Cost-effectiveness analysis in R using a multi-state modelling survival analysis framework: a tutorial

This tutorial provides a step-by-step guide to performing cost-effectiveness analysis using a multi-state modelling approach. Alongside the tutorial we provide easy-to-use functions in the statistics package R. We argue this multi-state modelling approach using a package such as R has advantages over approaches where models are built in a spreadsheet package. In particular, using a syntax-based approach means there is a written record of what was done and the calculations are transparent. Reproducing the analysis is straightforward as the syntax just needs to be run again. The approach can be thought of as an alternative way to build a Markov decision analytic model, which also has the option to use a state-arrival extended approach if the Markov property does not hold. In the state-arrival extended multi-state model a covariate that represents patients’ history is included allowing the Markov property to be tested. We illustrate the building of multi-state survival models, making predictions from the models and assessing fits. We then proceed to perform a cost-effectiveness analysis including deterministic and probabilistic sensitivity analyses. Finally, we show how to create two common methods of visualising the results, namely cost-effectiveness planes and cost-effectiveness acceptability curves. The analysis is implemented entirely within R. It is based on adaptions to functions in the existing R package mstate, to accommodate parametric multi-state modelling which facilitates extrapolation of survival curves

Effects of vildagliptin on ventricular function in patients with type 2 diabetes mellitus and heart failure: a randomized placebo-controlled trial

Objectives: This study sought to examine the safety of the dipeptidyl peptidase-4 inhibitor, vildagliptin, in patients with heart failure and reduced ejection fraction. Background: Many patients with type 2 diabetes mellitus have heart failure and it is important to know about the safety of new treatments for diabetes in these individuals. Methods: Patients 18 to 85 years of age with type 2 diabetes and heart failure (New York Heart Association functional class I to III and left ventricular ejection fraction [LVEF] <0.40) were randomized to 52 weeks treatment with vildagliptin 50 mg twice daily (50 mg once daily if treated with a sulfonylurea) or matching placebo. The primary endpoint was between-treatment change from baseline in echocardiographic LVEF using a noninferiority margin of −3.5%. Results: A total of 254 patients were randomly assigned to vildagliptin (n = 128) or placebo (n = 126). Baseline LVEF was 30.6 ± 6.8% in the vildagliptin group and 29.6 ± 7.7% in the placebo group. The adjusted mean change in LVEF was 4.95 ± 1.25% in vildagliptin treated patients and 4.33 ± 1.23% in placebo treated patients, a difference of 0.62 (95% confidence interval [CI]: −2.21 to 3.44; p = 0.667). This difference met the predefined noninferiority margin of −3.5%. Left ventricular end-diastolic and end-systolic volumes increased more in the vildagliptin group by 17.1 ml (95% CI: 4.6 to 29.5 ml; p = 0.007) and 9.4 ml (95% CI: −0.49 to 19.4 ml; p = 0.062), respectively. Decrease in hemoglobin A1c from baseline to 16 weeks, the main secondary endpoint, was greater in the vildagliptin group: −0.62% (95% CI: −0.93 to −0.30%; p < 0.001; −6.8 mmol/mol; 95% CI: −10.2 to −3.3 mmol/mol). Conclusions: Compared with placebo, vildagliptin had no major effect on LVEF but did lead to an increase in left ventricular volumes, the cause and clinical significance of which is unknown. More evidence is needed regarding the safety of dipeptidyl peptidase-4 inhibitors in patients with heart failure and left ventricular systolic dysfunction. (Effect of Vildagliptin on Left Ventricular Function in Patients With Type 2 Diabetes and Congestive Heart Failure; NCT00894868

Evidence synthesis for constructing directed acyclic graphs (ESC-DAGs): a novel and systematic method for building directed acyclic graphs

Background: Directed acyclic graphs (DAGs) are popular tools for identifying appropriate adjustment strategies for epidemiological analysis. However, a lack of direction on how to build them is problematic. As a solution, we propose using a combination of evidence synthesis strategies and causal inference principles to integrate the DAG-building exercise within the review stages of research projects. We demonstrate this idea by introducing a novel protocol: ‘Evidence Synthesis for Constructing Directed Acyclic Graphs’ (ESC-DAGs)’.\ud Methods: ESC-DAGs operates on empirical studies identified by a literature search, ideally a novel systematic review or review of systematic reviews. It involves three key stages: (i) the conclusions of each study are ‘mapped’ into a DAG; (ii) the causal structures in these DAGs are systematically assessed using several causal inference principles and are corrected accordingly; (iii) the resulting DAGs are then synthesised into one or more ‘integrated DAGs’. This demonstration article didactically applies ESC-DAGs to the literature on parental influences on offspring alcohol use during adolescence. Conclusions: ESC-DAGs is a practical, systematic and transparent approach for developing DAGs from background knowledge. These DAGs can then direct primary data analysis and DAG-based sensitivity analysis. ESC-DAGs has a modular design to allow researchers who are experienced DAG users to both use and improve upon the approach. It is also accessible to researchers with limited experience of DAGs or evidence synthesis

Estimation of Survival Probabilities for Use in Cost-effectiveness Analyses: A Comparison of a Multi-state Modeling Survival Analysis Approach with Partitioned Survival and Markov Decision-Analytic Modeling.

Modeling of clinical-effectiveness in a cost-effectiveness analysis typically involves some form of partitioned survival or Markov decision-analytic modeling. The health states progression-free, progression and death and the transitions between them are frequently of interest. With partitioned survival, progression is not modeled directly as a state; instead, time in that state is derived from the difference in area between the overall survival and the progression-free survival curves. With Markov decision-analytic modeling, a priori assumptions are often made with regard to the transitions rather than using the individual patient data directly to model them. This article compares a multi-state modeling survival regression approach to these two common methods. As a case study, we use a trial comparing rituximab in combination with fludarabine and cyclophosphamide v. fludarabine and cyclophosphamide alone for the first-line treatment of chronic lymphocytic leukemia. We calculated mean Life Years and QALYs that involved extrapolation of survival outcomes in the trial. We adapted an existing multi-state modeling approach to incorporate parametric distributions for transition hazards, to allow extrapolation. The comparison showed that, due to the different assumptions used in the different approaches, a discrepancy in results was evident. The partitioned survival and Markov decision-analytic modeling deemed the treatment cost-effective with ICERs of just over £16,000 and £13,000, respectively. However, the results with the multi-state modeling were less conclusive, with an ICER of just over £29,000. This work has illustrated that it is imperative to check whether assumptions are realistic, as different model choices can influence clinical and cost-effectiveness results

Beyond 10-Year Risk: A Cost-Effectiveness Analysis of Statins for the Primary Prevention of Cardiovascular Disease.

BACKGROUND: Cholesterol guidelines typically prioritize primary prevention statin therapy on the basis of 10-year risk of cardiovascular disease. The advent of generic pricing may justify expansion of statin eligibility. Moreover, 10-year risk may not be the optimal approach for statin prioritization. We estimated the cost-effectiveness of expanding preventive statin eligibility and evaluated novel approaches to prioritization from a Scottish health sector perspective. METHODS: A computer simulation model predicted long-term health and cost outcomes in Scottish adults ≥40 years of age. Epidemiologic analysis was completed using the Scottish Heart Health Extended Cohort, Scottish Morbidity Records, and National Records of Scotland. A simulation cohort was constructed with data from the Scottish Health Survey 2011 and contemporary population estimates. Treatment and cost inputs were derived from published literature and health service cost data. The main outcome measure was the lifetime incremental cost-effectiveness ratio, evaluated as cost (2020 GBP) per quality-adjusted life-year (QALY) gained. Three approaches to statin prioritization were analyzed: 10-year risk scoring using the ASSIGN score, age-stratified risk thresholds to increase treatment rates in younger individuals, and absolute risk reduction (ARR)-guided therapy to increase treatment rates in individuals with elevated cholesterol levels. For each approach, 2 policies were considered: treating the same number of individuals as those with an ASSIGN score ≥20% (age-stratified risk threshold 20, ARR 20) and treating the same number of individuals as those with an ASSIGN score ≥10% (age-stratified risk threshold 10, ARR 10). RESULTS: Compared with an ASSIGN score ≥20%, reducing the risk threshold for statin initiation to 10% expanded eligibility from 804 000 (32% of adults ≥40 years of age without CVD) to 1 445 500 individuals (58%). This policy would be cost-effective (incremental cost-effectiveness ratio, £12 300/QALY [95% CI, £7690/QALY-£26 500/QALY]). Incremental to an ASSIGN score ≥20%, ARR 20 produced ≈8800 QALYs and was cost-effective (£7050/QALY [95% CI, £4560/QALY-£10 700/QALY]). Incremental to an ASSIGN score ≥10%, ARR 10 produced ≈7950 QALYs and was cost-effective (£11 700/QALY [95% CI, £9250/QALY-£16 900/QALY]). Both age-stratified risk threshold strategies were dominated (ie, more expensive and less effective than alternative treatment strategies). CONCLUSIONS: Generic pricing has rendered preventive statin therapy cost-effective for many adults. ARR-guided therapy is more effective than 10-year risk scoring and is cost-effective

Comparison of conventional lipoprotein tests and apolipoproteins in the prediction of cardiovascular disease: data from UK Biobank

Background: Total cholesterol and high-density lipoprotein cholesterol (HDL-C) measurements are central to cardiovascular disease (CVD) risk assessment, but there is continuing debate around the utility of other lipids for risk prediction. Methods: Participants from UK Biobank without baseline CVD and not taking statins, with relevant lipid measurements (n=346 686), were included in the primary analysis. An incident fatal or nonfatal CVD event occurred in 6216 participants (1656 fatal) over a median of 8.9 years. Associations of nonfasting lipid measurements (total cholesterol, HDL-C, non–HDL-C, direct and calculated low-density lipoprotein cholesterol [LDL-C], and apolipoproteins [Apo] A1 and B) with CVD were compared using Cox models adjusting for classical risk factors, and predictive utility was determined by the C-index and net reclassification index. Prediction was also tested in 68 649 participants taking a statin with or without baseline CVD (3515 CVD events). Results: ApoB, LDL-C, and non–HDL-C were highly correlated (r>0.90), while HDL-C was strongly correlated with ApoA1 (r=0.92). After adjustment for classical risk factors, 1 SD increase in ApoB, direct LDL-C, and non–HDL-C had similar associations with composite fatal/nonfatal CVD events (hazard ratio, 1.23, 1.20, 1.21, respectively). Associations for 1 SD increase in HDL-C and ApoA1 were also similar (hazard ratios, 0.81 [both]). Adding either total cholesterol and HDL-C, or ApoB and ApoA, to a CVD risk prediction model (C-index, 0.7378) yielded similar improvement in discrimination (C-index change, 0.0084; 95% CI, 0.0065, 0.0104, and 0.0089; 95% CI, 0.0069, 0.0109, respectively). Once total and HDL-C were in the model, no further substantive improvement was achieved with the addition of ApoB (C-index change, 0.0004; 95% CI, 0.0000, 0.0008) or any measure of LDL-C. Results for predictive utility were similar for a fatal CVD outcome, and in a discordance analysis. In participants taking a statin, classical risk factors (C-index, 0.7118) were improved by non–HDL-C (C-index change, 0.0030; 95% CI, 0.0012, 0.0048) or ApoB (C-index change, 0.0030; 95% CI, 0.0011, 0.0048). However, adding ApoB or LDL-C to a model already containing non–HDL-C did not further improve discrimination. Conclusions: Measurement of total cholesterol and HDL-C in the nonfasted state is sufficient to capture the lipid-associated risk in CVD prediction, with no meaningful improvement from addition of apolipoproteins, direct or calculated LDL-C

Glycated hemoglobin, prediabetes and the links to cardiovascular disease: data from UK Biobank

OBJECTIVE: HbA1c levels are increasingly measured in screening for diabetes; we investigated whether HbA1c may simultaneously improve cardiovascular disease (CVD) risk assessment, using QRISK3, American College of Cardiology/American Heart Association (ACC/AHA), and Systematic COronary Risk Evaluation (SCORE) scoring systems. RESEARCH DESIGN AND METHODS: UK Biobank participants without baseline CVD or known diabetes (n = 357,833) were included. Associations of HbA1c with CVD was assessed using Cox models adjusting for classical risk factors. Predictive utility was determined by the C-index and net reclassification index (NRI). A separate analysis was conducted in 16,596 participants with known baseline diabetes. RESULTS: Incident fatal or nonfatal CVD, as defined in the QRISK3 prediction model, occurred in 12,877 participants over 8.9 years. Of participants, 3.3% (n = 11,665) had prediabetes (42.0–47.9 mmol/mol [6.0–6.4%]) and 0.7% (n = 2,573) had undiagnosed diabetes (≥48.0 mmol/mol [≥6.5%]). In unadjusted models, compared with the reference group (<42.0 mmol/mol [<6.0%]), those with prediabetes and undiagnosed diabetes were at higher CVD risk: hazard ratio (HR) 1.83 (95% CI 1.69–1.97) and 2.26 (95% CI 1.96–2.60), respectively. After adjustment for classical risk factors, these attenuated to HR 1.11 (95% CI 1.03–1.20) and 1.20 (1.04–1.38), respectively. Adding HbA1c to the QRISK3 CVD risk prediction model (C-index 0.7392) yielded a small improvement in discrimination (C-index increase of 0.0004 [95% CI 0.0001–0.0007]). The NRI showed no improvement. Results were similar for models based on the ACC/AHA and SCORE risk models. CONCLUSIONS: The near twofold higher unadjusted risk for CVD in people with prediabetes is driven mainly by abnormal levels of conventional CVD risk factors. While HbA1c adds minimally to cardiovascular risk prediction, those with prediabetes should have their conventional cardiovascular risk factors appropriately measured and managed

Lipoprotein(a) and cardiovascular disease: prediction, attributable risk fraction and estimating benefits from novel interventions

Aims:   To investigate the population attributable fraction due to elevated lipoprotein (a) (Lp(a)) and the utility of measuring Lp(a) in cardiovascular disease (CVD) risk prediction. Methods and results:   In 413 734 participants from UK Biobank, associations of serum Lp(a) with composite fatal/non-fatal CVD (n = 10 066 events), fatal CVD (n = 3247), coronary heart disease (CHD; n = 18 292), peripheral vascular disease (PVD; n = 2716), and aortic stenosis (n = 901) were compared using Cox models. Median Lp(a) was 19.7 nmol/L (interquartile interval 7.6–75.3 nmol/L). About 20.8% had Lp(a) values >100 nmol/L; 9.2% had values >175 nmol/L. After adjustment for classical risk factors, 1 SD increment in log Lp(a) was associated with a hazard ratio for fatal/non-fatal CVD of 1.12 [95% confidence interval (CI) 1.10–1.15]. Similar associations were observed with fatal CVD, CHD, PVD, and aortic stenosis. Adding Lp(a) to a prediction model containing traditional CVD risk factors in a primary prevention group improved the C-index by +0.0017 (95% CI 0.0008–0.0026). In the whole cohort, Lp(a) above 100 nmol/L was associated with a population attributable fraction (PAF) of 5.8% (95% CI 4.9–6.7%), and for Lp(a) above 175 nmol/L the PAF was 3.0% (2.4–3.6%). Assuming causality and an achieved Lp(a) reduction of 80%, an ongoing trial to lower Lp(a) in patients with CVD and Lp(a) above 175 nmol/L may reduce CVD risk by 20.0% and CHD by 24.4%. Similar benefits were also modelled in the whole cohort, regardless of baseline CVD. Conclusion:   Population screening for elevated Lp(a) may help to predict CVD and target Lp(a) lowering drugs, if such drugs prove efficacious, to those with markedly elevated levels

Protocol for the development of a CONSORT extension for RCTs using cohorts and routinely collected health data.

Background: Randomized controlled trials (RCTs) are often complex and expensive to perform. Less than one third achieve planned recruitment targets, follow-up can be labor-intensive, and many have limited real-world generalizability. Designs for RCTs conducted using cohorts and routinely collected health data, including registries, electronic health records, and administrative databases, have been proposed to address these challenges and are being rapidly adopted. These designs, however, are relatively recent innovations, and published RCT reports often do not describe important aspects of their methodology in a standardized way. Our objective is to extend the Consolidated Standards of Reporting Trials (CONSORT) statement with a consensus-driven reporting guideline for RCTs using cohorts and routinely collected health data. Methods: The development of this CONSORT extension will consist of five phases. Phase 1 (completed) consisted of the project launch, including fundraising, the establishment of a research team, and development of a conceptual framework. In phase 2, a systematic review will be performed to identify publications (1) that describe methods or reporting considerations for RCTs conducted using cohorts and routinely collected health data or (2) that are protocols or report results from such RCTs. An initial "long list" of possible modifications to CONSORT checklist items and possible new items for the reporting guideline will be generated based on the Strengthening the Reporting of Observational Studies in Epidemiology (STROBE) and The REporting of studies Conducted using Observational Routinely-collected health Data (RECORD) statements. Additional possible modifications and new items will be identified based on the results of the systematic review. Phase 3 will consist of a three-round Delphi exercise with methods and content experts to evaluate the "long list" and generate a "short list" of key items. In phase 4, these items will serve as the basis for an in-person consensus meeting to finalize a core set of items to be included in the reporting guideline and checklist. Phase 5 will involve drafting the checklist and elaboration-explanation documents, and dissemination and implementation of the guideline. Discussion: Development of this CONSORT extension will contribute to more transparent reporting of RCTs conducted using cohorts and routinely collected health data

HMG-coenzyme A reductase inhibition, type 2 diabetes, and bodyweight: evidence from genetic analysis and randomised trials.

BACKGROUND: Statins increase the risk of new-onset type 2 diabetes mellitus. We aimed to assess whether this increase in risk is a consequence of inhibition of 3-hydroxy-3-methylglutaryl-CoA reductase (HMGCR), the intended drug target. METHODS: We used single nucleotide polymorphisms in the HMGCR gene, rs17238484 (for the main analysis) and rs12916 (for a subsidiary analysis) as proxies for HMGCR inhibition by statins. We examined associations of these variants with plasma lipid, glucose, and insulin concentrations; bodyweight; waist circumference; and prevalent and incident type 2 diabetes. Study-specific effect estimates per copy of each LDL-lowering allele were pooled by meta-analysis. These findings were compared with a meta-analysis of new-onset type 2 diabetes and bodyweight change data from randomised trials of statin drugs. The effects of statins in each randomised trial were assessed using meta-analysis. FINDINGS: Data were available for up to 223 463 individuals from 43 genetic studies. Each additional rs17238484-G allele was associated with a mean 0·06 mmol/L (95% CI 0·05-0·07) lower LDL cholesterol and higher body weight (0·30 kg, 0·18-0·43), waist circumference (0·32 cm, 0·16-0·47), plasma insulin concentration (1·62%, 0·53-2·72), and plasma glucose concentration (0·23%, 0·02-0·44). The rs12916 SNP had similar effects on LDL cholesterol, bodyweight, and waist circumference. The rs17238484-G allele seemed to be associated with higher risk of type 2 diabetes (odds ratio [OR] per allele 1·02, 95% CI 1·00-1·05); the rs12916-T allele association was consistent (1·06, 1·03-1·09). In 129 170 individuals in randomised trials, statins lowered LDL cholesterol by 0·92 mmol/L (95% CI 0·18-1·67) at 1-year of follow-up, increased bodyweight by 0·24 kg (95% CI 0·10-0·38 in all trials; 0·33 kg, 95% CI 0·24-0·42 in placebo or standard care controlled trials and -0·15 kg, 95% CI -0·39 to 0·08 in intensive-dose vs moderate-dose trials) at a mean of 4·2 years (range 1·9-6·7) of follow-up, and increased the odds of new-onset type 2 diabetes (OR 1·12, 95% CI 1·06-1·18 in all trials; 1·11, 95% CI 1·03-1·20 in placebo or standard care controlled trials and 1·12, 95% CI 1·04-1·22 in intensive-dose vs moderate dose trials). INTERPRETATION: The increased risk of type 2 diabetes noted with statins is at least partially explained by HMGCR inhibition. FUNDING: The funding sources are cited at the end of the paper