the evaluation of health care, educational, and screening strategies. Group-randomized trials represent a subset of a larger class of designs often labeled nested, hierarchical, or multilevel and are characterized by the randomization of intact social units or groups, rather than individuals. The application of random effects models to group-randomized trials requires the specification of fixed and random components of the model. The underlying assumption is usually that these random components are normally distributed. This research is intended to determine if the Type I error rate and power are affected when the assumption of normality for the random component representing the group effect is violated. ^ In this study, simulated data are used to examine the Type I error rate, power, bias and mean squared error of the estimates of the fixed effect and the observed intraclass correlation coefficient (ICC) when the random component representing the group effect possess distributions with non-normal characteristics, such as heavy tails or severe skewness. The simulated data are generated with various characteristics (e.g. number of schools per condition, number of students per school, and several within school ICCs) observed in most small, school-based, group-randomized trials. The analysis is carried out using SAS PROC MIXED, Version 6.12, with random effects specified in a random statement and restricted maximum likelihood (REML) estimation specified. The results from the non-normally distributed data are compared to the results obtained from the analysis of data with similar design characteristics but normally distributed random effects. ^ The results suggest that the violation of the normality assumption for the group component by a skewed or heavy-tailed distribution does not appear to influence the estimation of the fixed effect, Type I error, and power. Negative biases were detected when estimating the sample ICC and dramatically increased in magnitude as the true ICC increased. These biases were not as pronounced when the true ICC was within the range observed in most group-randomized trials (i.e. 0.00 to 0.05). The normally distributed group effect also resulted in bias ICC estimates when the true ICC was greater than 0.05. However, this may be a result of higher correlation within the data. ^

A MORTALITY STUDY OF BUTYL-CHLOROBUTYL RUBBER WORKERS

Worker populations are potentially exposed to multiple chemical substances simultaneously during the performance of routine tasks. The acute health effects from exposure to toxic concentrations of these substances are usually well-described. However, very little is known about the long-term health effects of chronic low dose exposure to all except a few chemical substances. A mortality study was performed on a population of workers employed at a butyl rubber manufacturing plant in Baton Rouge, Louisiana for the period 1943-1978, with special emphasis on potential exposure to methyl chloride.^ The study population was enumerated using company records. The mortality experience among the population was evaluated by comparing the number of observed deaths (total and cause-specific) to the expected number of deaths, based on the U.S. general age, race, sex specific rates. An internal comparison population was assembled to address the issue of lack of comparability when the U.S. rates are used to calculate expected deaths in an employed population.^ There were 18% fewer total observed deaths compared to the expected when the U.S. death rates were used to obtain the expected. Deaths from specific causes were also less than expected except when numbers of observed and expected deaths were small. Similar results were obtained when the population was characterized by intensity and duration of potential exposure to methyl chloride. When the internal comparison population was utilized to evaluate overall mortality of the study population, the relative risk was about 1.2.^ The study results were discussed and conclusions drawn in light of certain limitations of the methodology and study population size. ^

Multilevel analysis for a longitudinal clinical trial

This study applies the multilevel analysis technique to longitudinal data of a large clinical trial. The technique accounts for the correlation at different levels when modeling repeated blood pressure measurements taken throughout the trial. This modeling allows for closer inspection of the remaining correlation and non-homogeneity of variance in the data. Three methods of modeling the correlation were compared. ^

Modeling a health promotion campaign process

In this work we will present a model that describes how the number of healthy and unhealthy subjects that belong to a cohort, changes through time when there are occurrences of health promotion campaigns aiming to change the undesirable behavior. This model also includes immigration and emigration components for each group and a component taking into account when a subject that used to perform a healthy behavior changes to perform the unhealthy behavior. We will express the model in terms of a bivariate probability generating function and in addition we will simulate the model. ^ An illustrative example on how to apply the model to the promotion of condom use among adolescents will be created and we will use it to compare the results obtained from the simulations and the results obtained by the probability generating function. ^

Analysis of recurrent failure times: A time-dependent Yule process approach

Analysis of recurrent events has been widely discussed in medical, health services, insurance, and engineering areas in recent years. This research proposes to use a nonhomogeneous Yule process with the proportional intensity assumption to model the hazard function on recurrent events data and the associated risk factors. This method assumes that repeated events occur for each individual, with given covariates, according to a nonhomogeneous Yule process with intensity function λx(t) = λ 0(t) · exp( x′β). One of the advantages of using a non-homogeneous Yule process for recurrent events is that it assumes that the recurrent rate is proportional to the number of events that occur up to time t. Maximum likelihood estimation is used to provide estimates of the parameters in the model, and a generalized scoring iterative procedure is applied in numerical computation. ^ Model comparisons between the proposed method and other existing recurrent models are addressed by simulation. One example concerning recurrent myocardial infarction events compared between two distinct populations, Mexican-American and Non-Hispanic Whites in the Corpus Christi Heart Project is examined. ^

Forecasting cost based on a stochastic utilization plan and a fixed cost function

The application of Markov processes is very useful to health-care problems. The objective of this study is to provide a structured methodology of forecasting cost based upon combining a stochastic model of utilization (Markov Chain) and deterministic cost function. The perspective of the cost in this study is the reimbursement for the services rendered. The data to be used is the OneCare database of claim records of their enrollees over a two-year period of January 1, 1996–December 31, 1997. The model combines a Markov Chain that describes the utilization pattern and its variability where the use of resources by risk groups (age, gender, and diagnosis) will be considered in the process and a cost function determined from a fixed schedule based on real costs or charges for those in the OneCare claims database. The cost function is a secondary application to the model. Goodness-of-fit will be used checked for the model against the traditional method of cost forecasting. ^

Traditional linkage analysis in admixed families

Currently there is no general method to study the impact of population admixture within families on the assumptions of random mating and consequently, Hardy-Weinberg equilibrium (HWE) and linkage equilibrium (LE) and on the inference obtained from traditional linkage analysis. ^ First, through simulation, the effect of admixture of two populations on the log of the odds (LOD) score was assessed, using Prostate Cancer as the typical disease model. Comparisons between simulated mixed and homogeneous families were performed. LOD scores under both models of admixture (within families and within a data set of homogeneous families) were closest to the homogeneous family scores of the population having the highest mixing proportion. Random sampling of families or ascertainment of families with disease affection status did not affect this observation, nor did the mode of inheritance (dominant/recessive) or sample size. ^ Second, after establishing the effect of admixture on the LOD score and inference for linkage, the presence of induced disequilibria by population admixture within families was studied and an adjustment procedure was developed. The adjustment did not force all disequilibria to disappear but because the families were adjusted for the population admixture, those replicates where the disequilibria exist are no longer affected by the disequilibria in terms of maximization for linkage. Furthermore, the adjustment was able to exclude uninformative families or families that had such a high departure from HWE and/or LE that their LOD scores were not reliable. ^ Together these observations imply that the presence of families of mixed population ancestry impacts linkage analysis in terms of the LOD score and the estimate of the recombination fraction. ^

Mixed effects model in negative exponential curve

Despite many researches on development in education and psychology, not often is the methodology tested with real data. A major barrier to test the growth model is that the design of study includes repeated observations and the nature of the growth is nonlinear. The repeat measurements on a nonlinear model require sophisticated statistical methods. In this study, we present mixed effects model in a negative exponential curve to describe the development of children's reading skills. This model can describe the nature of the growth on children's reading skills and account for intra-individual and inter-individual variation. We also apply simple techniques including cross-validation, regression, and graphical methods to determine the most appropriate curve for data, to find efficient initial values of parameters, and to select potential covariates. We illustrate with an example that motivated this research: a longitudinal study of academic skills from grade 1 to grade 12 in Connecticut public schools. ^

Familial aggregation, candidate genes and genome scans: Analyzing the role of genetics in stroke

The genetic etiology of stroke likely reflects the influence of multiple loci with small effects, each modulating different pathophysiological processes. This research project utilized three analytical strategies to address the paucity of information related to the identification and characterization of genetic variation associated with stroke in the general population. ^ First, the general contribution of familial factors to stroke susceptibility was evaluated in a population-based sample of unrelated individuals. Increased risk of subclinical cerebral infarction was observed among individuals with a positive parental history of stroke. This association did not appear to be mediated by established stroke risk factors, specifically blood pressure levels or hypertension status. ^ The need to identify specific gene variation associated with stroke in the general population was addressed by evaluating seven candidate gene polymorphisms in a population-based sample of unrelated individuals. Three polymorphisms were significantly associated with increased subclinical cerebral infarction or incident clinical ischemic stroke risk. These relationships include the G-protein β3 subunit 825C/T polymorphism and clinical stroke in Whites, the lipoprotein lipase S/X447 polymorphism and subclinical and clinical stroke in men, and the angiotensin I-converting enzyme Ins/Del polymorphism and subclinical stroke in White men. These associations did not appear to be obfuscated by the stroke risk factors adjusted for in the analysis models specifically blood pressure levels or anti-hypertensive medication use. ^ The final research strategy considered, on a genome-wide scale, the idea that genetic variation may contribute to the occurrence of hypertension or stroke through a common etiologic pathway. Genomic regions were identified for which significant evidence of heterogeneity was observed among hypertensive sibpairs stratified by family history of stroke information. Regions identified on chromosome 15 in African Americans, and chromosome 13 in Whites and African Americans, suggest the presence of genes influencing hypertension and stroke susceptibility. ^ Insight into the role of genetics in stroke is useful for the potential early identification of individuals at increased risk for stroke and improved understanding of the etiology of the disease. The ultimate goal of these endeavors is to guide the development of therapeutic intervention and informed prevention to provide a lasting and positive impact on public health. ^

Risk Index Score (RISc)

The main objective of this study was to develop and validate a computer-based statistical algorithm based on a multivariable logistic model that can be translated into a simple scoring system in order to ascertain stroke cases using hospital admission medical records data. This algorithm, the Risk Index Score (RISc), was developed using data collected prospectively by the Brain Attack Surveillance in Corpus Christ (BASIC) project. The validity of the RISc was evaluated by estimating the concordance of scoring system stroke ascertainment to stroke ascertainment accomplished by physician review of hospital admission records. The goal of this study was to develop a rapid, simple, efficient, and accurate method to ascertain the incidence of stroke from routine hospital admission hospital admission records for epidemiologic investigations. ^ The main objectives of this study were to develop and validate a computer-based statistical algorithm based on a multivariable logistic model that could be translated into a simple scoring system to ascertain stroke cases using hospital admission medical records data. (Abstract shortened by UMI.)^

Comparison of a traditional and a multilevel Cox Proportional Hazards model

Hierarchically clustered populations are often encountered in public health research, but the traditional methods used in analyzing this type of data are not always adequate. In the case of survival time data, more appropriate methods have only begun to surface in the last couple of decades. Such methods include multilevel statistical techniques which, although more complicated to implement than traditional methods, are more appropriate. ^ One population that is known to exhibit a hierarchical structure is that of patients who utilize the health care system of the Department of Veterans Affairs where patients are grouped not only by hospital, but also by geographic network (VISN). This project analyzes survival time data sets housed at the Houston Veterans Affairs Medical Center Research Department using two different Cox Proportional Hazards regression models, a traditional model and a multilevel model. VISNs that exhibit significantly higher or lower survival rates than the rest are identified separately for each model. ^ In this particular case, although there are differences in the results of the two models, it is not enough to warrant using the more complex multilevel technique. This is shown by the small estimates of variance associated with levels two and three in the multilevel Cox analysis. Much of the differences that are exhibited in identification of VISNs with high or low survival rates is attributable to computer hardware difficulties rather than to any significant improvements in the model. ^

Survival analysis of longevity in siblings

Do siblings of centenarians tend to have longer life spans? To answer this question, life spans of 184 siblings for 42 centenarians have been evaluated. Two important questions have been addressed in analyzing the sibling data. First, a standard needs to be established, to which the life spans of 184 siblings are compared. In this report, an external reference population is constructed from the U.S. life tables. Its estimated mortality rates are treated as baseline hazards from which the relative mortality of the siblings are estimated. Second, the standard survival models which assume independent observations are invalid when correlation within family exists, underestimating the true variance. Methods that allow correlations are illustrated by three different methods. First, the cumulative relative excess mortality between siblings and their comparison group is calculated and used as an effective graphic tool, along with the Product Limit estimator of the survival function. The variance estimator of the cumulative relative excess mortality is adjusted for the potential within family correlation using Taylor linearization approach. Second, approaches that adjust for the inflated variance are examined. They are adjusted one-sample log-rank test using design effect originally proposed by Rao and Scott in the correlated binomial or Poisson distribution setting and the robust variance estimator derived from the log-likelihood function of a multiplicative model. Nether of these two approaches provide correlation estimate within families, but the comparison with the comparison with the standard remains valid under dependence. Last, using the frailty model concept, the multiplicative model, where the baseline hazards are known, is extended by adding a random frailty term that is based on the positive stable or the gamma distribution. Comparisons between the two frailty distributions are performed by simulation. Based on the results from various approaches, it is concluded that the siblings of centenarians had significant lower mortality rates as compared to their cohorts. The frailty models also indicate significant correlations between the life spans of the siblings. ^

Multiple imputation for missing continuous and dichotomous data: The effects of patterns of missingness and variable correlations on type I error with small samples

The purpose of this study is to investigate the effects of predictor variable correlations and patterns of missingness with dichotomous and/or continuous data in small samples when missing data is multiply imputed. Missing data of predictor variables is multiply imputed under three different multivariate models: the multivariate normal model for continuous data, the multinomial model for dichotomous data and the general location model for mixed dichotomous and continuous data. Subsequent to the multiple imputation process, Type I error rates of the regression coefficients obtained with logistic regression analysis are estimated under various conditions of correlation structure, sample size, type of data and patterns of missing data. The distributional properties of average mean, variance and correlations among the predictor variables are assessed after the multiple imputation process. ^ For continuous predictor data under the multivariate normal model, Type I error rates are generally within the nominal values with samples of size n = 100. Smaller samples of size n = 50 resulted in more conservative estimates (i.e., lower than the nominal value). Correlation and variance estimates of the original data are retained after multiple imputation with less than 50% missing continuous predictor data. For dichotomous predictor data under the multinomial model, Type I error rates are generally conservative, which in part is due to the sparseness of the data. The correlation structure for the predictor variables is not well retained on multiply-imputed data from small samples with more than 50% missing data with this model. For mixed continuous and dichotomous predictor data, the results are similar to those found under the multivariate normal model for continuous data and under the multinomial model for dichotomous data. With all data types, a fully-observed variable included with variables subject to missingness in the multiple imputation process and subsequent statistical analysis provided liberal (larger than nominal values) Type I error rates under a specific pattern of missing data. It is suggested that future studies focus on the effects of multiple imputation in multivariate settings with more realistic data characteristics and a variety of multivariate analyses, assessing both Type I error and power. ^

Descriptive epidemiology of cancer in three regions of Kazakhstan

The current study investigated data quality and estimated cancer incidence and mortality rates using data provided by Pavlodar, Semipalatinsk and Ust-Kamenogorsk Regional Cancer Registries of Kazakhstan during the period of 1996–1998. Assessment of data quality was performed using standard quality indicators including internal database checks, proportion of cases verified from death certificates only, mortality:incidence ratio, data patterns, proportion of cases with unknown primary site, proportion of cases with unknown age. Crude and age-adjusted incidence and mortality rates and 95% confidence intervals were calculated, by gender, for all cancers combined and for 28 specific cancer sites for each year of the study period. The five most frequent cancers were identified and described for every population. The results of the study provide the first simultaneous assessment of data quality and standardized incidence and mortality rates for Kazakh cancer registries. ^