Ofer Harel

The estimation of R2 and adjusted R2 in incomplete data sets using multiple imputation

The coefficient of determination, known also as the R 2, is a common measure in regression analysis. Many scientists use the R 2 and the adjusted R 2 on a regular basis. In most cases, the researchers treat the coefficient of determination as an index of ‘usefulness’ or ‘goodness of fit,’ and in some cases, they even treat it as a model selection tool. In cases in which the data is incomplete, most researchers and common statistical software will use complete case analysis in order to estimate the R 2, a procedure that might lead to biased results. In this paper, I introduce the use of multiple imputation for the estimation of R 2 and adjusted R 2 in incomplete data sets. I illustrate my methodology using a biomedical example.

Education, cognitive function, and severity of neuropathology in Alzheimer disease

Background: Education may modulate the degree to which the neuropathology of Alzheimer disease (AD) is expressed as impaired cognitive performance. Methods: We studied 2,051 participants age 65+ years at 27 AD Centers who died and underwent autopsy. All took the Mini-Mental State Examination (MMSE) within 2 years before death. Braak & Braak stage, neuritic plaque density, and Consortium to Establish a Registry for Alzheimer’s Disease and National Institute on Aging (NIA)/Reagan diagnostic classifications quantified AD neuropathologic severity. Multivariate analyses modeled MMSE in relation to education and neuropathologic severity, adjusting for age at death, Lewy body pathology, and vascular dementia. Results: Higher education was associated with higher MMSE scores when AD neuropathology was absent or mild. But with more advanced neuropathology, differences in MMSE scores among education levels were attenuated. For example, among patients without AD by NIA/Reagan criteria, fitted MMSE scores ranged from 19.6 for patients with less than high school education to 25.9 with education beyond high school. But among patients with neuropathologically advanced AD, the range of scores by education was only 7.1 to 8.6. Conclusions: We found no evidence of larger education-related differences in cognitive function when Alzheimer disease (AD) neuropathology was more advanced. Higher Mini-Mental State Examination scores among more educated persons with mild or no AD may reflect better test-taking skills or cognitive reserve, but these advantages may ultimately be overwhelmed by AD neuropathology.

If you stock it, will they buy it? Healthy food availability and customer purchasing behaviour within corner stores in Hartford, CT, USA

OBJECTIVE Literature on food environments has expanded rapidly, yet most research focuses on stores and community characteristics without integrating customer-level data. The present study combines customer shopping behaviour with store food inventory data. DESIGN Face-to-face interviews were conducted with customers shopping in corner stores to measure food shopping behaviour, household food security and demographics. Store inventories were conducted to measure availability of healthy food in corner stores. Multilevel logistic regression models estimated the probability of customers purchasing a food item given the availability of that item in the store. SETTING Nineteen corner stores in Hartford, CT, USA, average size 669 ft(2) (62.15 m(2)). SUBJECTS Sample of 372 customers. RESULTS The majority of customers were Black or Hispanic (54 % and 40 %, respectively) and 61 % experienced food insecurity. For each additional type of fruits or vegetables available in the store, the estimated odds of a customer purchasing fruits increased by 12 % (P = 0.03) and the odds for purchasing vegetables increased by 15 % (P = 0.01). Customers receiving the Supplemental Nutrition Assistance Program (SNAP) were 1.7 times as likely to purchase fruit as those not receiving SNAP (P = 0.04). Greater availability of reduced-fat milk was not associated with increased likelihood of customers purchasing reduced-fat milk. CONCLUSIONS There is a positive association between fruit and vegetable variety and the probability that a customer purchases fruits and vegetables. Increasing the selection of produce in corner stores may increase their consumption by food-insecure and low-income residents at risk for health disparities. These findings have implications for future store interventions and food policies.

Data confidentiality: A review of methods for statistical disclosure limitation and methods for assessing privacy

There is an ever increasing demand from researchers for access to useful microdata files. However, there are also growing concerns regarding the privacy of the individuals contained in the microdata. Ideally, microdata could be released in such a way that a balance between usefulness of the data and privacy is struck. This paper presents a review of proposed methods of statistical disclosure control and techniques for assessing the privacy of such methods under different definitions of disclosure. AMS 2000 subject classifications: Primary 62A01.

How well quantified is the limit of quantification

Background: Raw data on the relationship between known and measured values of an analyte are collected and analyzed to determine the limit of quantification (LOQ) of an assay. In most LOQ problems, the researcher is given an observed value for the marker of interest if this value is greater than the LOQ, and a missing value (<LOQ) otherwise. From a statistical perspective, the implicit assumption is that there is no measurement error for values greater than the LOQ, and unacceptable measurement error for values less than the LOQ. A more plausible assumption is that there is measurement error throughout the measures support. Methods: We describe a Bayesian measurement error model that yields prediction intervals for the true assay value throughout the range of analyte values, and allows for heteroscedasticity of the measurement errors. Results: We illustrate our model on calibration data for fat-soluble vitamins, focusing particularly on beta-cryptoxanthin. Prediction intervals for values above the LOQ are wide, and the width increases with the measured value. Prediction intervals below the LOQ provide more information than the statement that the value is less than the LOQ. Conclusion: The current approach to transmitting data from calibration assays is flawed, since it provides a distorted picture of the actual measurement error. Implications for subsequent analyses of assay measurements are discussed.

Patterns of alcohol use and sexual behaviors among current drinkers in Cape Town, South Africa.

OBJECTIVE This study examined the association between alcohol use and sexual behaviors among South African adults who reported current drinking. METHOD Street-intercept surveys were administered to adults residing in neighborhoods in a South African township. RESULTS Analyses were restricted to participants reporting current drinking (N=1285; mean age=32; 27% women; 98% Black). Most participants (60%) reported heavy episodic drinking (i.e., 5 or more drinks on a single occasion) at least once per week in the past 30 days. Compared to non-heavy episodic drinkers, participants who reported heavy episodic drinking were more likely to drink before sex (79% vs. 66%) and have sex with a partner who had been drinking (59% vs. 44%). Overall, drinking before sex (self or partner) and heavy episodic drinking was associated with multiple sexual partners, discussing condom use with sexual partner(s), and proportion of protected sex. The frequency of condom use varied among participants with steady, casual, or both steady and casual sexual partners. CONCLUSIONS Alcohol use among South African adults is associated with sexual risk behaviors, but this association differs by partner type. Findings suggest the need to strengthen alcohol use components in sexual risk reduction interventions especially for participants with both steady and casual sex partners.

Heterosexual anal intercourse and HIV infection risks in the context of alcohol serving venues, Cape Town, South Africa

BackgroundThe most efficient sexual behavior for HIV transmission is unprotected receptive anal intercourse. However, it is unclear what role heterosexual unprotected anal sex is playing in the worlds worst HIV epidemics of southern Africa. The objective is to examine the prevalence of heterosexual unprotected anal intercourse among men and women who drink at informal alcohol serving establishments (shebeens) in South Africa.MethodsCross-sectional surveys were collected from a convenience sample of 5037 patrons of 10 shebeens in a peri-urban township of Cape Town, South Africa. Analyses concentrated on establishing the rates of unprotected anal intercourse practiced by men and women as well as the factors associated with practicing anal intercourse.ResultsWe found that 15% of men and 11% of women reported anal intercourse in the previous month, with 8% of men and 7% of women practicing any unprotected anal intercourse. Multiple logistic regression showed that younger age, having primary and casual sex partners, and meeting sex partners at shebeens were independently associated with engaging in anal intercourse. Mathematical modeling showed that individual risks are significantly impacted by anal intercourse but probably not to the degree needed to drive a generalized HIV epidemic.ConclusionsAnal intercourse likely plays a significant role in HIV infections among a small minority of South Africans who patronize alcohol serving establishments. Heterosexual anal intercourse, the most risky sexual behavior for HIV transmission, should not be ignored in HIV prevention for South African heterosexuals. However, this relatively infrequent behavior should not become the focus of prevention efforts.

Can we spin straw into gold? An evaluation of immigrant legal status imputation approaches.

Researchers have developed logical, demographic, and statistical strategies for imputing immigrants’ legal status, but these methods have never been empirically assessed. We used Monte Carlo simulations to test whether, and under what conditions, legal status imputation approaches yield unbiased estimates of the association of unauthorized status with health insurance coverage. We tested five methods under a range of missing data scenarios. Logical and demographic imputation methods yielded biased estimates across all missing data scenarios. Statistical imputation approaches yielded unbiased estimates only when unauthorized status was jointly observed with insurance coverage; when this condition was not met, these methods overestimated insurance coverage for unauthorized relative to legal immigrants. We next showed how bias can be reduced by incorporating prior information about unauthorized immigrants. Finally, we demonstrated the utility of the best-performing statistical method for increasing power. We used it to produce state/regional estimates of insurance coverage among unauthorized immigrants in the Current Population Survey, a data source that contains no direct measures of immigrants’ legal status. We conclude that commonly employed legal status imputation approaches are likely to produce biased estimates, but data and statistical methods exist that could substantially reduce these biases.

Are We Missing the Importance of Missing Values in HIV Prevention Randomized Clinical Trials? Review and Recommendations

Missing data in HIV prevention trials is a common complication to interpreting outcomes. Even a small proportion of missing values in randomized trials can cause bias, inefficiency and loss of power. We examined the extent of missing data and methods in which HIV prevention randomized clinical trials (RCT) have managed missing values. We used a database maintained by the HIV/AIDS Prevention Research Synthesis (PRS) Project at the Centers for Disease Control and Prevention (CDC) to identify related trials for our review. The PRS cumulative database was searched on June 15, 2010 and all citations that met the following criteria were retrieved: All RCTs which reported HIV/STD/HBV/HCV behavioral interventions with a biological outcome from 2005 to present. Out of the 57 intervention trials identified, all had some level of missing values. We found that the average missing values per study ranged between 3 and 97%. Averaging over all studies the percent of missing values was 26%. None of the studies reported any assumptions for managing missing data in their RCTs. Under some relaxed assumptions discussed below, we expect only 12% of studies to report unbiased results. There is a need for more detailed and thoughtful consideration of the missing data problem in HIV prevention trials. In the current state of managing missing data we risk major biases in interpretations. Several viable alternatives are available for improving the internal validity of RCTs by managing missing data.

Maternal consumption of a DHA-containing functional food benefits infant sleep patterning: An early neurodevelopmental measure

BACKGROUND Docosahexaenoic acid (DHA; 22:6n-3) is highly important during pregnancy for optimal development and functioning of fetal neural tissue. Infant ability to organize sleep and wake states following parturition is highly associated with later developmental outcomes. The impact of maternal DHA intake on sleep organization has not been previously investigated. AIMS To examine the effect of a DHA-containing functional food consumed during pregnancy on early neurobehavioral development as assessed by infant sleep patterning in the first 48 postnatal hours. STUDY DESIGN A longitudinal, randomized, double-blinded, placebo-controlled design was used. SUBJECTS Women (18-35 y) with no pregnancy complications consumed a cereal-based functional food (92 kcal) containing 300 mg DHA an average of 5 d/week or placebo bars (n=27 DHA, n=21 Placebo). The intervention began at 24 weeks gestation and continued until delivery (38-40 weeks). OUTCOME MEASURES Infant sleep/wake states were measured on postnatal days 1 (D1) and 2 (D2) using a pressure sensitive mattress recording respiration and body movements. RESULTS Using ANCOVA and controlling for ethnic variation, there were significant group differences in arousals in quiet sleep on D1 (P=0.006) and D2 (P=0.011) with fewer arousals in the DHA intervention group compared to the placebo group. Similarly, arousals in active sleep on D1 were significantly lower in the DHA-intervention group (P=0.012) compared to the placebo group. CONCLUSIONS We conclude that increased prenatal supply of dietary DHA has a beneficial impact on infant sleep organization.