Causation and familial confounding as explanations for the associations of polygenic risk scores with breast cancer: Evidence from innovative ICE FALCON and ICE CRISTAL analyses.

A polygenic risk score (PRS) combines the associations of multiple genetic variants that could be due to direct causal effects, indirect genetic effects, or other sources of familial confounding. We have developed new approaches to assess evidence for and against causation by using family data for pairs of relatives (Inference about Causation from Examination of FAmiliaL CONfounding [ICE FALCON]) or measures of family history (Inference about Causation from Examining Changes in Regression coefficients and Innovative STatistical AnaLyses [ICE CRISTAL]). Inference is made from the changes in regression coefficients of relatives' PRSs or PRS and family history before and after adjusting for each other. We applied these approaches to two breast cancer PRSs and multiple studies and found that (a) for breast cancer diagnosed at a young age, for example, <50 years, there was no evidence that the PRSs were causal, while (b) for breast cancer diagnosed at later ages, there was consistent evidence for causation explaining increasing amounts of the PRS-disease association. The genetic variants in the PRS might be in linkage disequilibrium with truly causal variants and not causal themselves. These PRSs cause minimal heritability of breast cancer at younger ages. There is also evidence for nongenetic factors shared by first-degree relatives that explain breast cancer familial aggregation. Familial associations are not necessarily due to genes, and genetic associations are not necessarily causal.

Breast and bowel cancers diagnosed in people 'too young to have cancer': A blueprint for research using family and twin studies.

Young breast and bowel cancers (e.g., those diagnosed before age 40 or 50 years) have far greater morbidity and mortality in terms of years of life lost, and are increasing in incidence, but have been less studied. For breast and bowel cancers, the familial relative risks, and therefore the familial variances in age-specific log(incidence), are much greater at younger ages, but little of these familial variances has been explained. Studies of families and twins can address questions not easily answered by studies of unrelated individuals alone. We describe existing and emerging family and twin data that can provide special opportunities for discovery. We present designs and statistical analyses, including novel ideas such as the VALID (Variance in Age-specific Log Incidence Decomposition) model for causes of variation in risk, the DEPTH (DEPendency of association on the number of Top Hits) and other approaches to analyse genome-wide association study data, and the within-pair, ICE FALCON (Inference about Causation from Examining FAmiliaL CONfounding) and ICE CRISTAL (Inference about Causation from Examining Changes in Regression coefficients and Innovative STatistical AnaLysis) approaches to causation and familial confounding. Example applications to breast and colorectal cancer are presented. Motivated by the availability of the resources of the Breast and Colon Cancer Family Registries, we also present some ideas for future studies that could be applied to, and compared with, cancers diagnosed at older ages and address the challenges posed by young breast and bowel cancers.

Leveraging LD eigenvalue regression to improve the estimation of SNP heritability and confounding inflation.

Heritability is a fundamental concept in genetic studies, measuring the genetic contribution to complex traits and bringing insights about disease mechanisms. The advance of high-throughput technologies has provided many resources for heritability estimation. Linkage disequilibrium (LD) score regression (LDSC) estimates both heritability and confounding biases, such as cryptic relatedness and population stratification, among single-nucleotide polymorphisms (SNPs) by using only summary statistics released from genome-wide association studies. However, only partial information in the LD matrix is utilized in LDSC, leading to loss in precision. In this study, we propose LD eigenvalue regression (LDER), an extension of LDSC, by making full use of the LD information. Compared to state-of-the-art heritability estimating methods, LDER provides more accurate estimates of SNP heritability and better distinguishes the inflation caused by polygenicity and confounding effects. We demonstrate the advantages of LDER both theoretically and with extensive simulations. We applied LDER to 814 complex traits from UK Biobank, and LDER identified 363 significantly heritable phenotypes, among which 97 were not identified by LDSC.

Leveraging the local genetic structure for trans-ancestry association mapping.

Over the past two decades, genome-wide association studies (GWASs) have successfully advanced our understanding of the genetic basis of complex traits. Despite the fruitful discovery of GWASs, most GWAS samples are collected from European populations, and these GWASs are often criticized for their lack of ancestry diversity. Trans-ancestry association mapping (TRAM) offers an exciting opportunity to fill the gap of disparities in genetic studies between non-Europeans and Europeans. Here, we propose a statistical method, LOG-TRAM, to leverage the local genetic architecture for TRAM. By using biobank-scale datasets, we showed that LOG-TRAM can greatly improve the statistical power of identifying risk variants in under-represented populations while producing well-calibrated p values. We applied LOG-TRAM to the GWAS summary statistics of various complex traits/diseases from BioBank Japan, UK Biobank, and African populations. We obtained substantial gains in power and achieved effective correction of confounding biases in TRAM. Finally, we showed that LOG-TRAM can be successfully applied to identify ancestry-specific loci and the LOG-TRAM output can be further used for construction of more accurate polygenic risk scores in under-represented populations.

Patterns of Unwanted Biological and Technical Expression Variation Among 49 Human Tissues.

Tissue gene expression studies are impacted by biological and technical sources of variation, which can be broadly classified into wanted and unwanted variation. The latter, if not addressed, results in misleading biological conclusions. Methods have been proposed to reduce unwanted variation, such as normalization and batch correction. A more accurate understanding of all causes of variation could significantly improve the ability of these methods to remove unwanted variation while retaining variation corresponding to the biological question of interest. We used 17,282 samples from 49 human tissues in the Genotype-Tissue Expression data set (v8) to investigate patterns and causes of expression variation. Transcript expression was transformed to z-scores, and only the most variable 2% of transcripts were evaluated and clustered based on coexpression patterns. Clustered gene sets were assigned to different biological or technical causes based on histologic appearances and metadata elements. We identified 522 variable transcript clusters (median: 11 per tissue) among the samples. Of these, 63% were confidently explained, 16% were likely explained, 7% were low confidence explanations, and 14% had no clear cause. Histologic analysis annotated 46 clusters. Other common causes of variability included sex, sequencing contamination, immunoglobulin diversity, and compositional tissue differences. Less common biological causes included death interval (Hardy score), disease status, and age. Technical causes included blood draw timing and harvesting differences. Many of the causes of variation in bulk tissue expression were identifiable in the Tabula Sapiens data set of single-cell expression. This is among the largest explorations of the underlying sources of tissue expression variation. It uncovered expected and unexpected causes of variable gene expression and demonstrated the utility of matched histologic specimens. It further demonstrated the value of acquiring meaningful tissue harvesting metadata elements to use for improved normalization, batch correction, and analysis of both bulk and single-cell RNA-seq data.

A simulation-based bias analysis to assess the impact of unmeasured confounding when designing non-randomized database studies.

BACKGROUND: Unmeasured confounding is often raised as a source of potential bias during the design of non-randomized studies but quantifying such concerns is challenging. METHODS: We developed a simulation-based approach to assess the potential impact of unmeasured confounding during the study design stage. The approach involved generation of hypothetical individual-level cohorts using realistic parameters including a binary treatment (prevalence 25%), a time-to-event outcome (incidence 5%), 13 measured covariates, a binary unmeasured confounder (u1, 10%), and a binary measured 'proxy' variable (p1) correlated with u1. Strength of unmeasured confounding and correlations between u1 and p1 were varied in simulation scenarios. Treatment effects were estimated with, a) no adjustment, b) adjustment for measured confounders (Level 1), c) adjustment for measured confounders and their proxy (Level 2). We computed absolute standardized mean differences in u1 and p1 and relative bias with each level of adjustment. RESULTS: Across all scenarios, Level 2 adjustment led to improvement in balance of u1, but this improvement was highly dependent on the correlation between u1 and p1. Level 2 adjustments also had lower relative bias than Level 1 adjustments (in strong u1 scenarios: relative bias of 9.2%, 12.2%, 13.5% at correlations 0.7, 0.5, and 0.3, respectively versus 16.4%, 15.8%, 15.0% for Level 1, respectively). CONCLUSION: An approach using simulated individual-level data was useful to explicitly convey the potential for bias due to unmeasured confounding while designing non-randomized studies and can be helpful in informing design choices.

Recent Methodological Trends in Epidemiology: No Need for Data-Driven Variable Selection?

Variable selection in regression models is a particularly important issue in epidemiology, where one usually encounters observational studies. In contrast to randomized trials or experiments, confounding is often not controlled by the study design, but has to be accounted for by suitable statistical methods. For instance, when risk factors should be identified with unconfounded effect estimates, multivariable regression techniques can help to adjust for confounders. We investigated the current practice of variable selection in 4 major epidemiologic journals in 2019 and found that the majority of articles used subject-matter knowledge to determine a priori the set of included variables. In comparison with previous reviews from 2008 and 2015, fewer articles applied data-driven variable selection. Furthermore, for most articles the main aim of analysis was hypothesis-driven effect estimation in rather low-dimensional data situations (i.e., large sample size compared with the number of variables). Based on our results, we discuss the role of data-driven variable selection in epidemiology.

Targeted Learning with an Undersmoothed Lasso Propensity Score Model for Large-Scale Covariate Adjustment in Healthcare Database Studies.

Lasso regression is widely used for large-scale propensity score (PS) estimation in healthcare database studies. In these settings, previous work has shown that undersmoothing (overfitting) Lasso PS models can improve confounding control, but it can also cause problems of non-overlap in covariate distributions. It remains unclear how to select the degree of undersmoothing when fitting large-scale Lasso PS models to improve confounding control while avoiding issues that can result from reduced covariate overlap. Here, we used simulations to evaluate the performance of using collaborative-controlled targeted learning to data-adaptively select the degree of undersmoothing when fitting large-scale PS models within both singly and doubly robust frameworks to reduce bias in causal estimators. Simulations showed that collaborative learning can data-adaptively select the degree of undersmoothing to reduce bias in estimated treatment effects. Results further showed that when fitting undersmoothed Lasso PS-models, the use of cross-fitting was important for avoiding non-overlap in covariate distributions and reducing bias in causal estimates.

On adjustment for temperature in heatwave epidemiology: a new method and toward clarification of methods to estimate health effects of heatwaves.

Defining the effect of exposure of interest and selecting an appropriate estimation method are prerequisite for causal inference. Understanding the ways in which association between heatwaves (i.e., consecutive days of extreme high temperature) and an outcome depends on whether adjustment was made for temperature and how such adjustment was conducted, is limited. This paper aims to investigate this dependency, demonstrate that temperature is a confounder in heatwave-outcome associations, and introduce a new modeling approach to estimate a new heatwave-outcome relation: E[R(Y)|HW=1, Z]/E[R(Y)|T=OT, Z], where HW is a daily binary variable to indicate the presence of a heatwave; R(Y) is the risk of an outcome, Y; T is a temperature variable; OT is optimal temperature; and Z is a set of confounders including typical confounders but also some types of T as a confounder. We recommend characterization of heatwave-outcome relations and careful selection of modeling approaches to understand the impacts of heatwaves under climate change. We demonstrate our approach using real-world data for Seoul, which suggests that the total effect of heatwaves may be larger than what may be inferred from the extant literature. An R package, HEAT (Heatwave effect Estimation via Adjustment for Temperature), was developed and made publicly available.

It's not all about residual confounding: a plea for QBA for epidemiologic researchers and educators.

We spend a great deal of time on confounding in our teaching, in our methods development and in our assessment of study results. This may give the impression that uncontrolled confounding is the biggest problem that observational epidemiology faces, when in fact, other sources of bias such as selection bias, measurement error, missing data, and misalignment of zero time may often (especially if they are all present in a single study) lead to a stronger deviation from the truth. Compared to the amount of time we spend teaching how to address confounding in a data analysis, we spend relatively little time teaching methods for simulating confounding (and other sources of bias) to learn their impact and develop plans to mitigate or quantify the bias. We review a paper by Desai et al that uses simulation methods to quantify the impact of an unmeasured confounder when it is completely missing or when a proxy of the confounder is measured. We use this article to discuss how we can use simulations of sources of bias to ensure we generate better and more valid study estimates, and we discuss the importance of simulating realistic datasets with plausible bias structures to guide data collection. If an advanced life form exists outside of our current universe and they came to earth with the goal of scouring the published epidemiologic literature to understand what the biggest problem epidemiologists have, they would quickly discover that the limitations section of publications would provide them with all the information they needed. And most likely what they would conclude is that the biggest problem that we face is uncontrolled confounding. It seems to be an obsession of ours.

Confounder Adjustment Using the Disease Risk Score: A Proposal for Weighting Methods.

Propensity score analysis is a common approach to addressing confounding in nonrandomized studies. Its implementation, however, requires important assumptions (e.g., positivity). The disease risk score (DRS) is an alternative confounding score that can relax some of these assumptions. Like the propensity score, the DRS summarizes multiple confounders into a single score, on which conditioning by matching allows the estimation of causal effects. However, matching relies on arbitrary choices for pruning out data (e.g., matching ratio, algorithm, and caliper width) and may be computationally demanding. Alternatively, weighting methods, common in propensity score analysis, are easy to implement and may entail fewer choices, yet none have been developed for the DRS. Here we present 2 weighting approaches: One derives directly from inverse probability weighting; the other, named target distribution weighting, relates to importance sampling. We empirically show that inverse probability weighting and target distribution weighting display performance comparable to matching techniques in terms of bias but outperform them in terms of efficiency (mean squared error) and computational speed (up to >870 times faster in an illustrative study). We illustrate implementation of the methods in 2 case studies where we investigate placebo treatments for multiple sclerosis and administration of aspirin in stroke patients.

The State of Use and Utility of Negative Controls in Pharmacoepidemiologic Studies.

Uses of real-world data in drug safety and effectiveness studies are often challenged by various sources of bias. We undertook a systematic search of the published literature through September 2020 to evaluate the state of use and utility of negative controls to address bias in pharmacoepidemiologic studies. Two reviewers independently evaluated study eligibility and abstracted data. Our search identified 184 eligible studies for inclusion. Cohort studies (115, 63%) and administrative data (114, 62%) were, respectively, the most common study design and data type used. Most studies used negative control outcomes (91, 50%), and for most studies the target source of bias was unmeasured confounding (93, 51%). We identified 4 utility domains of negative controls: 1) bias detection (149, 81%), 2) bias correction (16, 9%), 3) P-value calibration (8, 4%), and 4) performance assessment of different methods used in drug safety studies (31, 17%). The most popular methodologies used were the 95% confidence interval and P-value calibration. In addition, we identified 2 reference sets with structured steps to check the causality assumption of the negative control. While negative controls are powerful tools in bias detection, we found many studies lacked checking the underlying assumptions. This article is part of a Special Collection on Pharmacoepidemiology.

A Cautionary Note on Using Propensity Score Calibration to Control for Unmeasured Confounding Bias When the Surrogacy Assumption Is Absent.

Conventional propensity score methods encounter challenges when unmeasured confounding is present, as it becomes impossible to accurately estimate the gold-standard propensity score when data on certain confounders are unavailable. Propensity score calibration (PSC) addresses this issue by constructing a surrogate for the gold-standard propensity score under the surrogacy assumption. This assumption posits that the error-prone propensity score, based on observed confounders, is independent of the outcome when conditioned on the gold-standard propensity score and the exposure. However, this assumption implies that confounders cannot directly impact the outcome and that their effects on the outcome are solely mediated through the propensity score. This raises concerns regarding the applicability of PSC in practical settings where confounders can directly affect the outcome. While PSC aims to target a conditional treatment effect by conditioning on a subject's unobservable propensity score, the causal interest in the latter case lies in a conditional treatment effect conditioned on a subject's baseline characteristics. Our analysis reveals that PSC is generally biased unless the effects of confounders on the outcome and treatment are proportional to each other. Furthermore, we identify 2 sources of bias: 1) the noncollapsibility of effect measures, such as the odds ratio or hazard ratio and 2) residual confounding, as the calibrated propensity score may not possess the properties of a valid propensity score.

Assessing Etiologic Heterogeneity for Multinomial Outcome with Two-Phase Outcome-Dependent Sampling Design.

Etiologic heterogeneity occurs when distinct sets of events or exposures give rise to different subtypes of disease. Inference about subtype-specific exposure effects from two-phase outcome-dependent sampling data requires adjustment for both confounding and the sampling design. Common approaches to inference for these effects do not necessarily appropriately adjust for these sources of bias, or allow for formal comparisons of effects across different subtypes. Herein, using inverse probability weighting (IPW) to fit a multinomial model is shown to yield valid inference with this sampling design for subtype-specific exposure effects and contrasts thereof. The IPW approach is compared to common regression-based methods for assessing exposure effect heterogeneity using simulations. The methods are applied to estimate subtype-specific effects of various exposures on breast cancer risk in the Carolina Breast Cancer Study.

Overcoming Time-Varying Confounding in Self-Controlled Case Series with Active Comparators: Application and Recommendations.

Confounding by indication is a key challenge for pharmacoepidemiologists. Although self-controlled study designs address time-invariant confounding, indications sometimes vary over time. For example, infection might act as a time-varying confounder in a study of antibiotics and uveitis, because it is time-limited and a direct cause both of receiving antibiotics and uveitis. Methods for incorporating active comparators in self-controlled studies to address such time-varying confounding by indication have only recently been developed. In this paper we formalize these methods, and provide a detailed description for how the active comparator rate ratio can be derived in a self-controlled case series (SCCS): either by explicitly comparing the regression coefficients for a drug of interest and an active comparator under certain circumstances using a simple ratio approach, or through the use of a nested regression model. The approaches are compared in two case studies, one examining the association between thiazolidinediones and fractures, and one examining the association between fluoroquinolones and uveitis using the UK Clinical Practice Research DataLink. Finally, we provide recommendations for the use of these methods, which we hope will support the design, execution and interpretation of SCCS using active comparators and thereby increase the robustness of pharmacoepidemiological studies.

Nonparametric causal mediation analysis for stochastic interventional (in)direct effects.

Causal mediation analysis has historically been limited in two important ways: (i) a focus has traditionally been placed on binary exposures and static interventions and (ii) direct and indirect effect decompositions have been pursued that are only identifiable in the absence of intermediate confounders affected by exposure. We present a theoretical study of an (in)direct effect decomposition of the population intervention effect, defined by stochastic interventions jointly applied to the exposure and mediators. In contrast to existing proposals, our causal effects can be evaluated regardless of whether an exposure is categorical or continuous and remain well-defined even in the presence of intermediate confounders affected by exposure. Our (in)direct effects are identifiable without a restrictive assumption on cross-world counterfactual independencies, allowing for substantive conclusions drawn from them to be validated in randomized controlled trials. Beyond the novel effects introduced, we provide a careful study of nonparametric efficiency theory relevant for the construction of flexible, multiply robust estimators of our (in)direct effects, while avoiding undue restrictions induced by assuming parametric models of nuisance parameter functionals. To complement our nonparametric estimation strategy, we introduce inferential techniques for constructing confidence intervals and hypothesis tests, and discuss open-source software, the $\texttt{medshift}$$\texttt{R}$ package, implementing the proposed methodology. Application of our (in)direct effects and their nonparametric estimators is illustrated using data from a comparative effectiveness trial examining the direct and indirect effects of pharmacological therapeutics on relapse to opioid use disorder.

Alleviating spatial confounding in frailty models.

The confounding between fixed effects and (spatial) random effects in a regression setup is termed spatial confounding. This topic continues to gain attention and has been studied extensively in recent years, given that failure to account for this may lead to a suboptimal inference. To mitigate this, a variety of projection-based approaches under the class of restricted spatial models are available in the context of generalized linear mixed models. However, these projection approaches cannot be directly extended to the spatial survival context via frailty models due to dimension incompatibility between the fixed and spatial random effects. In this work, we introduce a two-step approach to handle this, which involves (i) projecting the design matrix to the dimension of the spatial effect (via dimension reduction) and (ii) assuring that the random effect is orthogonal to this new design matrix (confounding alleviation). Under a fully Bayesian paradigm, we conduct fast estimation and inference using integrated nested Laplace approximation. Both simulation studies and application to a motivating data evaluating respiratory cancer survival in the US state of California reveal the advantages of our proposal in terms of model performance and confounding alleviation, compared to alternatives.

Assessing the causal effects of a stochastic intervention in time series data: are heat alerts effective in preventing deaths and hospitalizations?

The methodological development of this article is motivated by the need to address the following scientific question: does the issuance of heat alerts prevent adverse health effects? Our goal is to address this question within a causal inference framework in the context of time series data. A key challenge is that causal inference methods require the overlap assumption to hold: each unit (i.e., a day) must have a positive probability of receiving the treatment (i.e., issuing a heat alert on that day). In our motivating example, the overlap assumption is often violated: the probability of issuing a heat alert on a cooler day is near zero. To overcome this challenge, we propose a stochastic intervention for time series data which is implemented via an incremental time-varying propensity score (ItvPS). The ItvPS intervention is executed by multiplying the probability of issuing a heat alert on day $t$-conditional on past information up to day $t$-by an odds ratio $\delta_t$. First, we introduce a new class of causal estimands, which relies on the ItvPS intervention. We provide theoretical results to show that these causal estimands can be identified and estimated under a weaker version of the overlap assumption. Second, we propose nonparametric estimators based on the ItvPS and derive an upper bound for the variances of these estimators. Third, we extend this framework to multisite time series using a spatial meta-analysis approach. Fourth, we show that the proposed estimators perform well in terms of bias and root mean squared error via simulations. Finally, we apply our proposed approach to estimate the causal effects of increasing the probability of issuing heat alerts on each warm-season day in reducing deaths and hospitalizations among Medicare enrollees in 2837 US counties.

Isolating the effect of confounding from the observed survival benefit of screening participants - a methodological approach illustrated by data from the German mammography screening programme.

BACKGROUND: Mammography screening programmes (MSP) aim to reduce breast cancer mortality by shifting diagnoses to earlier stages. However, it is difficult to evaluate the effectiveness of current MSP because analyses can only rely on observational data, comparing women who participate in screening with women who do not. These comparisons are subject to several biases: one of the most important is self-selection into the MSP, which introduces confounding and is difficult to control for. Here, we propose an approach to quantify confounding based on breast cancer survival analyses using readily available routine data sources. METHODS: Using data from the Cancer Registry of North Rhine-Westphalia, Germany, we estimate the relative contribution of confounding to the observed survival benefit of participants of the German MSP. This is accomplished by comparing non-participants, participants with screen-detected and participants with interval breast cancers for the endpoints "death from breast cancer" and "death from all causes other than breast cancer" - the latter being assumed to be unrelated to any MSP effect. By using different contrasts, we eliminate the effects of stage shift, lead and length time bias. The association of breast cancer detection mode with survival is analysed using Cox models in 68,230 women, aged 50-69 years, with breast cancer diagnosed in 2006-2014 and followed up until 2018. RESULTS: The hazard of dying from breast cancer was lower in participants with screen-detected cancer than in non-participants (HR = 0.21, 95% CI: 0.20-0.22), but biased by lead and length time bias, and confounding. When comparing participants with interval cancers and non-participants, the survival advantage was considerably smaller (HR = 0.62, 95% CI: 0.58-0.66), due to the elimination of stage shift and lead time bias. Finally, considering only mortality from causes other than breast cancer in the latter comparison, length time bias was minimised, but a survival advantage was still present (HR = 0.63, 95% CI: 0.56-0.70), which we attribute to confounding. CONCLUSIONS: This study shows that, in addition to stage shift, lead and length time bias, confounding is an essential component when comparing the survival of MSP participants and non-participants. We further show that the confounding effect can be quantified without explicit knowledge of potential confounders by using a negative control outcome.

Broadcasters, receivers, functional groups of metabolites, and the link to heart failure by revealing metabolomic network connectivity.

BACKGROUND AND OBJECTIVE: Blood-based small molecule metabolites offer easy accessibility and hold significant potential for insights into health processes, the impact of lifestyle, and genetic variation on disease, enabling precise risk prevention. In a prospective study with records of heart failure (HF) incidence, we present metabolite profiling data from individuals without HF at baseline. METHODS: We uncovered the interconnectivity of metabolites using data-driven and causal networks augmented with polygenic factors. Exploring the networks, we identified metabolite broadcasters, receivers, mediators, and subnetworks corresponding to functional classes of metabolites, and provided insights into the link between metabolomic architecture and regulation in health. We incorporated the network structure into the identification of metabolites associated with HF to control the effect of confounding metabolites. RESULTS: We identified metabolites associated with higher and lower risk of HF incidence, such as glycine, ureidopropionic and glycocholic acids, and LPC 18:2. These associations were not confounded by the other metabolites due to uncovering the connectivity among metabolites and adjusting each association for the confounding metabolites. Examples of our findings include the direct influence of asparagine on glycine, both of which were inversely associated with HF. These two metabolites were influenced by polygenic factors and only essential amino acids, which are not synthesized in the human body and are obtained directly from the diet. CONCLUSION: Metabolites may play a critical role in linking genetic background and lifestyle factors to HF incidence. Revealing the underlying connectivity of metabolites associated with HF strengthens the findings and facilitates studying complex conditions like HF.