The Bias Dynamics Model: Correcting for Meta-biases in Therapeutic Prediction

Abstract

Inferences from clinical research results to estimates of therapeutic effectiveness suffer due to various biases. I argue that predictions of medical effectiveness are prone to failure because current medical research overlooks the impacts of a particularly detrimental set of biases: meta-biases. Meta-biases are linked to higher-level characteristics of medical research and their effects are only observed when comparing sets of studies that share certain meta-level properties. I offer a model for correcting research results based on meta-research evidence, the bias dynamics model, which employs regularly updated empirical bias coefficients to attenuate estimates of therapeutic effectiveness.

1. Therapeutic Prediction

It’s commonly assumed that clinical research results can be used to make predictions about the effectiveness of medical interventions. This is done by inferring from measurements of therapeutic efficacy—an intervention’s capacity to cause its intended outcome in a study population—to estimations of therapeutic effectiveness—the capacity of the intervention to bring about its desired effects in populations outside the study setting. In this article, I argue that predictions of medical effectiveness are prone to failure because current policies and guidelines don’t account for the impacts of a particularly nefarious set of biases: meta-biases. To help remedy this, I offer a model for correcting the results of clinical studies based on evidence about these meta-biases. I refer to this framework as the bias dynamics model.

Researchers quantify therapeutic efficacy as an effect size using some outcome measure. This is a measure of the net difference that exposure to an intervention makes to a particular outcome in a population. Effect sizes are calculated by performing statistical tests on data gathered in clinical trials, such as cohort studies or randomized control trials (RCTs). If a trial meets certain standards of internal validity, then the measured effect size is thought to accurately quantify the relationship between exposure to the treatment and the outcome for the study population. The results from the trial are then used to predict the intervention’s therapeutic effectiveness.

One major challenge facing clinical trials is that they may be internally valid and nevertheless fail to be externally valid. That is, a therapeutic efficacy measure may be accurate for a study population but inaccurate for a target population. Several factors contribute to the problem of external validity, including problems related to extrapolation and a neglect of mechanistic evidence. Another particularly important consideration is the impact of biases on therapeutic prediction.

Discussions about biases typically focus on how they manifest in the methods of a clinical study, threatening internal validity. Such biases include confounding, confirmation bias, and reporting bias. However, another form of biases that affects medical research at the meta-level indirectly impacts the reliability of research results. I call these meta-biases. Widespread meta-biases present a serious challenge to the reliability of medical evidence, particularly when that evidence is used to estimate therapeutic effectiveness. Some argue that ubiquitous research biases contribute to a large proportion of published scientific conclusions being false (Ioannidis 2005). More recently, others have suggested that biases, including meta-biases, can, and typically do, lead to systematically exaggerated claims of therapeutic effectiveness (Fuller 2018; Stegenga 2018).

My first aim expands on these claims, arguing that, despite a growing body of evidence about their impacts, we often fail to account for the effects of meta-biases on therapeutic prediction. I distinguish between what I refer to as methodological biases and the higher-level concept of meta-biases. Methodological biases are directly linked to the methodological features of clinical research. Meta-biases, in contrast, are connected to meta-level properties of a scientific discipline. This distinction has not been explicitly drawn in the literature on biases, yet it is an important one to make. The concept of meta-bias effectively captures how meta-level properties of scientific disciplines can generate systemic distortions in clinical result and helps demonstrate that disciplinary guidance, with its typical focus on methodological biases, overlooks the effects of meta-biases. Thus, it has the potential to improve policies and research on bias.

My second aim is to offer a strategy to help remedy the problem of meta-bias. I outline a framework for correcting measures of efficacy in line with empirical evidence about the prevalence and effects of meta-biases prior to estimating therapeutic effectiveness. The model I propose takes inspiration from the methods used in dynamics wherein calculations of the forces impinging on objects’ motions are adjusted to account for friction. Just as such calculations employ empirical friction coefficients to estimate the forces acting on objects, I propose the use of empirical bias coefficients to attenuate estimates of therapeutic effectiveness. These bias coefficients, I argue, should be regularly updated to reflect the best current evidence about meta-biases. Because of its relation to dynamics calculations, and because I propose that bias coefficients be amended frequently based on empirical findings, I refer to my proposed framework as the bias dynamics model for estimating the effectiveness of medical interventions.

2. What are meta-biases?

Medical research is plagued by various forms of bias—errors or deviations from the truth in results (Higgins et al. 2022). Biases are typically thought to occur due to some property of either the design or implementation of a research method or the interpretation of the data gathered through experimentation. But this conception of bias doesn’t capture the full range of systemic distortions that occur medical research.

2.1. Methodological bias and meta-bias

Standard examples of bias include confounding, confirmation bias, and reporting bias. Biases like these are directly linked to methodological features of clinical research and are thus relatively well understood. We have a good idea of how they manifest and have invested a great deal into developing strategies to mitigate or prevent them. Take confounding, the underdetermination of the association between a treatment and an outcome due to an imbalance of some factor in the experimental and control groups of a study. Some strategies for lowering the chance of confounding in clinical research are randomization, matching, and multivariate analysis. Because of their direct relation to the processes within clinical trial methodology, I call these methodological biases.

Perhaps the most damaging form of methodological bias is reporting bias, a distortion in results due to selective disclosure of analyses performed and results obtained in a clinical trial. Practices that lead to reporting bias include withholding unfavorable or nonsignificant results, publishing only a subset of the analyzed data, reporting secondary outcomes as primary outcomes when the latter yielded nonsignificant results, and adding entirely new outcomes to a published study. While difficult to detect, there’s substantial evidence of rampant practices that constitute reporting bias (Goldacre et al. 2016).

Because of the scrutiny reporting bias has received, the mechanisms responsible for it are well understood and we have developed relatively successful strategies to prevent it. For instance, one study found a reduction in some of these mechanisms, including questionable design and analytic practices, after a requirement that studies be recorded on official trial registries was introduced at the turn of the millennium (Kaplan and Irvin 2015).

Methodological biases are emphasized in influential evidence-based medicine (EBM) guidelines. For example, the Cochrane Group’s “risk of bias” tool for evaluating clinical studies lists six broad categories of bias: selection bias, performance bias, detection bias, attrition bias, reporting bias, and a final category for other bias (Higgins et al. 2022). Researchers are advised to assess the risk of a particular bias by looking at methodological aspects of a clinical trial. Determining the risk of detection bias, for instance, entails assessing the extent to which analysts in a study were blinded when analyzing outcomes. Confounding, confirmation bias, and detection bias (and other methodological biases) fit well under the standard characterization of bias in medicine. They are indeed linked to problematic procedures in data collection, analysis, and interpretation.

Another set of biases, however, cannot be so explicitly connected to features of the experimental process. Instead, these biases are linked to meta-level properties of science, such as a scientific community’s entrenched values or its inveterate research norms. Because of their connection to meta-level properties that are external to experimental methodology, I call these meta-biases. Meta-biases may precipitate or manifest through questionable practices such as p-hacking or selective reporting. Yet, in contrast to those of methodological biases, their effects cannot be seen by looking at single studies. Distortions in results due to meta-biases are only seen when comparing sets of studies with particular meta-level properties.

An exemplar of meta-bias is publication bias, the tendency of trials with negative results, indicating no causal relationship between a treatment and an outcome, to go unpublished. There’s strong evidence for this. Murad et al. (2018) found that studies with positive results are 3.90 times more likely to be published than those with negative results. This leads to a general weighting toward positive results in published medical research. Here, the distortion is observed by comparing the set of all published studies to the set of all completed studies.

Another example of meta-bias involves observed differences between the findings of industry-funded studies and those of nonindustry-funded studies. A vast majority of clinical trials are funded and/or conducted by private organizations that have vested interests in those trials’ outcomes. There’s evidence that industry-funded studies tend to generate a higher ratio of results that promote the interests of the funding organization when compared to nonindustry-funded studies. A recent Cochrane systematic review concluded that industry sponsored trials were 1.27 times more likely to report beneficial outcomes, 1.34 times more likely to show less evidence of harms, and 1.37 times more likely to present more favorable overall conclusions when compared with nonindustry-funded studies (Lundh et al. 2017). This tendency of clinical trials to generate results that promote a sponsor’s interests know as sponsorship bias. ¹

Seeing that sponsorship bias is a meta-bias is less straightforward than it is for publication bias. This is because it’s common for methodological biases, such as reporting bias, to occur in efforts to generate findings that benefit a trial sponsor. Nevertheless, there’s clear evidence that the meta-level properties of studies, namely “industry funded” and “nonindustry funded,” are associated with a systemic distortion toward results that favor trial sponsors’ interests. Indeed, industry sponsorship is not a necessary feature of trials in which related methodological biases occur. Nor is it necessarily the case that researchers in industry-sponsored trials with positive findings always commit practices that constitute methodological biases. It’s simply that industry-sponsored trials tend to generate findings in favor of sponsors’ interests. And because most trials are industry funded, and most industry-funded studies report positive findings in favor of their sponsor, industry funding leads to a positive skew in research results.

One might argue that, on its own, evidence that industry-sponsored trials tend to report beneficial outcomes when compared to nonindustry-funded trials is insufficient for establishing the existence of sponsorship bias. After all, pharmaceutical companies often halt research programs that run the risk of failure before they reach clinical trials. And nonsponsored research is typically slow off the mark in this regard. This provides an ostensible explanation for the higher rates of positive results from sponsored trials. However, sponsored head-to-head trials tend to generate results that favor the sponsor’s drug over a competitor when compared to nonsponsored head-to-head trials (Flacco et al. 2015). In other words, industry-funded trials are more likely to conclude that their drug is superior, or at least not inferior, to competitors than nonindustry-funded trials. This failure to reach similar conclusions regarding particular treatments further supports the existence of sponsorship bias.

2.2. The neglect of meta-biases

Meta-biases have not been explored to the same extent as methodological biases. As a result, strategies to help prevent them are nascent and somewhat limited. The Cochrane risk of bias tool gestures toward this concern in its “other bias” category, recommending that systematic reviewers simply “[s]tate any important concerns about bias not addressed in the other domains in the tool” (Higgins et al. 2022). Sadly, this leaves much open to interpretation.

Failing to commit resources to meta-biases hinders efforts to limit their effects. To prevent publication bias, for instance, some journals have committed to soliciting and publishing research with negative results. Yet, other factors that lead to publication bias, such as the higher likelihood of positive results being cited thus increasing one’s chance of funding and career promotion, go unchecked. And governmental and organizational policy requiring that the results of certain studies be reported on clinical trial registries within a year of completion are often undercut by noncompliance on behalf of researchers and through regulatory loopholes (Goldacre et al. 2018). A more recent strategy, the use of funnel plots, aims at detecting publication bias without requiring access to unpublished research (see Holman 2019). While useful for assessing the risk of publication bias in meta-analytic research, funnel plots don’t correct for its effects. Researchers who find a risk of publication bias typically caveat it in the discussion sections of their studies. Thus, funnel plots don’t directly tackle the challenge of publication bias, but rather reveal the extent of the problem further. Overall, publication bias is a multifaceted problem and preventing it requires immense coordinated efforts.

The same can be said of sponsorship bias. Doucet and Sismondo (2008) outline several proposed solutions to sponsorship bias, including financial disclosures, standardized reporting, and trial registration. Such policies, however, fail to cover all the contributing factors. Financial disclosure has been common practice for many years, yet industry-funded trials continue to regularly favor sponsors’ interests. Standardized reporting cannot fully address trial design concerns. And while it may make it more difficult, developing strict reporting guidelines will not fully deter those whose goal is to manipulate data through outright fraud. Furthermore, the complexities of rhetoric in articles are hardly solved by introducing reporting standards. Such standardization may contribute to what Steel (2018) refers to as inferential asymmetries in the interpretation of clinical results, whereby some stakeholders are less able to infer true conclusions than others due to the way in which research results are reported. Trial registries may help solve sponsorship bias as it relates to publication bias, but one could follow registration procedures correctly and still introduce industry favoring design features, directly manipulate data, and present findings in a way that promotes sponsors’ interests.

Ultimately, sponsorship bias cannot be so easily reduced to particular issues of methodology. The effect can manifest using multiple first-order methodological biases or through outright fraud. It is, in this sense, multiply realizable—in individual trials, different constellations of biases may be responsible for generating results that favor sponsor interests. However, it’s often difficult to know whether methodological biases have occurred in a trial, and when we do know, it’s difficult to explicitly connect these to a desire or tendency to favor a sponsor’s interests. Moreover, existing quality assessment tools (QATs) for evaluating evidence, including the risk of bias tool, often have poor interrater and intertool reliability (Stegenga 2018). In other words, there are often epistemic gaps regarding first-order methodological biases connected to sponsorship bias and their effects on the quality of evidence. Here, the higher-order concept of sponsorship bias is useful because we can have clear evidence to show how industry funding is correlated with favorable results.

Sponsorship bias should, in this sense, be thought of as a higher-level bias responsible for systemic distortions in clinical research in comparison to the more fundamental methodological biases that it precipitates. Indeed, it’s the entrenched seating of private sponsors as the majority curators of clinical research, not merely pervasive methodological biases, that’s ultimately responsible for the observed distortion in results. That’s what makes sponsorship bias a meta-bias. Thus, preventing sponsorship bias involves the mammoth task of completely overhauling clinical research, requiring an enormous amount of time and resources, all while the effects of the bias persist.

The systematic distortions in results caused by pervasive meta-biases are a serious problem for medical research. Growing evidence shows that publication bias leads to the systemic overestimation of effect sizes generated through meta-analyses of clinical research (Murad et al. 2018). Because there’s a higher proportion of positive findings than negative findings in the published literature, the pooled results of the published studies will show greater effectiveness than if all studies were included (Stegenga 2018). Likewise, we can infer from evidence about sponsorship bias that it generally skews results such that therapeutic effectiveness is overestimated. If most clinical trials are industry funded, and if industry-funded trials tend to generate industry favoring results when compared to nonindustry-funded trials, then this gives us good reason to believe that (1) any given industry-funded trial is more likely to be biased that any nonindustry-funded trial, and (2) amalgamations of evidence from all relevant published trials will bake sponsorship bias into their results. Therefore, there are principled reasons to lower our confidence in the results of industry-funded RCTs and meta-analyses that include industry-funded trials (Fuller 2018).

The concept of meta-bias, and its distinction from methodological bias, is significant for at least four reasons. First, the concept of meta-bias provides a clear way to understand how systemic distortions in medical research can arise through meta-level properties of a scientific discipline. Second, it helps guide research to gather evidence about such systemic distortions in cases where epistemic access to first-order, methodological biases is limited. Third, it helps reveal flaws in current guidelines and efforts aimed at preventing biases by highlighting their neglect of meta-biases. Finally, it illustrates that the problem of meta-biases is difficult to solve because such biases are linked to high-level properties of a scientific discipline. Preventing meta-biases entails an immense overhaul of the medical research system. In the absence of effective strategies for preventing meta-biases, there should be a way to attenuate efficacy measures based on what we know about the influence of meta-biases. In the next section, I describe a model for how this can be done.

3. The bias dynamics model

The model I propose uses empirical bias coefficients to modulate therapeutic efficacy measures to account for the effects of meta-biases. This allows us to correct for meta-biases in our estimations of therapeutic effectiveness. I refer to this model as the bias dynamics model. ²

Assume a meta-analysis is conducted to measure the effect of some treatment on some dichotomous outcome. After completing data collection and analysis, the researchers calculate an effect size measured as an absolute risk reduction (ARR). Let ARR_S refer to the measure of therapeutic efficacy—calculated for a given study population—quantified as an absolute risk reduction. When conducting such a study, we are not just interested in therapeutic efficacy but also therapeutic effectiveness—estimated for some target population. Because we usually don’t have direct evidence about the extent to which an intervention will work in a target population, ARR_S is used to infer the general capacity of the treatment in that target population. Let ARR_T refer to a prediction of therapeutic effectiveness, estimated as an absolute risk reduction. ³ In this case, ARR_T is the absolute expected effectiveness of the intervention in questions, representing the predicted rate individuals in the target population who would benefit from the intervention in question.

The aim is to take what we believe to be a true measure of a treatment’s effect in the study and infer the capacity of the intervention that’s as close to the truth as possible for a target population. Many in the EBM movement assume that barring threats to internal validity and relevant differences between study and target populations, we can straightforwardly apply such results. Thus:

$${\rm{AR}}{{\rm{R}}_{\rm{T}}} = {\rm{AR}}{{\rm{R}}_{\rm{S}}}$$

However, as noted, pervasive meta-biases should lead us to attenuate clinical trial results—there’s good reason, besides differences between populations and traditional failures of internal validity, to expect that the effectiveness represented by ARR_T is lower than the estimated efficacy represented by ARR_S.

Lowering the expected effect size can be done by introducing what I refer to as a bias coefficient for the ARR, δ, where 0 ≤ δ ≤ 1. Ideally, the bias coefficient represents the effect of all meta-biases on effectiveness claims. By multiplying the therapeutic efficacy measure by the bias coefficient, we lower the expected effectiveness of the treatment in question:

$${\rm{AR}}{{\rm{R}}_{\rm{T}}} = {\rm{\delta AR}}{{\rm{R}}_{\rm{S}}}$$

Because the magnitude of the bias coefficient is between 0 and 1, it will always attenuate the value of ARR_T. The closer δ is to 0, the more meta-biases affect ARR_T, and likewise, the closer δ is to 1, the less meta-biases affect ARR_T. It’s theoretically possible that the effects of meta-biases are sufficient (δ = 0) for us to expect that the intervention will have no effect in the target (ARR_T = 0). Conversely, meta-biases could, in principle, have no effect (δ = 1), and thus we could conclude (assuming no other problems related to generalization and no other threats to internal validity) that the therapeutic effectiveness will be equal to the therapeutic efficacy (ARR_T = ARR_T). However, given the prevalence of meta-biases, these scenarios are unlikely.

The bias dynamics model provides a way to correct therapeutic effectiveness estimates by taking the effects of meta-biases into account. As mentioned, the bias coefficient ideally represents the effect of all meta-biases on research results, yet, in practice, it’s unlikely that we could have access to such knowledge. This doesn’t, however, preclude the use of the model. We can determine bias coefficients based on what is known about meta-biases. This is the next step to calls for the use of meta-research evidence—evidence about the evidential support provided by clinical research—in adjusting confidence in clinical findings (Fuller 2018). Furthermore, bias coefficients can fill the gap left in recognized guidelines on biases by helping researchers account for the effects of meta-biases, which are not explicitly listed in QATs. For example, once Cochrane’s risk of bias tool has been used to rate single studies for bias, the bias coefficient can be used to determine an overall rating for a given research program based on evidence about meta-biases. In line with this, an organization like Cochrane should publish domain specific bias coefficients. And, at least in the case of publication bias, bias coefficients can be used in conjunction with funnel plot analyses. Here, researchers may detect publication bias and be more justified in applying the bias dynamics model.

Bias coefficients should be categorized by research area and outcome. Meta-biases occur at various rates in different research programs—the prevalence of publication bias in cancer research differs to that in research on antidepressants (cf. Peters et al. 2021; Turner et al. 2022). Likewise, different outcomes within each research program will have different rates of meta-biases—the rate of publication bias in research on the association between statins and heart attack may differ from that in research on the association between statins and stroke. Naturally, because of this, the values of bias coefficients for given outcomes in particular fields will differ.

Unlike their analog in physics, bias coefficients should be dynamic. Their values should be updated over time with the observation of new evidence about meta-biases. That is, bias coefficients should be derived using current meta-research evidence and modeling data about the effects of publication bias, sponsorship bias, and other meta-biases. Such an approach is in keeping with the central tenets of EBM and its related organizations, which aim to update guidelines based on the best available evidence. The Cochrane Group has already gestured toward this sort of approach with updates to its research into the effects of industry funding on research outcomes (cf. Lundh et al. 2017).

To briefly demonstrate the bias dynamics model, consider a meta-analysis that found statin therapy is associated with a 0.81% decrease in heart attacks over six years (Chou et al. 2016). Thus, ARR_S = 0.81%. We want to know if using statins will decrease the risk of heart attack in a target population of individuals with high cholesterol, a risk factor for heart attack; in other words, we want to estimate ARR_T. Most would assume that ARR_T = 0.81%. However, evidence about meta-biases in statin research should be considered.

Bero et al. (2007) found that the odds of statistically significant results in favor of statin therapy in drug-drug comparisons were sixteen times greater for industry-funded trials than for nonindustry-funded trials. While these findings don’t indicate the exact effects of meta-biases on statin research, they do warrant a relatively low bias coefficient (indicating a large effect from meta-biases). In line with this, assume a bias coefficient δ = 0.45. This would attenuate the estimate of therapeutic effectiveness for statin therapy; ARR_T = 0.37%.

Overall, the bias dynamics model provides a relatively straightforward strategy for researchers correct for the effects of meta-biases. Bias coefficient function as regularly updated attenuating variables representing the known effects of meta-biases. The implementation of such a tool would go some way to producing more reliable predictions of therapeutic effectiveness.

4. Conclusion

Estimations of therapeutic effectiveness suffer greatly due to widespread neglect of the effects of meta-biases. Meta-biases are distinct from methodological biases in that they are not directly linked to the methodological features of clinical research. Rather, they are connected to meta-level properties of a scientific discipline, such as the deep-rooted values of the medical research community or entrenched norms of the system in which medical research is conducted. Current research guidance focuses on methodological biases at the expense of accounting for meta-biases.

The bias dynamics model provides a way to modulate therapeutic predictions. Using evidence on the effects of meta-biases, estimates of therapeutic effectiveness can be attenuated using empirical bias coefficients. The bias dynamics model, and its use of bias coefficients, is appealing for at least two reasons. First, it has the potential to fill a gap in current EBM guidelines, which emphasize the risks of methodological biases, and do not account for meta-bias effects. And second, using empirical bias coefficients, the model provides a clear way for researchers to use up-to-date evidence to generate more accurate estimations of medical effectiveness.

Further study is necessary. For instance, there needs to be a reliable program for determining bias coefficients. There’s promising work in this domain. Tabatabaei Ghomi and Stegenga (2021) simulate trial-level data using the higher-order reported results of published trials, such as means and effect sizes. Using simulations allows researchers to not only specify the true effectiveness of the intervention in question prior to analyzing the effects of meta-biases but also control for methodological biases and researcher idiosyncrasies. Such studies can be conducted using meta-research findings on the rates and prevalence of various meta-biases. In doing so, we can measure their effects on different outcomes in different subdomains of medicine, and from there determine bias coefficients for specific areas of research that can be published on a regular basis to reflect the latest meta-research evidence.