A novel method for evaluating an interaction effect of correlated continuous covariates in a linear model

Interaction effect is an important scientific interest for many areas of research. Common approach for investigating the interaction effect of two continuous covariates on a response variable is through a cross-product term in multiple linear regression. In epidemiological studies, the two-way analysis of variance (ANOVA) type of method has also been utilized to examine the interaction effect by replacing the continuous covariates with their discretized levels. However, the implications of model assumptions of either approach have not been examined and the statistical validation has only focused on the general method, not specifically for the interaction effect.^ In this dissertation, we investigated the validity of both approaches based on the mathematical assumptions for non-skewed data. We showed that linear regression may not be an appropriate model when the interaction effect exists because it implies a highly skewed distribution for the response variable. We also showed that the normality and constant variance assumptions required by ANOVA are not satisfied in the model where the continuous covariates are replaced with their discretized levels. Therefore, naïve application of ANOVA method may lead to an incorrect conclusion. ^ Given the problems identified above, we proposed a novel method modifying from the traditional ANOVA approach to rigorously evaluate the interaction effect. The analytical expression of the interaction effect was derived based on the conditional distribution of the response variable given the discretized continuous covariates. A testing procedure that combines the p-values from each level of the discretized covariates was developed to test the overall significance of the interaction effect. According to the simulation study, the proposed method is more powerful then the least squares regression and the ANOVA method in detecting the interaction effect when data comes from a trivariate normal distribution. The proposed method was applied to a dataset from the National Institute of Neurological Disorders and Stroke (NINDS) tissue plasminogen activator (t-PA) stroke trial, and baseline age-by-weight interaction effect was found significant in predicting the change from baseline in NIHSS at Month-3 among patients received t-PA therapy.^

Impact of medications prescribed for treatment of attention-deficit hyperactivity disorder on physical growth in children and adolescents with HIV.

OBJECTIVE: To examine the relationships between physical growth and medications prescribed for symptoms of attention-deficit hyperactivity disorder in children with HIV. METHODS: Analysis of data from children with perinatally acquired HIV (N = 2251; age 3-19 years), with and without prescriptions for stimulant and nonstimulant medications used to treat attention-deficit hyperactivity disorder, in a long-term observational study. Height and weight measurements were transformed to z scores and compared across medication groups. Changes in z scores during a 2-year interval were compared using multiple linear regression models adjusting for selected covariates. RESULTS: Participants with (n = 215) and without (n = 2036) prescriptions were shorter than expected based on US age and gender norms (p < .001). Children without prescriptions weighed less at baseline than children in the general population (p < .001) but gained height and weight at a faster rate (p < .001). Children prescribed stimulants were similar to population norms in baseline weight; their height and weight growth velocities were comparable with the general population and children without prescriptions (for weight, p = .511 and .100, respectively). Children prescribed nonstimulants had the lowest baseline height but were similar to population norms in baseline weight. Their height and weight growth velocities were comparable with the general population but significantly slower than children without prescriptions (p = .01 and .02, respectively). CONCLUSION: The use of stimulants to treat symptoms of attention-deficit hyperactivity disorder does not significantly exacerbate the potential for growth delay in children with HIV and may afford opportunities for interventions that promote physical growth. Prospective studies are needed to confirm these findings.

Genes to blood pressure: The effects of variation in genes of the renin-angiotensin system on the hormonal and renal control of blood pressure

Objective. Essential hypertension affects 25% of the US adult population and is a leading contributor to morbidity and mortality. Because BP is a multifactorial phenotype that resists simple genetic analysis, intermediate phenotypes within the complex network of BP regulatory systems may be more accessible to genetic dissection. The Renin-Angiotensin System (RAS) is known to influence intermediate and long-term blood pressure regulation through alterations in vascular tone and renal sodium and fluid resorption. This dissertation examines associations between renin (REN), angiotensinogen (AGT), angiotensin-converting enzyme (ACE) and angiotensin II type 1 receptor (AT1) gene variation and interindividual differences in plasma hormone levels, renal hemodynamics, and BP homeostasis.^ Methods. A total of 150 unrelated men and 150 unrelated women, between 20.0 and 49.9 years of age and free of acute or chronic illness except for a history of hypertension (11 men and 7 women, all off medications), were studied after one week on a controlled sodium diet. RAS plasma hormone levels, renal hemodynamics and BP were determined prior to and during angiotensin II (Ang II) infusion. Individuals were genotyped by PCR for a variable number tandem repeat (VNTR) polymorphism in REN, and for the following restriction fragment length polymorphisms (RFLP): AGT M235T, ACE I/D, and AT1 A1166C. Associations between clinical measurements and allelic variation were examined using multiple linear regression statistical models.^ Results. Women homozygous for the AT1 1166C allele demonstrated higher intracellular levels of sodium (p = 0.044). Men homozygous for the AGT T235 allele demonstrated a blunted decrement in renal plasma flow in response to Ang II infusion (p = 0.0002). There were no significant associations between RAS gene variation and interindividual variation in RAS plasma hormone levels or BP.^ Conclusions. Rather than identifying new BP controlling genes or alleles, the study paradigm employed in this thesis (i.e., measured genes, controlled environments and interventions) may provide mechanistic insight into how candidate genes affect BP homeostasis. ^

Association between temperament and physical activity in a population of minority women

Physical activity has been, and remains, a significant public health issue. Thus, increasing physical activity has been identified as a top priority according to Healthy People 2010. Various behavioral variables have been associated with participation in physical activity, including the Type A behavior pattern (TABP). This study was a secondary data analysis of the Women On The Move pilot study data and examined the relationship between Type A behavior with physical activity. The study population consisted of fifty-six (56) adult minority women 40 years of age and above. The Thurstone Activity Scale was adapted for use in this study to measure TABP. Physical activity behavior was measured using an accelerometer (Computer Science Application, [CSA]) and a physical activity diary. All study questions were examined using multiple linear regression analysis. In all analyses age, household income, and level of education were entered as covariates. The results found no association with TABP and exercise or physical activity. More research involving a larger, more active study population is recommended in order to more precisely determine the relationship of TABP and physical activity. ^

Dietary intake patterns and relationships to polybrominated diphenyl ether (PBDE) and phthalate body burden

Polybrominated diphenyl ethers (PBDEs) and phthalates are chemicals of concern because of high levels measured in people and the environment as well as the demonstrated toxicity in animal studies and limited epidemiological studies. Exposure to these chemicals has been associated with a range of toxicological outcomes, including developmental effects, behavioral changes, endocrine disruption, effects on sexual health, and cancer. Previous research has shown that both of these classes of chemicals contaminate food in the United States and worldwide. However, how large a role diet plays in exposure to these chemicals is currently unknown. To address this question, an exploratory analysis of data collected as part of the 2003-04 National Health and Nutrition Examination Survey (NHANES) was conducted. Associations between dietary intake (assessed by 24-hour dietary recalls) for a range of food types (meat, poultry, fish, and dairy) and levels PBDEs and phthalate metabolites were analyzed using multiple linear regression modeling. Levels of individual PBDE congeners 28, 47, 99, 100 as well as total PBDEs were found to be significantly associated with the consumption of poultry. Metabolites of di-(2-ethylhexyl) phthalate (DEHP) were found to be associated with the consumption of poultry, as well as with an increased consumption of fat of animal origin. These results, combined with results from previous studies, suggest that diet is an important route of intake for both PBDEs and phthalates. Further research needs to be conducted to determine the sources of food contamination with these toxic chemicals as well as to describe the levels of contamination of US food in a large, representative sample.^

Evidence of reliability and validity of IPAQ for Mexican-American adults

Physical activity is a key component of life-style modification process which helps to reduce the risk of developing chronic diseases. It is important to have accurate estimates of physical activity to identify sedentary populations where interventions might be helpful. The International Physical Activity Questionnaire (IPAQ) short version has been used to estimate physical activity in diverse populations. However, there is little literature depicting the use of the IPAQ short version in Mexican America population. This study addressed the predictive validity and test-retest reliability of the IPAQ short version in Mexican American adults. The analysis was performed on 97 participants enrolled in the Cameron County Hispanic Cohort. Individuals selected in this study were 18 years of age or older. The predictive validity was evaluated by studying the relationship between physical activity and biomarkers known to be correlated with physical activity, namely, TNF-α, Adiponectin, and HDL. Multiple linear regression analysis was performed to delineate predictive validity. To assess test-retest reliability, two IPAQ-short last seven days questionnaires were interviewer administered to the participants on the same day, approximately two hours apart. Test-Retest reliability of IPAQ was estimated by performing intraclass correlations between the readings at two different time periods. The study showed that the IPAQ – short version used in the above study had acceptable test-retest reliability in the Mexican American population. This study showed that the IPAQ – short version did not have acceptable predictive validity when looking at physical activity and TNF-α, Adiponectin, and HDL in this sample.^

Low birthweight and the risk of developing subsequent high blood pressure and/or dyslipidemia in childhood

The association between birthweight and blood pressure (BP), and birthweight and serum lipid concentrations at age 7 through 11 years was examined in 1446 black and white children. The prevalence ratio (with 95% confidence interval) for being in the race-, sex- and age-specific upper decile of diastolic BP in children born with low birthweight (LBW, $<$2500 grams) versus children with birthweight $\geq$2500 grams was for black boys, 2.66 (1.24-5.70). In the other race-sex groups for diastolic BP, and in all race-sex groups for systolic BP this ratio did not differ from one. Among white boys with LBW, but not in the other race-sex groups, higher than expected percentages of subjects were in the highest decile group of triglyceride concentrations (0.01 $<$ p $<$ 0.05). The prevalence ratio was 2.42 (1.19-4.91). When prematures were excluded only more than expected white girls with LBW were in the highest decile group of triglyceride concentrations. The prevalence ratio was 3.23 (1.16-9.00). Prevalence ratios for triglyceride concentrations in black boys and girls, and for LDL/HDL-C ratio, cholesterol and VLDL-C concentrations in all race-sex groups were not different from one in analyses including and in those excluding prematures. Mean triglyceride concentrations stratified by tertiles of Quetelet Index, race and sex showed a strongly positive association between triglyceride concentrations and Quetelet Index, and in the upper tertile of the Quetelet Index an association between LBW and raised triglyceride concentrations. Multiple linear regression analyses showed that after adjusting for sex, race and age present Quetelet Index (p $<$ 0.001) is a much stronger predictor of systolic and diastolic BP, and also of LDL-C/HDL-C ratio and triglyceride concentrations in this age group than birthweight (p $>$ 0.05). Thus, an association between LBW and subsequent risk for elevated BP was confirmed for diastolic BP in black boys, but not for the other race-sex groups, and not for systolic BP in any group. This is the first study finding an association between LBW and elevated triglyceride concentrations in boys (white and black) and girls (white). A follow-up study to assess whether the findings can be confirmed at adult age is recommended. ^

The role of serotonin in depression and clotting in the coronary artery disease population

Background: The mechanisms underlying the relationship between depression and acute coronary syndrome (ACS) remain unclear. Platelet serotonin has been associated with both depression and coronary artery disease in stable outpatients. Understanding the association between depression and platelet serotonin, during ACS, may explain some of the acute cardiovascular events seen in some individuals with depression. ^ Objectives: This study was designed to evaluate whether levels of platelet serotonin, during ACS, differ between individuals who screen positive for depression and individuals who screen negative for depression and to determine if a dose-response relationship exists between depressive symptoms and platelet serotonin levels. ^ Methods: In this cross-sectional study, data was collected on 51 patients hospitalized for ACS. Multiple linear regression models were used to determine if a relationship exists between depression and platelet serotonin levels. ^ Results: Of the 51 ACS patients, 24 screened positive for depression and 27 screened negative for depression. Platelet serotonin levels were not significantly different between the depressed group (942.10 ± 461.3) and the non-depressed group (1192.41 ± 764.3) (p= .293 and β= -4.093) and a dose-response relationship between depressive symptoms and platelet serotonin levels was not found (p= .250 and β= -.254). ^ Discussion: In this study, a relationship between depression and platelet serotonin levels was not found. Future research should focus on gaining a better understanding of the variables that may influence platelet serotonin levels in the ACS population. ^

Identification of genetic variants that influence atherosclerosis in young persons

Atherosclerosis is widely accepted as a complex genetic phenotype and is the usual cause of cardiovascular disease, the world’s leading killer. Genetic factors have been proven to be important risk contributors for atherosclerosis and much work has been done to identify promising candidates that might play a role in the development of atherosclerosis. It is well known that many independent replications are needed to unequivocally establish a valid genotype-phenotype association across different populations before the findings are extended to clinical settings and to the expensive follow-up studies designed to identify causal genetic variants. Aiming to replicate the association with atherosclerosis in the Pathobiological Determinants of Atherosclerosis in Youth (PDAY) study, we assessed the relationship of 32 atherosclerosis candidate SNPs to atherosclerosis in the PDAY cohort, consisting of AA and EA young people aged 15-34 years who died of non-medical causes. Two association studies, a whole sample study and a 1:1 matched case control study were performed by use of multiple linear regression and logistic regression analyses, respectively. For the whole sample association study, 32 SNPs among 2,650 individuals (1,369 AA and 1,281 EA) were tested for the association with six early atherosclerosis phenotypes: abdominal aorta fatty streaks, abdominal aorta raised lesions, right coronary artery fatty streaks, right coronary artery raised lesions, thoracic aorta fatty streaks, and thoracic aorta raised lesions. For the matched case-control association study, 337 case-control paired samples were included; cases were chosen with the highest total raised lesion scores from the studied population, while controls were randomly selected from individuals that had no raised lesions and matched to cases by age, gender and race. Sixteen SNPs in 13 genes were found to be significantly associated with atherosclerosis in at least one of the PDAY association studies. Among these 16 findings: eight SNPs (rs9579646, rs6053733, rs3849150, rs10499903, rs2148079, rs5073691, rs10116277, and rs17228212) successfully replicated previous results, six SNPs (rs17222814, rs10811661, rs7028570, rs7291467, rs16996148 and rs10401969) were reported as new findings exclusive to our study, the last two of the 16 SNPs, rs501120 and rs6922269, showed either intriguing or conflicting result. SNP rs17222814 in ALOX5AP and SNP rs3849150 in LRRC18 were consistently associated with atherosclerosis in both prior and the two PDAY association studies. SNP rs3849150 was also identified to be highly correlated with a non-synonymous coding SNP, rs17772611, which may damage the protein (polyphen score = 0.996), suggesting that SNP rs17772611 may be the causal functional variant.^ In conclusion, our study added more support for the association of these candidate genes with atherosclerosis. SNPs rs3849150 and rs17772611 of LRRC18, as well as SNP rs17222814 of ALOX5AP, were the most significant findings from our study, and may be ranked among the best for further study.^

A comparison of worker risk of injury while working on fully automated side loaders and other residential collection trucks at a large solid waste collection company

The study aim was to determine whether using automated side loader (ASL) trucks in higher proportions compared to other types of trucks for residential waste collection results in lower injury rates (from all causes). The primary hypothesis was that the risk of injury to workers was lower for those who work with ASL trucks than for workers who work with other types of trucks used in residential waste collection. To test this hypothesis, data were collected from one of the nation’s largest companies in the solid waste management industry. Different local operating units (i.e. facilities) in the company used different types of trucks to varying degrees, which created a special opportunity to examine refuse collection injuries and illnesses and the risk reduction potential of ASL trucks.^ The study design was ecological and analyzed end-of-year data provided by the company for calendar year 2007. During 2007, there were a total of 345 facilities which provided residential services. Each facility represented one observation.^ The dependent variable – injury and illness rate, was defined as a facility’s total case incidence rate (TCIR) recorded in accordance with federal OSHA requirements for the year 2007. The TCIR is the rate of total recordable injury and illness cases per 100 full-time workers. The independent variable, percent of ASL trucks, was calculated by dividing the number of ASL trucks by the total number of residential trucks at each facility.^ Multiple linear regression models were estimated for the impact of the percent of ASL trucks on TCIR per facility. Adjusted analyses included three covariates: median number of hours worked per week for residential workers; median number of months of work experience for residential workers; and median age of residential workers. All analyses were performed with the statistical software, Stata IC (version 11.0).^ The analyses included three approaches to classifying exposure, percent of ASL trucks. The first approach included two levels of exposure: (1) 0% and (2) >0 - <100%. The second approach included three levels of exposure: (1) 0%, (2) ≥ 1 - < 100%, and (3) 100%. The third approach included six levels of exposure to improve detection of a dose-response relationship: (1) 0%, (2) 1 to <25%, (3) 25 to <50%, (4) 50 to <75%, (5) 75 to <100%, and (6) 100%. None of the relationships between injury and illness rate and percent ASL trucks exposure levels was statistically significant (i.e., p<0.05), even after adjustment for all three covariates.^ In summary, the present study shows that there is some risk reduction impact of ASL trucks but not statistically significant. The covariates demonstrated a varied yet more modest impact on the injury and illness rate but again, none of the relationships between injury and illness rate and the covariates were statistically significant (i.e., p<0.05). However, as an ecological study, the present study also has the limitations inherent in such designs and warrants replication in an individual level cohort design. Any stronger conclusions are not suggested.^

Postoperative renal function preservation with nonischemic femoral arterial cannulation for thoracoabdominal aortic repair.

BACKGROUND: Renal failure after thoracoabdominal aortic repair is a significant clinical problem. Distal aortic perfusion for organ and spinal cord protection requires cannulation of the left femoral artery. In 2006, we reported the finding that direct cannulation led to leg ischemia in some patients and was associated with increased renal failure. After this finding, we modified our perfusion technique to eliminate leg ischemia from cannulation. In this article, we present the effects of this change on postoperative renal function. METHODS: Between February 1991 and July 2008, we repaired 1464 thoracoabdominal aortic aneurysms. Distal aortic perfusion was used in 1088, and these were studied. Median patient age was 68 years, and 378 (35%) were women. In September 2006, we began to adopt a sidearm femoral cannulation technique that provides distal aortic perfusion while maintaining downstream flow to the leg. This was used in 167 patients (15%). We measured the joint effects of preoperative glomerular filtration rate (GFR) and cannulation technique on the highest postoperative creatinine level, postoperative renal failure, and death. Analysis was by multiple linear or logistic regression with interaction. RESULTS: The preoperative GFR was the strongest predictor of postoperative renal dysfunction and death. No significant main effects of sidearm cannulation were noted. For peak creatinine level and postoperative renal failure, however, strong interactions between preoperative GFR and sidearm cannulation were present, resulting in reductions of postoperative renal complications of 15% to 20% when GFR was <60 mL>/min/1.73 m(2). For normal GFR, the effect was negated or even reversed at very high levels of GFR. Mortality, although not significantly affected by sidearm cannulation, showed a similar trend to the renal outcomes. CONCLUSION: Use of sidearm cannulation is associated with a clinically important and highly statistically significant reduction in postoperative renal complications in patients with a low GFR. Reduced renal effect of skeletal muscle ischemia is the proposed mechanism. Effects among patients with good preoperative renal function are less clear. A randomized trial is needed.

Understanding causes of hospitalization and access to care among newly diagnosed HIV patients in Houston, TX

More than a quarter of patients with HIV in the United States are diagnosed in hospital settings most often with advanced HIV related conditions.(1) There has been little research done on the causes of hospitalization when the patients are first diagnosed with HIV. The aim of this study was to determine if the patients are hospitalized due to an HIV related cause or due to some other co-morbidity. Reduced access to care could be one possible reason why patients are diagnosed late in the course of the disease. This study compared the access to care of patients diagnosed with HIV in hospital and outpatient setting. The data used for the study was a part of the ongoing study “Attitudes and Beliefs and Steps of HIV Care”. The participants in the study were newly diagnosed with HIV and recruited from both inpatient and outpatient settings. The primary and the secondary diagnoses from hospital discharge reports were extracted and a primary reason for hospitalization was ascertained. These were classified as HIV-related, other infectious causes, non–infectious causes, other systemic causes, and miscellaneous causes. Access to care was determined by a score based on responses to a set of questions derived from the HIV Cost and Services Utilization Study (HCSUS) on a 6 point scale. The mean score of the hospitalized patients and mean score of the patients diagnosed in an outpatient setting was compared. We used multiple linear regressions to compare mean differences in the two groups after adjusting for age, sex, race, household income educational level and health insurance at the time of diagnosis. There were 185 participants in the study, including 78 who were diagnosed in hospital settings and 107 who were diagnosed in outpatient settings. We found that HIV-related conditions were the leading cause of hospitalization, accounting for 60% of admissions, followed by non-infectious causes (20%) and then other infectious causes (17%). The inpatient diagnosed group did not have greater perceived access-to-care as compared to the outpatient group. Regression analysis demonstrated a statistically significant improvement in access-to-care with advancing education level (p=0.04) and with better health insurance (p=0.004). HIV-related causes account for many hospitalizations when patients are first diagnosed with HIV. Many of these HIV-related hospitalizations could have been prevented if patients were diagnosed early and linked to medical care. Programs to increase HIV awareness need to be an integral part of activities aimed at control of spread of HIV in the community. Routine testing for HIV infection to promote early HIV diagnosis can prevent significant morbidity and mortality.^

Statistical and methodological challenges for disaster preparedness and medical needs assessment in Rio Grande Valley of Texas

In recent years, disaster preparedness through assessment of medical and special needs persons (MSNP) has taken a center place in public eye in effect of frequent natural disasters such as hurricanes, storm surge or tsunami due to climate change and increased human activity on our planet. Statistical methods complex survey design and analysis have equally gained significance as a consequence. However, there exist many challenges still, to infer such assessments over the target population for policy level advocacy and implementation. ^ Objective. This study discusses the use of some of the statistical methods for disaster preparedness and medical needs assessment to facilitate local and state governments for its policy level decision making and logistic support to avoid any loss of life and property in future calamities. ^ Methods. In order to obtain precise and unbiased estimates for Medical Special Needs Persons (MSNP) and disaster preparedness for evacuation in Rio Grande Valley (RGV) of Texas, a stratified and cluster-randomized multi-stage sampling design was implemented. US School of Public Health, Brownsville surveyed 3088 households in three counties namely Cameron, Hidalgo, and Willacy. Multiple statistical methods were implemented and estimates were obtained taking into count probability of selection and clustering effects. Statistical methods for data analysis discussed were Multivariate Linear Regression (MLR), Survey Linear Regression (Svy-Reg), Generalized Estimation Equation (GEE) and Multilevel Mixed Models (MLM) all with and without sampling weights. ^ Results. Estimated population for RGV was 1,146,796. There were 51.5% female, 90% Hispanic, 73% married, 56% unemployed and 37% with their personal transport. 40% people attained education up to elementary school, another 42% reaching high school and only 18% went to college. Median household income is less than $15,000/year. MSNP estimated to be 44,196 (3.98%) [95% CI: 39,029; 51,123]. All statistical models are in concordance with MSNP estimates ranging from 44,000 to 48,000. MSNP estimates for statistical methods are: MLR (47,707; 95% CI: 42,462; 52,999), MLR with weights (45,882; 95% CI: 39,792; 51,972), Bootstrap Regression (47,730; 95% CI: 41,629; 53,785), GEE (47,649; 95% CI: 41,629; 53,670), GEE with weights (45,076; 95% CI: 39,029; 51,123), Svy-Reg (44,196; 95% CI: 40,004; 48,390) and MLM (46,513; 95% CI: 39,869; 53,157). ^ Conclusion. RGV is a flood zone, most susceptible to hurricanes and other natural disasters. People in the region are mostly Hispanic, under-educated with least income levels in the U.S. In case of any disaster people in large are incapacitated with only 37% have their personal transport to take care of MSNP. Local and state government’s intervention in terms of planning, preparation and support for evacuation is necessary in any such disaster to avoid loss of precious human life. ^ Key words: Complex Surveys, statistical methods, multilevel models, cluster randomized, sampling weights, raking, survey regression, generalized estimation equations (GEE), random effects, Intracluster correlation coefficient (ICC).^

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. ^

FEMALE SEXUAL MATURATION AND BLOOD PRESSURE (SECONDARY-SEX CHARACTERISTICS, GROWTH, DEVELOPMENT)

This study described the relationship of sexual maturation and blood pressure in a sample (n = 361) of white females, ages seven through 18, attending public schools in a defined area of Central Texas during October through December, 1984. Other correlates of blood pressure were also described for this sample.^ A survey was performed to obtain the data on height, weight, body mass, pulse rate, upper arm circumference and length, and blood pressure. Each subject self-assessed her secondary sex characteristics (breast and pubic hair) according to drawings of the Tanner stages of maturation. The subjects were interviewed to obtain data on personal health habits and menstrual status. Student age, ethnic group and place of residence were abstracted from school records. Parents or guardians of the subjects responded to a questionnaire pertaining to parental and subject health history and parents' occupation and educational attainment.^ In the simple linear regression analysis, sexual maturation and variables of body size were significantly (p < 0.001) and positively associated with systolic and fourth- and fifth-phase diastolic blood pressure. The demographic and socioeconomic variables were not sufficiently variant in this population to have differential effects on the relation between blood pressure and maturation. Stepwise multiple regression was used to assess the contribution of sexual maturation to the variance of blood pressure after accounting for the variables of body size. Sexual maturation (breast stage) along with weight, height and body mass remained in the multiple regression models for fourth- and fifth-phase diastolic blood pressure. Only height and body mass remained in the regression model for systolic blood pressure; sexual maturation did not contribute more to the explanation of the systolic blood pressure variance.^ The association of sexual maturation with blood pressure level was established in this sample of young white females. More research is needed first, to determine if this relationship prevails in other populations of young females, and second, to determine the relationship of sexual maturation sequence and change with the change of blood pressure during childhood and adolescence. ^