Comment on Oberman & Vink: Should we fix or simulate the complete data in simulation studies evaluating missing data methods?

For simulation studies that evaluate methods of handling missing data, we argue that generating partially observed data by fixing the complete data and repeatedly simulating the missingness indicators is a superficially attractive idea but only rarely appropriate to use.

Standard and reference-based conditional mean imputation.

Clinical trials with longitudinal outcomes typically include missing data due to missed assessments or structural missingness of outcomes after intercurrent events handled with a hypothetical strategy. Approaches based on Bayesian random multiple imputation and Rubin's rules for pooling results across multiple imputed data sets are increasingly used in order to align the analysis of these trials with the targeted estimand. We propose and justify deterministic conditional mean imputation combined with the jackknife for inference as an alternative approach. The method is applicable to imputations under a missing-at-random assumption as well as for reference-based imputation approaches. In an application and a simulation study, we demonstrate that it provides consistent treatment effect estimates with the Bayesian approach and reliable frequentist inference with accurate standard error estimation and type I error control. A further advantage of the method is that it does not rely on random sampling and is therefore replicable and unaffected by Monte Carlo error.

Robustness of ANCOVA in randomized trials with unequal randomization.

Randomized trials with continuous outcomes are often analyzed using analysis of covariance (ANCOVA), with adjustment for prognostic baseline covariates. The ANCOVA estimator of the treatment effect is consistent under arbitrary model misspecification. In an article recently published in the journal, Wang et al proved the model-based variance estimator for the treatment effect is also consistent under outcome model misspecification, assuming the probability of randomization to each treatment is 1/2. In this reader reaction, we derive explicit expressions which show that when randomization is unequal, the model-based variance estimator can be biased upwards or downwards. In contrast, robust sandwich variance estimators can provide asymptotically valid inferences under arbitrary misspecification, even when randomization probabilities are not equal.

Multiple imputation of missing data in nested case-control and case-cohort studies.

The nested case-control and case-cohort designs are two main approaches for carrying out a substudy within a prospective cohort. This article adapts multiple imputation (MI) methods for handling missing covariates in full-cohort studies for nested case-control and case-cohort studies. We consider data missing by design and data missing by chance. MI analyses that make use of full-cohort data and MI analyses based on substudy data only are described, alongside an intermediate approach in which the imputation uses full-cohort data but the analysis uses only the substudy. We describe adaptations to two imputation methods: the approximate method (MI-approx) of White and Royston (2009) and the "substantive model compatible" (MI-SMC) method of Bartlett et al. (2015). We also apply the "MI matched set" approach of Seaman and Keogh (2015) to nested case-control studies, which does not require any full-cohort information. The methods are investigated using simulation studies and all perform well when their assumptions hold. Substantial gains in efficiency can be made by imputing data missing by design using the full-cohort approach or by imputing data missing by chance in analyses using the substudy only. The intermediate approach brings greater gains in efficiency relative to the substudy approach and is more robust to imputation model misspecification than the full-cohort approach. The methods are illustrated using the ARIC Study cohort. Supplementary Materials provide R and Stata code.

Covariate adjustment and estimation of mean response in randomised trials.

Analyses of randomised trials are often based on regression models which adjust for baseline covariates, in addition to randomised group. Based on such models, one can obtain estimates of the marginal mean outcome for the population under assignment to each treatment, by averaging the model-based predictions across the empirical distribution of the baseline covariates in the trial. We identify under what conditions such estimates are consistent, and in particular show that for canonical generalised linear models, the resulting estimates are always consistent. We show that a recently proposed variance estimator underestimates the variance of the estimator around the true marginal population mean when the baseline covariates are not fixed in repeated sampling and provide a simple adjustment to remedy this. We also describe an alternative semiparametric estimator, which is consistent even when the outcome regression model used is misspecified. The different estimators are compared through simulations and application to a recently conducted trial in asthma.

White matter hyperintensities are associated with disproportionate progressive hippocampal atrophy.

This study investigates relationships between white matter hyperintensity (WMH) volume, cerebrospinal fluid (CSF) Alzheimer's disease (AD) pathology markers, and brain and hippocampal volume loss. Subjects included 198 controls, 345 mild cognitive impairment (MCI), and 154 AD subjects with serial volumetric 1.5-T MRI. CSF Aß42 and total tau were measured (n = 353). Brain and hippocampal loss were quantified from serial MRI using the boundary shift integral (BSI). Multiple linear regression models assessed the relationships between WMHs and hippocampal and brain atrophy rates. Models were refitted adjusting for (a) concurrent brain/hippocampal atrophy rates and (b) CSF Aß42 and tau in subjects with CSF data. WMH burden was positively associated with hippocampal atrophy rate in controls (P = 0.002) and MCI subjects (P = 0.03), and with brain atrophy rate in controls (P = 0.03). The associations with hippocampal atrophy rate remained following adjustment for concurrent brain atrophy rate in controls and MCIs, and for CSF biomarkers in controls (P = 0.007). These novel results suggest that vascular damage alongside AD pathology is associated with disproportionately greater hippocampal atrophy in nondemented older adults. © 2016 The Authors Hippocampus Published by Wiley Periodicals, Inc.

Missing covariates in competing risks analysis.

Studies often follow individuals until they fail from one of a number of competing failure types. One approach to analyzing such competing risks data involves modeling the cause-specific hazards as functions of baseline covariates. A common issue that arises in this context is missing values in covariates. In this setting, we first establish conditions under which complete case analysis (CCA) is valid. We then consider application of multiple imputation to handle missing covariate values, and extend the recently proposed substantive model compatible version of fully conditional specification (SMC-FCS) imputation to the competing risks setting. Through simulations and an illustrative data analysis, we compare CCA, SMC-FCS, and a recent proposal for imputing missing covariates in the competing risks setting.

Missing binary outcomes under covariate-dependent missingness in cluster randomised trials.

Missing outcomes are a commonly occurring problem for cluster randomised trials, which can lead to biased and inefficient inference if ignored or handled inappropriately. Two approaches for analysing such trials are cluster-level analysis and individual-level analysis. In this study, we assessed the performance of unadjusted cluster-level analysis, baseline covariate-adjusted cluster-level analysis, random effects logistic regression and generalised estimating equations when binary outcomes are missing under a baseline covariate-dependent missingness mechanism. Missing outcomes were handled using complete records analysis and multilevel multiple imputation. We analytically show that cluster-level analyses for estimating risk ratio using complete records are valid if the true data generating model has log link and the intervention groups have the same missingness mechanism and the same covariate effect in the outcome model. We performed a simulation study considering four different scenarios, depending on whether the missingness mechanisms are the same or different between the intervention groups and whether there is an interaction between intervention group and baseline covariate in the outcome model. On the basis of the simulation study and analytical results, we give guidance on the conditions under which each approach is valid. © 2017 The Authors. Statistics in Medicine Published by John Wiley & Sons Ltd.

Growth of HIV-exposed uninfected, compared with HIV-unexposed, Zambian children: a longitudinal analysis from infancy to school age.

BACKGROUND: Early growth of HIV-exposed, uninfected (HEU) children is poorer than that of their HIV-unexposed, uninfected (HUU) counterparts but there is little longitudinal or longer term information about the growth effects of early HIV exposure. METHODS: We performed a longitudinal analysis to compare growth of HEU and HUU infants and children using data from two cohort studies in Lusaka, Zambia. Initially 207 HUU and 200 HEU infants from the Breastfeeding and Postpartum Health (BFPH) study and 580 HUU and 165 HEU from the Chilenje Infant Growth, Nutrition and Infection Study (CIGNIS) had anthropometric measurements taken during infancy and again when school-aged, at which time 66 BFPH children and 326 CIGNIS children were available. We analysed the data from the two cohorts separately using linear mixed models. Linear regression models were used as a secondary analysis at the later time points, adjusting for breastfeeding duration. We explored when the main group differences in growth emerged in order to estimate the largest 'effect periods'. RESULTS: After adjusting for socioeconomic status and maternal education, HEU children had lower weight-for-age, length-for-age and BMI-for-age Z-scores during early growth and these differences still existed when children were school-aged. Exposure group differences changed most between 1 and 6 weeks and between 18 months and ~7.5 years. CONCLUSIONS: HEU children have poorer early growth than HUU children which persists into later growth. Interventions to improve growth of HEU children need to target pregnant women and infants.

Multiple imputation of missing covariates for the Cox proportional hazards cure model.

We explore several approaches for imputing partially observed covariates when the outcome of interest is a censored event time and when there is an underlying subset of the population that will never experience the event of interest. We call these subjects 'cured', and we consider the case where the data are modeled using a Cox proportional hazards (CPH) mixture cure model. We study covariate imputation approaches using fully conditional specification. We derive the exact conditional distribution and suggest a sampling scheme for imputing partially observed covariates in the CPH cure model setting. We also propose several approximations to the exact distribution that are simpler and more convenient to use for imputation. A simulation study demonstrates that the proposed imputation approaches outperform existing imputation approaches for survival data without a cure fraction in terms of bias in estimating CPH cure model parameters. We apply our multiple imputation techniques to a study of patients with head and neck cancer. Copyright © 2016 John Wiley & Sons, Ltd.

Asymptotically Unbiased Estimation of Exposure Odds Ratios in Complete Records Logistic Regression.

Missing data are a commonly occurring threat to the validity and efficiency of epidemiologic studies. Perhaps the most common approach to handling missing data is to simply drop those records with 1 or more missing values, in so-called "complete records" or "complete case" analysis. In this paper, we bring together earlier-derived yet perhaps now somewhat neglected results which show that a logistic regression complete records analysis can provide asymptotically unbiased estimates of the association of an exposure of interest with an outcome, adjusted for a number of confounders, under a surprisingly wide range of missing-data assumptions. We give detailed guidance describing how the observed data can be used to judge the plausibility of these assumptions. The results mean that in large epidemiologic studies which are affected by missing data and analyzed by logistic regression, exposure associations may be estimated without bias in a number of settings where researchers might otherwise assume that bias would occur.

Improving upon the efficiency of complete case analysis when covariates are MNAR.

Missing values in covariates of regression models are a pervasive problem in empirical research. Popular approaches for analyzing partially observed datasets include complete case analysis (CCA), multiple imputation (MI), and inverse probability weighting (IPW). In the case of missing covariate values, these methods (as typically implemented) are valid under different missingness assumptions. In particular, CCA is valid under missing not at random (MNAR) mechanisms in which missingness in a covariate depends on the value of that covariate, but is conditionally independent of outcome. In this paper, we argue that in some settings such an assumption is more plausible than the missing at random assumption underpinning most implementations of MI and IPW. When the former assumption holds, although CCA gives consistent estimates, it does not make use of all observed information. We therefore propose an augmented CCA approach which makes the same conditional independence assumption for missingness as CCA, but which improves efficiency through specification of an additional model for the probability of missingness, given the fully observed variables. The new method is evaluated using simulations and illustrated through application to data on reported alcohol consumption and blood pressure from the US National Health and Nutrition Examination Survey, in which data are likely MNAR independent of outcome.

Comparison of random forest and parametric imputation models for imputing missing data using MICE: a CALIBER study.

Multivariate imputation by chained equations (MICE) is commonly used for imputing missing data in epidemiologic research. The "true" imputation model may contain nonlinearities which are not included in default imputation models. Random forest imputation is a machine learning technique which can accommodate nonlinearities and interactions and does not require a particular regression model to be specified. We compared parametric MICE with a random forest-based MICE algorithm in 2 simulation studies. The first study used 1,000 random samples of 2,000 persons drawn from the 10,128 stable angina patients in the CALIBER database (Cardiovascular Disease Research using Linked Bespoke Studies and Electronic Records; 2001-2010) with complete data on all covariates. Variables were artificially made "missing at random," and the bias and efficiency of parameter estimates obtained using different imputation methods were compared. Both MICE methods produced unbiased estimates of (log) hazard ratios, but random forest was more efficient and produced narrower confidence intervals. The second study used simulated data in which the partially observed variable depended on the fully observed variables in a nonlinear way. Parameter estimates were less biased using random forest MICE, and confidence interval coverage was better. This suggests that random forest imputation may be useful for imputing complex epidemiologic data sets in which some patients have missing data.

Evaluation of two-fold fully conditional specification multiple imputation for longitudinal electronic health record data.

Most implementations of multiple imputation (MI) of missing data are designed for simple rectangular data structures ignoring temporal ordering of data. Therefore, when applying MI to longitudinal data with intermittent patterns of missing data, some alternative strategies must be considered. One approach is to divide data into time blocks and implement MI independently at each block. An alternative approach is to include all time blocks in the same MI model. With increasing numbers of time blocks, this approach is likely to break down because of co-linearity and over-fitting. The new two-fold fully conditional specification (FCS) MI algorithm addresses these issues, by only conditioning on measurements, which are local in time. We describe and report the results of a novel simulation study to critically evaluate the two-fold FCS algorithm and its suitability for imputation of longitudinal electronic health records. After generating a full data set, approximately 70% of selected continuous and categorical variables were made missing completely at random in each of ten time blocks. Subsequently, we applied a simple time-to-event model. We compared efficiency of estimated coefficients from a complete records analysis, MI of data in the baseline time block and the two-fold FCS algorithm. The results show that the two-fold FCS algorithm maximises the use of data available, with the gain relative to baseline MI depending on the strength of correlations within and between variables. Using this approach also increases plausibility of the missing at random assumption by using repeated measures over time of variables whose baseline values may be missing.

Infection and telomere length: a systematic review protocol.

INTRODUCTION: Telomeres are a measure of cellular ageing with potential links to diseases such as cardiovascular diseases and cancer. Studies have shown that some infections may be associated with telomere shortening, but whether an association exists across all types and severities of infections and in which populations is unclear. Therefore we aim to collate available evidence to enable comparison and to inform future research in this field. METHODS AND ANALYSIS: We will search for studies involving telomere length and infection in various databases including MEDLINE (Ovid interface), EMBASE (Ovid interface), Web of Science, Scopus, Global Health and the Cochrane Library. For grey literature, the British Library of electronic theses databases (ETHOS) will be explored. We will not limit by study type, geographical location, infection type or method of outcome measurement. Two researchers will independently carry out study selection, data extraction and risk of bias assessment using the ROB2 and ROBINS-E tools. The overall quality of the studies will be determined using the Grading of Recommendations Assessment, Development and Evaluation criteria. We will also evaluate study heterogeneity with respect to study design, exposure and outcome measurement and if there is sufficient homogeneity, a meta-analysis will be conducted. Otherwise, we will provide a narrative synthesis with results grouped by exposure category and study design. ETHICS AND DISSEMINATION: The present study does not require ethical approval. Results will be disseminated via publishing in a peer-reviewed journal and conference presentations. PROSPERO REGISTRATION NUMBER: CRD42023444854.

Comparative effectiveness of second line oral antidiabetic treatments among people with type 2 diabetes mellitus: emulation of a target trial using routinely collected health data.

OBJECTIVE: To compare the effectiveness of three commonly prescribed oral antidiabetic drugs added to metformin for people with type 2 diabetes mellitus requiring second line treatment in routine clinical practice. DESIGN: Cohort study emulating a comparative effectiveness trial (target trial). SETTING: Linked primary care, hospital, and death data in England, 2015-21. PARTICIPANTS: 75 739 adults with type 2 diabetes mellitus who initiated second line oral antidiabetic treatment with a sulfonylurea, DPP-4 inhibitor, or SGLT-2 inhibitor added to metformin. MAIN OUTCOME MEASURES: Primary outcome was absolute change in glycated haemoglobin A1c (HbA1c) between baseline and one year follow-up. Secondary outcomes were change in body mass index (BMI), systolic blood pressure, and estimated glomerular filtration rate (eGFR) at one year and two years, change in HbA1c at two years, and time to ≥40% decline in eGFR, major adverse kidney event, hospital admission for heart failure, major adverse cardiovascular event (MACE), and all cause mortality. Instrumental variable analysis was used to reduce the risk of confounding due to unobserved baseline measures. RESULTS: 75 739 people initiated second line oral antidiabetic treatment with sulfonylureas (n=25 693, 33.9%), DPP-4 inhibitors (n=34 464 ,45.5%), or SGLT-2 inhibitors (n=15 582, 20.6%). SGLT-2 inhibitors were more effective than DPP-4 inhibitors or sulfonylureas in reducing mean HbA1c values between baseline and one year. After the instrumental variable analysis, the mean differences in HbA1c change between baseline and one year were -2.5 mmol/mol (95% confidence interval (CI) -3.7 to -1.3) for SGLT-2 inhibitors versus sulfonylureas and -3.2 mmol/mol (-4.6 to -1.8) for SGLT-2 inhibitors versus DPP-4 inhibitors. SGLT-2 inhibitors were more effective than sulfonylureas or DPP-4 inhibitors in reducing BMI and systolic blood pressure. For some secondary endpoints, evidence for SGLT-2 inhibitors being more effective was lacking-the hazard ratio for MACE, for example, was 0.99 (95% CI 0.61 to 1.62) versus sulfonylureas and 0.91 (0.51 to 1.63) versus DPP-4 inhibitors. SGLT-2 inhibitors had reduced hazards of hospital admission for heart failure compared with DPP-4 inhibitors (0.32, 0.12 to 0.90) and sulfonylureas (0.46, 0.20 to 1.05). The hazard ratio for a ≥40% decline in eGFR indicated a protective effect versus sulfonylureas (0.42, 0.22 to 0.82), with high uncertainty in the estimated hazard ratio versus DPP-4 inhibitors (0.64, 0.29 to 1.43). CONCLUSIONS: This emulation study of a target trial found that SGLT-2 inhibitors were more effective than sulfonylureas or DPP-4 inhibitors in lowering mean HbA1c, BMI, and systolic blood pressure and in reducing the hazards of hospital admission for heart failure (v DPP-4 inhibitors) and kidney disease progression (v sulfonylureas), with no evidence of differences in other clinical endpoints.

Socioeconomic and early-life factors and risk of being overweight or obese in children of Swedish- and foreign-born parents.

BACKGROUND: Ethnic minorities/immigrants have differential health as compared with natives. The epidemic in child overweight/obesity (OW/OB) in Sweden is leveling off, but lower socioeconomic groups and immigrants/ethnic minorities may not have benefited equally from this trend. We investigated whether nonethnic Swedish children are at increased risk for being OW/OB and whether these associations are mediated by parental socioeconomic position (SEP) and/or early-life factors such as birth weight, maternal smoking, BMI, and breastfeeding. METHODS: Data on 10,628 singleton children (51% boys, mean age: 4.8 y, born during the period 2000-2004) residing in Uppsala were analyzed. OW/OB was computed using the International Obesity Task Force's sex- and age-specific cutoffs. The mother's nativity was used as proxy for ethnicity. Logistic regression was used to analyze ethnicity-OW/OB associations. RESULTS: Children of North African, Iranian, South American, and Turkish ethnicity had increased odds for being overweight/obese as compared with children of Swedish ethnicity (adjusted odds ratio (OR): 2.60 (95% confidence interval (CI): 1.57-4.27), 1.67 (1.03-2.72), 3.00 (1.86-4.80), and 2.90 (1.73-4.88), respectively). Finnish children had decreased odds for being overweight/obese (adjusted OR: 0.53 (0.32-0.90)). CONCLUSION: Ethnic differences in a child's risk for OW/OB exist in Sweden that cannot be explained by SEP or maternal or birth factors. As OW/OB often tracks into adulthood, more effective public health policies that intervene at an early age are needed.

Multiple imputation for handling systematically missing confounders in meta-analysis of individual participant data.

A variable is 'systematically missing' if it is missing for all individuals within particular studies in an individual participant data meta-analysis. When a systematically missing variable is a potential confounder in observational epidemiology, standard methods either fail to adjust the exposure-disease association for the potential confounder or exclude studies where it is missing. We propose a new approach to adjust for systematically missing confounders based on multiple imputation by chained equations. Systematically missing data are imputed via multilevel regression models that allow for heterogeneity between studies. A simulation study compares various choices of imputation model. An illustration is given using data from eight studies estimating the association between carotid intima media thickness and subsequent risk of cardiovascular events. Results are compared with standard methods and also with an extension of a published method that exploits the relationship between fully adjusted and partially adjusted estimated effects through a multivariate random effects meta-analysis model. We conclude that multiple imputation provides a practicable approach that can handle arbitrary patterns of systematic missingness. Bias is reduced by including sufficient between-study random effects in the imputation model.

The value of hippocampal and temporal horn volumes and rates of change in predicting future conversion to AD.

Hippocampal pathology occurs early in Alzheimer disease (AD), and atrophy, measured by volumes and volume changes, may predict which subjects will develop AD. Measures of the temporal horn (TH), which is situated adjacent to the hippocampus, may also indicate early changes in AD. Previous studies suggest that these metrics can predict conversion from amnestic mild cognitive impairment (MCI) to AD with conversion and volume change measured concurrently. However, the ability of these metrics to predict future conversion has not been investigated. We compared the abilities of hippocampal, TH, and global measures to predict future conversion from MCI to AD. TH, hippocampi, whole brain, and ventricles were measured using baseline and 12-month scans. Boundary shift integral was used to measure the rate of change. We investigated the prediction of conversion between 12 and 24 months in subjects classified as MCI from baseline to 12 months. All measures were predictive of future conversion. Local and global rates of change were similarly predictive of conversion. There was evidence that the TH expansion rate is more predictive than the hippocampal atrophy rate (P=0.023) and that the TH expansion rate is more predictive than the TH volume (P=0.036). Prodromal atrophy rates may be useful predictors of future conversion to sporadic AD from amnestic MCI.