Aleatory and epistemic uncertainties can completely derail medical research results.

Aleatory uncertainties are generated by intrinsic factors such as studying a sample rather than the whole population and the source of epistemic uncertainties is extraneous such as limitations of knowledge. These uncertainties inflict all the findings in empirical medical research, but they are rarely appreciated. This article highlights these uncertainties and shows with the help of an example how apparently valid and reliable findings can completely derail due to these uncertainties. We conclude that aleatory and epistemic uncertainties should get due consideration while drawing conclusions and before the results are put into practice. Methods to reduce their impact on results are also presented.

Introduction

Despite enormous progress in medicine in recent times, the reports of non-reproducible findings[1] keep coming up. Thus, legitimate questions are raised on the actual worth of enormous resources invested in medical research around the world.

Most of the research in health and medicine is empirical where a set of data is collected on the patients or healthy subjects and analyzed with the help of statistical methods to come up to a result. The expectation is that such results are reliable and valid, and can be used to advance the science of medicine when accompanied by rational thinking. As many as 761,674 citations appeared in MedLine database with 2017 as the year of publication[2] but perhaps only a small fraction of them succeeded in advancing the practice of medicine. Chalmers[3] and Yordanov et al.[4] have highlighted this enormous waste in medical research. Among several reasons, such as choice of topic, design, sample size, confounding, and bias and errors, one important reason for this waste is the failure to take proper account of the aleatory and epistemic uncertainties. In medical research, these uncertainties are common and afflict the results in unpredictable ways. The conclusion, which is supposed to consider not just the result but also factors such as biological plausibility, previous knowledge, and corroborative evidence, can also go haywire. The net consequence is that many results lack reproducibility and are unusable. This communication first explains aleatory and epistemic uncertainties for the benefit of those who are not aware and then illustrates them with the help of an example. The example shows how apparently valid result loses credibility because of these uncertainties. In the end, we suggest some methods to reduce the impact of these uncertainties on the results.

Aleatory and Epistemic Uncertainties

Aleatory uncertainties are intrinsic to the study and arise mostly due to sampling fluctuations. Results from one sample of patients generally differ from another sample from the same target population due to interindividual variation. The factors causing these variations can be categorized as biological (such as age, gender, hereditary, immunity level, physiological functions, and biochemical parameters), environmental (life style, stress and anxiety, climate, pollution exposure, infection, and such other factors), and social support (family ties, interaction with friends, financial security, etc.). In addition, imperfect tools also contribute to aleatory uncertainties. When my blood pressure differs from yours, it is not merely due to differences in age and gender but also due to the variation in several other associated factors. At the study level, results differ from one study to another due to differences in design, method of collection of data, variables under consideration, confounding, method of analysis, interpretations, and reporting. Most aleatory uncertainties can be minimized by controlling the individual factors and by being more careful at each step of the study. However, the effect of these uncertainties cannot be completely eliminated. Two identical studies in the same population can still lead to different results due to uncontrollable sampling fluctuations.

Epistemic uncertainties are more intricate and require deeper explanation. These were first highlighted in the context of medical research by Indrayan in 2008[5] but still not fully appreciated. These uncertainties arise mainly due to the limitation of our knowledge. According to one paradigm, what we do not know is much more than what we know. All the studies are necessarily based on existing knowledge and that can be very incomplete in some situations. For example, only those risk factors of cancer of the prostate are studied that can be conjectured, and these conjectures depend on our present knowledge. Nobody tries to find how echographic findings modify this risk because that is not in our conjecture yet. As the knowledge expands, more and more factors are added and they tend to get more exactitude. In science, the unknown domain contributes to what we generally call chance.

In the context of medicine, at least two types of limitations of knowledge can be identified. One is the global ignorance as mentioned in the previous paragraph and the other is incomplete knowledge at the personal level. There may be aspects about which a particular researcher does not know although that knowledge is available with others through literature, experience, discussion with colleagues, and such other sources. Sometimes the researcher knows but fails to consider while planning a study, either due to negligence and lack of resources, or lack of knowledge about how to take care of various factors. Global ignorance and personal inadequacy both result in unknown inaccuracies but the former affects at the macro level (such as for all studies on peritonitis) and second only a particular study. In research set up in an institution, these two may be confounded and can hardly be segregated once the study is completed.

Another source of epistemic uncertainty is incomplete information on the patients under research. If it is on patients, some of whom come in coma, nothing much can be elicited and the patients’ management has to start based on whatever can be observed. Many patients, who are in full senses, are not able to provide complete history as they forget and do not have records. Some even suppress the information as for an injury or for drug abuse to avoid hassles. Such instances also put in a question mark on the results of some research.

All these uncertainties have the potential to adversely affect the credibility of results. We illustrate this with the help of a fictitious but simple example.

Example: Estimating the Incidence of Sexual Adverse Effects of Finasteride in a Population

Finasteride is commonly prescribed for male-pattern hair loss but is known to cause side effects, particularly adverse effect on sexual functions such as decreased libido and erectile dysfunction.[6] The incidence of such side effects is low and varies from population to population because of its possible dependence on factors such as age distribution of the patients, their pre-existing physical health condition, and the prevalence of anxiety-stress syndrome. Such risk factors seem to have not been studied for side effects of finasteride, but we consider them for this made-up example for illustration. An estimate of the incidence of such side effects is important for discussing this with patients while prescribing the drug.

Suppose a study was carried out on a group of 1,000 consecutive male patients who were prescribed finasteride orally 1 mg daily for 12 months. They reported that they never took finasteride earlier and agreed to participate in the study. They answered questions on their background information such as age, physical health, and anxiety-stress syndrome at the time of recruitment. No question was asked about sexual functions at this time as that could have alerted them about such side effects. At the end of the 12-month period, 800 of them could be assessed for their sexual functions – others dropped out. Only questions regarding libido and erection relative to their initial status were asked for a focused response. These are the only side effects under this study. In total, 5.1% reported such adverse effects. This is the point estimate. No other information was recorded. What kind of uncertainties does this express for the estimate of the incidence of sexual adverse effects of finasteride?

The most obvious source of aleatory uncertainty is the sampling fluctuations. Another group of 800 patients from the same population may reveal sexual adverse effects in 4.1% or 5.2% or any other. If the sample is simple random from a specified target population, a statistical confidence interval (CI) can be easily built around the point estimate. The convention is 95% CI. In this example, this would be 3.6%–6.6% as per the established procedure. Note that this is quite wide despite a large n and shows the high vulnerability of the estimate. Another problem is that the CI is based on simple random sample, which is not the case in this example. However, consecutive cases in this example can be considered to simulate simple random sampling and no adjustment is needed. But the requirement of consent has the potential to make it biased as the consent is affected by factors such as knowledge, anxiety, and satisfaction with the consent process.[7] This can have a major impact but let us assume for this example that it is minor and the plausible range is marginally higher to 3.5%–6.7% instead of the CI of 3.6%–6.6%. Specific values of the wider range are only guesses just to illustrate the point about the effect of unaccounted uncertainties.

The major problem, however, is nonresponse by 20% of the subjects in this example. This is substantial and can severely affect the estimate depending on whether none or many of them had the side effects under consideration. The nonresponders are generally those who belong to low socioeconomic status, high illness burden, etc.[8] and adds to the uncertainty to the estimate of the incidence of side effects in this case. The reasons for nonresponse are generally not known, hard to elicit, and come mostly under the epistemic domain. Let the new plausible range incorporating this uncertainty be 3.3%–6.9%.

Now consider the fact that these 800 patients were those who were prescribed finasteride, but their actual intake is not known. Some may have missed intermittently for a short period each time and some may have discontinued for a long period after observing side effects. Suppose this was asked at the end of the 12-month period and all reported regular intake, where regularity is defined as at least 90% intake. We assume for our example that there is no misreporting. This may not be so in other setups.

The antecedents under this study are age, physical health, and anxiety-stress syndrome. Other antecedents such as hand preference and sexual orientation[9] are excluded. We will come to their measurement in a while but realize for now that the incidence of side effects should be different in different age-groups, and similarly for different levels of physical health and anxiety-stress levels. The point estimate of 5.1% obtained in this study is the average over the variation in these antecedents in the study group. The same is true for our plausible range of 3.3%–6.9% stated above. These should have been calculated separately for younger subjects and older subjects, and similarly for different physical health groups and anxiety-stress groups. If a patient of age 29 years in good physical health and no anxiety comes for a consultation, he cannot be told that the incidence of side effects is between 3.3% and 6.9% for his kind of patients. It is likely to be much lower for such patients and much higher for patients of age, say, 50 years and in debilitating condition. Considering this variation in various subgroups, it would be wise to consider a much wider plausible range such as 3.0%–7.2% in place of 3.3%–6.9% arrived earlier. There is no way to calculate this exactly but the plausible range illustrates the point that the CI widens. Note how the original CI for average incidence loses reliability due to such aleatory uncertainties. We have not considered all aleatory uncertainties yet. For example, we have not considered confounders such as co-morbidities and exercise which may or may not have been considered for assessment of physical health. These can further dilute the estimate but we ignore these for our example.

We have assumed that all the assessments were correctly made and properly recorded with no error. This is a tall order for most empirical research but we are not considering their effect in this communication because they are errors and do not fall in the ambit of uncertainties that we are presently discussing.

Uncertainties are attached to the measurements also. In this example, whereas age can be exactly obtained, there is no widely accepted scale for measuring the level of physical health and anxiety-stress syndrome. Surrogates are used and that causes epistemic uncertainties because the correct method to measure them is not available. If these are self-assessments, the response may depend on the condition of the patient at the time of response. In the case of an interview, the answer would also depend on the type of questions asked, who asked, and the type of rapport the interviewer could establish with the respondent.[10] These uncertainties will ultimately reflect on the plausible interval of the estimate of the incidence of side effects. Suppose the new interval is 2.8%–7.4% against 3.0–7.2 reached earlier. These are conservative estimates – if we actually calculate, the interval may be wider.

On the outcome side, this example restricts to decreased libido and erectile dysfunction. There is an epistemic gap regarding the method to measure them exactly as no widely acceptable scale is available. The impact of this uncertainty on the incidence of side effects is also largely unpredictable but it is easy to imagine that this would add to the uncertainty in the estimate. For illustration, let us say that this uncertainty increases the plausible interval from 2.8%–7.4% to 2.6%–7.6%. Note also that the side effects in this study were assessed by interview method where the response would depend on the perception of the responder. This will not contribute to uncertainty if the study aims to assess this perception and is explicitly stated.

The bigger problem, however, is that the side effects studied in this study are only decreased libido and erectile dysfunction. Even if other side effects such as depression, rash and gingival hypertrophy[11] are excluded, other sexual adverse effects such as lower sperm count and trouble having orgasm can also occur. There might be others in the epistemic domain about which we do not know yet. These will increase the incidence and not decrease it if all sexual adverse effects are to be considered. Suppose the new range to account for this, raises the upper limit from 7.6% to 8.0%. The lower limit remains at 2.6% as guessed earlier. This adjustment is required only if the patient is to be informed of regarding incidence of all the sexual adverse effects and not restricted to the two considered in this study.

In this example, the actual 95% confidence interval (CI) was 3.6%–6.6%. This is what is generally reported. But the plausible range as just explained could be 2.6%–8.0%. This is the conservative range considering that we have ignored the effect of certain uncertainties as stated in the preceding paragraphs. It may be alleged that we have inflated the range too much but our experience suggests that we are conservative for the effect of the specified uncertainties. The CI is based on widely accepted statistical methods but further widening is our conjecture with hardly any scientific basis. Perhaps, there is no way to delineate this exactly and that is not important either. The explanation of the aleatory and epistemic uncertainties in this setup should leave no doubt that the actual plausible limits are much wider than the CI. Thus, the point estimate of 5.1% and 95% CI of 3.6%–6.7% can be hardly believed despite the study following all the steps for an adequate prevalence study in this example.

We have not considered one more aspect of epistemic uncertainty and not many seem to be alive to this problem. Almost any result in medical research is derived from the existing or past cases but is generally used on future cases. No future case can be in any sample – thus, even the most immaculately drawn sample remains imperfect representation. It is presumed that future cases, at least in immediate future, would be similar to those studied. The experience suggests that this works well in most situations but may not hold in some situations such as when some new development occurs, say, for the assessment of sexual adverse effects. The other aspect is using the result for one population on the other without making any adjustment. For example, the normal body temperature 98.6°F was obtained for the German population.[12] This is accepted almost all over the world but no large scale study has been carried out in developing countries to confirm that this is valid for them. The same can be stated also for a large number of laboratory based parameters.

Our example illustrates the sizeable impact of aleatory and epistemic uncertainties in the simple case of estimating the incidence of side effects. The objective in most medical studies is more complex such as finding the relative importance of various risk factors. In such studies, the role of covariates and confounding factors can be prominent, and the aleatory and epistemic uncertainties in the assessment of these factors can make a substantial dent on the validity and reliability of the results. At present, these uncertainties are mostly ignored and the results become unreproducible.

Minimizing the Impact of Uncertainties

The realization of the presence of aleatory and epistemic uncertainties in an empirical result is an achievement by itself because these are rarely discussed in the context of medical research. The steps to control these uncertainties can be taken only after such a realization.

Aleatory and epistemic uncertainties remain but their impact on results can be controlled by taking certain steps. Some of these are already well known and many studies routinely adopt them, although without proper contextualization. For example, the proper choice of design can control most aleatory uncertainties caused by variation in antecedent factors, their interaction, and the confounders.[13,p.38,93] Strict inclusion and exclusion criteria help to remove many sources of aleatory uncertainties and to focus on a specific type of subjects but the generalizability suffers in this process. The results should have explicit mention of this limitation and no tall claims should be made for the general class of patients. Random selection and randomization in clinical trials is done to ameliorate the effect of unknown factors in the epistemic domain in the hope that these will average out. These methods are effective in their mandate in the case of large samples but can fail in studies with small samples.[13, p.122] A large sample, particularly when drawn by one of the random methods, is a great help in minimizing the uncertainties generated by sampling fluctuations. When random sampling is not feasible, consecutive cases meeting the inclusion and exclusion criteria without any other consideration simulate random sampling for those who meet the criteria. Although informed consent is a pre-requisite for most medical research, efforts should be made to secure maximum consent by explaining the benefits of the study, offering an incentive, or any such method. If the attrition is substantial, assess how it would have affected the results in the worst scenario. This will bring humility to conclusions. The statement of results should include a qualifying clause that the results are valid for only the consenting cases and interpret the results accordingly.

Synthesis methods such as systematic reviews and meta-analysis could be helpful to average out the effect of aleatory uncertainties since the subjects across studies are likely to represent a case-mix of the type we expect in actual practice. The conclusion, in any case, from such synthesis is more reliable because of a substantially higher base. However, if all or most studies in systematic reviews or meta-analysis are based on consenting individuals, the results can provide a false sense of security because the final result cannot be extended to nonconsenting persons.

The epistemic uncertainty also comes while associating the side effects with the treatment. WHO has discussed the division of causes into possibly due to, probably due to, and definitely due to a particular antecedent.[14] In our example, the question was asked regarding the adverse effect relative to the initial status, and we assume that all such effects can be attributed to the drug. This may not be so in other setups and an adjustment will be needed.

We have earlier mentioned epistemic uncertainties in the context of the exact measurement of the antecedents and outcome in our example. There are a large number of medical factors that defy direct measurement. The usual practice for such factors is to devise a scoring system and use it after proper validation. Many scoring systems such as quality of life scores and APACHE scores have been validated in different populations but no validated scoring system is available for many other factors. Thus, the first step for reproducible research in such cases should be to develop a scoring system and validate it for the population under study. The procedure for this has been described by several workers for different conditions.[15161718]

For the epistemic uncertainties generated by global ignorance, perhaps the only alternative is to expand the horizon and conduct more focused research on possible conjectures. Development and use of improved medical methods are always helpful in furthering research. This is a long term process and possibly no short-cuts are available. Till that time, we have to live with it but we need to be cautious in our conclusions and accept uncertainty.[19] However, for incomplete medical knowledge of individual workers, help can be taken from tools such as expert systems.[20] These are available for some conditions and more can be developed. This is easily said than done because of problems such as congregating a set of real experts for each topic. Such experts are rare, and they are extremely busy in their profession and generally not available for this kind of exercise. The other such tool is the etiology diagram of the type presented by Indrayan and Malhotra[13, p.297] for myocardial infarction. This kind of diagram helps in not missing out factors of importance in its causation. More such diagrams can be developed to facilitate general practitioners and researchers.

The steps suggested in this communication may make it difficult to reach a conclusion but that is the price we should be willing to pay for valid and reliable research results.

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Conflicts of interest

There are no conflicts of interest.