Evaluation of the accuracy of multilevel analysis parameter estimates for intra-cluster correlation in correlated binary data

Many studies in biostatistics deal with binary data. Some of these studies involve correlated observations, which can complicate the analysis of the resulting data. Studies of this kind typically arise when a high degree of commonality exists between test subjects. If there exists a natural hierarchy in the data, multilevel analysis is an appropriate tool for the analysis. Two examples are the measurements on identical twins, or the study of symmetrical organs or appendages such as in the case of ophthalmic studies. Although this type of matching appears ideal for the purposes of comparison, analysis of the resulting data while ignoring the effect of intra-cluster correlation has been shown to produce biased results.^ This paper will explore the use of multilevel modeling of simulated binary data with predetermined levels of correlation. Data will be generated using the Beta-Binomial method with varying degrees of correlation between the lower level observations. The data will be analyzed using the multilevel software package MlwiN (Woodhouse, et al, 1995). Comparisons between the specified intra-cluster correlation of these data and the estimated correlations, using multilevel analysis, will be used to examine the accuracy of this technique in analyzing this type of data. ^

AN INVESTIGATION INTO THE EFFECT OF TESTOSTERONE ON THE QUANTITATIVE MAINTENANCE OF SPERMATOGENESIS IN THE HYPOPHYSECTOMIZED ADULT RAT (PHARMACOKINETICS, MORPHOMETRY, STATISTICS)

Administration of gonadotropins or testosterone (T) will maintain qualitatively normal spermatogenesis and fertility in hypophysectomized (APX) rats. However, quantitative maintenance of the spermatogenic process in APX rats treated with T alone or in combination with follicle stimulating hormone (FSH) has not been demonstrated. Studies reported here were conducted to determine whether it would be possible to increase intratesticular testosterone (ITT) levels in APX rats to those found in normal animals by administration of appropriate amounts of testosterone propionate (TP) and if under these conditions spermatogenesis can be maintained quantitatively. Quantitative analysis of spermatogenesis was performed on stages VI and VII of the spermatogenic cycle utilizing criteria of Leblond and Clermont (1952) all cell types were enumerated. In a series of experiments designed to investigate the effects of T on spermatogenesis, TP was administered to 60 day old APX rats twice daily for 30 days in doses ranging from 0.6 to 15 mg/day or from 0.6 to 6.0 mg/day in combination with FSH. The results of this study demonstrate that the efficiency of transformation of type A to type B spermatogonia and the efficacy of the meiotic prophase are related to ITT levels, and that quantitatively normal completion of the reduction division requires normal ITT levels. The ratio of spermatids to spermatocytes in the vehicle-treated APX rats was 1:1.38; in the APX rats treated with 15 mg of TP it was 1:4.0 (the theoretically expected number). This study is probably the first to demonstrate: (1) the pharmacokinetics of TP, (2) the profile and quantity of T-immunoactivity in both serum and testicular tissue of APX and IC rats as well as APX rats treated with TP alone or in combination with FSH, (3) the direct correlation of serum T and ITT levels in treated APX rats (r = 0.9, p < 0.001) as well as in the IC rats (r = 0.9, p < 0.001), (4) the significant increase in the number of Type B spermatogonia, preleptotene and pachytene spermatocytes and round spermatids in TP-treated APX rats, (5) the correlation of the number of round spermatids formed in IC rats to ITT levels (r = 0.9, p < 0.001), and (6) the correlation of the quantitative maintenance of spermatogenesis with ITT levels (r = 0.7, p < 0.001) in the testes of TP-treated APX rats. These results provide direct experimental evidence for the key role of T in the spermatogenic process. ^

Assessment of the effect on statistical power of regression model misspecification by using techniques of mathematical statistics and simulation study

Objectives. This paper seeks to assess the effect on statistical power of regression model misspecification in a variety of situations. ^ Methods and results. The effect of misspecification in regression can be approximated by evaluating the correlation between the correct specification and the misspecification of the outcome variable (Harris 2010).In this paper, three misspecified models (linear, categorical and fractional polynomial) were considered. In the first section, the mathematical method of calculating the correlation between correct and misspecified models with simple mathematical forms was derived and demonstrated. In the second section, data from the National Health and Nutrition Examination Survey (NHANES 2007-2008) were used to examine such correlations. Our study shows that comparing to linear or categorical models, the fractional polynomial models, with the higher correlations, provided a better approximation of the true relationship, which was illustrated by LOESS regression. In the third section, we present the results of simulation studies that demonstrate overall misspecification in regression can produce marked decreases in power with small sample sizes. However, the categorical model had greatest power, ranging from 0.877 to 0.936 depending on sample size and outcome variable used. The power of fractional polynomial model was close to that of linear model, which ranged from 0.69 to 0.83, and appeared to be affected by the increased degrees of freedom of this model.^ Conclusion. Correlations between alternative model specifications can be used to provide a good approximation of the effect on statistical power of misspecification when the sample size is large. When model specifications have known simple mathematical forms, such correlations can be calculated mathematically. Actual public health data from NHANES 2007-2008 were used as examples to demonstrate the situations with unknown or complex correct model specification. Simulation of power for misspecified models confirmed the results based on correlation methods but also illustrated the effect of model degrees of freedom on power.^

A Bayesian approach to estimating the intraclass correlation coefficient

A Bayesian approach to estimating the intraclass correlation coefficient was used for this research project. The background of the intraclass correlation coefficient, a summary of its standard estimators, and a review of basic Bayesian terminology and methodology were presented. The conditional posterior density of the intraclass correlation coefficient was then derived and estimation procedures related to this derivation were shown in detail. Three examples of applications of the conditional posterior density to specific data sets were also included. Two sets of simulation experiments were performed to compare the mean and mode of the conditional posterior density of the intraclass correlation coefficient to more traditional estimators. Non-Bayesian methods of estimation used were: the methods of analysis of variance and maximum likelihood for balanced data; and the methods of MIVQUE (Minimum Variance Quadratic Unbiased Estimation) and maximum likelihood for unbalanced data. The overall conclusion of this research project was that Bayesian estimates of the intraclass correlation coefficient can be appropriate, useful and practical alternatives to traditional methods of estimation. ^

Correlation of tuberculosis and human immunodeficiency virus in Harris County, Texas from 2009 through 2010 using Geographic Information Systems

A population based ecological study was conducted to identify areas with a high number of TB and HIV new diagnoses in Harris County, Texas from 2009 through 2010 by applying Geographic Information Systems to determine whether distinguished spatial patterns exist at the census tract level through the use of exploratory mapping. As of 2010, Texas has the fourth highest occurrence of new diagnoses of HIV/AIDS and TB.[31] The Texas Department of State Health Services (DSHS) has identified HIV infected persons as a high risk population for TB in Harris County.[29] In order to explore this relationship further, GIS was utilized to identify spatial trends. ^ The specific aims were to map TB and HIV new diagnoses rates and spatially identify hotspots and high value clusters at the census tract level. The potential association between HIV and TB was analyzed using spatial autocorrelation and linear regression analysis. The spatial statistics used were ArcGIS 9.3 Hotspot Analysis and Cluster and Outlier Analysis. Spatial autocorrelation was determined through Global Moran's I and linear regression analysis. ^ Hotspots and clusters of TB and HIV are located within the same spatial areas of Harris County. The areas with high value clusters and hotspots for each infection are located within the central downtown area of the city of Houston. There is an additional hotspot area of TB located directly north of I-10 and a hotspot area of HIV northeast of Interstate 610. ^ The Moran's I Index of 0.17 (Z score = 3.6 standard deviations, p-value = 0.01) suggests that TB is statistically clustered with a less than 1% chance that this pattern is due to random chance. However, there were a high number of features with no neighbors which may invalidate the statistical properties of the test. Linear regression analysis indicated that HIV new diagnoses rates (β=−0.006, SE=0.147, p=0.970) and census tracts (β=0.000, SE=0.000, p=0.866) were not significant predictors of TB new diagnoses rates. ^ Mapping products indicate that census tracts with overlapping hotspots and high value clusters of TB and HIV should be a targeted focus for prevention efforts, most particularly within central Harris County. While the statistical association was not confirmed, evidence suggests that there is a relationship between HIV and TB within this two year period.^