Binary Covariate Research Articles

Improving measurement of binary covariates in claims data: A simulation study.

When investigators have two claims-based definitions for a binary confounder, it is unclear whether to prefer the more sensitive or more specific definition. Our objective was to compare adjusting for the sensitive or specific definition alone vs two novel approaches combining both definitions: a "two-algorithm indicator" and a "two-algorithm restriction" approach. Each simulated patient had a binary exposure, outcome, and confounder. We created two nested, misclassified versions of the confounder using validated heart failure definitions. The sensitive definition had a sensitivity/specificity of 0.98/0.83, while the specific definition had a sensitivity/specificity of 0.77/0.99. Patients were classified into 3 groups: group 0 did not meet either definition, group 1 met the sensitive but not specific definition, and group 2 met both. The two-algorithm indicator approach adjusted using indicators for groups 1 and 2, while the two-algorithm restriction approach excluded patients in group 1 and adjusted using an indicator for group 2. Adjusted exposure odds ratios (ORs) were estimated for each approach using logistic regression. The crude OR was 1.33 (95% CI, 1.07-1.63). Adjusting for the specific or sensitive definitions resulted in ORs of 1.09 (95% CI, 0.87-1.35) and 1.14 (95% CI, 0.91-1.40). The two-algorithm indicator method returned an OR of 1.07 (95% CI, 0.86-1.33). The two-algorithm restriction approach returned an OR of 1.02 (95% CI, 0.79-1.29) but excluded 20% of the cohort. The two-algorithm indicator approach may improve adjustment for claims-based confounders by returning a point estimate at least as unbiased as the better of the two component definitions.

MDiNE: a model to estimate differential co-occurrence networks in microbiome studies.

MotivationThe human microbiota is the collection of microorganisms colonizing the human body, and plays an integral part in human health. A growing trend in microbiome analysis is to construct a network to estimate the co-occurrence patterns among taxa through precision matrices. Existing methods do not facilitate investigation into how these networks change with respect to covariates.ResultsWe propose a new model called Microbiome Differential Network Estimation (MDiNE) to estimate network changes with respect to a binary covariate. The counts of individual taxa in the samples are modeled through a multinomial distribution whose probabilities depend on a latent Gaussian random variable. A sparse precision matrix over all the latent terms determines the co-occurrence network among taxa. The model fit is obtained and evaluated using Hamiltonian Monte Carlo methods. The performance of our model is evaluated through an extensive simulation study and is shown to outperform existing methods in terms of estimation of network parameters. We also demonstrate an application of the model to estimate changes in the intestinal microbial network topology with respect to Crohn’s disease.Availability and implementation MDiNE is implemented in a freely available R package: https://github.com/kevinmcgregor/mdine.Supplementary information Supplementary data are available at Bioinformatics online.

Lymphopenia and neutropenia are associated with subsequent incident proteinuria in Danish patients with systemic lupus erythematosus

Objective: The aim of this study was to investigate whether incident proteinuria in patients with systemic lupus erythematosus (SLE) was preceded by changes in blood lymphocytes and neutrophil counts and/or neutrophil–lymphocyte ratio (NLR).Method: SLE patients with no proteinuria before or at the time of classification were included. Longitudinal data on SLE manifestations, vital status, and SLE-associated medications were collected during clinical visits and chart review. Laboratory data were collected through a nationwide database. Lymphopenia, severe lymphopenia, and neutropenia were defined as values below 0.8 × 109, 0.5 × 109, and 2.0 × 109 cells/L, respectively. High NLR was defined as values above the median. Proteinuria was defined by at least two measurements of elevated urine protein excretion (> 0.5 g/day). Hazard ratios (HRs) were calculated by Cox modelling using time-dependent continuous and binary covariates based on multiple laboratory measurements adjusted for use of immunosuppressants.Results: In total, 260 SLE patients were available for the analysis, of whom 30 (12%) developed incident proteinuria following the diagnosis of SLE. Median follow-up time was 73.5 months. Lymphocyte and neutrophil counts, but not NLR, were associated with incident proteinuria. HRs for incident proteinuria were 2.71 for lymphopenia [95% confidence interval (CI) 1.20–6.11], 4.73 for severe lymphopenia (95% CI 1.93–11.59), and 2.54 for neutropenia (95% CI 1.14–5.65).Conclusion: Lymphopenia and neutropenia predicted the risk of first-time proteinuria independently of immunosuppressants.

Association between both maternal and fetal angiotensinogen gene single nucleotide polymorphism and preeclampsia/eclampsia

Objective: To explore the association between preeclampsia/eclampsia and maternal and fetal angiotensinogen SNPs. Methods: From January 2008 to October 2015, a case-parents/mother-control designed study was conducted among 347 preeclampsia/eclampsia cases and 700 controls to collect related information on their demographic characteristics and to detect the related angiotensinogen SNPs' genotypes. Both log-linear and unconditional logistic regression methods were employed to investigate the genetic effects of maternal/fetal angiotensinogen SNPs on preeclampsia/eclampsia. Multivariate binary unconditional logistic regression model and covariance were used to analyze the relationship between BMI before pregnancy, weight gain during pregnancy and overweight and obesity in preschool children. Results: Both fetal angiotensinogen rs3789679 GA and AA genotype were associated with the reduced risks of preeclampsia/eclampsia, with ORs as 0.73 (95%CI: 0.55-0.96) and 0.62 (95%CI: 0.39-0.98), respectively. For fetal angiotensinogen rs2493132, individuals that carrying the TT genotype, presented a positive association with the risk of preeclampsia/eclampsia, with OR as 1.60 (95%CI: 1.08-2.37). However, these associations were not statistically significant after the correction of the false discovery rate. It was observed that fetal rs3789679 could reduce the risk of preeclampsia/eclampsia (OR=0.73, 95%CI: 0.55-0.96) under the dominant model (GA+AA/GG) while fetal rs2493132 increased the risk of preeclampsia/eclampsia (OR=1.66, 95%CI: 1.13-2.44) under the recessive model (TT/CC+CT). Maternal rs5051 presented an association with preeclampsia/eclampsia (OR=1.33, 95%CI: 1.01-1.76) under the dominant model (TC+CC/TT). Conclusions: Results from the dominant model showed that both fetal rs3789679 GA and AA genotype reduced the risk of preeclampsia/eclampsia and maternal rs5051 TC while CC genotype increased the risk of preeclampsia/eclampsia. Fetal rs2493132 TT genotype seemed to be associated with the risk of preeclampsia/eclampsia under the recessive model.

A General and Robust Estimation Method for the Case-Time-Control Design

The case-time-control design is a tool to control for measured, time-varying covariates that increase montonically in time within each subject while also controlling for all unmeasured covariates that are constant within each subject across time. Until recently, the design was restricted to data with only two timepoints and a single binary covariate, or data with a binary exposure. Sjölander (2017) made an important extension that allows for an arbitrary number of timepoints and covariates and a nonbinary exposure. However, his estimation method requires fairly strong model assumptions, and it may create bias if these assumptions are violated. We propose a novel estimation method for the case-time-control design, which to a large extent relaxes the model assumptions in Sjölander. We show in simulations that this estimation method performs well under a range of scenarios and gives consistent estimates when Sjölander’s estimation does not.

Multiple imputation in the presence of an incomplete binary variable created from an underlying continuous variable.

Multiple imputation (MI) is used to handle missing at random (MAR) data. Despite warnings from statisticians, continuous variables are often recoded into binary variables. With MI it is important that the imputation and analysis models are compatible; variables should be imputed in the same form they appear in the analysis model. With an encoded binary variable more accurate imputations may be obtained by imputing the underlying continuous variable. We conducted a simulation study to explore how best to impute a binary variable that was created from an underlying continuous variable. We generated a completely observed continuous outcome associated with an incomplete binary covariate that is a categorized version of an underlying continuous covariate, and an auxiliary variable associated with the underlying continuous covariate. We simulated data with several sample sizes, and set 25% and 50% of data in the covariate to MAR dependent on the outcome and the auxiliary variable. We compared the performance of five different imputation methods: (a) Imputation of the binary variable using logistic regression; (b) imputation of the continuous variable using linear regression, then categorizing into the binary variable; (c, d) imputation of both the continuous and binary variables using fully conditional specification (FCS) and multivariate normal imputation; (e) substantive-model compatible (SMC) FCS. Bias and standard errors were large when the continuous variable only was imputed. The other methods performed adequately. Imputation of both the binary and continuous variables using FCS often encountered mathematical difficulties. We recommend the SMC-FCS method as it performed best in our simulation studies.

Impact of legislation to reduce the drink-drive limit on road traffic accidents and alcohol consumption in Scotland: a natural experiment study

Background It is widely recognised that drink driving is a leading cause of road traffic accidents (RTAs). There is evidence that changing the drink-drive limit from a blood alcohol concentration of 0.08 to 0.05 g/dl is effective in reducing RTAs. Scotland changed the blood alcohol concentration limit to 0.05 g/dl on 5 December 2014. Aims To assess whether or not the numbers and rates of RTAs and per capita alcohol consumption in Scotland were reduced because of the 2014 drink-drive legislation. To assess whether or not the 2014 change in legislation provided good value for money. Design A natural experimental, quantitative study. The control group was England and Wales, that is, the other countries in Great Britain, where the drink-drive legislation remained unchanged. Setting Great Britain. Participants The entire population of Scotland, England and Wales for the period of January 2013–December 2016. Intervention The change to drink-drive legislation in Scotland. Outcome measures The counts and rates of RTAs; and per capita alcohol consumption. Methods For the numbers and rates of RTAs (both traffic flow and population denominators were used), and separately for the intervention and control trial groups, negative binomial regression models were fitted to panel data sets to test for a change in outcome level after the new 2014 legislation was in place. To obtain a ‘difference-in-differences’ (DiD)-type measure of effect, an interaction term between the intervention group indicator and the binary covariate for indicating pre and post change in legislation (‘pseudo’-change for the control group) was assessed. For off- and on-trade per capita alcohol sales, and separately for the intervention and control trial group, seasonal autoregressive integrated moving average error models were fitted to the relevant time series. Results The change to drink-drive legislation was associated with a 2% relative decrease in RTAs in Scotland [relative risk (RR) 0.98, 95% CI 0.91 to 1.04; p = 0.53]. However, the pseudo-change in legislation was associated with a 5% decrease in RTAs in England and Wales (RR 0.95, 95% CI 0.90 to 1.00; p = 0.05). For RTA rates, with traffic flow as the denominator, the DiD-type estimate indicated a 7% increase in rates for Scotland relative to England and Wales (unadjusted RR 1.07, 95% CI 0.98 to 1.17; p = 0.1). The change to drink-drive legislation was associated with a 0.3% relative decrease in per capita off-trade sales (–0.3%, 95% CI –1.7% to 1.1%; p = 0.71) and a 0.7% decrease in per capita on-trade sales (–0.7%, 95% CI –0.8% to –0.5%; p < 0.001). Conclusion The change to drink-drive legislation in Scotland in December 2014 did not have the expected effect of reducing RTAs in the country, and nor did it change alcohol drinking levels in Scotland. This main finding for RTAs was unexpected and the research has shown that a lack of enforcement is the most likely reason for legislation failure. Future work Investigations into how the public interpret and act on changes in drink-drive legislation would be welcome, as would research into whether or not previous change in drink-drive legislation effects on RTAs in other jurisdictions are associated with the level of enforcement that took place. Trial registration Current Controlled Trials ISRCTN38602189. Funding This project was funded by the National Institute for Health Research (NIHR) Public Health Research programme and will be published in full in Public Health Research; Vol. 7, No. 12. See the NIHR Journals Library website for further project information.

Joint modelling of longitudinal binary data and survival data

The medical costs in an ageing society substantially increase when the incidences of chronic diseases, disabilities and inability to live independently are high. Healthy lifestyles not only affect elderly individuals but also influence the entire community. When assessing treatment efficacy, survival and quality of life should be considered simultaneously. This paper proposes the joint likelihood approach for modelling survival and longitudinal binary covariates simultaneously. Because some unobservable information is present in the model, the Monte Carlo EM algorithm and Metropolis-Hastings algorithm are used to find the estimators. Monte Carlo simulations are performed to evaluate the performance of the proposed model based on the accuracy and precision of the estimates. Real data are used to demonstrate the feasibility of the proposed model.

The effect of neutropenia on the clinical pharmacokinetics of vancomycin in adults

AimThere is accumulating evidence that neutropenic patients require higher dosages of vancomycin. To prevent sub-therapeutic drug exposure, it is of utmost importance to obtain adequate exposure from the first dose onwards. We aimed to quantify the effect of neutropenia on the pharmacokinetics of vancomycin.MethodsData were extracted from a matched patient cohort of patients known with (1) hematological disease, (2) solid malignancy, and (3) patients not known with cancer. Pharmacokinetic analysis was performed using non-linear mixed effects modeling with neutropenia investigated as a binary covariate on clearance and volume of distribution of vancomycin.ResultsA total of 116 patients were included (39 hematologic patients, 39 solid tumor patients, and 38 patients not known with cancer). In total, 742 paired time-concentration observations were available for the pharmacokinetic analysis. Presence of neutropenia showed to significantly (p = 0.00157) increase the clearance of vancomycin by 27.7% (95% CI 10.2–46.2%), whereas it did not impact the volume of distribution (p = 0.704).ConclusionsThis study shows that vancomycin clearance is increased in patients with neutropenia by 27.7%. Therefore, the vancomycin maintenance dose should be pragmatically increased by 25% in neutropenic patients at the start of treatment. Since the volume of distribution appeared unaffected, no adjustment in loading dose is required. These dose adjustments do not rule out the necessity of further dose individualization by means of therapeutic drug monitoring.

Renal Function and Risk Stratification of Patients With Embolic Stroke of Undetermined Source

Background and Purpose- We aimed to assess if renal function can aid in risk stratification for ischemic stroke or transient ischemic attack (TIA) recurrence and death in patients with embolic stroke of undetermined source (ESUS). Methods- We pooled 12 ESUS datasets from Europe and America. Renal function was evaluated using the estimated glomerular filtration rate (eGFR) and analyzed in continuous, binary, and categorical way. Cox-regression analyses assessed if renal function was independently associated with the risk for ischemic stroke/TIA recurrence and death. The Kaplan-Meier product limit method estimated the cumulative probability of ischemic stroke/TIA recurrence and death. Results- In 1530 patients with ESUS followed for 3260 patient-years, there were 237 recurrences (15.9%) and 201 deaths (13.4%), corresponding to 7.3 ischemic stroke/TIA recurrences and 5.6 deaths per 100 patient-years, respectively. Renal function was not associated with the risk for ischemic stroke/TIA recurrence when forced into the final multivariate model, regardless if it was analyzed as continuous (hazard ratio, 1.00; 95% CI, 0.99-1.00 for every 1 mL/min), binary (hazard ratio, 1.27; 95% CI, 0.87-1.73) or categorical covariate (likelihood-ratio test 2.59, P=0.63 for stroke recurrence). The probability of ischemic stroke/TIA recurrence across stages of renal function was 11.9% for eGFR ≥90, 16.6% for eGFR 60-89, 21.7% for eGFR 45-59, 19.2% for eGFR 30-44, and 24.9% for eGFR <30 (likelihood-ratio test 2.59, P=0.63). The results were similar for the outcome of death. Conclusions- The present study is the largest pooled individual patient-level ESUS dataset, and does not provide evidence that renal function can be used to stratify the risk of ischemic stroke/TIA recurrence or death in patients with ESUS.

Statistical Methods in the Evaluation of Cardio-Respiratory Parameters in Young Childhood Cancer Survivors and Healthy Peers

Abstract This study concerns the problem of late complications of antineo-plastic therapy. Reduced parameters of the cardiorespiratory system in childhood may have a tremendous impact on health. In order to assess the selected parameters, to evaluate physical endurance, and compare the results with those obtained for healthy children, a test was carried out on a treadmill, until 80% of maximum pulse rate was reached. To compare the differences between the treatment group and the control group, three approaches were used. The first one was the classical statistical inference, the second consisted in forming a multidimensional normal model and also involved modelling of the correlation between variables. The unstructured type of the working correlation matrix was chosen to obtain the results and correct standard errors. In the last approach, logistic regression was used to model the relationship between binary outcome and covariates, and to differentiate between the groups of patients on the basis of their cardiovascular parameters.

Application of the Misclassification Simulation Extrapolation Procedure to Log-Logistic Accelerated Failure Time Models in Survival Analysis

Misclassification of binary covariates is pervasive in survival data, leading to inaccurate parameter estimates. Despite extensive research of misclassification error in Cox proportional hazards models, it has not been adequately researched in the context of accelerated failure time models. The log-logistic distribution plays an important role in evaluating non-monotonic hazards. However, the performance of misclassification correction methods has not been explored in such scenarios. We aim to fill this gap in the literature by investigating a method involving the simulation and extrapolation algorithm, to correct for misclassification error in log-logistic AFT models and later apply this method in real survival data.

Erratum: High-dimensional Propensity Score Adjustment in Studies of Treatment Effects Using Health Care Claims Data.

In the article titled “High-dimensional Propensity Score Adjustment in Studies of Treatment Effects Using Health Care Claims Data,” the authors introduce a semiautomated variable selection algorithm for high-dimensional proxy adjustment within insurance health care claims databases.1 The high-dimensional propensity score (HDPS) algorithm evaluates thousands of diagnostic, procedural, and medication claims codes and, for each code, generates binary variables based on the frequency of occurrence for each code during a defined pre-exposure covariate assessment period. The HDPS then prioritizes or ranks each variable based on its potential for bias by assessing the variable’s prevalence and univariate association with the treatment and outcome according to the Bross formula.1,2 From this ordered list, investigators then specify the number of variables to include in the HDPS model along with prespecified variables such as age and sex.1 A full description of the HDPS algorithm is provided elsewhere.1 In the original article by Schneeweiss et al.,1 the Bross bias multiplier for prioritizing covariates was defined as follows: where represents the prevalence of the binary covariate within the exposed group, the prevalence of the binary covariate within the unexposed group, and the relative risk for the univariate association between the binary covariate and the study outcome. One of us (B.F.) noted that for correct assessment of a binary covariate’s confounding impact, the Bross bias multiplier should be defined simply as follows: We repeated a subset of the analyses from the original manuscript using a revised HDPS that included the correct implementation of the Bross formula. A full description of the data sources that were used for the empirical analyses is provided in the original article.1,3 The Table shows that there was almost no change from the results reported in the original manuscript after using the above Bross formula for covariate prioritization. For the nonsteroidal anti-inflammatory drugs data example (Table), 199 out of the top 200 ranked variables and 476 out of the top 500 ranked variables were common to both the ordering from the revised HDPS and the ordering from the original manuscript. For the Statin data example (Table), 193 out of the top 200 ranked variables and 486 out of the top 500 ranked variables were common to both the ordering from the revised HDPS and the ordering from the original manuscript.TABLE 1.: Comparison of Results for a Subset of Analyses Reported in Schneeweiss et al.1 (2009) With Results Using the Revised HDPSThe HDPS software that is distributed online has been updated to include the modified implementation of the Bross formula.4 Results from analyses that have been conducted using older versions of the HDPS algorithm are unlikely to change meaningfully after this correction.

A novel calibration framework for survival analysis when a binary covariate is measured at sparse time points.

The goals in clinical and cohort studies often include evaluation of the association of a time-dependent binary treatment or exposure with a survival outcome. Recently, several impactful studies targeted the association between initiation of aspirin and survival following colorectal cancer (CRC) diagnosis. The value of this exposure is zero at baseline and may change its value to one at some time point. Estimating this association is complicated by having only intermittent measurements on aspirin-taking. Commonly used methods can lead to substantial bias. We present a class of calibration models for the distribution of the time of status change of the binary covariate. Estimates obtained from these models are then incorporated into the proportional hazard partial likelihood in a natural way. We develop non-parametric, semiparametric, and parametric calibration models, and derive asymptotic theory for the methods that we implement in the aspirin and CRC study. We further develop a risk-set calibration approach that is more useful in settings in which the association between the binary covariate and survival is strong.

Inference on local average treatment effects for misclassified treatment

We develop point-identification for the local average treatment effect when the binary treatment contains a measurement error. The standard instrumental variable estimator is inconsistent for the parameter since the measurement error is nonclassical by construction. We correct the problem by identifying the distribution of the measurement error based on the use of an exogenous variable that can even be a binary covariate. The moment conditions derived from the identification lead to generalized method of moments estimation with asymptotically valid inferences. Monte Carlo simulations and an empirical illustration demonstrate the usefulness of the proposed procedure.

A11199 Prevalence of Cardio-cerebrovascular Risk Factors in the Middle-aged and Elderly Community Population

Objectives: We investigated the prevalence of cardio-cerebrovascular risk factors in the middle-aged and elderly community population to determine the 10-year risk for coronary heart disease for the further risk management. Methods: 1140 subjects aged 40 years or older was selected from May 2016 to July 2016 in two communities in Fujian Province. The demographic information, physical examination and laboratory examination were conducted. Binary logistic regression or covariance analysis was used to analyze the relationship between cardio-cerebrovascular risk factors and education levels or average income levels. Results: 1. The subjects including 382 men and 758 women, with the average age of 57.9 ± 10.1 years. 198 subjects with high risk of stroke were screened out (17.4%). The 10-year risk for coronary heart disease was 2% (1%, 8%). 2. Prevalence of hypertension and diabetes, which standardized by age in the population, were significant lower while prevalence of dyslipidemia and atrial fibrillation were higher in men than those in women (all P < 0.05). 3. There were higher proportion of high risk of stroke among men, urban residents, population with higher education levels, higher income levels and older population (all P < 0.05). 4. The 10-year risk of coronary heart disease was higher in urban residents, the population with higher education levels, higher income levels, higher risk of stroke, heavy drinking and diabetes (all P < 0.05). Conclusion: The prevalence of cardio-cerebrovascular risk factors and proportion of high risk of stroke were higher in the middle aged and elderly population. Framingham risk score and stroke risk rating can be complementary for the prediction of cardiovascular and cerebrovascular diseases.

Sample size calculation for a proportional hazards mixture cure model with nonbinary covariates

ABSTRACTSample size calculation is a critical issue in clinical trials because a small sample size leads to a biased inference and a large sample size increases the cost. With the development of advanced medical technology, some patients can be cured of certain chronic diseases, and the proportional hazards mixture cure model has been developed to handle survival data with potential cure information. Given the needs of survival trials with potential cure proportions, a corresponding sample size formula based on the log-rank test statistic for binary covariates has been proposed by Wang et al. [25]. However, a sample size formula based on continuous variables has not been developed. Herein, we presented sample size and power calculations for the mixture cure model with continuous variables based on the log-rank method and further modified it by Ewell's method. The proposed approaches were evaluated using simulation studies for synthetic data from exponential and Weibull distributions. A program for calculating necessary sample size for continuous covariates in a mixture cure model was implemented in R.

Multiple imputation in Cox regression when there are time-varying effects of covariates.

In Cox regression, it is important to test the proportional hazards assumption and sometimes of interest in itself to study time‐varying effects (TVEs) of covariates. TVEs can be investigated with log hazard ratios modelled as a function of time. Missing data on covariates are common and multiple imputation is a popular approach to handling this to avoid the potential bias and efficiency loss resulting from a “complete‐case” analysis. Two multiple imputation methods have been proposed for when the substantive model is a Cox proportional hazards regression: an approximate method (Imputing missing covariate values for the Cox model in Statistics in Medicine (2009) by White and Royston) and a substantive‐model‐compatible method (Multiple imputation of covariates by fully conditional specification: accommodating the substantive model in Statistical Methods in Medical Research (2015) by Bartlett et al). At present, neither accommodates TVEs of covariates. We extend them to do so for a general form for the TVEs and give specific details for TVEs modelled using restricted cubic splines. Simulation studies assess the performance of the methods under several underlying shapes for TVEs. Our proposed methods give approximately unbiased TVE estimates for binary covariates with missing data, but for continuous covariates, the substantive‐model‐compatible method performs better. The methods also give approximately correct type I errors in the test for proportional hazards when there is no TVE and gain power to detect TVEs relative to complete‐case analysis. Ignoring TVEs at the imputation stage results in biased TVE estimates, incorrect type I errors, and substantial loss of power in detecting TVEs. We also propose a multivariable TVE model selection algorithm. The methods are illustrated using data from the Rotterdam Breast Cancer Study. R code is provided.

Sequential rerandomization.

The seminal work of Morgan & Rubin (2012) considers rerandomization for all the units at one time.In practice, however, experimenters may have to rerandomize units sequentially. For example, a clinician studying a rare disease may be unable to wait to perform an experiment until all the experimental units are recruited. Our work offers a mathematical framework for sequential rerandomization designs, where the experimental units are enrolled in groups. We formulate an adaptive rerandomization procedure for balancing treatment/control assignments over some continuous or binary covariates, using Mahalanobis distance as the imbalance measure. We prove in our key result that given the same number of rerandomizations, in expected value, under certain mild assumptions, sequential rerandomization achieves better covariate balance than rerandomization at one time.

Sensitivity analysis on the ecological bias for Seoul tuberculosis data

In ecological studies, researchers often try to convey the analysis results to individual level based on aggregate data. In order to do this correctly, the possibility of ecological bias should be studied and addressed. One of the key ideas used to address the ecological bias issue is to derive the ecological model from the individual model and to check whether the parameter of interest in the individual model is identifiable in the ecological model. However, the procedure depends on unverifiable assumptions, and we recommend checking how sensitive the results are to these unverifiable assumptions. We analyzed the tuberculosis data that was collected in Seoul in 2005 using a spatial ecological regression model for the aggregate count data with spatial correlation, and found that the deprivation index is likely to have a small positive effect on the occurrence risk of tuberculosis in individual level in Seoul. We considered this finding in various aspects by performing in depth sensitivity analyses. In particular, our findings are shown to be robust to the distribution assumptions for the individual exposure and missing binary covariate across various scenarios.