Robust effect sizes and their confidence intervals for group difference between trajectories in hierarchical linear growth model

Hierarchical linear growth model (HLGM), as a flexible and powerful analytic method, has played an increased important role in psychology, public health and medical sciences in recent decades. Mostly, researchers who conduct HLGM are interested in the treatment effect on individual trajectories, which can be indicated by the cross-level interaction effects. However, the statistical hypothesis test for the effect of cross-level interaction in HLGM only show us whether there is a significant group difference in the average rate of change, rate of acceleration or higher polynomial effect; it fails to convey information about the magnitude of the difference between the group trajectories at specific time point. Thus, reporting and interpreting effect sizes have been increased emphases in HLGM in recent years, due to the limitations and increased criticisms for statistical hypothesis testing. However, most researchers fail to report these model-implied effect sizes for group trajectories comparison and their corresponding confidence intervals in HLGM analysis, since lack of appropriate and standard functions to estimate effect sizes associated with the model-implied difference between grouping trajectories in HLGM, and also lack of computing packages in the popular statistical software to automatically calculate them. ^ The present project is the first to establish the appropriate computing functions to assess the standard difference between grouping trajectories in HLGM. We proposed the two functions to estimate effect sizes on model-based grouping trajectories difference at specific time, we also suggested the robust effect sizes to reduce the bias of estimated effect sizes. Then, we applied the proposed functions to estimate the population effect sizes (d ) and robust effect sizes (du) on the cross-level interaction in HLGM by using the three simulated datasets, and also we compared the three methods of constructing confidence intervals around d and du recommended the best one for application. At the end, we constructed 95% confidence intervals with the suitable method for the effect sizes what we obtained with the three simulated datasets. ^ The effect sizes between grouping trajectories for the three simulated longitudinal datasets indicated that even though the statistical hypothesis test shows no significant difference between grouping trajectories, effect sizes between these grouping trajectories can still be large at some time points. Therefore, effect sizes between grouping trajectories in HLGM analysis provide us additional and meaningful information to assess group effect on individual trajectories. In addition, we also compared the three methods to construct 95% confident intervals around corresponding effect sizes in this project, which handled with the uncertainty of effect sizes to population parameter. We suggested the noncentral t-distribution based method when the assumptions held, and the bootstrap bias-corrected and accelerated method when the assumptions are not met.^

LONGITUDINAL GROWTH PARAMETERS AND THEIR ECOLOGICAL DETERMINANTS (SEASONALITY)

The growth patterns of weight from birth through the first twelve months of life among rural Taiwanese infants were investigated with the following objectives: (i) compare each of the parameters of the Count model estimated for infants who were nutritionally at risk with those for a reference population from the United States; and (ii) within the Taiwanese infants, account for the variance in the growth patterns in the first and second six months of life on the basis of selected ecological factors.^ The significance between group differences were observed in the patterns of the weight growth in both linear growth and in the timing and the direction of velocity changes. A significant decline in growth velocity was observed among Taiwanese infants at about the fourth month of life. The decline is in keeping with a recent proposal made by J. C. Waterlow regarding the timing of change in growth velocity among nutritionally at risk populations in developing countries. The growth course of a nutritionally at risk infant during the first three months is apparently protected by the nurturance of the mother and innate biological properties of the infant.^ A highly significant portion of the growth variance in the second six months of life was accounted for by exogenous factors and biological factors related to the infant. Conversely, none of the growth variance in the first six months of life was accounted for by predictor variables. The most potent determinant of growth in the second six months of life was seasonality which represents a multiple environmental event.^ The model parameters estimated from the Count model represent different aspect of physical growth; yet the correlation coefficients between parameters b and c are high (r > .80). Clearly, the biological interpretation of the model parameters requires analysis of the whole function in the specific context of a given age period. ^

RNAi reduces expression and intracellular retention of mutant cartilage oligomeric matrix protein.

Mutations in cartilage oligomeric matrix protein (COMP), a large extracellular glycoprotein expressed in musculoskeletal tissues, cause two skeletal dysplasias, pseudoachondroplasia and multiple epiphyseal dysplasia. These mutations lead to massive intracellular retention of COMP, chondrocyte death and loss of growth plate chondrocytes that are necessary for linear growth. In contrast, COMP null mice have only minor growth plate abnormalities, normal growth and longevity. This suggests that reducing mutant and wild-type COMP expression in chondrocytes may prevent the toxic cellular phenotype causing the skeletal dysplasias. We tested this hypothesis using RNA interference to reduce steady state levels of COMP mRNA. A panel of shRNAs directed against COMP was tested. One shRNA (3B) reduced endogenous and recombinant COMP mRNA dramatically, regardless of expression levels. The activity of the shRNA against COMP mRNA was maintained for up to 10 weeks. We also demonstrate that this treatment reduced ER stress. Moreover, we show that reducing steady state levels of COMP mRNA alleviates intracellular retention of other extracellular matrix proteins associated with the pseudoachondroplasia cellular pathology. These findings are a proof of principle and the foundation for the development of a therapeutic intervention based on reduction of COMP expression.

The use of second-generation antipsychotics and the changes in physical growth in children and adolescents with perinatally acquired HIV.

Second-generation antipsychotics (SGAs) are increasingly prescribed to treat psychiatric symptoms in pediatric patients infected with HIV. We examined the relationship between prescribed SGAs and physical growth in a cohort of youth with perinatally acquired HIV-1 infection. Pediatric AIDS Clinical Trials Group (PACTG), Protocol 219C (P219C), a multicenter, longitudinal observational study of children and adolescents perinatally exposed to HIV, was conducted from September 2000 until May 2007. The analysis included P219C participants who were perinatally HIV-infected, 3-18 years old, prescribed first SGA for at least 1 month, and had available baseline data prior to starting first SGA. Each participant prescribed an SGA was matched (based on gender, age, Tanner stage, baseline body mass index [BMI] z score) with 1-3 controls without antipsychotic prescriptions. The main outcomes were short-term (approximately 6 months) and long-term (approximately 2 years) changes in BMI z scores from baseline. There were 236 participants in the short-term and 198 in the long-term analysis. In linear regression models, youth with SGA prescriptions had increased BMI z scores relative to youth without antipsychotic prescriptions, for all SGAs (short-term increase = 0.192, p = 0.003; long-term increase = 0.350, p < 0.001), and for risperidone alone (short-term = 0.239, p = 0.002; long-term = 0.360, p = 0.001). Participants receiving both protease inhibitors (PIs) and SGAs showed especially large increases. These findings suggest that growth should be carefully monitored in youth with perinatally acquired HIV who are prescribed SGAs. Future research should investigate the interaction between PIs and SGAs in children and adolescents with perinatally acquired HIV infection.

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.

Left ventricular growth from age 8 to 18 and its anthropometric determinants: Longitudinal results from Project Heartbeat!

Left ventricular mass (LVM) is a strong predictor of cardiovascular disease (CVD) in adults. However, normal growth of LVM in healthy children is not well understood, and previous results on independent effects of body size and body fatness on LVM have been inconsistent. The purpose of this study was (1) to establish the normal growth curve of LVM from age 8 to age 18, and evaluate the determinants of change in LVM with age, and (2) to assess the independent effects of body size and body fatness on LVM.^ In Project HeartBeat!, 678 healthy children aged 8, 11 and 14 years at baseline were enrolled and examined at 4-monthly intervals for up to 4 years. A synthetic cohort with continuous observations from age 8 to 18 years was constructed. A total of 4608 LVM measurements was made from M-mode echocardiography. The multilevel linear model was used for analysis.^ Sex-specific trajectories of normal growth of LVM from age 8 to 18 was displayed. On average, LVM was 15 g higher in males than females. Average LVM increased linearly in males from 78 g at age 8 to 145 g at age 18. For females, the trajectory was curvilinear, nearly constant after age 14. No significant racial differences were found. After adjustment for the effects of body size and body fatness, average LVM decreased slightly from age 8 to 18, and sex differences in changes of LVM remained constant.^ The impact of body size on LVM was examined by adding to a basic LVM-sex-age model one of 9 body size indicators. The impact of body fatness was tested by further introducing into each of the 9 LVM models (with one or another of the body size indicators) one of 4 body fatness indicators, yielding 36 models with different body size and body fatness combinations. The results indicated that effects of body size on LVM can be distinguished between fat-free body mass and fat body mass, both being independent, positive predictors. The former is the stronger determinant. When a non-fat-free body size indicator is used as predictor, the estimated residual effect of body fatness on LVM becomes negative. ^

Physical activity, body composition, exogenous estrogen use and their association with insulin-like growth factors

Obesity and physical inactivity are modifiable risk factors that are associated with several health issues; they are major factors in up to 30% of major cancers. Elevated levels of circulating insulin-like growth factor-I (IGF-I) have been associated with high body composition measurements and high cancer risk; exogenous estrogen use is associated with low circulating IGF-I levels and high cancer risk. The relationship between physical activity and circulating IGF levels is complex and findings of previous studies of their relationship remain inconsistent; however, these studies included vague definitions of physical activity. In this study, we used cross-sectional data from the Women's Health Initiative to determine the relationship between specific measures of physical activity (e.g., intensity, duration, and frequency) and circulating IGF-I levels, accounting for exogenous estrogen use and body composition. These data were collected from women enrolled at Women's Health Initiative clinical centers at Baylor College of Medicine and Wake Forest University School of Medicine. Multivariate linear regression analysis showed that circulating IGF-I and IGF-binding protein (BP) 3 levels were positively associated with frequency, duration, and intensity of physical activity. Circulating IGF-I levels and the molar IGF-I:IGF-BP3 ratio were significantly associated with frequency of walking, whereas circulating IGF-BP3 levels were significantly associated with strenuous physical activity, suggesting that different aspects of physical activity and their effects on fitness affect members of the IGF family differently. The results from our study support the recommendation of a regular exercise routine, particularly that of strenuous intensity, for postmenopausal women as a means to prevention of cancer.^

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. ^

Analysis of life expectancy using linear and nonlinear models

Life expectancy has consistently increased over the last 150 years due to improvements in nutrition, medicine, and public health. Several studies found that in many developed countries, life expectancy continued to rise following a nearly linear trend, which was contrary to a common belief that the rate of improvement in life expectancy would decelerate and was fit with an S-shaped curve. Using samples of countries that exhibited a wide range of economic development levels, we explored the change in life expectancy over time by employing both nonlinear and linear models. We then observed if there were any significant differences in estimates between linear models, assuming an auto-correlated error structure. When data did not have a sigmoidal shape, nonlinear growth models sometimes failed to provide meaningful parameter estimates. The existence of an inflection point and asymptotes in the growth models made them inflexible with life expectancy data. In linear models, there was no significant difference in the life expectancy growth rate and future estimates between ordinary least squares (OLS) and generalized least squares (GLS). However, the generalized least squares model was more robust because the data involved time-series variables and residuals were positively correlated. ^