A Bayesian approach to estimating COVID-19 incidence and infection fatality rates.

Naive estimates of incidence and infection fatality rates (IFR) of coronavirus disease 2019 suffer from a variety of biases, many of which relate to preferential testing. This has motivated epidemiologists from around the globe to conduct serosurveys that measure the immunity of individuals by testing for the presence of SARS-CoV-2 antibodies in the blood. These quantitative measures (titer values) are then used as a proxy for previous or current infection. However, statistical methods that use this data to its full potential have yet to be developed. Previous researchers have discretized these continuous values, discarding potentially useful information. In this article, we demonstrate how multivariate mixture models can be used in combination with post-stratification to estimate cumulative incidence and IFR in an approximate Bayesian framework without discretization. In doing so, we account for uncertainty from both the estimated number of infections and incomplete deaths data to provide estimates of IFR. This method is demonstrated using data from the Action to Beat Coronavirus erosurvey in Canada.

Comparative Analysis of Instrumental Variables on the Assignment of Buprenorphine/Naloxone or Methadone for the Treatment of Opioid Use Disorder.

BACKGROUND: Instrumental variable (IV) analysis provides an alternative set of identification assumptions in the presence of uncontrolled confounding when attempting to estimate causal effects. Our objective was to evaluate the suitability of measures of prescriber preference and calendar time as potential IVs to evaluate the comparative effectiveness of buprenorphine/naloxone versus methadone for treatment of opioid use disorder (OUD). METHODS: Using linked population-level health administrative data, we constructed five IVs: prescribing preference at the individual, facility, and region levels (continuous and categorical variables), calendar time, and a binary prescriber's preference IV in analyzing the treatment assignment-treatment discontinuation association using both incident-user and prevalent-new-user designs. Using published guidelines, we assessed and compared each IV according to the four assumptions for IVs, employing both empirical assessment and content expertise. We evaluated the robustness of results using sensitivity analyses. RESULTS: The study sample included 35,904 incident users (43.3% on buprenorphine/naloxone) initiated on opioid agonist treatment by 1585 prescribers during the study period. While all candidate IVs were strong (A1) according to conventional criteria, by expert opinion, we found no evidence against assumptions of exclusion (A2), independence (A3), monotonicity (A4a), and homogeneity (A4b) for prescribing preference-based IV. Some criteria were violated for the calendar time-based IV. We determined that preference in provider-level prescribing, measured on a continuous scale, was the most suitable IV for comparative effectiveness of buprenorphine/naloxone and methadone for the treatment of OUD. CONCLUSIONS: Our results suggest that prescriber's preference measures are suitable IVs in comparative effectiveness studies of treatment for OUD.

Application of causal inference methods in individual-participant data meta-analyses in medicine: addressing data handling and reporting gaps with new proposed reporting guidelines.

Observational data provide invaluable real-world information in medicine, but certain methodological considerations are required to derive causal estimates. In this systematic review, we evaluated the methodology and reporting quality of individual-level patient data meta-analyses (IPD-MAs) conducted with non-randomized exposures, published in 2009, 2014, and 2019 that sought to estimate a causal relationship in medicine. We screened over 16,000 titles and abstracts, reviewed 45 full-text articles out of the 167 deemed potentially eligible, and included 29 into the analysis. Unfortunately, we found that causal methodologies were rarely implemented, and reporting was generally poor across studies. Specifically, only three of the 29 articles used quasi-experimental methods, and no study used G-methods to adjust for time-varying confounding. To address these issues, we propose stronger collaborations between physicians and methodologists to ensure that causal methodologies are properly implemented in IPD-MAs. In addition, we put forward a suggested checklist of reporting guidelines for IPD-MAs that utilize causal methods. This checklist could improve reporting thereby potentially enhancing the quality and trustworthiness of IPD-MAs, which can be considered one of the most valuable sources of evidence for health policy.

Issues in Implementing Regression Calibration Analyses.

Regression calibration is a popular approach for correcting biases in estimated regression parameters when exposure variables are measured with error. This approach involves building a calibration equation to estimate the value of the unknown true exposure given the error-prone measurement and other covariates. The estimated, or calibrated, exposure is then substituted for the unknown true exposure in the health outcome regression model. When used properly, regression calibration can greatly reduce the bias induced by exposure measurement error. Here, we first provide an overview of the statistical framework for regression calibration, specifically discussing how a special type of error, called Berkson error, arises in the estimated exposure. We then present practical issues to consider when applying regression calibration, including: 1) how to develop the calibration equation and which covariates to include; 2) valid ways to calculate standard errors of estimated regression coefficients; and 3) problems arising if one of the covariates in the calibration model is a mediator of the relationship between the exposure and outcome. Throughout, we provide illustrative examples using data from the Hispanic Community Health Study/Study of Latinos (United States, 2008-2011) and simulations. We conclude with recommendations for how to perform regression calibration.

Combining parametric and nonparametric models to estimate treatment effects in observational studies.

Performing causal inference in observational studies requires we assume confounding variables are correctly adjusted for. In settings with few discrete-valued confounders, standard models can be employed. However, as the number of confounders increases these models become less feasible as there are fewer observations available for each unique combination of confounding variables. In this paper, we propose a new model for estimating treatment effects in observational studies that incorporates both parametric and nonparametric outcome models. By conceptually splitting the data, we can combine these models while maintaining a conjugate framework, allowing us to avoid the use of Markov chain Monte Carlo (MCMC) methods. Approximations using the central limit theorem and random sampling allow our method to be scaled to high-dimensional confounders. Through simulation studies we show our method can be competitive with benchmark models while maintaining efficient computation, and illustrate the method on a large epidemiological health survey.

Is the cholesterol-perfluoroalkyl substance association confounded by dietary fiber intake?: a Bayesian analysis of NHANES data with adjustment for measurement error in fiber intake.

BACKGROUND: Serum concentrations of total cholesterol and related lipid measures have been associated with serum concentrations of per- and polyfluoroalkyl substances (PFAS) in humans, even among those with only background-level exposure to PFAS. Fiber is known to decrease serum cholesterol and a recent report based on National Health and Nutrition Examination Survey (NHANES) showed that PFAS and fiber are inversely associated. We hypothesized that confounding by dietary fiber may account for some of the association between cholesterol and PFAS. METHODS: We implemented a Bayesian correction for measurement error in estimated intake of dietary fiber to evaluate whether fiber confounds the cholesterol-PFAS association. The NHANES measure of diet, two 24-h recalls, allowed calculation of an estimate of the "true" long-term fiber intake for each subject. We fit models to the NHANES data on serum cholesterol and serum concentration of perfluorooctanoic acid (PFOA) and two other PFAS for 7,242 participants in NHANES. RESULTS: The Bayesian model, after adjustment for soluble fiber intake, suggested a decrease in the size of the coefficient for PFOA by 6.4% compared with the fiber-unadjusted model. CONCLUSIONS: The results indicated that the association of serum cholesterol with PFAS was not substantially confounded by fiber intake.

Invited Commentary: Quantitative Bias Analysis Can See the Forest for the Trees.

The accompanying article by Jiang et al. (Am J Epidemiol. 2021;190(9):1830-1840) extends quantitative bias analysis from the realm of statistical models to the realm of machine learning algorithms. Given the rooting of statistical models in the spirit of explanation and the rooting of machine learning algorithms in the spirt of prediction, this extension is thought-provoking indeed. Some such thoughts are expounded upon here.

Invited Commentary: Toward Better Bias Analysis.

In this issue of the Journal, Lash et al. (Am J Epidemiol. 2021;190(8):1604-1612) show how some previously published bias analyses could have been better. In investigation of one of their examples, we add some thoughts about routes to better bias analysis, particularly via exploration of a joint distribution of bias parameters and target parameters.

Incorporating partial adherence into the principal stratification analysis framework.

Participants in pragmatic clinical trials often partially adhere to treatment. However, to simplify the analysis, most studies dichotomize adherence (supposing that subjects received either full or no treatment), which can introduce biases in the results. For example, the popular approach of principal stratification is based on the concept that the population can be separated into strata based on how they will react to treatment assignment, but this framework does not include strata in which a partially adhering participant would belong. We expanded the principal stratification framework to allow partial adherers to have their own principal stratum and treatment level. The expanded approach is feasible in pragmatic settings. We have designed a Monte Carlo posterior sampling method to obtain the relevant parameter estimates. Simulations were completed under a range of settings where participants partially adhered to treatment, including a hypothetical setting from a published simulation trial on the topic of partial adherence. The inference method is additionally applied to data from a real randomized clinical trial that features partial adherence. Comparison of the simulation results indicated that our method is superior in most cases to the biased estimators obtained through standard principal stratification. Simulation results further suggest that our proposed method may lead to increased accuracy of inference in settings where study participants only partially adhere to assigned treatment.

Geospatial indicators of exposure, sensitivity, and adaptive capacity to assess neighbourhood variation in vulnerability to climate change-related health hazards.

BACKGROUND: Although the frequency and magnitude of climate change-related health hazards (CCRHHs) are likely to increase, the population vulnerabilities and corresponding health impacts are dependent on a community's exposures, pre-existing sensitivities, and adaptive capacities in response to a hazard's impact. To evaluate spatial variability in relative vulnerability, we: 1) identified climate change-related risk factors at the dissemination area level; 2) created actionable health vulnerability index scores to map community risks to extreme heat, flooding, wildfire smoke, and ground-level ozone; and 3) spatially evaluated vulnerability patterns and priority areas of action to address inequity. METHODS: A systematic literature review was conducted to identify the determinants of health hazards among populations impacted by CCRHHs. Identified determinants were then grouped into categories of exposure, sensitivity, and adaptive capacity and aligned with available data. Data were aggregated to 4188 Census dissemination areas within two health authorities in British Columbia, Canada. A two-step principal component analysis (PCA) was then used to select and weight variables for each relative vulnerability score. In addition to an overall vulnerability score, exposure, adaptive capacity, and sensitivity sub-scores were computed for each hazard. Scores were then categorised into quintiles and mapped. RESULTS: Two hundred eighty-one epidemiological papers met the study criteria and were used to identify 36 determinant indicators that were operationalized across all hazards. For each hazard, 3 to 5 principal components explaining 72 to 94% of the total variance were retained. Sensitivity was weighted much higher for extreme heat, wildfire smoke and ground-level ozone, and adaptive capacity was highly weighted for flooding vulnerability. There was overall varied contribution of adaptive capacity (16-49%) across all hazards. Distinct spatial patterns were observed - for example, although patterns varied by hazard, vulnerability was generally higher in more deprived and more outlying neighbourhoods of the study region. CONCLUSIONS: The creation of hazard and category-specific vulnerability indices (exposure, adaptive capacity and sensitivity sub-scores) supports evidence-based approaches to prioritize public health responses to climate-related hazards and to reduce inequity by assessing relative differences in vulnerability along with absolute impacts. Future studies can build upon this methodology to further understand the spatial variation in vulnerability and to identify and prioritise actionable areas for adaptation.

A threshold-free summary index for quantifying the capacity of covariates to yield efficient treatment rules.

When data on treatment assignment, outcomes, and covariates from a randomized trial are available, a question of interest is to what extent covariates can be used to optimize treatment decisions. Statistical hypothesis testing of covariate-by-treatment interaction is ill-suited for this purpose. The application of decision theory results in treatment rules that compare the expected benefit of treatment given the patient's covariates against a treatment threshold. However, determining treatment threshold is often context-specific, and any given threshold might seem arbitrary when the overall capacity towards predicting treatment benefit is of concern. We propose the Concentration of Benefit index (Cb ), a threshold-free metric that quantifies the combined performance of covariates towards finding individuals who will benefit the most from treatment. The construct of the proposed index is comparing expected treatment outcomes with and without knowledge of covariates when one of a two randomly selected patients is to be treated. We show that the resulting index can also be expressed in terms of the integrated efficiency of individualized treatment decision over the entire range of treatment thresholds. We propose parametric and semiparametric estimators, the latter being suitable for out-of-sample validation and correction for optimism. We used data from a clinical trial to demonstrate the calculations in a step-by-step fashion. The proposed index has intuitive and theoretically sound interpretation and can be estimated with relative ease for a wide class of regression models. Beyond the conceptual developments, various aspects of estimation and inference for such a metric need to be pursued in future research. R code that implements the method for a variety of regression models is provided at (https://github.com/msadatsafavi/txBenefit).

STRATOS guidance document on measurement error and misclassification of variables in observational epidemiology: Part 2-More complex methods of adjustment and advanced topics.

We continue our review of issues related to measurement error and misclassification in epidemiology. We further describe methods of adjusting for biased estimation caused by measurement error in continuous covariates, covering likelihood methods, Bayesian methods, moment reconstruction, moment-adjusted imputation, and multiple imputation. We then describe which methods can also be used with misclassification of categorical covariates. Methods of adjusting estimation of distributions of continuous variables for measurement error are then reviewed. Illustrative examples are provided throughout these sections. We provide lists of available software for implementing these methods and also provide the code for implementing our examples in the Supporting Information. Next, we present several advanced topics, including data subject to both classical and Berkson error, modeling continuous exposures with measurement error, and categorical exposures with misclassification in the same model, variable selection when some of the variables are measured with error, adjusting analyses or design for error in an outcome variable, and categorizing continuous variables measured with error. Finally, we provide some advice for the often met situations where variables are known to be measured with substantial error, but there is only an external reference standard or partial (or no) information about the type or magnitude of the error.

STRATOS guidance document on measurement error and misclassification of variables in observational epidemiology: Part 1-Basic theory and simple methods of adjustment.

Measurement error and misclassification of variables frequently occur in epidemiology and involve variables important to public health. Their presence can impact strongly on results of statistical analyses involving such variables. However, investigators commonly fail to pay attention to biases resulting from such mismeasurement. We provide, in two parts, an overview of the types of error that occur, their impacts on analytic results, and statistical methods to mitigate the biases that they cause. In this first part, we review different types of measurement error and misclassification, emphasizing the classical, linear, and Berkson models, and on the concepts of nondifferential and differential error. We describe the impacts of these types of error in covariates and in outcome variables on various analyses, including estimation and testing in regression models and estimating distributions. We outline types of ancillary studies required to provide information about such errors and discuss the implications of covariate measurement error for study design. Methods for ascertaining sample size requirements are outlined, both for ancillary studies designed to provide information about measurement error and for main studies where the exposure of interest is measured with error. We describe two of the simpler methods, regression calibration and simulation extrapolation (SIMEX), that adjust for bias in regression coefficients caused by measurement error in continuous covariates, and illustrate their use through examples drawn from the Observing Protein and Energy (OPEN) dietary validation study. Finally, we review software available for implementing these methods. The second part of the article deals with more advanced topics.

Towards reduction in bias in epidemic curves due to outcome misclassification through Bayesian analysis of time-series of laboratory test results: case study of COVID-19 in Alberta, Canada and Philadelphia, USA.

BACKGROUND: Despite widespread use, the accuracy of the diagnostic test for SARS-CoV-2 infection is poorly understood. The aim of our work was to better quantify misclassification errors in identification of true cases of COVID-19 and to study the impact of these errors in epidemic curves using publicly available surveillance data from Alberta, Canada and Philadelphia, USA. METHODS: We examined time-series data of laboratory tests for SARS-CoV-2 viral infection, the causal agent for COVID-19, to try to explore, using a Bayesian approach, the sensitivity and specificity of the diagnostic test. RESULTS: Our analysis revealed that the data were compatible with near-perfect specificity, but it was challenging to gain information about sensitivity. We applied these insights to uncertainty/bias analysis of epidemic curves under the assumptions of both improving and degrading sensitivity. If the sensitivity improved from 60 to 95%, the adjusted epidemic curves likely falls within the 95% confidence intervals of the observed counts. However, bias in the shape and peak of the epidemic curves can be pronounced, if sensitivity either degrades or remains poor in the 60-70% range. In the extreme scenario, hundreds of undiagnosed cases, even among the tested, are possible, potentially leading to further unchecked contagion should these cases not self-isolate. CONCLUSION: The best way to better understand bias in the epidemic curves of COVID-19 due to errors in testing is to empirically evaluate misclassification of diagnosis in clinical settings and apply this knowledge to adjustment of epidemic curves.

Explaining the variation in the attained power of a stepped-wedge trial with unequal cluster sizes.

BACKGROUND: In a cross-sectional stepped-wedge trial with unequal cluster sizes, attained power in the trial depends on the realized allocation of the clusters. This attained power may differ from the expected power calculated using standard formulae by averaging the attained powers over all allocations the randomization algorithm can generate. We investigated the effect of design factors and allocation characteristics on attained power and developed models to predict attained power based on allocation characteristics. METHOD: Based on data simulated and analyzed using linear mixed-effects models, we evaluated the distribution of attained powers under different scenarios with varying intraclass correlation coefficient (ICC) of the responses, coefficient of variation (CV) of the cluster sizes, number of cluster-size groups, distributions of group sizes, and number of clusters. We explored the relationship between attained power and two allocation characteristics: the individual-level correlation between treatment status and time period, and the absolute treatment group imbalance. When computational time was excessive due to a scenario having a large number of possible allocations, we developed regression models to predict attained power using the treatment-vs-time period correlation and absolute treatment group imbalance as predictors. RESULTS: The risk of attained power falling more than 5% below the expected or nominal power decreased as the ICC or number of clusters increased and as the CV decreased. Attained power was strongly affected by the treatment-vs-time period correlation. The absolute treatment group imbalance had much less impact on attained power. The attained power for any allocation was predicted accurately using a logistic regression model with the treatment-vs-time period correlation and the absolute treatment group imbalance as predictors. CONCLUSION: In a stepped-wedge trial with unequal cluster sizes, the risk that randomization yields an allocation with inadequate attained power depends on the ICC, the CV of the cluster sizes, and number of clusters. To reduce the computational burden of simulating attained power for allocations, the attained power can be predicted via regression modeling. Trial designers can reduce the risk of low attained power by restricting the randomization algorithm to avoid allocations with large treatment-vs-time period correlations.

Effects of Multiple Forms of Information Bias on Estimated Prevalence of Suicide Attempts According to Sexual Orientation: An Application of a Bayesian Misclassification Correction Method to Data From a Systematic Review.

Multiple epidemiologic studies demonstrate a disparity in suicide risk between sexual minority (lesbian, gay, bisexual) and heterosexual populations; however, both "exposure" (sexual minority status) and outcome (suicide attempts) may be affected by information bias related to errors in self-reporting. We therefore applied a Bayesian misclassification correction method to account for possible information biases. A systematic literature search identified studies of lifetime suicide attempts in sexual minority and heterosexual adults, and frequentist meta-analysis was used to generate unadjusted estimates of relative risk. A Bayesian model accounting for prior information about sensitivity and specificity of exposure and outcome measures was used to adjust for misclassification biases. In unadjusted frequentist analysis, the relative risk of lifetime suicide attempt comparing sexual minority with heterosexual groups was 3.38 (95% confidence interval: 2.65, 4.32). In Bayesian reanalysis, the estimated prevalence was slightly reduced in heterosexual adults and increased in sexual minority adults, yielding a relative risk of 4.67 (95% credible interval: 3.94, 5.73). The disparity in lifetime suicide attempts between sexual minority and heterosexual adults is greater than previously estimated, when accounting for multiple forms of information bias. Additional research on the impact of information bias in studies of sexual minority health should be pursued.

Reconciling randomized trial evidence on proximal versus distal outcomes, with application to trials of influenza vaccination for healthcare workers.

When synthesizing the body of evidence concerning a clinical intervention, impacts on both proximal and distal outcome variables may be relevant. Assessments will be more defensible if results concerning a proximal outcome align with those concerning a corresponding distal outcome. We present a method to assess the coherence of empirical clinical trial results with biologic and mathematical first principles in situations where the intervention can only plausibly impact the distal outcome indirectly via the proximal outcome. The method comprises a probabilistic sensitivity analysis, where plausible ranges for key parameters are specified, resulting in a constellation of plausible pairs of estimated intervention effects, for the proximal and distal outcomes, respectively. Both outcome misclassification and sampling variability are reflected in the method. We apply our methodology in the context of cluster randomized trials to evaluate the impacts of vaccinating healthcare workers on the health of elderly patients, where the proximal outcome is suspected influenza and the distal outcome is death. However, there is scope to apply the method for other interventions in other disease areas.

Adjusting for differential misclassification in matched case-control studies utilizing health administrative data.

In epidemiological studies of secondary data sources, lack of accurate disease classifications often requires investigators to rely on diagnostic codes generated by physicians or hospital systems to identify case and control groups, resulting in a less-than-perfect assessment of the disease under investigation. Moreover, because of differences in coding practices by physicians, it is hard to determine the factors that affect the chance of an incorrectly assigned disease status. What results is a dilemma where assumptions of non-differential misclassification are questionable but, at the same time, necessary to proceed with statistical analyses. This paper develops an approach to adjust exposure-disease association estimates for disease misclassification, without the need of simplifying non-differentiality assumptions, or prior information about a complicated classification mechanism. We propose to leverage rich temporal information on disease-specific healthcare utilization to estimate each participant's probability of being a true case and to use these estimates as weights in a Bayesian analysis of matched case-control data. The approach is applied to data from a recent observational study into the early symptoms of multiple sclerosis (MS), where MS cases were identified from Canadian health administrative databases and matched to population controls that are assumed to be correctly classified. A comparison of our results with those from non-differentially adjusted analyses reveals conflicting inferences and highlights that ill-suited assumptions of non-differential misclassification can exacerbate biases in association estimates.

Bayesian inference for unidirectional misclassification of a binary response trait.

When assessing association between a binary trait and some covariates, the binary response may be subject to unidirectional misclassification. Unidirectional misclassification can occur when revealing a particular level of the trait is associated with a type of cost, such as a social desirability or financial cost. The feasibility of addressing misclassification is commonly obscured by model identification issues. The current paper attempts to study the efficacy of inference when the binary response variable is subject to unidirectional misclassification. From a theoretical perspective, we demonstrate that the key model parameters possess identifiability, except for the case with a single binary covariate. From a practical standpoint, the logistic model with quantitative covariates can be weakly identified, in the sense that the Fisher information matrix may be near singular. This can make learning some parameters difficult under certain parameter settings, even with quite large samples. In other cases, the stronger identification enables the model to provide more effective adjustment for unidirectional misclassification. An extension to the Poisson approximation of the binomial model reveals the identifiability of the Poisson and zero-inflated Poisson models. For fully identified models, the proposed method adjusts for misclassification based on learning from data. For binary models where there is difficulty in identification, the method is useful for sensitivity analyses on the potential impact from unidirectional misclassification.