Testing for genetic association with constrained models using triads.

It has been shown that it is preferable to use a robust model that incorporated constraints on the genotype relative risk rather than rely on a model that assumes the disease operates in a recessive or dominant fashion. Previous methods are applicable to case-control studies, but not to family based studies of case children along with their parents (triads). We show here how to implement analogous constraints while analyzing triad data. The likelihood, conditional on the parents genotype, is maximized over the appropriately constrained parameter space. The asymptotic distribution for the maximized likelihood ratio statistic is found and used to estimate the null distribution of the test statistics. The properties of several methods of testing for association are compared by simulation. The constrained method provides higher power across a wide range of genetic models with little cost when compared to methods that restrict to a dominant, recessive, or multiplicative model, or make no modeling restriction. The methods are applied to two SNPs on the methylenetetrahydrofolate reductase (MTHFR) gene with neural tube defect (NTD) triads.

Identifying pre-post chemotherapy differences in gene expression in breast tumours: a statistical method appropriate for this aim.

Although widely used for the analysis of gene expression microarray data, cluster analysis may not be the most appropriate statistical technique for some study aims. We demonstrate this by considering a previous analysis of microarray data obtained on breast tumour specimens, many of which were paired specimens from the same patient before and after chemotherapy. Reanalysing the data using statistical methods that appropriately utilise the paired differences for identification of differentially expressed genes, we find 17 genes that we can confidently identify as more expressed after chemotherapy than before. These findings were not reported by the original investigators who analysed the data using cluster analysis techniques.

Risks of hypertensive disorders in the second pregnancy.

This study examined the incidence of and risk factors for recurrent and newly developed hypertensive disorders in the second pregnancy. We analysed data on 1641 women who had both the first and second pregnancies in the Collaborative Perinatal Project, a large prospective cohort study at 12 hospitals in the US. Nineteen per cent [95% CI 14%, 24%] of women who had gestational hypertension in the first pregnancy, 32% [95% CI 17%, 48%] of those with pre-eclampsia and 46% [95% CI 32%, 60%] of patients with gestational hypertension or pre-eclampsia superimposed on chronic hypertension, had recurrent hypertensive disorders in the second pregnancy. Risk factors for recurrence included history of chronic hypertension and thromboembolism, early onset of hypertension in the first pregnancy or persistent hypertension after 5 weeks postpartum and high baseline blood pressure in the second pregnancy. Women with a normotensive first pregnancy but a severe small-for-gestational-age birth had twice the risk of developing hypertension in the second pregnancy (RR = 2.1, 95% CI, 1.1, 4.0). In summary, hypertensive disorders have a 20--50% recurrence rate in the second pregnancy. The earlier the onset of hypertension in the first pregnancy, the higher the overall recurrence rate. Intrauterine growth restriction of the first birth is an independent risk factor for hypertension in the second pregnancy.

Unbiased confidence intervals for the odds ratio of two independent binomial samples with application to case-control data.

The problem of confidence interval construction for the odds ratio of two independent binomial samples is considered. Two methods of eliminating the nuisance parameter from the exact likelihood, conditioning and maximization, are described. A conditionally exact tail method exists by putting together upper and lower bounds. A shorter interval can be obtained by simultaneous consideration of both tails. We present here new methods that extend the tail and simultaneous approaches to the maximized likelihood. The methods are unbiased and applicable to case-control data, for which the odds ratio is important. The confidence interval procedures are compared unconditionally for small sample sizes in terms of their expected length and coverage probability. A Bayesian confidence interval method and a large-sample chi2 procedure are included in the comparisons.

Effect of growth hormone treatment on testicular function, puberty, and adrenarche in boys with non-growth hormone-deficient short stature: a randomized, double-blind, placebo-controlled trial.

OBJECTIVE: To evaluate the effect of growth hormone (GH) therapy on pubertal onset, pubertal pace, adult testicular function, and adrenarche in boys with non-GH-deficient short stature. STUDY DESIGN: Randomized, double-blind, placebo-controlled trial. GH (0.074 mg/kg, subcutaneously, 3 times per week) or placebo treatment was initiated in prepubertal or early pubertal boys and continued until near final height was reached (n = 49). Statistical significance was assessed by survival analysis, repeated-measures analysis of variance, and Student t test. RESULTS: GH therapy did not affect the age at pubertal onset, defined either by testicular volume >4 mL or by testosterone concentration >1.0 nmol/L (30 ng/dL). GH treatment also did not affect the pace of puberty, defined either by the rate of change in testicular volume or testosterone concentration during the 4 years after pubertal onset. In boys followed up to age > or =16 years during the study, there were no significant differences in final testicular volume or in plasma testosterone, luteinizing hormone, or follicle-stimulating hormone concentrations. The pace of adrenarche, assessed by change in dehydroepiandrosterone sulfate levels over time, also did not differ significantly between the GH and placebo groups. CONCLUSION: Our findings suggest that GH treatment does not cause testicular damage, alter the onset or pace of puberty, or alter the pace of adrenarche in boys with non-GH-deficient short stature.

Stature, weight, and body mass among young US children born at term with appropriate birth weights.

OBJECTIVE: To describe weight, stature, and body mass index (BMI) changes occurring before the age of 7 years, which may influence the prevalence of overweight in adolescence and adulthood. METHODS: Regression models predicting height and weight at ages 2 months to 6. 75 years were based on the third National Health and Nutrition Examination Survey. Birth certificate data were used to adjust ethnic-specific models for birth weight for gestational age. RESULTS: Attained height is higher for non-Hispanic black children than for either non-Hispanic white or Mexican American children (P 85th percentile than either non-Hispanic white or black children (boys = 25.6%, SE = 2.7 compared with 14.1%, SE = 1.7 and 16.5%, SE = 1.7, respectively; girls = 21.9%, SE = 3.6 compared with 13.0%, SE = 1.7 and 13.7%, SE = 2.2, respectively). For non-Hispanic whites and Mexican Americans and for non-Hispanic black boys, BMI decreased slightly between ages 2 and 6.75 years; BMI for non-Hispanic black girls did not. CONCLUSION: Size differences before the age of 7 years may influence later ethnic-specific overweight prevalence, independent of prenatal influences.

Early infant feeding and growth status of US-born infants and children aged 4-71 mo: analyses from the third National Health and Nutrition Examination Survey, 1988-1994.

BACKGROUND: There is controversy over what growth references to use in evaluating breast-fed infants and concern about whether never-breast-fed infants are at risk of overweight in childhood. OBJECTIVE: The objective of this study was to determine whether infants who are exclusively breast-fed for 4 mo differ in average size from infants who are fed in other ways and whether such differences persist through age 5 y. DESIGN: Data from the third National Health and Nutrition Examination Survey (NHANES III) were linked to birth certificates of US-born infants and children. Feeding groups were defined on the basis of feeding patterns over the first 4 mo of life: exclusively breast-fed for 4 mo, partially breast-fed, breast-fed for <4 mo, and never breast-fed. Growth status, indexed as internally derived z scores (SD units) for weight, length (height), weight-for-length (height), midupper arm circumference, and triceps skinfold thickness, was compared among feeding groups. RESULTS: The final sample consisted of 5594 non-Hispanic white, non-Hispanic black, and Mexican American infants and children aged 4-71 mo. Of these, 21% were exclusively breast-fed for 4 mo, 10% were partially breast-fed, 24% were breast-fed for <4 mo, and 45% were never breast-fed. At 8-11 mo, infants who were exclusively breast-fed for4 mo had adjusted mean z scores for weight (-0.21; -0.2 kg), weight-for-length (-0.27), and midupper arm circumference (-0.15) that differed significantly from zero (P < 0. 05). By 12-23 mo, the differences had dissipated; there were no significant differences subsequent to 5 y. Triceps skinfold thickness was not related to early infant feeding. CONCLUSION: Infants who were exclusively breast-fed for 4 mo weighed less at 8-11 mo than did infants who were fed in other ways, but there were few other significant differences in growth status through age 5 y associated with early infant feeding.

Suppression and recovery of GH secretion after GH injection in non-GH deficient short children.

OBJECTIVE: To identify the effect of exogenous GH on endogenous GH secretion in 48 non-GH deficient short children participating in a placebo-controlled trial of GH therapy on final adult height. DESIGN: Night GH secretion (mean of levels every 20 min from 20.00 to 08.00 h) was evaluated at baseline, 6 months before starting placebo or GH (somatotropin, 0.222 mg/kg/ week, divided into 3 doses each week). At 6 months after starting injections, blood samples for GH were obtained hourly for 24 h after an injection, and every 20 min on each of the next two nights (with no additional placebo or GH injection). RESULTS: IGF-I levels in the treatment group were elevated at 12 and 24 h but not at 36 h compared to the placebo group. Mean GH levels in the placebo group did not vary significantly among the four sampling periods. In the treatment group, the mean serum GH rose to a supraphysiological peak at an average time of 4 h after injection. Subsequently, mean GH level was significantly suppressed compared to placebo on the second night following GH injection, but returned to normal by the third night. CONCLUSION: After 6 months of a thrice weekly GH treatment regimen in non-GH deficient short children, endogenous GH secretion was reduced from 24 to 36 h after injection compared to placebo and returned to control levels by 48 to 60 h after injection.

Approximating the power of Wilcoxon's rank-sum test against shift alternatives.

Three methods of approximating the power of Wilcoxon's rank-sum test against shift alternatives are studied. They are obtained by using a Gaussian assumption, Edgeworth expansion, or bootstrap. It is assumed that a historical data set is available to use in estimating the shape of the distribution. The methods are compared through simulation across several different distributional types. The results indicate that the bootstrap generally gives the most reliable approximation, however the Edgeworth expansion has the practical advantage that a lower bound on the power can be roughly approximated. The methods are illustrated on muscle strength data from patients with osteogenesis imperfecta. Published in 1999 by John Wiley & Sons, Ltd. This is US Government work and is in the public domain in the United States.

A comparison of one-sided methods to identify significant individual outcomes in a multiple outcome setting: stepwise tests or global tests with closed testing.

We compare two approaches to the identification of individual significant outcomes when a comparison of two groups involves multiple outcome variables. The approaches are all designed to control the familywise error rate (FWE) with any subset of the null hypothesis being true (in the strong sense). The first approach is initially to use a global test of the overall hypothesis that the groups are equivalent for all variables, followed by an application of the closed testing algorithm of Marcus, Peritz and Gabriel. The global tests considered here are ordinary least squares (OLS), generalized least squares (GLS), an approximation to a likelihood ratio test (ALR), and a new test based on an approximation to the most powerful similar test for simple alternatives. The second approach is that of stepwise testing, which tests the univariate hypotheses in a specific order with appropriate adjustment to the univariate p-values for multiplicity. The stepwise tests considered include both step-down and step-up tests of a general type, and likewise permutation tests that incorporate the dependence structure of the data. We illustrate the tests with two examples of birth outcomes: a comparison of cocaine-exposed new-borns to control new-borns on neurobehavioural and physical growth variables, and, in a separate study, a comparison of babies born to diabetic mothers and babies born to non-diabetic mothers on minor malformations. After describing the methods and analysing the birth outcome data, we use simulations on Gaussian data to provide guidelines for the use of these procedures in terms of power and computation.

Infectious disease mortality among infants in the United States, 1983 through 1987.

OBJECTIVE: The purpose of this study was to determine the relative importance of infectious disease as a cause of infant mortality in the United States and to identify characteristics at birth associated with subsequent infectious disease mortality. METHODS: Birth and infant death certificate data from the National Center for Health Statistics (NCHS) 1983 through 1987 Linked Birth/ Infant Death Data Sets were analyzed. RESULTS: Infection was the underlying cause of death for over 16000 infants, representing the fourth leading cause of mortality in this cohort. Almost 90% of infectious disease deaths during infancy were due to noncongenital infections, and the majority of these deaths occurred during the postneonatal period. Low birthweight, preterm birth, and male gender were independently associated with postneonatal mortality due to noncongenital infection. CONCLUSIONS: NCHS should revise its classification system for causes of infant mortality to incorporate an "Infectious Diseases" category. Future research should be directed toward clarifying the low birthweight-infectious disease mortality relationship and determining the degree to which infection-related infant deaths might be prevented by existing vaccines or improved access to health care.

Parametric and non-parametric tests for the overall comparison of several treatments to a control when treatment is expected to increase variability.

We consider the problem of making an overall comparison of several treatments to a control where experimental units are randomly assigned to either the 'control' group which receives no treatment or to one of k-1 'treatment' groups. We assume that the effect of the treatments is, if anything, a location shift possibly accompanied by an increase in scale relative to that of the control group. The ANOVA F test loses considerable power in such circumstances. A modification of the ANOVA F test has been proposed which uses the variance estimate from the controls in place of the usual pooled variance estimate. However, this modification has shortcomings when k exceeds two and the variances of the treatment groups are not inflated. We develop a combination procedure to avoid the pitfalls of the modified and usual F tests. We then propose parametric and non-parametric implementations of a likelihood ratio test that more efficiently incorporates the assumptions of this problem, yielding a test with a high power profile over a large range of normal alternatives. We use simulations to compare the power of the competing tests against several alternatives for normal and non-normal data.

A permutational step-up method of testing multiple outcomes.

This paper describes a permutational step-up multiple comparison procedure to adjust the p values from k related hypotheses. The method is applicable when two groups of subjects are being compared on each of k outcomes. It is related to the step-down method of Westfall and Young (1993, Resampling-Based Multiple Testing: Examples and Methods for P-Value Adjustment, Volume 1) and Troendle (1995, Journal of the American Statistical Association 90, 370-378) and is an alternative to the analytic step-up method of Dunnett and Tamhane (1992, Journal of the American Statistical Association 87, 162-170), which requires a specific distribution and correlation structure. By conditioning on the data observed, this permutational method avoids any specific distribution or correlation assumption. It is shown very generally that the method asymptotically controls the familywise probability of a type I error.

Control of familywise errors in multiple endpoint assessments via stepwise permutation tests.

We describe permutation based sequentially rejective multiple comparison procedures useful in multiple endpoint assessments. We used Monte Carlo methods to compare the power of these newly devised tests to that of tests due to Holm and Rom as well as to the classical Bonferroni method. We illustrate applications of the methods with analysis of visual field data collected from optic neuritis patients. We conclude that the new methods are particularly useful when there are many endpoints involved, the data are significantly correlated, and/or the distributional assumptions are questionable.

A note on testing the Hardy-Weinberg law across strata.

The problem of testing the Hardy-Weinberg law when the data are stratified in K strata is considered. Previous methods lose power when the departure from the law is irregular from stratum to stratum. Two methods based on the squared distance are proposed to overcome this problem. Simulations show that the new methods can have a dramatic improvement over the previous methods. The methods are applied to red cell glyoxalase genotype data from populations in India.

Development of a practical screening tool to identify preterm, low-birthweight neonates in Ethiopia.

Preterm, low-birthweight (LBW) newborn infants are at high risk of neonatal mortality and morbidity and need early referral for special paediatric care. In developing countries, birthweight and gestational age often cannot be measured and a practical screening tool based on surrogate neonatal body measurements to identify high-risk infants would be very useful. We studied a consecutive series of 843 singleton infants born at a referral hospital in Addis Ababa, Ethiopia. Gestational age, birthweight, and four body measurements (chest, head, and mid-arm circumferences and length) were accurately recorded. We randomly divided the series into equal-sized training and validation groups. In the training group, we used a recursive partitioning technique to develop a simple predictive algorithm--infants were classified as high risk if head circumference was 31 cm or less or if chest circumference was 30 cm or less, and were classified as low risk otherwise. When tested in the validation group, this algorithm had sensitivity, specificity, and negative predictive value for prediction of preterm and LBW births above 90%. Thus, neonatal body measurements can be combined into a pragmatic, accurate screening tool suitable for clinical use in developing countries.