Three-phase generalized raking and multiple imputation estimators to address error-prone data.

Validation studies are often used to obtain more reliable information in settings with error-prone data. Validated data on a subsample of subjects can be used together with error-prone data on all subjects to improve estimation. In practice, more than one round of data validation may be required, and direct application of standard approaches for combining validation data into analyses may lead to inefficient estimators since the information available from intermediate validation steps is only partially considered or even completely ignored. In this paper, we present two novel extensions of multiple imputation and generalized raking estimators that make full use of all available data. We show through simulations that incorporating information from intermediate steps can lead to substantial gains in efficiency. This work is motivated by and illustrated in a study of contraceptive effectiveness among 83 671 women living with HIV, whose data were originally extracted from electronic medical records, of whom 4732 had their charts reviewed, and a subsequent 1210 also had a telephone interview to validate key study variables.

Associations Between Gestational Weight Gain, Gestational Diabetes, and Childhood Obesity Incidence.

INTRODUCTION: Excessive maternal gestational weight gain (GWG) is strongly correlated with childhood obesity, yet how excess maternal weight gain and gestational diabetes mellitus (GDM) interact to affect early childhood obesity is poorly understood. The purpose of this study was to investigate whether overall and trimester-specific maternal GWG and GDM were associated with obesity in offspring by age 6 years. METHODS: A cohort of 10,335 maternal-child dyads was established from electronic health records. Maternal weights at conception and delivery were estimated from weight trajectory fits using functional principal components analysis. Kaplan-Meier curves and Cox regression, together with generalized raking, examined time-to-childhood-obesity. RESULTS: Obesity diagnosed prior to age 6 years was estimated at 19.7% (95% CI: 18.3, 21.1). Maternal weight gain during pregnancy was a strong predictor of early childhood obesity (p < 0.0001). The occurrence of early childhood obesity was lower among mothers with GDM compared with those without diabetes (adjusted hazard ratio = 0.58, p = 0.014). There was no interaction between maternal weight gain and GDM (p = 0.55). Higher weight gain during the first trimester was associated with lower risk of early childhood obesity (p = 0.0002) whereas higher weight gain during the second and third trimesters was associated with higher risk (p < 0.0001). DISCUSSION: Results indicated total and trimester-specific maternal weight gain was a strong predictor of early childhood obesity, though obesity risk by age 6 was lower for children of mothers with GDM. Additional research is needed to elucidate underlying mechanisms directly related to trimester-specific weight gain and GDM that impede or protect against obesity prevalence during early childhood.

Excessive maternal gestational weight gain (GWG) and gestational diabetes mellitus (GDM) have been linked to childhood obesity. Yet, research on how excessive total and trimester-specific GWG and GDM interact to affect early childhood obesity remains inconclusive. This study found that inadequate weight gain in the first trimester and excessive weight gain in the second and third trimester were associated with higher risks of childhood obesity by age 6. No significant interaction between maternal GWG and GDM was noted suggesting that these two important maternal conditions do not have a combined effect on the risk of early childhood obesity.

Practical considerations for sandwich variance estimation in two-stage regression settings.

We present a practical approach for computing the sandwich variance estimator in two-stage regression model settings. As a motivating example for two-stage regression, we consider regression calibration, a popular approach for addressing covariate measurement error. The sandwich variance approach has been rarely applied in regression calibration, despite it requiring less computation time than popular resampling approaches for variance estimation, specifically the bootstrap. This is likely due to requiring specialized statistical coding. We first outline the steps needed to compute the sandwich variance estimator. We then develop a convenient method of computation in R for sandwich variance estimation, which leverages standard regression model outputs and existing R functions and can be applied in the case of a simple random sample or complex survey design. We use a simulation study to compare the sandwich to a resampling variance approach for both settings. Finally, we further compare these two variance estimation approaches for data examples from the Women's Health Initiative (WHI) and Hispanic Community Health Study/Study of Latinos (HCHS/SOL). The sandwich variance estimator typically had good numerical performance, but simple Wald bootstrap confidence intervals were unstable or over-covered in certain settings, particularly when there was high correlation between covariates or large measurement error.

Discussion on "A formal causal interpretation of the case-crossover design" by Zach Shahn, Miguel A. Hernán, and James M. Robins.

It has always been clear that the case-crossover design works, for some definition of "works," but some of the details have been surprisingly elusive, and it is good to see more of them nailed down by Shahn et al. My interest in case-crossover analyses has mostly been in the context of air pollution epidemiology mentioned at the end of the paper. The air pollution setting is distinctive for several reasons: as the exposure variable is plausibly exogenous, it is possible to use control times after the case time, the effects of interest are quite small, and the same measured exposure series is shared over many-perhaps all-of the cohort.

Multiwave validation sampling for error-prone electronic health records.

Electronic health record (EHR) data are increasingly used for biomedical research, but these data have recognized data quality challenges. Data validation is necessary to use EHR data with confidence, but limited resources typically make complete data validation impossible. Using EHR data, we illustrate prospective, multiwave, two-phase validation sampling to estimate the association between maternal weight gain during pregnancy and the risks of her child developing obesity or asthma. The optimal validation sampling design depends on the unknown efficient influence functions of regression coefficients of interest. In the first wave of our multiwave validation design, we estimate the influence function using the unvalidated (phase 1) data to determine our validation sample; then in subsequent waves, we re-estimate the influence function using validated (phase 2) data and update our sampling. For efficiency, estimation combines obesity and asthma sampling frames while calibrating sampling weights using generalized raking. We validated 996 of 10,335 mother-child EHR dyads in six sampling waves. Estimated associations between childhood obesity/asthma and maternal weight gain, as well as other covariates, are compared to naïve estimates that only use unvalidated data. In some cases, estimates markedly differ, underscoring the importance of efficient validation sampling to obtain accurate estimates incorporating validated data.

Atrial fibrillation incidence and outcomes in two cohorts of octogenarians: LiLACS NZ.

BACKGROUND: Atrial fibrillation (AF), the most common cardiac arrhythmia in the general population, has significant healthcare burden. Little is known about AF in octogenarians. OBJECTIVE: To describe the prevalence and incidence rate of AF in New Zealand (NZ) octogenarians and the risk of stroke and mortality at 5-year follow-up. DESIGN: Longitudinal Cohort Study. SETTING: Bay of Plenty and Lakes health regions of New Zealand. SUBJECTS: Eight-hundred-seventy-seven (379 indigenous Maori, 498 non-Maori) were included in the analysis. METHODS: AF, stroke/TIA events and relevant co-variates were established annually using self-report and hospital records (and ECG for AF). Cox proportional-hazards regression models were used to determine the time dependent AF risk of stroke/TIA. RESULTS: AF was present in 21% at baseline (Maori 26%, non-Maori 18%), the prevalence doubled over 5-years (Maori 50%, non-Maori 33%). 5-year AF incidence was 82.6 /1000-person years and at all times AF incidence for Maori was twice that of non-Maori. Five-year stroke/TIA prevalence was 23% (22% in Maori and 24% non- Maori), higher in those with AF than without. AF was not independently associated with 5-year new stroke/TIA; baseline systolic blood pressure was. Mortality was higher for Maori, men, those with AF and CHF and statin use was protective. In summary, AF is more prevalent in indigenous octogenarians and should have an increased focus in health care management. Further research could examine treatment in more detail to facilitate ethnic specific impact and risks and benefits of treating AF in octogenarians.

Optimal sampling for design-based estimators of regression models.

Two-phase designs measure variables of interest on a subcohort where the outcome and covariates are readily available or cheap to collect on all individuals in the cohort. Given limited resource availability, it is of interest to find an optimal design that includes more informative individuals in the final sample. We explore the optimal designs and efficiencies for analyses by design-based estimators. Generalized raking is an efficient class of design-based estimators, and they improve on the inverse-probability weighted (IPW) estimator by adjusting weights based on the auxiliary information. We derive a closed-form solution of the optimal design for estimating regression coefficients from generalized raking estimators. We compare it with the optimal design for analysis via the IPW estimator and other two-phase designs in measurement-error settings. We consider general two-phase designs where the outcome variable and variables of interest can be continuous or discrete. Our results show that the optimal designs for analyses by the two classes of design-based estimators can be very different. The optimal design for analysis via the IPW estimator is optimal for IPW estimation and typically gives near-optimal efficiency for generalized raking estimation, though we show there is potential improvement in some settings.

On the Use of Regression Calibration in a Complex Sampling Design With Application to the Hispanic Community Health Study/Study of Latinos.

Regression calibration is the most widely used method to adjust regression parameter estimates for covariate measurement error. Yet its application in the context of a complex sampling design, for which the common bootstrap variance estimator can be less straightforward, has been less studied. We propose 2 variance estimators for a multistage probability-based sampling design, a parametric and a resampling-based multiple imputation approach, where a latent mean exposure needed for regression calibration is the target of imputation. This work was motivated by the Hispanic Community Health Study/Study of Latinos (HCHS/SOL) data from 2008 to 2011, for which relationships between several outcomes and diet, an error-prone self-reported exposure, are of interest. We assessed the relative performance of these variance estimation strategies in an extensive simulation study built on the HCHS/SOL data. We further illustrate the proposed estimators with an analysis of the cross-sectional association of dietary sodium intake with hypertension-related outcomes in a subsample of the HCHS/SOL cohort. We have provided guidelines for the application of regression models with regression-calibrated exposures. Practical considerations for implementation of these 2 variance estimators in the setting of a large multicenter study are also discussed. Code to replicate the presented results is available online.

The clock is ticking: Temporally prioritizing eradications on islands.

Achieving conservation objectives is time critical, but the vast number of threats and potential actions means some form of ranking is necessary to aid prioritization. Objective methods for ranking conservation actions based on when they are differentially likely to become feasible, or to succeed, are currently unavailable within existing decision-making frameworks but are critical for making informed management decisions. We demonstrate how statistical tools developed for survival (or time-to-event) analysis can be used to rank conservation actions over time, through the lens of invasive mammal eradications on islands. Here we forecast the probability of eradicating commensal rat species (Rattus rattus, R. norvegicus, R. exulans) from the New Zealand archipelago by the government's stated target of year 2050. Our methods provide temporally ranked eradication trajectories for the entire country, thus facilitating meeting nationwide policy goals. This demonstration highlights the relevance and applicability of such an approach and its utility for prioritizing globally effective conservation actions.

Combining multiple imputation with raking of weights: An efficient and robust approach in the setting of nearly true models.

Multiple imputation (MI) provides us with efficient estimators in model-based methods for handling missing data under the true model. It is also well-understood that design-based estimators are robust methods that do not require accurately modeling the missing data; however, they can be inefficient. In any applied setting, it is difficult to know whether a missing data model may be good enough to win the bias-efficiency trade-off. Raking of weights is one approach that relies on constructing an auxiliary variable from data observed on the full cohort, which is then used to adjust the weights for the usual Horvitz-Thompson estimator. Computing the optimally efficient raking estimator requires evaluating the expectation of the efficient score given the full cohort data, which is generally infeasible. We demonstrate MI as a practical method to compute a raking estimator that will be optimal. We compare this estimator to common parametric and semi-parametric estimators, including standard MI. We show that while estimators, such as the semi-parametric maximum likelihood and MI estimator, obtain optimal performance under the true model, the proposed raking estimator utilizing MI maintains a better robustness-efficiency trade-off even under mild model misspecification. We also show that the standard raking estimator, without MI, is often competitive with the optimal raking estimator. We demonstrate these properties through several numerical examples and provide a theoretical discussion of conditions for asymptotically superior relative efficiency of the proposed raking estimator.

Raking and regression calibration: Methods to address bias from correlated covariate and time-to-event error.

Medical studies that depend on electronic health records (EHR) data are often subject to measurement error, as the data are not collected to support research questions under study. These data errors, if not accounted for in study analyses, can obscure or cause spurious associations between patient exposures and disease risk. Methodology to address covariate measurement error has been well developed; however, time-to-event error has also been shown to cause significant bias, but methods to address it are relatively underdeveloped. More generally, it is possible to observe errors in both the covariate and the time-to-event outcome that are correlated. We propose regression calibration (RC) estimators to simultaneously address correlated error in the covariates and the censored event time. Although RC can perform well in many settings with covariate measurement error, it is biased for nonlinear regression models, such as the Cox model. Thus, we additionally propose raking estimators which are consistent estimators of the parameter defined by the population estimating equation. Raking can improve upon RC in certain settings with failure-time data, require no explicit modeling of the error structure, and can be utilized under outcome-dependent sampling designs. We discuss features of the underlying estimation problem that affect the degree of improvement the raking estimator has over the RC approach. Detailed simulation studies are presented to examine the performance of the proposed estimators under varying levels of signal, error, and censoring. The methodology is illustrated on observational EHR data on HIV outcomes from the Vanderbilt Comprehensive Care Clinic.

Primary Care Variation in Rates of Unplanned Hospitalizations, Functional Ability, and Quality of Life of Older People.

PURPOSE: To investigate variability in older people's outcomes according to general practitioner (GP) and practice characteristics in New Zealand and the Netherlands. METHODS: We used data from 2 primary care-based, cluster-randomized, controlled trials to separately fit mixed models of unplanned admission rates, functional ability, and quality of life (QOL) and examine variation according to GP- and practice-level characteristics after adjusting for participant-level characteristics. For the New Zealand sample (n = 3,755 aged 75+ years in 60 practices), we modeled 36-month unplanned admission rates, Nottingham Extended Activities of Daily Living (NEADL) scale, and QOL domain ratings from the brief version of the World Health Organization Quality of Life assessment tool. For the Netherlands sample (n = 3,141 aged 75+ years in 59 practices), we modeled 12-month unplanned admission rates, Groningen Activity Restriction Scale scores, and EuroQOL 5 dimensions (EQ-5D) summary index. RESULTS: None of the GP or practice characteristics were significantly associated with rates of unplanned admissions in the New Zealand sample, but we found greater rates of admission in larger practices (incidence rate ratio [IRR], 1.45; 95% CI, 1.15-1.81) and practices staffed with a practice nurse (IRR, 1.74; 95% CI, 1.20-2.52) in the Netherlands sample. In both samples, differences were consistently small where there were significant associations with function (range, -0.26 to 0.19 NEADL points in the New Zealand sample; no associations in the Netherlands sample) and QOL (range, -1.64 to 0.97 QOL points in New Zealand; -0.01 EQ-5D points in the Netherlands). CONCLUSIONS: In the absence of substantial differences in older people's function and QOL, it remains unclear whether intriguing GP- or practice-related variations in admission rates represent low- or high-quality practice.

A Bayesian analysis of mortality outcomes in multicentre clinical trials in critical care.

BACKGROUND: Multicentre RCTs are widely used by critical care researchers to answer important clinical questions. However, few trials evaluating mortality outcomes report statistically significant results. We hypothesised that the low proportion of trials reporting statistically significant differences for mortality outcomes is plausibly explained by lower-than-expected effect sizes combined with a low proportion of participants who could realistically benefit from studied interventions. METHODS: We reviewed multicentre trials in critical care published over a 10-yr period in the New England Journal of Medicine, the Journal of the American Medical Association, and the Lancet. To test our hypothesis, we analysed the results using a Bayesian model to investigate the relationship between the proportion of effective interventions and the proportion of statistically significant results for prior distributions of effect size and trial participant susceptibility. RESULTS: Five of 54 trials (9.3%) reported a significant difference in mortality between the control and the intervention groups. The median expected and observed differences in absolute mortality were 8.0% and 2.0%, respectively. Our modelling shows that, across trials, a lower-than-expected effect size combined with a low proportion of potentially susceptible participants is consistent with the observed proportion of trials reporting significant differences even when most interventions are effective. CONCLUSIONS: When designing clinical trials, researchers most likely overestimate true population effect sizes for critical care interventions. Bayesian modelling demonstrates that that it is not necessarily the case that most studied interventions lack efficacy. In fact, it is plausible that many studied interventions have clinically important effects that are missed.

Improved generalized raking estimators to address dependent covariate and failure-time outcome error.

Biomedical studies that use electronic health records (EHR) data for inference are often subject to bias due to measurement error. The measurement error present in EHR data is typically complex, consisting of errors of unknown functional form in covariates and the outcome, which can be dependent. To address the bias resulting from such errors, generalized raking has recently been proposed as a robust method that yields consistent estimates without the need to model the error structure. We provide rationale for why these previously proposed raking estimators can be expected to be inefficient in failure-time outcome settings involving misclassification of the event indicator. We propose raking estimators that utilize multiple imputation, to impute either the target variables or auxiliary variables, to improve the efficiency. We also consider outcome-dependent sampling designs and investigate their impact on the efficiency of the raking estimators, either with or without multiple imputation. We present an extensive numerical study to examine the performance of the proposed estimators across various measurement error settings. We then apply the proposed methods to our motivating setting, in which we seek to analyze HIV outcomes in an observational cohort with EHR data from the Vanderbilt Comprehensive Care Clinic.

The Galaxy Plot: A New Visualization Tool for Bivariate Meta-Analysis Studies.

Funnel plots have been widely used to detect small-study effects in the results of univariate meta-analyses. However, there is no existing visualization tool that is the counterpart of the funnel plot in the multivariate setting. We propose a new visualization method, the galaxy plot, which can simultaneously present the effect sizes of bivariate outcomes and their standard errors in a 2-dimensional space. We illustrate the use of the galaxy plot with 2 case studies, including a meta-analysis of hypertension trials with studies from 1979-1991 (Hypertension. 2005;45(5):907-913) and a meta-analysis of structured telephone support or noninvasive telemonitoring with studies from 1966-2015 (Heart. 2017;103(4):255-257). The galaxy plot is an intuitive visualization tool that can aid in interpreting results of multivariate meta-analysis. It preserves all of the information presented by separate funnel plots for each outcome while elucidating more complex features that may only be revealed by examining the joint distribution of the bivariate outcomes.

Optimal multiwave sampling for regression modeling in two-phase designs.

Two-phase designs involve measuring extra variables on a subset of the cohort where some variables are already measured. The goal of two-phase designs is to choose a subsample of individuals from the cohort and analyse that subsample efficiently. It is of interest to obtain an optimal design that gives the most efficient estimates of regression parameters. In this article, we propose a multiwave sampling design to approximate the optimal design for design-based estimators. Influence functions are used to compute the optimal sampling allocations. We propose to use informative priors on regression parameters to derive the wave-1 sampling probabilities because any prespecified sampling probabilities may be far from optimal and decrease the design efficiency. The posterior distributions of the regression parameters derived from the current wave will then be used as priors for the next wave. Generalized raking is used in the final statistical analysis. We show that a two-wave sampling with reasonable informative priors will end up with a highly efficient estimation for the parameter of interest and be close to the underlying optimal design.

Incorporating sampling weights into robust estimation of Cox proportional hazards regression model, with illustration in the Multi-Ethnic Study of Atherosclerosis.

BACKGROUND: Cox proportional hazards regression models are used to evaluate associations between exposures of interest and time-to-event outcomes in observational data. When exposures are measured on only a sample of participants, as they are in a case-cohort design, the sampling weights must be incorporated into the regression model to obtain unbiased estimating equations. METHODS: Robust Cox methods have been developed to better estimate associations when there are influential outliers in the exposure of interest, but these robust methods do not incorporate sampling weights. In this paper, we extend these robust methods, which already incorporate influence weights, so that they also accommodate sampling weights. RESULTS: Simulations illustrate that in the presence of influential outliers, the association estimate from the weighted robust method is closer to the true value than the estimate from traditional weighted Cox regression. As expected, in the absence of outliers, the use of robust methods yields a small loss of efficiency. Using data from a case-cohort study that is nested within the Multi-Ethnic Study of Atherosclerosis (MESA) longitudinal cohort study, we illustrate differences between traditional and robust weighted Cox association estimates for the relationships between immune cell traits and risk of stroke. CONCLUSIONS: Robust weighted Cox regression methods are a new tool to analyze time-to-event data with sampling, e.g. case-cohort data, when exposures of interest contain outliers.

GP- and practice-related variation in ambulatory sensitive hospitalisations of older primary care patients.

BACKGROUND: Reducing ambulatory sensitive hospitalisations (ASHs) is a strategy to control spending on hospital care and to improve quality of primary health care. This research investigated whether ASH rates in older people varied by GP and practice characteristics. METHODS: We identified ASHs from the national dataset of hospital events for 3755 community-dwelling participants aged 75+ enrolled in a cluster randomised controlled trial involving 60 randomly selected general practices in three regions in New Zealand. Poisson mixed models of 36-month ASH rates were fitted for the entire sample, for complex participants, and non-complex participants. We examined variation in ASH rates according to GP- and practice-level characteristics after adjusting for patient-level predictors of ASH. RESULTS: Lower rates of ASHs were observed in female GPs (IRR 0.83, CI 0.71 to 0.98). In non-complex participants, but not complex participants, practices in more deprived areas had lower ASH rates (4% lower per deprivation decile higher, IRR 0.96, CI 0.92 to 1.00), whereas main urban centre practices had higher rates (IRR 1.84, CI 1.15 to 2.96). Variance explained by these significant factors was small (0.4% of total variance for GP sex, 0.2% for deprivation, and 0.5% for area type). None of the modifiable practice-level characteristics such as home visiting and systematically contacting patients were significantly associated with ASH rates. CONCLUSIONS: Only a few GP and non-modifiable practice characteristics were associated with variation in ASH rates in 60 New Zealand practices interested in a trial about care of older people. Where there were significant associations, the contribution to overall variance was minimal. It also remains unclear whether lower ASH rates in older people represents underservicing or less overuse of hospital services, particularly for the relatively well patient attending practices in less central, more disadvantaged communities. Thus, reducing ASHs through primary care redesign for older people should be approached carefully. TRIAL REGISTRATION: Australian and New Zealand Clinical Trials Register ACTRN12609000648224 .

FastSKAT: Sequence kernel association tests for very large sets of markers.

The sequence kernel association test (SKAT) is widely used to test for associations between a phenotype and a set of genetic variants that are usually rare. Evaluating tail probabilities or quantiles of the null distribution for SKAT requires computing the eigenvalues of a matrix related to the genotype covariance between markers. Extracting the full set of eigenvalues of this matrix (an n×n matrix, for n subjects) has computational complexity proportional to n3 . As SKAT is often used when n>104 , this step becomes a major bottleneck in its use in practice. We therefore propose fastSKAT, a new computationally inexpensive but accurate approximations to the tail probabilities, in which the k largest eigenvalues of a weighted genotype covariance matrix or the largest singular values of a weighted genotype matrix are extracted, and a single term based on the Satterthwaite approximation is used for the remaining eigenvalues. While the method is not particularly sensitive to the choice of k, we also describe how to choose its value, and show how fastSKAT can automatically alert users to the rare cases where the choice may affect results. As well as providing faster implementation of SKAT, the new method also enables entirely new applications of SKAT that were not possible before; we give examples grouping variants by topologically associating domains, and comparing chromosome-wide association by class of histone marker.

Genetic Diversity and Association Studies in US Hispanic/Latino Populations: Applications in the Hispanic Community Health Study/Study of Latinos.

US Hispanic/Latino individuals are diverse in genetic ancestry, culture, and environmental exposures. Here, we characterized and controlled for this diversity in genome-wide association studies (GWASs) for the Hispanic Community Health Study/Study of Latinos (HCHS/SOL). We simultaneously estimated population-structure principal components (PCs) robust to familial relatedness and pairwise kinship coefficients (KCs) robust to population structure, admixture, and Hardy-Weinberg departures. The PCs revealed substantial genetic differentiation within and among six self-identified background groups (Cuban, Dominican, Puerto Rican, Mexican, and Central and South American). To control for variation among groups, we developed a multi-dimensional clustering method to define a "genetic-analysis group" variable that retains many properties of self-identified background while achieving substantially greater genetic homogeneity within groups and including participants with non-specific self-identification. In GWASs of 22 biomedical traits, we used a linear mixed model (LMM) including pairwise empirical KCs to account for familial relatedness, PCs for ancestry, and genetic-analysis groups for additional group-associated effects. Including the genetic-analysis group as a covariate accounted for significant trait variation in 8 of 22 traits, even after we fit 20 PCs. Additionally, genetic-analysis groups had significant heterogeneity of residual variance for 20 of 22 traits, and modeling this heteroscedasticity within the LMM reduced genomic inflation for 19 traits. Furthermore, fitting an LMM that utilized a genetic-analysis group rather than a self-identified background group achieved higher power to detect previously reported associations. We expect that the methods applied here will be useful in other studies with multiple ethnic groups, admixture, and relatedness.