Missing data in randomized clinical trials for weight loss: scope of the problem, state of the field, and performance of statistical methods.

BACKGROUND: Dropouts and missing data are nearly-ubiquitous in obesity randomized controlled trails, threatening validity and generalizability of conclusions. Herein, we meta-analytically evaluate the extent of missing data, the frequency with which various analytic methods are employed to accommodate dropouts, and the performance of multiple statistical methods. METHODOLOGY/PRINCIPAL FINDINGS: We searched PubMed and Cochrane databases (2000-2006) for articles published in English and manually searched bibliographic references. Articles of pharmaceutical randomized controlled trials with weight loss or weight gain prevention as major endpoints were included. Two authors independently reviewed each publication for inclusion. 121 articles met the inclusion criteria. Two authors independently extracted treatment, sample size, drop-out rates, study duration, and statistical method used to handle missing data from all articles and resolved disagreements by consensus. In the meta-analysis, drop-out rates were substantial with the survival (non-dropout) rates being approximated by an exponential decay curve (e(-lambdat)) where lambda was estimated to be .0088 (95% bootstrap confidence interval: .0076 to .0100) and t represents time in weeks. The estimated drop-out rate at 1 year was 37%. Most studies used last observation carried forward as the primary analytic method to handle missing data. We also obtained 12 raw obesity randomized controlled trial datasets for empirical analyses. Analyses of raw randomized controlled trial data suggested that both mixed models and multiple imputation performed well, but that multiple imputation may be more robust when missing data are extensive. CONCLUSION/SIGNIFICANCE: Our analysis offers an equation for predictions of dropout rates useful for future study planning. Our raw data analyses suggests that multiple imputation is better than other methods for handling missing data in obesity randomized controlled trials, followed closely by mixed models. We suggest these methods supplant last observation carried forward as the primary method of analysis.

Importance of prostate volume in the European Randomised Study of Screening for Prostate Cancer (ERSPC) risk calculators: results from the prostate biopsy collaborative group.

OBJECTIVES: To compare the predictive performance and potential clinical usefulness of risk calculators of the European Randomized Study of Screening for Prostate Cancer (ERSPC RC) with and without information on prostate volume. METHODS: We studied 6 cohorts (5 European and 1 US) with a total of 15,300 men, all biopsied and with pre-biopsy TRUS measurements of prostate volume. Volume was categorized into 3 categories (25, 40, and 60 cc), to reflect use of digital rectal examination (DRE) for volume assessment. Risks of prostate cancer were calculated according to a ERSPC DRE-based RC (including PSA, DRE, prior biopsy, and prostate volume) and a PSA + DRE model (including PSA, DRE, and prior biopsy). Missing data on prostate volume were completed by single imputation. Risk predictions were evaluated with respect to calibration (graphically), discrimination (AUC curve), and clinical usefulness (net benefit, graphically assessed in decision curves). RESULTS: The AUCs of the ERSPC DRE-based RC ranged from 0.61 to 0.77 and were substantially larger than the AUCs of a model based on only PSA + DRE (ranging from 0.56 to 0.72) in each of the 6 cohorts. The ERSPC DRE-based RC provided net benefit over performing a prostate biopsy on the basis of PSA and DRE outcome in five of the six cohorts. CONCLUSIONS: Identifying men at increased risk for having a biopsy detectable prostate cancer should consider multiple factors, including an estimate of prostate volume.

Methods for Imputing Missing Values and Synthesizing Confidential Values for Continuous and Magnitude Data

Abstract

Continuous variable is one of the major data types collected by the survey organizations. It can be incomplete such that the data collectors need to fill in the missingness. Or, it can contain sensitive information which needs protection from re-identification. One of the approaches to protect continuous microdata is to sum them up according to different cells of features. In this thesis, I represents novel methods of multiple imputation (MI) that can be applied to impute missing values and synthesize confidential values for continuous and magnitude data.

The first method is for limiting the disclosure risk of the continuous microdata whose marginal sums are fixed. The motivation for developing such a method comes from the magnitude tables of non-negative integer values in economic surveys. I present approaches based on a mixture of Poisson distributions to describe the multivariate distribution so that the marginals of the synthetic data are guaranteed to sum to the original totals. At the same time, I present methods for assessing disclosure risks in releasing such synthetic magnitude microdata. The illustration on a survey of manufacturing establishments shows that the disclosure risks are low while the information loss is acceptable.

The second method is for releasing synthetic continuous micro data by a nonstandard MI method. Traditionally, MI fits a model on the confidential values and then generates multiple synthetic datasets from this model. Its disclosure risk tends to be high, especially when the original data contain extreme values. I present a nonstandard MI approach conditioned on the protective intervals. Its basic idea is to estimate the model parameters from these intervals rather than the confidential values. The encouraging results of simple simulation studies suggest the potential of this new approach in limiting the posterior disclosure risk.

The third method is for imputing missing values in continuous and categorical variables. It is extended from a hierarchically coupled mixture model with local dependence. However, the new method separates the variables into non-focused (e.g., almost-fully-observed) and focused (e.g., missing-a-lot) ones. The sub-model structure of focused variables is more complex than that of non-focused ones. At the same time, their cluster indicators are linked together by tensor factorization and the focused continuous variables depend locally on non-focused values. The model properties suggest that moving the strongly associated non-focused variables to the side of focused ones can help to improve estimation accuracy, which is examined by several simulation studies. And this method is applied to data from the American Community Survey.

Risk Prediction for Epithelial Ovarian Cancer in 11 United States-Based Case-Control Studies: Incorporation of Epidemiologic Risk Factors and 17 Confirmed Genetic Loci.

Previously developed models for predicting absolute risk of invasive epithelial ovarian cancer have included a limited number of risk factors and have had low discriminatory power (area under the receiver operating characteristic curve (AUC) < 0.60). Because of this, we developed and internally validated a relative risk prediction model that incorporates 17 established epidemiologic risk factors and 17 genome-wide significant single nucleotide polymorphisms (SNPs) using data from 11 case-control studies in the United States (5,793 cases; 9,512 controls) from the Ovarian Cancer Association Consortium (data accrued from 1992 to 2010). We developed a hierarchical logistic regression model for predicting case-control status that included imputation of missing data. We randomly divided the data into an 80% training sample and used the remaining 20% for model evaluation. The AUC for the full model was 0.664. A reduced model without SNPs performed similarly (AUC = 0.649). Both models performed better than a baseline model that included age and study site only (AUC = 0.563). The best predictive power was obtained in the full model among women younger than 50 years of age (AUC = 0.714); however, the addition of SNPs increased the AUC the most for women older than 50 years of age (AUC = 0.638 vs. 0.616). Adapting this improved model to estimate absolute risk and evaluating it in prospective data sets is warranted.