Skip to main content
NCBI home page
Sleep logoLink to Sleep
. 2024 Mar 7;47(9):zsae064. doi: 10.1093/sleep/zsae064

Pro: comparing adherent to non-adherent patients can provide useful estimates of the effect of continuous positive airway pressure on cardiovascular outcomes

Brendan T Keenan 1,✉, Ulysses J Magalang 2, Greg Maislin 3
PMCID: PMC12104147  PMID: 38452013

This article is a written debate between the author(s) of this article and the author(s) of the opposing argument [1].

Argument

The following argument was prepared in response to the question without the knowledge of the contents of the opposing argument.

Whether or not there are cardiovascular benefits of using continuous positive airway pressure (CPAP) for patients with obstructive sleep apnea (OSA) is a foundational question for sleep medicine research. Answering this question is also essential to clinical practice, both for cardiovascular endpoints and other health outcomes experienced by patients. We strongly contend not only that comparing adherent to non-adherent patients can provide estimates of the causal effect of CPAP that are useful for patients, clinicians, and policymakers, but also that these comparisons are the most appropriate way to answer this foundational question.

Given the high health costs of cardiovascular disease (CVD) [2] and established links between OSA and CVD [3, 4], many have investigated whether and in whom CPAP has cardiovascular benefits. Observational studies indicate that OSA is an independent risk factor for cardiovascular endpoints, including myocardial infarction [5], stroke [6], heart failure [7], and mortality [8]. Similarly, longitudinal studies demonstrate that CPAP reduces cardiovascular risk [9]. However, recent randomized trials (RCTs) building on this evidence have not found reductions in cardiovascular risk in participants randomized to CPAP [10–12]. Among several issues that may explain these inconsistent results [13–15], one particularly relevant to the present argument is poor adherence among those randomized to CPAP [16]. Without methods for ensuring high adherence among all participants randomized to therapy, which have not yet proven effective [16–19], RCTs are answering the question of whether assigning CPAP improves outcomes. This differs from the foundational question of the benefits of using CPAP, which can only be answered in RCTs using per-protocol analyses that lose the benefits of randomization.

Given poor adherence in RCTs, the most sensible way to understand the benefits of using CPAP is to directly compare adherent versus non-adherent patients. Notably, when recent RCTs performed these comparisons using causal inference techniques, results supported the benefits of CPAP consistent with observational data [10–13, 20]. However, RCTs often enroll patients who are not representative of those seen clinically [21]. The common exclusion of excessively sleepy patients is particularly problematic, as most recent studies [22–26], but not all [27, 28], suggest that these patients are more likely to experience adverse cardiovascular outcomes and, thus, cardiovascular benefits from CPAP. Thus, we assert that causal effects from comparisons of adherent versus non-adherent patients are most useful when estimated in real-world observational datasets containing more representative samples of patients.

Estimating treatment effects from this seemingly straightforward comparison requires causal inference techniques and consideration of the appropriate causal estimands [29–33]. The “potential outcomes” framework [34], which considers the outcomes (Yi) a specific patient would have experienced if they were adherent [Yi(adherent)] or non-adherent [Yi(non-adherent)] to CPAP, is helpful to formalize these concepts. As “each potential outcome is observable, but we can never observe them all” [35], the goal of causal inference is to estimate the unobserved potential outcome and quantify the causal effect of treatment (i.e. the expected difference in potential outcomes, denoted E[Yi(adherent)−Yi(non-adherent)]). Three such causal estimands are often defined based on the target population of interest:

  1. The average treatment effect (ATE) is the average effect of CPAP within the full population of adherent and non-adherent individuals.

  2. The ATE on the treated (ATT) is the average effect of CPAP among adherent patients (i.e. the “treated”), or the benefit these patients received from adhering to CPAP compared to their potential outcomes had these specific patients been non-adherent.

  3. The ATE on the Control (ATC) is the equivalent estimand among non-adherent patients (i.e. the “controls”).

To obtain these estimands, the expected differences in potential outcomes are derived with respect to all participants (ATE), only treated participants (ATT), or only controls (ATC), using appropriate weighting of samples or group differences (see further below) [30, 33]. Conditional causal estimands (CATE, CATT, and CATC) may also be defined by further restricting the target populations based on specific covariate values. While these estimands are, in theory, identical in RCTs, they may differ in observational data due to differences in the characteristics of each target sample (e.g. covariate differences between adherent versus non-adherent patients). When estimating the benefits of using CPAP from non-randomized comparisons, the ATT estimand may be of particular interest, as it provides a valid causal estimate of the benefit of CPAP in a population with characteristics similar to adherent patients.

The robustness of these causal estimands relies on the ability to satisfy three assumptions – conditional exchangeability, positivity, and consistency [32, 36–39]. Exchangeability asserts that the adherent and non-adherent groups share similar distributions of outcome predictors (e.g. no unmeasured confounding), with conditional exchangeability implying this holds conditional on covariates (e.g. within matched pairs or covariate-based subclasses). Positivity asserts that the probability of being adherent cannot be 0 or 1 for any subset defined by combinations of covariates; violating this extrapolates beyond observed data. Consistency assumes that the exposure is defined such that the observed outcome accurately represents the true (potential) outcome on treatment (e.g. there are not multiple versions of the exposure that differentially affect outcomes) [37, 38]. Rubin [35] expresses these concepts in terms of a “stable unit treatment value (SUTV)” assumption containing two components: no interference (i.e. each participant’s potential outcomes are not affected by other participants’ outcomes) and no hidden versions of treatment (related to consistency). Methods for deriving causal estimands within observational data focus on creating samples and estimates for which these assumptions hold.

Propensity score (PS) designs are one common approach to deriving causal estimands from non-randomized comparisons [29, 30]. These designs focus on creating a sample of treated (e.g. adherent) and untreated (e.g. non-adherent) patients balanced with respect to a rich set of baseline covariates related to the outcome of interest. When effectively implemented, PS designs permit valid causal interpretations of the estimated group differences (under the above-mentioned assumptions) [40]. An optimal design should result in overlapping PS distributions (e.g. positivity) and very small differences in baseline covariates between groups after accounting for the design (e.g. conditional exchangeability) [41], thereby greatly reducing potential bias, if not eliminating it entirely. Within this design, causal estimands can be derived by appropriately weighting the group differences [30, 33]. For example, in PS subclassification the ATE estimand is obtained by weighting the within-subclass differences by the total sample size in each subclass, whereas the ATT estimand is obtained by weighting within-subclass differences by the total number of treated patients in each subclass [30, 33].

A common misperception is that accurately predicting the exposure (e.g. CPAP adherence) is necessary in PS designs. Not only is this unnecessary, it can be counter-productive. Including variables related to exposure but unrelated to outcome will worsen precision of the estimated treatment effect without decreasing bias, while including variables in the design that are unrelated to exposure but related to outcome can improve precision without increasing bias [42]. This is profoundly important. It implies that it is vital to understand factors associated with the outcome (e.g. cardiovascular events) and then, through the design, ensure that the exposure groups are balanced on these factors. Thus, the ability to derive causal estimates from comparisons between adherent and non-adherent patients is limited by the ability to achieve exchangeability for variables related to cardiovascular endpoints. Hence, an essential part of the design process is engaging both cardiovascular and sleep experts to identify an extensive covariate set including most factors expected to influence cardiovascular risk. To avoid controlling for mediators or inducing biased associations, it is important to carefully consider the expected relationships and pathways linking adherence, covariates, and outcomes; drawing and interpreting directed acyclic graphs (or “DAGs”) can be particularly useful [39, 43, 44]. Ultimately, if adherent and non-adherent patients are balanced for all consensus confounders of cardiovascular outcomes, then it matters little how well we understand other factors related to CPAP adherence.

Notably, obtaining some of these data may require significant effort. Variables often overlooked or unmeasured include exercise [45], diet [46], and healthy user/healthy adherer status [47, 48]. Along with correlations with general health measures (e.g. obesity), validated questionnaires are likely to sufficiently capture bias due to imbalance in diet [49] or exercise [50]. Regarding healthy user/adherer biases, studies show patients adherent to placebo have improved cardiovascular outcomes [51, 52]. Although it is reasonable to assume that patients adherent to CPAP behave similarly to those adherent to placebo, data are mixed regarding whether CPAP adherent patients differ in their use of cardiovascular medications compared to non-adherent patients [53, 54]. To measure the propensity to be a healthy user/adherer, demographics, lifestyle and socioeconomic factors, and data from electronic health records (preventative screenings, vaccinations, prescriptions, and medication refills) are likely useful [47, 55, 56]. Creative designs can also mitigate bias [47]. Analyses could be restricted to patients engaging in specific behaviors correlated with healthy user/adherer status (e.g. requiring that all included patients received recommended vaccinations). Causal estimands that were conditional on being a healthy user/adherer can be compared to the same estimands in those not engaged in relevant health-related behaviors to understand bias or effect modification. Ultimately, to ensure meaningful comparisons between adherent and non-adherent patients, careful planning and resource allocation to measure these variables is needed.

Careful consideration of exposure definitions is also important. For longer-term outcomes, CPAP exposure may be constructed to represent adequate/consistent adherence over time and the unexposed condition constructed to represent no more than clinically trivial use. Thus, by design, there are only two observable treatment sequences. These constructions are especially appropriate for ATT estimands, where the objective is to replace the adherent patient’s “missing” potential outcome under the non-adherent condition using data from non-adherent patients that are exchangeable (e.g. have similar covariates). It is also possible to evaluate additional patterns of adherence (e.g. more variable use over time), which may be especially appropriate for shorter-term outcomes. Notably, adherence over time may depend on time-varying confounders. One way to account for these factors is using marginal structural models [57], where observations are weighted by the inverse of the estimated probability of receiving the observed sequence of treatments the individual actually received (termed “inverse probability of treatment weighting [IPTW]”).

After careful design and estimation of causal treatment effects, additional analyses can enhance understanding. For determining robustness to unobserved confounders, the E-value quantifies the magnitude of association that an unmeasured confounder needs to have with both exposure (e.g. CPAP adherence) and outcome (e.g. cardiovascular events), independent of included covariates, to negate the observed effects [58]. While this requires some subjectivity, put simply, the larger the E-value the more robust the association. Including a rich set of covariates can minimize the likelihood that an important independent confounder is missed. Data from observational designs may also be used to examine mediators (e.g. changes in BMI) or effect modifiers (e.g. subgroup analyses) of treatment effects to better understand generalizability. To evaluate effect modification, conditional causal estimands from PS designs in samples defined by each level of the covariate(s) can be compared. Together, these robustly designed comparisons and downstream analyses can maximize the usefulness of the estimated treatment effects.

Importantly, we must not lose sight of the clinical usefulness of these causal estimates, even if uncertainties remain. Often, RCTs are not required to provide evidence of sufficient quality for use by clinicians and policymakers [59]. Appropriately educating patients on the risks and likely outcomes of OSA could help to motivate acceptance and adherence to CPAP [19], which effectively treats OSA regardless of its long-term impact on cardiovascular risk. Should well-designed observational studies consistently show cardiovascular benefits of using CPAP, there is clinical utility in advising patients of the potential long-term benefits of adhering to therapy, even if we can never be 100% certain of no unmeasured confounding. Moreover, it seems preferable that this advice be rooted in comparisons from representative samples of patients who used CPAP versus those who did not, rather than a highly selected sample of patients randomized to therapy or no therapy (many of whom are non-adherent). Supporting the validity of this approach, the recent RCT-DUPLICATE initiative [60] shows good agreement between causal estimands from PS-designed observational studies and RCTs, particularly when the RCT can be closely emulated; similar studies on CPAP would be greatly beneficial. Consistent with this is the reality that differences between causal estimands in RCTs and observational data do not immediately imply a failure of the observational design, but could also reflect differences or limitations of the RCT.

Ultimately, it is crucial to recognize that estimating causal effects of CPAP on cardiovascular endpoints from comparisons between adherent and non-adherent patients is useful, rather than abandoning this knowledge in pursuit of a perfectly unbiased comparison or default to randomized comparisons of patients assigned to CPAP or no CPAP who do not represent patients seen in clinical practice [21].

Rebuttal to Opposing Argument

The following was prepared in response to the opposing argument [1].

We appreciate the viewpoint raised by Patel et al. in their opposing argument [1]. We agree on limitations of existing trials [13] and the need for carefully designed studies that include representative patients to understand the cardiovascular benefits of CPAP. However, as discussed below, there are flaws in the arguments leading to the authors’ conclusions that “opportunities to conduct feasible randomized clinical trials” [1] should be the focus of investigators seeking to understand the cardiovascular benefits of using CPAP.

The authors begin their argument against the usefulness of comparisons of adherent and non-adherent patients by noting that these comparisons “violate the core design principle of analysis by intent-to-treat” [1]. While it is true that reliance on a per protocol sample likely lessens the benefits of randomization, thereby requiring additional methods to mitigate bias, Patel et al overlook the fact that the estimand obtained from the intent-to-treat sample does not address the specific question at hand. Notably, the FDA [61] defines intention-to-treat as:

The principle that asserts that the effect of a treatment policy can be best assessed by evaluating on the basis of the intention to treat a subject (i.e., the planned treatment regimen) rather than the actual treatment given.

Thus, analyses under the intention-to-treat principle can inform treatment policy recommendations (e.g. regarding the cardiovascular benefit of prescribing CPAP). By design, intention-to-treat analyses do not estimate the benefits of actually using CPAP (the question of clinical/scientific interest in this debate). The same FDA guidance [61] defines per protocol as:

The set of data generated by the subset of subjects who complied with the protocol sufficiently to ensure that these data would be likely to exhibit the effects of treatment according to the underlying scientific model.

Therefore, to best understand the benefits of using treatment, rather than those attributable to the treatment policy, per protocol estimands are required. Without programs that ensure near-perfect adherence among those randomized to CPAP [18], the large proportion of patients excluded from such per-protocol analyses due to poor adherence requires well-designed causal inference approaches to derive these estimands through comparisons of adherent and non-adherent patients.

In considering these comparisons, the authors raise valid concerns surrounding the benefits of adherence to placebo. While we believe that there are unique challenges with complying with CPAP [53, 54], meaning that non-adherent patients will still exhibit other healthy behaviors, we concede that healthy user/adherer biases have likely not been sufficiently addressed in prior studies. However, this does not prevent future studies from doing so. Investment in well-designed studies that capture detailed information on healthy behaviors, which is becoming increasingly accessible through electronic health records, is needed. The same is true for known cardiovascular risk factors and determinants of cardiovascular health not readily available. As a first step, studies focused on identifying optimal approaches to quantifying healthy user/adherer biases and understanding how CPAP adherence is unique would be greatly beneficial. We contend that investment in causal inference will prove more worthwhile than investing in more large-scale randomized studies that do not include fully representative groups of patients [21] and are plagued by inadequate adherence [16], even if the opportunity for such trials arises.

When discussing causal inference designs, Patel et al. argue multiple times that predicting adherence to CPAP is required or that the inability to do so implies that these designs are not useful [1]. The authors go so far as to suggest that, “At a minimum, studies reporting such PS adjustments should report the proportion of variance in adherence that is explained by the PS” [1]. Here, they have succumbed to the common misperception noted in our Pro argument. The goal of PS designs specifically, and causal inference generally, is not to predict adherence but, rather, to create exchangeability between treated and untreated patients for covariates associated with outcomes [42, 62]. Efforts should focus on identifying, measuring, and creating balance on factors related to cardiovascular risk, not on predicting CPAP adherence. Importantly, studies have already shown an ability to predict future cardiovascular risk, including well-established risk factors and many clinically utilized risk scores [63, 64]. This literature, and not the literature on predictors of CPAP adherence, provides foundational information on factors to consider in the design of causal inference studies determining the cardiovascular benefits of using CPAP.

The authors raise important considerations regarding the potential for time-varying confounding in observational designs. However, overlooked is the fact that randomized trials, particularly with long-term endpoints, are not immune from post-randomization confounding and selection bias [65]. In addition to the IPTW approach noted in our counterpoint, Robins and Hernan [66] describe a broader class of approaches (termed g methods [67]) that should be considered when deriving causal estimates in the context of such confounding. If controlling for post-baseline factors, researchers must take care not to adjust for mediating variables.

Ultimately, we should not simply position randomization as a panacea for overcoming difficulties in understanding the benefits of CPAP. Randomized trials are important and powerful, but there is a tendency to overlook their shortcomings [68]. Data suggest that, despite common perceptions, well-designed observational studies generally do not overestimate treatment effects [69, 70] and can be complementary to randomized studies. While randomization may be preferred “all else being equal,” all else is not equal when attempting to understand the cardiovascular benefits of using CPAP. Patients in randomized studies do not represent those seen clinically [21] and, even if eligible, it seems unlikely that symptomatic patients will want to be randomized to no therapy for many years. Poor adherence to CPAP among randomized patients requires per-protocol comparisons of adherent versus non-adherent patients to understand the benefits of using treatment, rather than simply obtaining treatment policy insights from intention-to-treat analyses. These issues will persist even in opportunities where randomized trials are feasible.

Thus, rather than accepting “that the proliferation of studies comparing adherent to non-adherent patients does not provide useful estimates of the causal effect of CPAP” [1], we contend that the field needs to recognize the inability of randomized trials to answer some fundamental questions about the benefits of using CPAP, and commit to investing in well-designed causal inference studies that can better inform real-world clinical decisions.

Contributor Information

Brendan T Keenan, Division of Sleep Medicine, Department of Medicine, University of Pennsylvania Perelman School of Medicine, Philadelphia, PA, USA.

Ulysses J Magalang, Division of Pulmonary, Critical Care and Sleep Medicine, Department of Internal Medicine, The Ohio State University Wexner Medical Center, Columbus, OH, USA.

Greg Maislin, Division of Sleep Medicine, Department of Medicine, University of Pennsylvania Perelman School of Medicine, Philadelphia, PA, USA.

Funding

Professor Maislin and Mr. Keenan lead the Biostatistics Core in the Division of Sleep Medicine at the University of Pennsylvania, which is supported by National Heart, Lung, and Blood Institute (NHLBI) grant P01 HL160471 (Developing a P4 Medicine Approach to Obstructive Sleep Apnea).

Disclosure Statement

Professor Maislin is also Principal Biostatistician of Biomedical Statistical Consulting (Wynnewood, PA) and has supported numerous medical device studies that have used propensity score methods to achieve regulatory approval, unrelated to the present article. Mr. Keenan has supported these efforts in the role of the outcomes-blinded PS design statistician and receives compensation from Biomedical Statistical Consulting for this and other work. Dr. Magalang has no disclosures to report.

Data Availability

No new data were generated or analyzed in support of this research.

References

  • 1. Patel  SR, Sawyer  AM, Gottlieb  DJ.  Con: Can comparing adherent to non-adherent patients provide useful estimates of the effect of CPAP? Sleep.  2024;47(9):1–7. doi: 10.1093/sleep/zsae063 [DOI] [PubMed] [Google Scholar]
  • 2. Roth  GA, Mensah  GA, Johnson  CO, et al.; GBD-NHLBI-JACC Global Burden of Cardiovascular Diseases Writing Group. Global burden of cardiovascular diseases and risk factors, 1990-2019: update from the GBD 2019 study. J Am Coll Cardiol.  2020;76(25):2982–3021. doi: 10.1016/j.jacc.2020.11.010 [DOI] [PMC free article] [PubMed] [Google Scholar]
  • 3. Salman  LA, Shulman  R, Cohen  JB.  Obstructive sleep apnea, hypertension, and cardiovascular risk: epidemiology, pathophysiology, and management. Curr Cardiol Rep.  2020;22(2):6. doi: 10.1007/s11886-020-1257-y [DOI] [PubMed] [Google Scholar]
  • 4. Yeghiazarians  Y, Jneid  H, Tietjens  JR, et al. Obstructive sleep apnea and cardiovascular disease: a scientific statement from the American heart association. Circulation.  2021;144(3):e56–e67. doi: 10.1161/CIR.0000000000000988 [DOI] [PubMed] [Google Scholar]
  • 5. Shah  NA, Yaggi  HK, Concato  J, Mohsenin  V.  Obstructive sleep apnea as a risk factor for coronary events or cardiovascular death. Sleep Breath.  2010;14(2):131–136. doi: 10.1007/s11325-009-0298-7 [DOI] [PubMed] [Google Scholar]
  • 6. Yaggi  HK, Concato  J, Kernan  WN, Lichtman  JH, Brass  LM, Mohsenin  V.  Obstructive sleep apnea as a risk factor for stroke and death. N Engl J Med.  2005;353(19):2034–2041. doi: 10.1056/NEJMoa043104 [DOI] [PubMed] [Google Scholar]
  • 7. Gottlieb  DJ, Yenokyan  G, Newman  AB, et al. Prospective study of obstructive sleep apnea and incident coronary heart disease and heart failure: the sleep heart health study. Circulation.  2010;122(4):352–360. doi: 10.1161/CIRCULATIONAHA.109.901801 [DOI] [PMC free article] [PubMed] [Google Scholar]
  • 8. Xie  C, Zhu  R, Tian  Y, Wang  K.  Association of obstructive sleep apnoea with the risk of vascular outcomes and all-cause mortality: a meta-analysis. BMJ Open. 2017;7(12):e013983. doi: 10.1136/bmjopen-2016-013983 [DOI] [PMC free article] [PubMed] [Google Scholar]
  • 9. Marin  JM, Carrizo  SJ, Vicente  E, Agusti  AG.  Long-term cardiovascular outcomes in men with obstructive sleep apnoea-hypopnoea with or without treatment with continuous positive airway pressure: an observational study. Lancet.  2005;365(9464):1046–1053. doi: 10.1016/S0140-6736(05)71141-7 [DOI] [PubMed] [Google Scholar]
  • 10. McEvoy  RD, Antic  NA, Heeley  E, et al.; SAVE Investigators and Coordinators. CPAP for prevention of cardiovascular events in obstructive sleep apnea. N Engl J Med.  2016;375(10):919–931. doi: 10.1056/NEJMoa1606599 [DOI] [PubMed] [Google Scholar]
  • 11. Peker  Y, Glantz  H, Eulenburg  C, Wegscheider  K, Herlitz  J, Thunstrom  E.  Effect of positive airway pressure on cardiovascular outcomes in coronary artery disease patients with nonsleepy obstructive sleep apnea. The RICCADSA randomized controlled trial. Am J Respir Crit Care Med.  2016;194(5):613–620. doi: 10.1164/rccm.201601-0088OC [DOI] [PubMed] [Google Scholar]
  • 12. Sanchez-de-la-Torre  M, Sanchez-de-la-Torre  A, Bertran  S, et al.; Spanish Sleep Network. Effect of obstructive sleep apnoea and its treatment with continuous positive airway pressure on the prevalence of cardiovascular events in patients with acute coronary syndrome (ISAACC study): a randomised controlled trial. Lancet Respir Med. 2020;8(4):359–367. doi: 10.1016/S2213-2600(19)30271-1 [DOI] [PubMed] [Google Scholar]
  • 13. Pack  AI, Magalang  UJ, Singh  B, Kuna  ST, Keenan  BT, Maislin  G.  Randomized clinical trials of cardiovascular disease in obstructive sleep apnea: understanding and overcoming bias. Sleep.  2021;44(2). doi: 10.1093/sleep/zsaa229 [DOI] [PMC free article] [PubMed] [Google Scholar]
  • 14. Javaheri  S, Martinez-Garcia  MA, Campos-Rodriguez  F.  CPAP treatment and cardiovascular prevention: we need to change the design and implementation of our trials. Chest.  2019;156(3):431–437. doi: 10.1016/j.chest.2019.04.092 [DOI] [PubMed] [Google Scholar]
  • 15. Gottlieb  DJ.  Does obstructive sleep apnea treatment reduce cardiovascular risk?: it is far too soon to say. JAMA.  2017;318(2):128–130. doi: 10.1001/jama.2017.7966 [DOI] [PubMed] [Google Scholar]
  • 16. Rotenberg  BW, Murariu  D, Pang  KP.  Trends in CPAP adherence over twenty years of data collection: a flattened curve. J Otolaryngol Head Neck Surg. 2016;45(1):43. doi: 10.1186/s40463-016-0156-0 [DOI] [PMC free article] [PubMed] [Google Scholar]
  • 17. Bakker  JP, Weaver  TE, Parthasarathy  S, Aloia  MS.  Adherence to CPAP: what should we be aiming for, and how can we get there? Chest.  2019;155(6):1272–1287. doi: 10.1016/j.chest.2019.01.012 [DOI] [PubMed] [Google Scholar]
  • 18. Sawyer  AM, Wallace  DM, Buenaver  LF, et al. Where to next for optimizing adherence in large-scale trials of continuous positive airway pressure? Sleep Med Clin. 2021;16(1):125–144. doi: 10.1016/j.jsmc.2020.10.007 [DOI] [PubMed] [Google Scholar]
  • 19. Weaver  TE.  Novel aspects of CPAP treatment and interventions to improve CPAP adherence. J Clin Med. 2019;8(12):2220. doi: 10.3390/jcm8122220 [DOI] [PMC free article] [PubMed] [Google Scholar]
  • 20. Sanchez-de-la-Torre  M, Gracia-Lavedan  E, Benitez  ID, et al. Adherence to CPAP treatment and the risk of recurrent cardiovascular events: a meta-analysis. JAMA.  2023;330(13):1255–1265. doi: 10.1001/jama.2023.17465 [DOI] [PMC free article] [PubMed] [Google Scholar]
  • 21. Reynor  A, McArdle  N, Shenoy  B, et al. Continuous positive airway pressure and adverse cardiovascular events in obstructive sleep apnea: are participants of randomized trials representative of sleep clinic patients? Sleep.  2022;45(4). doi: 10.1093/sleep/zsab264 [DOI] [PMC free article] [PubMed] [Google Scholar]
  • 22. Mazzotti  DR, Keenan  BT, Lim  DC, Gottlieb  DJ, Kim  J, Pack  AI.  Symptom subtypes of obstructive sleep apnea predict incidence of cardiovascular outcomes. Am J Respir Crit Care Med.  2019;200(4):493–506. doi: 10.1164/rccm.201808-1509OC [DOI] [PMC free article] [PubMed] [Google Scholar]
  • 23. Labarca  G, Dreyse  J, Salas  C, Letelier  F, Jorquera  J.  A validation study of four different cluster analyses of OSA and the incidence of cardiovascular mortality in a hispanic population. Chest.  2021;160(6):2266–2274. doi: 10.1016/j.chest.2021.06.047 [DOI] [PubMed] [Google Scholar]
  • 24. Allen  AJH, Jen  R, Mazzotti  DR, et al. Symptom subtypes and risk of incident cardiovascular and cerebrovascular disease in a clinic-based obstructive sleep apnea cohort. J Clin Sleep Med.  2022;18(9):2093–2102. doi: 10.5664/jcsm.9986 [DOI] [PMC free article] [PubMed] [Google Scholar]
  • 25. Gerves-Pinquie  C, Bailly  S, Goupil  F, et al. Positive airway pressure adherence, mortality and cardiovascular events in patients with sleep apnea. Am J Respir Crit Care Med.  2022;206(11):1393–1404. doi: 10.1164/rccm.202202-0366OC [DOI] [PubMed] [Google Scholar]
  • 26. Wu  B, Tarraf  W, Wallace  DM, et al. Cardiovascular correlates of sleep apnea phenotypes: Results from the Hispanic Community Health Study/Study of Latinos (HCHS/SOL). PLoS One.  2022;17(4):e0265151. doi: 10.1371/journal.pone.0265151 [DOI] [PMC free article] [PubMed] [Google Scholar]
  • 27. Trzepizur  W, Blanchard  M, Ganem  T, et al. Sleep apnea-specific hypoxic burden, symptom subtypes, and risk of cardiovascular events and all-cause mortality. Am J Respir Crit Care Med.  2022;205(1):108–117. doi: 10.1164/rccm.202105-1274OC [DOI] [PubMed] [Google Scholar]
  • 28. Eulenburg  C, Celik  Y, Redline  S, et al. Cardiovascular outcomes in adults with coronary artery disease and obstructive sleep apnea with vs without excessive daytime sleepiness in the RICCADSA cohort. Ann Am Thorac Soc. 2023;20(7):1048–1056. doi: 10.1513/AnnalsATS.202208-676OC [DOI] [PubMed] [Google Scholar]
  • 29. Austin  PC.  An introduction to propensity score methods for reducing the effects of confounding in observational studies. Multivariate Behav Res. 2011;46(3):399–424. doi: 10.1080/00273171.2011.568786 [DOI] [PMC free article] [PubMed] [Google Scholar]
  • 30. Stuart  EA.  Matching methods for causal inference: a review and a look forward. Stat Sci. 2010;25(1):1–21. doi: 10.1214/09-STS313 [DOI] [PMC free article] [PubMed] [Google Scholar]
  • 31. Lu  N, Xu  Y, Yue  LQ.  Some considerations on design and analysis plan on a nonrandomized comparative study using propensity score methodology for medical device premarket evaluation. Stat Biopharm Res. 2020;12(2):155–163. doi: 10.1080/19466315.2019.1647873 [DOI] [Google Scholar]
  • 32. Shiba  K, Kawahara  T.  Using propensity scores for causal inference: pitfalls and tips. J Epidemiol.  2021;31(8):457–463. doi: 10.2188/jea.JE20210145 [DOI] [PMC free article] [PubMed] [Google Scholar]
  • 33. Imbens  GW.  Nonparametric estimation of average treatment effects under exogeneity: a review. Rev Econ Stat. 2004;86(1):4–29. doi: 10.1162/003465304323023651 [DOI] [Google Scholar]
  • 34. Rubin  DB.  Estimating causal effects of treatments in randomized and nonrandomized studies. J Educ Psychol. 1974;66(5):688–701. doi: 10.1037/h0037350 [DOI] [Google Scholar]
  • 35. Rubin  DB.  Causal inference using potential outcomes. J Am Stat Assoc.  2005;100(469):322–331. doi: 10.1198/016214504000001880 [DOI] [Google Scholar]
  • 36. Zhu  Y, Hubbard  RA, Chubak  J, Roy  J, Mitra  N.  Core concepts in pharmacoepidemiology: violations of the positivity assumption in the causal analysis of observational data: consequences and statistical approaches. Pharmacoepidemiol Drug Saf.  2021;30(11):1471–1485. doi: 10.1002/pds.5338 [DOI] [PMC free article] [PubMed] [Google Scholar]
  • 37. VanderWeele  TJ.  Concerning the consistency assumption in causal inference. Epidemiology. 2009;20(6):880–883. doi: 10.1097/EDE.0b013e3181bd5638 [DOI] [PubMed] [Google Scholar]
  • 38. Cole  SR, Frangakis  CE.  The consistency statement in causal inference: a definition or an assumption? Epidemiology. 2009;20(1):3–5. doi: 10.1097/EDE.0b013e31818ef366 [DOI] [PubMed] [Google Scholar]
  • 39. Bettega  F, Leyrat  C, Tamisier  R, et al. Application of inverse-probability-of-treatment weighting to estimate the effect of daytime sleepiness in patients with obstructive sleep apnea. Ann Am Thorac Soc. 2022;19(9):1570–1580. doi: 10.1513/AnnalsATS.202109-1036OC [DOI] [PMC free article] [PubMed] [Google Scholar]
  • 40. Rubin  DB.  The design versus the analysis of observational studies for causal effects: parallels with the design of randomized trials. Stat Med.  2007;26(1):20–36. doi: 10.1002/sim.2739 [DOI] [PubMed] [Google Scholar]
  • 41. Austin  PC.  Balance diagnostics for comparing the distribution of baseline covariates between treatment groups in propensity-score matched samples. Stat Med.  2009;28(25):3083–3107. doi: 10.1002/sim.3697 [DOI] [PMC free article] [PubMed] [Google Scholar]
  • 42. Brookhart  MA, Schneeweiss  S, Rothman  KJ, Glynn  RJ, Avorn  J, Sturmer  T.  Variable selection for propensity score models. Am J Epidemiol.  2006;163(12):1149–1156. doi: 10.1093/aje/kwj149 [DOI] [PMC free article] [PubMed] [Google Scholar]
  • 43. Shrier  I, Platt  RW.  Reducing bias through directed acyclic graphs. BMC Med Res Methodol.  2008;8:70. doi: 10.1186/1471-2288-8-70 [DOI] [PMC free article] [PubMed] [Google Scholar]
  • 44. Lederer  DJ, Bell  SC, Branson  RD, et al. Control of confounding and reporting of results in causal inference studies. guidance for authors from editors of respiratory, sleep, and critical care journals. Ann Am Thorac Soc. 2019;16(1):22–28. doi: 10.1513/AnnalsATS.201808-564PS [DOI] [PubMed] [Google Scholar]
  • 45. Nystoriak  MA, Bhatnagar  A.  Cardiovascular effects and benefits of exercise. Front Cardiovasc Med. 2018;5:135. doi: 10.3389/fcvm.2018.00135 [DOI] [PMC free article] [PubMed] [Google Scholar]
  • 46. Casas  R, Castro-Barquero  S, Estruch  R, Sacanella  E.  Nutrition and cardiovascular health. Int J Mol Sci .  2018;19(12):3988. doi: 10.3390/ijms19123988 [DOI] [PMC free article] [PubMed] [Google Scholar]
  • 47. Shrank  WH, Patrick  AR, Brookhart  MA.  Healthy user and related biases in observational studies of preventive interventions: a primer for physicians. J Gen Intern Med.  2011;26(5):546–550. doi: 10.1007/s11606-010-1609-1 [DOI] [PMC free article] [PubMed] [Google Scholar]
  • 48. Silverman  SL, Gold  DT.  Healthy users, healthy adherers, and healthy behaviors? J Bone Miner Res.  2011;26(4):681–682. doi: 10.1002/jbmr.384 [DOI] [PubMed] [Google Scholar]
  • 49. Thompson  FE, Midthune  D, Kahle  L, Dodd  KW.  Development and evaluation of the national cancer institute’s dietary screener questionnaire scoring algorithms. J Nutr.  2017;147(6):1226–1233. doi: 10.3945/jn.116.246058 [DOI] [PMC free article] [PubMed] [Google Scholar]
  • 50. Sattler  MC, Jaunig  J, Tosch  C, et al. Current evidence of measurement properties of physical activity questionnaires for older adults: an updated systematic review. Sports Med.  2020;50(7):1271–1315. doi: 10.1007/s40279-020-01268-x [DOI] [PMC free article] [PubMed] [Google Scholar]
  • 51. Granger  BB, Swedberg  K, Ekman  I, et al.; CHARM investigators. Adherence to candesartan and placebo and outcomes in chronic heart failure in the CHARM programme: double-blind, randomised, controlled clinical trial. Lancet.  2005;366(9502):2005–2011. doi: 10.1016/S0140-6736(05)67760-4 [DOI] [PubMed] [Google Scholar]
  • 52. Kronish  IM, Ye  S.  Adherence to cardiovascular medications: lessons learned and future directions. Prog Cardiovasc Dis.  2013;55(6):590–600. doi: 10.1016/j.pcad.2013.02.001 [DOI] [PMC free article] [PubMed] [Google Scholar]
  • 53. Villar  I, Izuel  M, Carrizo  S, Vicente  E, Marin  JM.  Medication adherence and persistence in severe obstructive sleep apnea. Sleep.  2009;32(5):623–628. doi: 10.1093/sleep/32.5.623 [DOI] [PMC free article] [PubMed] [Google Scholar]
  • 54. Platt  AB, Kuna  ST, Field  SH, et al. Adherence to sleep apnea therapy and use of lipid-lowering drugs: a study of the healthy-user effect. Chest.  2010;137(1):102–108. doi: 10.1378/chest.09-0842 [DOI] [PMC free article] [PubMed] [Google Scholar]
  • 55. Kinjo  M, Chia-Cheng Lai  E, Korhonen  MJ, McGill  RL, Setoguchi  S.  Potential contribution of lifestyle and socioeconomic factors to healthy user bias in antihypertensives and lipid-lowering drugs. Open Heart. 2017;4(1):e000417. doi: 10.1136/openhrt-2016-000417 [DOI] [PMC free article] [PubMed] [Google Scholar]
  • 56. Eurich  DT, Achtymichuk  KA, Johnson  JA, Minhas-Sandhu  JK, Lin  M.  Development and validation of an index score to adjust for healthy user bias in observational studies. J Popul Ther Clin Pharmacol. 2017;24(3):e79–e89. doi: 10.22374/1710-6222.24.3.6 [DOI] [PubMed] [Google Scholar]
  • 57. Robins  JM, Hernan  MA, Brumback  B.  Marginal structural models and causal inference in epidemiology. Epidemiology.  2000;11(5):550–560. doi: 10.1097/00001648-200009000-00011 [DOI] [PubMed] [Google Scholar]
  • 58. VanderWeele  TJ, Ding  P.  Sensitivity analysis in observational research: introducing the E-Value. Ann Intern Med.  2017;167(4):268–274. doi: 10.7326/M16-2607 [DOI] [PubMed] [Google Scholar]
  • 59. Dreyer  NA, Tunis  SR, Berger  M, Ollendorf  D, Mattox  P, Gliklich  R.  Why observational studies should be among the tools used in comparative effectiveness research. Health Aff (Millwood).  2010;29(10):1818–1825. doi: 10.1377/hlthaff.2010.0666 [DOI] [PubMed] [Google Scholar]
  • 60. Wang  SV, Schneeweiss  S, Initiative  R-D, et al. Emulation of randomized clinical trials with nonrandomized database analyses: results of 32 clinical trials. JAMA.  2023;329(16):1376–1385. [DOI] [PMC free article] [PubMed] [Google Scholar]
  • 61. FDA Guidance for Industry:  E9 Statistical Principles for Clinical Trials. In. https://www.fda.gov/regulatory-information/search-fda-guidance-documents/e9-statistical-principles-clinical-trials. Accessed February 21, 2024.
  • 62. Chatton  A, Le Borgne  F, Leyrat  C, et al. G-computation, propensity score-based methods, and targeted maximum likelihood estimator for causal inference with different covariates sets: a comparative simulation study. Sci Rep.  2020;10(1):9219. doi: 10.1038/s41598-020-65917-x [DOI] [PMC free article] [PubMed] [Google Scholar]
  • 63. Arnett  DK, Blumenthal  RS, Albert  MA, et al. 2019 ACC/AHA guideline on the primary prevention of cardiovascular disease: executive summary: a report of the american college of cardiology/american heart association task force on clinical practice guidelines. Circulation.  2019;140(11):e563–e595. doi: 10.1161/CIR.0000000000000677 [DOI] [PMC free article] [PubMed] [Google Scholar]
  • 64. Flora  GD, Nayak  MK.  A brief review of cardiovascular diseases, associated risk factors and current treatment regimes. Curr Pharm Des.  2019;25(38):4063–4084. doi: 10.2174/1381612825666190925163827 [DOI] [PubMed] [Google Scholar]
  • 65. Hernan  MA, Hernandez-Diaz  S, Robins  JM.  Randomized trials analyzed as observational studies. Ann Intern Med.  2013;159(8):560–562. doi: 10.7326/0003-4819-159-8-201310150-00709 [DOI] [PMC free article] [PubMed] [Google Scholar]
  • 66. Robins  JM, Hernan  MA.  Estimation of the causal effects of time-varying exposures. In: Fitzmaurice  G, Davidian  M, Verbeke  G, Molenberghs  G, eds. Longitudinal Data Analysis. Chapman & Hall/CRC Handbooks of Modern Statistical Methods. 2008;553–599. doi: 10.1201/9781420011579 [Google Scholar]
  • 67. Naimi  AI, Cole  SR, Kennedy  EH.  An introduction to g methods. Int J Epidemiol.  2017;46(2):756–762. doi: 10.1093/ije/dyw323 [DOI] [PMC free article] [PubMed] [Google Scholar]
  • 68. Deaton  A, Cartwright  N.  Understanding and misunderstanding randomized controlled trials. Soc Sci Med.  2018;210:2–21. doi: 10.1016/j.socscimed.2017.12.005 [DOI] [PMC free article] [PubMed] [Google Scholar]
  • 69. Benson  K, Hartz  AJ.  A comparison of observational studies and randomized, controlled trials. N Engl J Med.  2000;342(25):1878–1886. doi: 10.1056/NEJM200006223422506 [DOI] [PubMed] [Google Scholar]
  • 70. Concato  J, Shah  N, Horwitz  RI.  Randomized, controlled trials, observational studies, and the hierarchy of research designs. N Engl J Med.  2000;342(25):1887–1892. doi: 10.1056/NEJM200006223422507 [DOI] [PMC free article] [PubMed] [Google Scholar]

Associated Data

This section collects any data citations, data availability statements, or supplementary materials included in this article.

Data Availability Statement

No new data were generated or analyzed in support of this research.

RESOURCES