Mild-to-Moderate Kidney Dysfunction and Cardiovascular Disease: Observational and Mendelian Randomization Analyses.

BACKGROUND: End-stage renal disease is associated with a high risk of cardiovascular events. It is unknown, however, whether mild-to-moderate kidney dysfunction is causally related to coronary heart disease (CHD) and stroke. METHODS: Observational analyses were conducted using individual-level data from 4 population data sources (Emerging Risk Factors Collaboration, EPIC-CVD [European Prospective Investigation into Cancer and Nutrition-Cardiovascular Disease Study], Million Veteran Program, and UK Biobank), comprising 648 135 participants with no history of cardiovascular disease or diabetes at baseline, yielding 42 858 and 15 693 incident CHD and stroke events, respectively, during 6.8 million person-years of follow-up. Using a genetic risk score of 218 variants for estimated glomerular filtration rate (eGFR), we conducted Mendelian randomization analyses involving 413 718 participants (25 917 CHD and 8622 strokes) in EPIC-CVD, Million Veteran Program, and UK Biobank. RESULTS: There were U-shaped observational associations of creatinine-based eGFR with CHD and stroke, with higher risk in participants with eGFR values <60 or >105 mL·min-1·1.73 m-2, compared with those with eGFR between 60 and 105 mL·min-1·1.73 m-2. Mendelian randomization analyses for CHD showed an association among participants with eGFR <60 mL·min-1·1.73 m-2, with a 14% (95% CI, 3%-27%) higher CHD risk per 5 mL·min-1·1.73 m-2 lower genetically predicted eGFR, but not for those with eGFR >105 mL·min-1·1.73 m-2. Results were not materially different after adjustment for factors associated with the eGFR genetic risk score, such as lipoprotein(a), triglycerides, hemoglobin A1c, and blood pressure. Mendelian randomization results for stroke were nonsignificant but broadly similar to those for CHD. CONCLUSIONS: In people without manifest cardiovascular disease or diabetes, mild-to-moderate kidney dysfunction is causally related to risk of CHD, highlighting the potential value of preventive approaches that preserve and modulate kidney function.

The impact of fatty acids biosynthesis on the risk of cardiovascular diseases in Europeans and East Asians: a Mendelian randomization study.

Despite early interest, the evidence linking fatty acids to cardiovascular diseases (CVDs) remains controversial. We used Mendelian randomization to explore the involvement of polyunsaturated (PUFA) and monounsaturated (MUFA) fatty acids biosynthesis in the etiology of several CVD endpoints in up to 1 153 768 European (maximum 123 668 cases) and 212 453 East Asian (maximum 29 319 cases) ancestry individuals. As instruments, we selected single nucleotide polymorphisms mapping to genes with well-known roles in PUFA (i.e. FADS1/2 and ELOVL2) and MUFA (i.e. SCD) biosynthesis. Our findings suggest that higher PUFA biosynthesis rate (proxied by rs174576 near FADS1/2) is related to higher odds of multiple CVDs, particularly ischemic stroke, peripheral artery disease and venous thromboembolism, whereas higher MUFA biosynthesis rate (proxied by rs603424 near SCD) is related to lower odds of coronary artery disease among Europeans. Results were unclear for East Asians as most effect estimates were imprecise. By triangulating multiple approaches (i.e. uni-/multi-variable Mendelian randomization, a phenome-wide scan, genetic colocalization and within-sibling analyses), our results are compatible with higher low-density lipoprotein (LDL) cholesterol (and possibly glucose) being a downstream effect of higher PUFA biosynthesis rate. Our findings indicate that PUFA and MUFA biosynthesis are involved in the etiology of CVDs and suggest LDL cholesterol as a potential mediating trait between PUFA biosynthesis and CVDs risk.

The EWAS Catalog: a database of epigenome-wide association studies.

Epigenome-wide association studies (EWAS) seek to quantify associations between traits/exposures and DNA methylation measured at thousands or millions of CpG sites across the genome. In recent years, the increase in availability of DNA methylation measures in population-based cohorts and case-control studies has resulted in a dramatic expansion of the number of EWAS being performed and published. To make this rich source of results more accessible, we have manually curated a database of CpG-trait associations (with p<1x10 -4) from published EWAS, each assaying over 100,000 CpGs in at least 100 individuals. From January 7, 2022, The EWAS Catalog contained 1,737,746 associations from 2,686 EWAS. This includes 1,345,398 associations from 342 peer-reviewed publications. In addition, it also contains summary statistics for 392,348 associations from 427 EWAS, performed on data from the Avon Longitudinal Study of Parents and Children (ALSPAC) and the Gene Expression Omnibus (GEO). The database is accompanied by a web-based tool and R package, giving researchers the opportunity to query EWAS associations quickly and easily, and gain insight into the molecular underpinnings of disease as well as the impact of traits and exposures on the DNA methylome. The EWAS Catalog data extraction team continue to update the database monthly and we encourage any EWAS authors to upload their summary statistics to our website. Details of how to upload data can be found here: http://www.ewascatalog.org/upload. The EWAS Catalog is available at http://www.ewascatalog.org.

Coding and regulatory variants are associated with serum protein levels and disease.

Circulating proteins can be used to diagnose and predict disease-related outcomes. A deep serum proteome survey recently revealed close associations between serum protein networks and common disease. In the current study, 54,469 low-frequency and common exome-array variants were compared to 4782 protein measurements in the serum of 5343 individuals from the AGES Reykjavik cohort. This analysis identifies a large number of serum proteins with genetic signatures overlapping those of many diseases. More specifically, using a study-wide significance threshold, we find that 2021 independent exome array variants are associated with serum levels of 1942 proteins. These variants reside in genetic loci shared by hundreds of complex disease traits, highlighting serum proteins' emerging role as biomarkers and potential causative agents of a wide range of diseases.

A robust mean and variance test with application to high-dimensional phenotypes.

Most studies of continuous health-related outcomes examine differences in mean levels (location) of the outcome by exposure. However, identifying effects on the variability (scale) of an outcome, and combining tests of mean and variability (location-and-scale), could provide additional insights into biological mechanisms. A joint test could improve power for studies of high-dimensional phenotypes, such as epigenome-wide association studies of DNA methylation at CpG sites. One possible cause of heterogeneity of variance is a variable interacting with exposure in its effect on outcome, so a joint test of mean and variability could help in the identification of effect modifiers. Here, we review a scale test, based on the Brown-Forsythe test, for analysing variability of a continuous outcome with respect to both categorical and continuous exposures, and develop a novel joint location-and-scale score (JLSsc) test. These tests were compared to alternatives in simulations and used to test associations of mean and variability of DNA methylation with gender and gestational age using data from the Accessible Resource for Integrated Epigenomics Studies (ARIES). In simulations, the Brown-Forsythe and JLSsc tests retained correct type I error rates when the outcome was not normally distributed in contrast to the other approaches tested which all had inflated type I error rates. These tests also identified > 7500 CpG sites for which either mean or variability in cord blood methylation differed according to gender or gestational age. The Brown-Forsythe test and JLSsc are robust tests that can be used to detect associations not solely driven by a mean effect.

Sclerostin Downregulation Globally by Naturally Occurring Genetic Variants, or Locally in Atherosclerotic Plaques, Does Not Associate With Cardiovascular Events in Humans.

Inhibition of sclerostin increases bone formation and decreases bone resorption, leading to increased bone mass, bone mineral density, and bone strength and reduced fracture risk. In a clinical study of the sclerostin antibody romosozumab versus alendronate in postmenopausal women (ARCH), an imbalance in adjudicated serious cardiovascular (CV) adverse events driven by an increase in myocardial infarction (MI) and stroke was observed. To explore whether there was a potential mechanistic plausibility that sclerostin expression, or its inhibition, in atherosclerotic (AS) plaques may have contributed to this imbalance, sclerostin was immunostained in human plaques to determine whether it was detected in regions relevant to plaque stability in 94 carotid and 50 femoral AS plaques surgically collected from older female patients (mean age 69.6 ± 10.4 years). Sclerostin staining was absent in most plaques (67%), and when detected, it was of reduced intensity compared with normal aorta and was located in deeper regions of the plaque/wall but was not observed in areas considered relevant to plaque stability (fibrous cap and endothelium). Additionally, genetic variants associated with lifelong reduced sclerostin expression were explored for associations with phenotypes including those related to bone physiology and CV risk factors/events in a population-based phenomewide association study (PheWAS). Natural genetic modulation of sclerostin by variants with a significant positive effect on bone physiology showed no association with lifetime risk of MI or stroke. These data do not support a causal association between the presence of sclerostin, or its inhibition, in the vasculature and increased risk of serious cardiovascular events. © 2021 The Authors. Journal of Bone and Mineral Research published by Wiley Periodicals LLC on behalf of American Society for Bone and Mineral Research (ASBMR).

A fast and efficient colocalization algorithm for identifying shared genetic risk factors across multiple traits.

Genome-wide association studies (GWAS) have identified thousands of genomic regions affecting complex diseases. The next challenge is to elucidate the causal genes and mechanisms involved. One approach is to use statistical colocalization to assess shared genetic aetiology across multiple related traits (e.g. molecular traits, metabolic pathways and complex diseases) to identify causal pathways, prioritize causal variants and evaluate pleiotropy. We propose HyPrColoc (Hypothesis Prioritisation for multi-trait Colocalization), an efficient deterministic Bayesian algorithm using GWAS summary statistics that can detect colocalization across vast numbers of traits simultaneously (e.g. 100 traits can be jointly analysed in around 1 s). We perform a genome-wide multi-trait colocalization analysis of coronary heart disease (CHD) and fourteen related traits, identifying 43 regions in which CHD colocalized with ≥1 trait, including 5 previously unknown CHD loci. Across the 43 loci, we further integrate gene and protein expression quantitative trait loci to identify candidate causal genes.

The Effect of Attention Deficit/Hyperactivity Disorder on Physical Health Outcomes: A 2-Sample Mendelian Randomization Study.

Attention-deficit/hyperactivity disorder (ADHD) is associated with a broad range of physical health problems. Using different research designs to test whether ADHD has a causal role in these associations is important because comorbid health problems increase the serious social and economic impacts of ADHD. We used 2-sample Mendelian randomization (MR) to infer causal relationships between ADHD and previously implicated physical health conditions. Different MR methods were used to test the robustness and plausibility of our findings. Consistent findings underwent bidirectional and multivariable MR. We found evidence of ADHD having a causal effect on childhood obesity (odds ratio = 1.29, 95% confidence interval: 1.02, 1.63) and coronary artery disease (odds ratio = 1.11, 95% confidence interval: 1.03, 1.19) with consistent results across MR approaches. There was additional MR evidence for a bidirectional relationship between ADHD and childhood obesity. The relationship with coronary artery disease attenuated when controlling for childhood obesity. There was little evidence for inferring a causal effect on other cardiometabolic, autoimmune, allergic, and neurological diseases. Our findings strengthen the argument for effective treatment of children with ADHD, and suggest that clinicians who manage ADHD need to be aware of the risk of childhood obesity to reduce future risks of coronary artery disease.

DNA methylation signatures of adolescent victimization: analysis of a longitudinal monozygotic twin sample.

Accumulating evidence suggests that individuals exposed to victimization at key developmental stages may have different epigenetic fingerprints compared to those exposed to no/minimal stressful events, however results are inconclusive. This study aimed to strengthen causal inference regarding the impact of adolescent victimization on the epigenome by controlling for genetic variation, age, gender, and shared environmental exposures. We conducted longitudinal epigenome-wide association analyses (EWAS) on DNA methylation (DNAm) profiles of 118 monozygotic (MZ) twin pairs from the Environmental Risk study with and without severe adolescent victimization generated using buccal DNA collected at ages 5, 10 and 18, and the Illumina EPIC array. Additionally, we performed cross-sectional EWAS on age-18 blood and buccal DNA from the same individuals to elucidate tissue-specific signatures of severe adolescent victimization. Our analyses identified 20 suggestive differentially methylated positions (DMPs) (P < 5e-05), with altered DNAm trajectories between ages 10-18 associated with severe adolescent victimization (∆Beta range = -5.5%-5.3%). Age-18 cross-sectional analyses revealed 72 blood (∆Beta range = -2.2%-3.4%) and 42 buccal (∆Beta range = -3.6%-4.6%) suggestive severe adolescent victimization-associated DMPs, with some evidence of convergent signals between these two tissue types. Downstream regional analysis identified significant differentially methylated regions (DMRs) in LGR6 and ANK3 (Sidák P = 5e-09 and 4.07e-06), and one upstream of CCL27 (Sidák P = 2.80e-06) in age-18 blood and buccal EWAS, respectively. Our study represents the first longitudinal MZ twin analysis of DNAm and severe adolescent victimization, providing initial evidence for altered DNA methylomic signatures in individuals exposed to adolescent victimization.

Phenome-wide Mendelian randomization mapping the influence of the plasma proteome on complex diseases.

The human proteome is a major source of therapeutic targets. Recent genetic association analyses of the plasma proteome enable systematic evaluation of the causal consequences of variation in plasma protein levels. Here we estimated the effects of 1,002 proteins on 225 phenotypes using two-sample Mendelian randomization (MR) and colocalization. Of 413 associations supported by evidence from MR, 130 (31.5%) were not supported by results of colocalization analyses, suggesting that genetic confounding due to linkage disequilibrium is widespread in naïve phenome-wide association studies of proteins. Combining MR and colocalization evidence in cis-only analyses, we identified 111 putatively causal effects between 65 proteins and 52 disease-related phenotypes ( https://www.epigraphdb.org/pqtl/ ). Evaluation of data from historic drug development programs showed that target-indication pairs with MR and colocalization support were more likely to be approved, evidencing the value of this approach in identifying and prioritizing potential therapeutic targets.

A robust and efficient method for Mendelian randomization with hundreds of genetic variants.

Mendelian randomization (MR) is an epidemiological technique that uses genetic variants to distinguish correlation from causation in observational data. The reliability of a MR investigation depends on the validity of the genetic variants as instrumental variables (IVs). We develop the contamination mixture method, a method for MR with two modalities. First, it identifies groups of genetic variants with similar causal estimates, which may represent distinct mechanisms by which the risk factor influences the outcome. Second, it performs MR robustly and efficiently in the presence of invalid IVs. Compared to other robust methods, it has the lowest mean squared error across a range of realistic scenarios. The method identifies 11 variants associated with increased high-density lipoprotein-cholesterol, decreased triglyceride levels, and decreased coronary heart disease risk that have the same directions of associations with various blood cell traits, suggesting a shared mechanism linking lipids and coronary heart disease risk mediated via platelet aggregation.

MendelianRandomization v0.5.0: updates to an R package for performing Mendelian randomization analyses using summarized data.

The MendelianRandomization package is a software package written for the R software environment that implements methods for Mendelian randomization based on summarized data. In this manuscript, we describe functions that have been added to the package or updated in recent years. These features can be divided into four categories: robust methods for Mendelian randomization, methods for multivariable Mendelian randomization, functions for data visualization, and the ability to load data into the package seamlessly from the PhenoScanner web-resource. We provide examples of the graphical output produced by the data visualization commands, as well as syntax for obtaining suitable data and performing a Mendelian randomization analysis in a single line of code.

PhenoScanner V2: an expanded tool for searching human genotype-phenotype associations.

SUMMARY: PhenoScanner is a curated database of publicly available results from large-scale genetic association studies in humans. This online tool facilitates 'phenome scans', where genetic variants are cross-referenced for association with many phenotypes of different types. Here we present a major update of PhenoScanner ('PhenoScanner V2'), including over 150 million genetic variants and more than 65 billion associations (compared to 350 million associations in PhenoScanner V1) with diseases and traits, gene expression, metabolite and protein levels, and epigenetic markers. The query options have been extended to include searches by genes, genomic regions and phenotypes, as well as for genetic variants. All variants are positionally annotated using the Variant Effect Predictor and the phenotypes are mapped to Experimental Factor Ontology terms. Linkage disequilibrium statistics from the 1000 Genomes project can be used to search for phenotype associations with proxy variants. AVAILABILITY AND IMPLEMENTATION: PhenoScanner V2 is available at www.phenoscanner.medschl.cam.ac.uk.

Body mass index and all cause mortality in HUNT and UK Biobank studies: linear and non-linear mendelian randomisation analyses.

OBJECTIVE: To investigate the shape of the causal relation between body mass index (BMI) and mortality. DESIGN: Linear and non-linear mendelian randomisation analyses. SETTING: Nord-Trøndelag Health (HUNT) Study (Norway) and UK Biobank (United Kingdom). PARTICIPANTS: Middle to early late aged participants of European descent: 56 150 from the HUNT Study and 366 385 from UK Biobank. MAIN OUTCOME MEASURES: All cause and cause specific (cardiovascular, cancer, and non-cardiovascular non-cancer) mortality. RESULTS: 12 015 and 10 344 participants died during a median of 18.5 and 7.0 years of follow-up in the HUNT Study and UK Biobank, respectively. Linear mendelian randomisation analyses indicated an overall positive association between genetically predicted BMI and the risk of all cause mortality. An increase of 1 unit in genetically predicted BMI led to a 5% (95% confidence interval 1% to 8%) higher risk of mortality in overweight participants (BMI 25.0-29.9) and a 9% (4% to 14%) higher risk of mortality in obese participants (BMI ≥30.0) but a 34% (16% to 48%) lower risk in underweight (BMI <18.5) and a 14% (-1% to 27%) lower risk in low normal weight participants (BMI 18.5-19.9). Non-linear mendelian randomisation indicated a J shaped relation between genetically predicted BMI and the risk of all cause mortality, with the lowest risk at a BMI of around 22-25 for the overall sample. Subgroup analyses by smoking status, however, suggested an always-increasing relation of BMI with mortality in never smokers and a J shaped relation in ever smokers. CONCLUSIONS: The previously observed J shaped relation between BMI and risk of all cause mortality appears to have a causal basis, but subgroup analyses by smoking status revealed that the BMI-mortality relation is likely comprised of at least two distinct curves, rather than one J shaped relation. An increased risk of mortality for being underweight was only evident in ever smokers.

Genomic atlas of the human plasma proteome.

Although plasma proteins have important roles in biological processes and are the direct targets of many drugs, the genetic factors that control inter-individual variation in plasma protein levels are not well understood. Here we characterize the genetic architecture of the human plasma proteome in healthy blood donors from the INTERVAL study. We identify 1,927 genetic associations with 1,478 proteins, a fourfold increase on existing knowledge, including trans associations for 1,104 proteins. To understand the consequences of perturbations in plasma protein levels, we apply an integrated approach that links genetic variation with biological pathway, disease, and drug databases. We show that protein quantitative trait loci overlap with gene expression quantitative trait loci, as well as with disease-associated loci, and find evidence that protein biomarkers have causal roles in disease using Mendelian randomization analysis. By linking genetic factors to diseases via specific proteins, our analyses highlight potential therapeutic targets, opportunities for matching existing drugs with new disease indications, and potential safety concerns for drugs under development.

Association of LPA Variants With Risk of Coronary Disease and the Implications for Lipoprotein(a)-Lowering Therapies: A Mendelian Randomization Analysis.

Importance: Human genetic studies have indicated that plasma lipoprotein(a) (Lp[a]) is causally associated with the risk of coronary heart disease (CHD), but randomized trials of several therapies that reduce Lp(a) levels by 25% to 35% have not provided any evidence that lowering Lp(a) level reduces CHD risk. Objective: To estimate the magnitude of the change in plasma Lp(a) levels needed to have the same evidence of an association with CHD risk as a 38.67-mg/dL (ie, 1-mmol/L) change in low-density lipoprotein cholesterol (LDL-C) level, a change that has been shown to produce a clinically meaningful reduction in the risk of CHD. Design, Setting, and Participants: A mendelian randomization analysis was conducted using individual participant data from 5 studies and with external validation using summarized data from 48 studies. Population-based prospective cohort and case-control studies featured 20 793 individuals with CHD and 27 540 controls with individual participant data, whereas summarized data included 62 240 patients with CHD and 127 299 controls. Data were analyzed from November 2016 to March 2018. Exposures: Genetic LPA score and plasma Lp(a) mass concentration. Main Outcomes and Measures: Coronary heart disease. Results: Of the included study participants, 53% were men, all were of white European ancestry, and the mean age was 57.5 years. The association of genetically predicted Lp(a) with CHD risk was linearly proportional to the absolute change in Lp(a) concentration. A 10-mg/dL lower genetically predicted Lp(a) concentration was associated with a 5.8% lower CHD risk (odds ratio [OR], 0.942; 95% CI, 0.933-0.951; P = 3 × 10-37), whereas a 10-mg/dL lower genetically predicted LDL-C level estimated using an LDL-C genetic score was associated with a 14.5% lower CHD risk (OR, 0.855; 95% CI, 0.818-0.893; P = 2 × 10-12). Thus, a 101.5-mg/dL change (95% CI, 71.0-137.0) in Lp(a) concentration had the same association with CHD risk as a 38.67-mg/dL change in LDL-C level. The association of genetically predicted Lp(a) concentration with CHD risk appeared to be independent of changes in LDL-C level owing to genetic variants that mimic the relationship of statins, PCSK9 inhibitors, and ezetimibe with CHD risk. Conclusions and Relevance: The clinical benefit of lowering Lp(a) is likely to be proportional to the absolute reduction in Lp(a) concentration. Large absolute reductions in Lp(a) of approximately 100 mg/dL may be required to produce a clinically meaningful reduction in the risk of CHD similar in magnitude to what can be achieved by lowering LDL-C level by 38.67 mg/dL (ie, 1 mmol/L).

Longitudinal analysis strategies for modelling epigenetic trajectories.

Background: DNA methylation levels are known to vary over time, and modelling these trajectories is crucial for our understanding of the biological relevance of these changes over time. However, due to the computational cost of fitting multilevel models across the epigenome, most trajectory modelling efforts to date have focused on a subset of CpG sites identified through epigenome-wide association studies (EWAS) at individual time-points. Methods: We propose using linear regression across the repeated measures, estimating cluster-robust standard errors using a sandwich estimator, as a less computationally intensive strategy than multilevel modelling. We compared these two longitudinal approaches, as well as three approaches based on EWAS (associated at baseline, at any time-point and at all time-points), for identifying epigenetic change over time related to an exposure using simulations and by applying them to blood DNA methylation profiles from the Accessible Resource for Integrated Epigenomics Studies (ARIES). Results: Restricting association testing to EWAS at baseline identified a less complete set of associations than performing EWAS at each time-point or applying the longitudinal modelling approaches to the full dataset. Linear regression models with cluster-robust standard errors identified similar sets of associations with almost identical estimates of effect as the multilevel models, while also being 74 times more efficient. Both longitudinal modelling approaches identified comparable sets of CpG sites in ARIES with an association with prenatal exposure to smoking (>70% agreement). Conclusions: Linear regression with cluster-robust standard errors is an appropriate and efficient approach for longitudinal analysis of DNA methylation data.

A comparison of Cox and logistic regression for use in genome-wide association studies of cohort and case-cohort design.

Logistic regression is often used instead of Cox regression to analyse genome-wide association studies (GWAS) of single-nucleotide polymorphisms (SNPs) and disease outcomes with cohort and case-cohort designs, as it is less computationally expensive. Although Cox and logistic regression models have been compared previously in cohort studies, this work does not completely cover the GWAS setting nor extend to the case-cohort study design. Here, we evaluated Cox and logistic regression applied to cohort and case-cohort genetic association studies using simulated data and genetic data from the EPIC-CVD study. In the cohort setting, there was a modest improvement in power to detect SNP-disease associations using Cox regression compared with logistic regression, which increased as the disease incidence increased. In contrast, logistic regression had more power than (Prentice weighted) Cox regression in the case-cohort setting. Logistic regression yielded inflated effect estimates (assuming the hazard ratio is the underlying measure of association) for both study designs, especially for SNPs with greater effect on disease. Given logistic regression is substantially more computationally efficient than Cox regression in both settings, we propose a two-step approach to GWAS in cohort and case-cohort studies. First to analyse all SNPs with logistic regression to identify associated variants below a pre-defined P-value threshold, and second to fit Cox regression (appropriately weighted in case-cohort studies) to those identified SNPs to ensure accurate estimation of association with disease.

Semiparametric methods for estimation of a nonlinear exposure-outcome relationship using instrumental variables with application to Mendelian randomization.

Mendelian randomization, the use of genetic variants as instrumental variables (IV), can test for and estimate the causal effect of an exposure on an outcome. Most IV methods assume that the function relating the exposure to the expected value of the outcome (the exposure-outcome relationship) is linear. However, in practice, this assumption may not hold. Indeed, often the primary question of interest is to assess the shape of this relationship. We present two novel IV methods for investigating the shape of the exposure-outcome relationship: a fractional polynomial method and a piecewise linear method. We divide the population into strata using the exposure distribution, and estimate a causal effect, referred to as a localized average causal effect (LACE), in each stratum of population. The fractional polynomial method performs metaregression on these LACE estimates. The piecewise linear method estimates a continuous piecewise linear function, the gradient of which is the LACE estimate in each stratum. Both methods were demonstrated in a simulation study to estimate the true exposure-outcome relationship well, particularly when the relationship was a fractional polynomial (for the fractional polynomial method) or was piecewise linear (for the piecewise linear method). The methods were used to investigate the shape of relationship of body mass index with systolic blood pressure and diastolic blood pressure.