Bootstrap Estimates Of Variance Research Articles

Health and oral health-related quality of life of children and adolescents with chronic kidney disease: a cross-sectional study.

The aim of this study was to evaluate if health and oral health status of children and adolescents with different stages of CKD are associated with their health-related quality of life (HRQoL), oral health-related quality of life (OHRQoL) and socioeconomic and demographic conditions. One hundred children and adolescents with CKD were age and gender matched to 100 individuals without CKD (mean age ± SD = 13.04 ± 2.57).Oral health was characterised by means of gingival bleeding index (GBI), plaque index (PI), the decayed, missing, and filled teeth(DMFT) index and the developmental enamel defect (DED) index. All children and adolescents answered two Peds QL® instruments (general and oral health scales). Comparing the mean scores of HRQoL and OHRQoL between groups, we observed that CKD group demonstrated worse perceptions when compared to non-CKD group. Multiple linear regression analysis with bootstrap estimation of variance (1000 replications) showed association between dental caries experience (p < 0.001), gingival inflammation (p < 0.001) and diagnosis of CKD (p = 0.027) with the OHRQoL and between physical and the emotional domain of HRQoL, when moderate/severe gingival inflammation and hypoplasia were present. The implementation of public policies that contemplate the early dental preventive intervention in CKD children and adolescents should occur aiming to improve their oral health, once oral manifestations can directly affect the aspects of the HRQoL and OHRQoL of these individuals.

Maternal serum uric acid levels and blood pressure during pregnancy: A community-based cohort study

ObjectiveStudies find both very low and high serum uric acid (UA) levels are related to oxidative stress and to conditions such as cardiovascular diseases and chronic kidney disease in the general population. Pregnancy studies have focused only on high maternal UA. In present study, we tested whether unusually high and low levels of maternal serum UA are associated with increases in blood pressure (BP) during pregnancy. Study designThe Pregnancy Outcomes and Community Health Study enrolled 3019 pregnant women between their 16th–27th week of pregnancy from 52 clinics in 5 Michigan communities (1998–2004). UA levels were measured in maternal blood collected at enrollment from a sub-cohort of 1223 participants. BP was abstracted from prenatal medical records; these analyses used highest recorded diastolic BP (DBP) and its companion systolic BP (SBP). Mean arterial pressure (MAP) was calculated using the formula of (2 × DBP + SBP)/3. Covariates, including maternal race/ethnicity, age at enrollment, education level, medical insurance status, body mass index before pregnancy, parity, smoking during pregnancy, alcohol use during pregnancy, and gestational week at blood collection, were considered as potential confounding variables. Associations between UA levels and BP were evaluated with linear spline or multiple linear regression models. Models’ robustness was examined with bootstrap estimation of variance, sensitivity analysis, and 10-fold cross-validation. ResultsBoth DBP and MAP had a J-shaped relationship with maternal UA; the breakpoints (nadirs) were 0.153 and 0.161 mmol/L UA, respectively. For DBP versus UA, adjusted regression coefficient (β) = −95.67 (standard error (SE) = 37.67 and p = 0.01) for the left and adjusted β = 48.95 (SE = 9.56 and p < 0.01) for the right; for MAP versus UA, adjusted β = −58.48 (SE = 31.42 and p = 0.06) for the left and adjusted β = 52.23 (SE = 11.39 and p < 0.01) for the right. Maternal SBP followed a positive linear trend with UA levels (adjusted β = 37.75, SE = 12.93, and p < 0.01). All results were robust. ConclusionExtreme high and low maternal serum UA levels may be informative in studying maternal blood pressure during pregnancy.

Variance estimation for stratified propensity score estimators

Propensity score methods are increasingly used to estimate the effect of a treatment or exposure on an outcome in non-randomised studies. We focus on one such method, stratification on the propensity score, comparing it with the method of inverse-probability weighting by the propensity score. The propensity score--the conditional probability of receiving the treatment given observed covariates--is usually an unknown probability estimated from the data. Estimators for the variance of treatment effect estimates typically used in practice, however, do not take into account that the propensity score itself has been estimated from the data. By deriving the asymptotic marginal variance of the stratified estimate of treatment effect, correctly taking into account the estimation of the propensity score, we show that routinely used variance estimators are likely to produce confidence intervals that are too conservative when the propensity score model includes variables that predict (cause) the outcome, but only weakly predict the treatment. In contrast, a comparison with the analogous marginal variance for the inverse probability weighted (IPW) estimator shows that routinely used variance estimators for the IPW estimator are likely to produce confidence intervals that are almost always too conservative. Because exact calculation of the asymptotic marginal variance is likely to be complex, particularly for the stratified estimator, we suggest that bootstrap estimates of variance should be used in practice.

Estimating medical care costs under conditions of censoring

A number of non-parametric estimators have been proposed to calculate average medical care costs in the presence of censoring. This paper assesses their performance both in terms of bias and efficiency under extreme conditions using a medical dataset which exhibits heavy censoring. The estimators are further investigated using artificially generated data. Their variances are derived from analytic formulae based on the estimators’ asymptotic properties and these are compared to empirically derived bootstrap estimates. The analysis revealed various performance patterns ranging from generally stable estimators under all conditions considered to estimators which become increasingly unstable with increasing levels of censoring. The bootstrap estimates of variance were consistent with the analytically derived asymptotic variance estimates. Of the two estimators that performed best, one imposes restrictions on the censoring distribution while the other is not restricted by the censoring pattern and on this basis the second may be preferred.

Jackknife Approximations to Bootstrap Estimates

Let $\hat{T}_n$ be an estimate of the form $\hat{T}_n = T(\hat{F}_n)$, where $\hat{F}_n$ is the sample $\operatorname{cdf}$ of $n \operatorname{iid}$ observations and $T$ is a locally quadratic functional defined on $\operatorname{cdf's}$. Then, the normalized jackknife estimates for bias, skewness, and variance of $\hat{T}_n$ approximate closely their bootstrap counterparts. Each of these estimates is consistent. Moreover, the jackknife and bootstrap estimates of variance are asymptotically normal and asymptotically minimax. The main results: the first-order Edgeworth expansion estimate for the distribution of $n^{1/2}(\hat{T}_n - T(F))$, with $F$ being the actual $\operatorname{cdf}$ of each observation and the expansion coefficients being estimated by jackknifing, is asymptotically equivalent to the corresponding bootstrap distribution estimate, up to and including terms of order $n^{-1/2}$. Both distribution estimates are asymptotically minimax. The jackknife Edgeworth expansion estimate suggests useful corrections for skewness and bias to upper and lower confidence bounds for $T(F)$.