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Counterintuitive results from observational data: a case study and discussion
  1. Erik Doty1,
  2. David J Stone2,3,
  3. Ned McCague3,4,
  4. Leo Anthony Celi5
  1. 1 Department of Biomedical Informatics, Harvard Medical School, Boston, Massachusetts, USA
  2. 2 University of Virginia School of Medicine, Charlottesville, Virginia, USA
  3. 3 Laboratory for Computational Physiology, Massachusetts Institute of Technology, Cambridge, Massachusetts, USA
  4. 4 Verily, Cambridge, Massachusetts, USA
  5. 5 Massachusetts Institute of Technology, Cambridge, Massachusetts, USA
  1. Correspondence to Dr Leo Anthony Celi; lceli{at}


Objective To explore the issue of counterintuitive data via analysis of a representative case in which the data obtained was unexpected and inconsistent with current knowledge. We then discuss the issue of counterintuitive data while developing a framework for approaching such findings.

Design The case study is a retrospective analysis of a cohort of coronary artery bypass graft (CABG) patients. Regression was used to examine the association between perceived pain in the intensive care unit (ICU) and selected outcomes.

Setting Medical Information Mart for Intensive Care-III, a publicly available, de-identified critical care patient database.

Participants 844 adult patients from the database who underwent CABG surgery and were extubated within 24 hours after ICU admission.

Outcomes 30 day mortality, 1 year mortality and hospital length of stay (LOS).

Results Increased pain levels were found to be significantly associated with reduced mortality at 30 days and 1 year, and shorter hospital LOS. A one-point increase in mean pain level was found to be associated with a reduction in the odds of 30 day and 1 year mortality by a factor of 0.457 (95% CI 0.304 to 0.687, p<0.01) and 0.710 (95% CI 0.571 to 0.881, p<0.01) respectively, and a 0.916 (95% CI −1.159 to –0.673, p<0.01) day decrease in hospital LOS.

Conclusion The finding of an association between increased pain and improved outcomes was unexpected and clinically counterintuitive. In an increasingly digitised age of medical big data, such results are likely to become more common. The reliability of such counterintuitive results must be carefully examined. We suggest several issues to consider in this analytic process. If the data is determined to be valid, consideration must then be made towards alternative explanations for the counterintuitive results observed. Such results may in fact indicate that current clinical knowledge is incomplete or not have been firmly based on empirical evidence and function to inspire further research into the factors involved.

  • pain
  • mortality
  • length of stay

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Strengths and limitations of this study

  • Large sample size with minimal covariate data missing.

  • Multiple regression models with multiple sensitivity analyses.

  • High internal validity shown by use of falsification hypothesis testing.

  • Lack of oral analgesic data.

  • Recognising that correlation does not equal causation and further work is needed to confirm case results.


What do we mean by counterintuitive data? It is data that presents unexpected results that may clash with common sense or what has been previously published and accepted by the medical community. In practice, clinicians have long dealt with such results in individual bits but have had the vast advantage of being able to examine the concurrent state of the patient and react in real time by repeating a lab test or tracking ongoing monitor data. These responses function to identify the prior result as a non-repeatable error or as a genuine anomaly. However, this approach is not applicable to the context of retrospective data analysis. Furthermore, the counterintuitive data revealed in such analyses is likely to be more involved than a single aberrant lab or vital sign value. In today’s data driven healthcare system, retrospective data analyses are becoming more and more common. We can therefore logically expect to encounter a greater incidence and variety of counterintuitive values and results that are impossible to confirm by repetition, difficult to confirm or deny by context, but still require interpretation.

The question then becomes how best to approach such results? Are they incorrect simply because they weren’t what was expected? And was the expectation itself based on subjective assumptions or objective conclusions? When our prior expectations are not met, are we dealing with truly faulty data or do our expectations need to be reset by what are reliable, but counterintuitive, results. For example, we have learnt that intensive care practices common in the past such as large tidal volume ventilation, the use of pulmonary artery catheters and the use of lidocaine infusions in myocardial infarction led to no benefit or injury.1–3 Were these unexpected negative outcomes initially missed because outcomes data was not being carefully analysed or perhaps ignored or interpreted as counterintuitive to the level of unbelievability? How can the situation be dissected retrospectively so that counterintuitive data can be identified as truly spurious versus simply not being consistent with our prior experience which may itself be faulty and require data driven correction?

In this paper, we explore a case in which the results contradicted previous reports and our clinical expectations. Using the Medical Information Mart for Intensive Care-III (MIMIC-III) a critical care database that was developed and maintained by the Laboratory for Computational Physiology at the Massachusetts Institute of Technology,4 we retrospectively selected a cohort of patients that underwent a coronary artery bypass graft (CABG) procedure and evaluated the effect of perceived pain on mortality and hospital length of stay (LOS). Our initial hypothesis was that increased levels of perceived pain would correlate with worse patient outcomes such as increased hospital length of stay. This would be in line with the current literature that suggest optimal pain control leads to increased mobility, earlier ambulation and improved outcomes.5–7 Contrary to the literature, we found that higher levels of pain were associated with reduced mortality and reduced LOS. We then discuss potential causes of these results and the general issue of dealing with counterintuitive results in retrospective data analyses.



We selected patients from the MIMIC database who met all of the following inclusion criteria and none of the exclusion criteria. Inclusion criteria included: (1) Adult >18 years old, (2) who underwent CABG surgery and (3) was extubated within 24 hours after arrival to the intensive care unit (ICU). Exclusion criteria were: (1) Non-CABG surgical procedure and (2) missing data on confounding variables. Patients were identified using Current Procedural Terminology (CPT) codes: The following CPT codes corresponded to the CABG procedure: 33 510 to 33 516 for venous grafting only for coronary artery bypass and 33 533 to 33 548 for arterial grafting for coronary bypass. The final study cohort contained 844 patients (figure 1).

Figure 1

Shows selection of patient cohort from MIMIC database. After selecting those who underwent CABG procedure and excluding those with no pain measurements, 844 patients were extubated within 24 hours following surgery and included in the cohort. CABG, coronary artery bypass graft; MIMIC, Medical Information Mart for Intensive Care.

The MIMIC-III database included 1917 patients who underwent CABG with 844 meeting the study criteria. CABG was chosen for the investigation as it is a common procedure with the majority of patients having no or few postoperative complications and relatively predictable recoveries.5 Due to the nature of the surgical procedure which requires sternal spreading for exposure, there is an expected high analgesic burden immediately after surgery.


The primary outcome assessed was mortality at 30 days. Secondary outcomes were mortality at 1 year and hospital LOS. In the MIMIC database, mortality data for patients who die after hospital discharge is derived from the social security death registry.4


The exposures of interest were pain levels reported by the patient immediately and in the subsequent interval after ICU extubation. Pain levels on a scale of 0 to 10 were regularly self-reported by patients to ICU nurses and recorded in the database, generating a continuum of measurements for each patient. The mean, median and maximum pain levels were used for separate analyses. Concomitant measurements of heart rates, respiratory rates and systolic blood pressures were also compared against their simultaneously recorded pain measurement.

Intravenous (IV) opiate administration was extracted from the database. MIMIC contained data for the following medications: Morphine, fentanyl, hydromorphone and meperidine. The was no data in MIMIC corresponding to the administration of oral analgesics.

We also looked for an association of pain and nausea for use in falsification hypothesis testing. The presence of nausea was derived from the nursing notes stored in the database. A positive nausea exposure was defined as the mention ‘nausea’ or ‘nauseous’ in the nursing note with no negative descriptor, such as ‘not nauseous’ or ‘denies nausea’, attached.


Several variables found to be linked to worse patient outcomes in previous studies were included to control for confounding in the regression models; demographic factors, comorbid conditions and illness severity score on admission to the ICU.8 9 Comorbid burden was represented by the Elixhauser index which is determined by the aggregate presence or absence of 30 different comorbid conditions as detected by International Classification of Diseases (ICD)-9 codes.10 These conditions include but are not limited to cardiovascular disorders such as hypertension, congestive heart failure, coronary artery disease and peripheral vascular disease; pulmonary disorders such as chronic obstructive pulmonary disease; endocrine disorders such as diabetes and hypothyroid; obesity; drug and alcohol use disorders; renal disease; liver disease. Illness severity was captured using the Oxford Acute Severity of Illness Score (OASIS), which is calculated on admission to the ICU and takes into account age, heart rate, Glasgow coma scale, mean arterial pressure, temperature, respiratory rate, ventilatory status, urine output, pre-ICU in-hospital LOS and whether or not the patient underwent elective surgery. Studies have shown OASIS is comparable to other illness severity ratings in predicting outcomes such as mortality and length of stay.11

Patient and public involvement

This research was done without patient or public involvement. They were not invited to contribute to the development of our methodology, our outcomes, nor the writing of our paper.

Statistical analysis

Analysis was carried out using R V.3.4.0 and SAS V.9.4. Binomial logistic regression models were fitted using maximum likelihood estimation to compare the pain measures with 30 day and 1 year mortality. Linear regression was used to model the relationship between mean pain scores and hospital LOS. Age, gender (male reference), Elixhauser index and OASIS score were included in the models to account for potential confounders. In a separate regression, mean pain levels were categorised into four ordinal groups of no pain (0/10), mild pain (1 to 3), moderate pain (3 to 6) and severe pain (7 to 10) in accordance with the National Institutes of Health (NIH) Pain Consortium.12

Analysis of variance (ANOVA) was used to determine if there was a significant variation in heart rate, respiratory rate and/or systolic blood pressure, when compared with the concurrent pain assessment.

IV analgesia medications were converted to their morphine equivalents based on the National Pharmaceutical Council guidelines.13 The IV analgesia was subdivided into total dose in the first 24 hours, mean dose per ICU course day and total dose during ICU course. ANOVA models were used to determine if there were any significant variation in administration of IV analgesics among the four categorised pain groups.

Two sensitivity analyses were performed to assess the robustness of the observed effects. The first included the same statistical tests in all postoperative CABG patients regardless of duration of intubation. The second sensitivity analysis excluded patients who died in the hospital.

To add validity to the potential observed associations, falsification hypothesis testing using Prasad and Jena’s methodology was employed. A distinct and highly unlikely hypothesis is tested against the exposure of interest, pain in this case.14 We used nausea, a symptom with no known correlation to pain, and tested it against the four different pain metrics.


The database included 844 patients who underwent a CABG procedure and were extubated within 24 hours. There were 68 patients who on average reported no pain during their ICU stay after extubation, 419 with mild pain, 336 with moderate pain and 21 with severe pain. The mean frequency of pain measurements was 19.8 measurements per patient. The distribution of patient characteristics, including age, gender, illness acuity on ICU admission (OASIS) and comorbidity index is reported in table 1. There was no significant difference noted in the frequency in which pain was assessed in those who experienced lower pain levels when compared with those who experienced increased pain levels. The number of comorbidities ranged from 0 to 9. Bivariate analysis showed increasing OASIS was significantly associated with increased mortality and increased LOS (p<0.05). No significant differences were found in the amount of IV analgesia administered among the pain subgroups.

Table 1

Shows the distribution of the outcomes and covariates in the patient cohort

Bivariate analysis (figure 2) shows a correlation between increasing pain levels and improved outcomes among these patients who had no intra-operative complications and were extubated within 24 hours of arrival in the ICU. Higher pain levels for this specific cohort of patients who were fast-tracked after CABG were found to be associated with decreased hospital LOS. Those who experienced lower levels of pain in the ICU were more likely to be dead at 30 days and 1 year.

Figure 2

Three plots demonstrating the bivariate relationship between the outcomes of interest and mean pain. Plot A shows decreased length of stays with increased mean pain levels. Plot B and Plot C show that, on average, those who expired at 30 days and 1 year marks experienced lower in hospital pain levels than those who did not expire. LOS, length of stay.

Multivariate regression analysis was performed to adjust for confounding. Four different models using mean, median and maximum pain scores and pain categories were tested against the clinical outcomes with the results displayed in table 2. The logistic regression models consistently showed that increasing pain was associated with reduced odds of death at 30 days and 1 year after adjustment for illness severity and comorbid conditions. All the linear models demonstrated that increasing pain levels were also associated with decreased hospital LOS, except for the model that looked at the maximum pain score, which showed an opposite effect. R-squared values for the linear regression models varied between 0.25 and 0.3 for all the models. Complete statistical data from all regression models can be found in the online supplementary materials file.

Table 2

Shows results from main analysis and the two sensitivity analyses

No significant variations were noted in heart rate, respiratory rate or blood pressure with increasing pain levels.

Sensitivity analysis was employed to examine all patients regardless of duration of intubation, expanding the sample size to 1889 patients. The results were similar for 30 day mortality and hospital LOS as regards effect size and statistical significance; however, the results were not statistically significant for 1 year mortality (table 2). A total of 22 CABG patients were noted to have expired in the hospital, our cohort included 15 of these in hospital deaths. An additional sensitivity analysis excluded patients who died in the hospital - these results were consistent with the prior models and were statistically significant for hospital LOS, but not for mortality (table 2).

As expected, the presence of nausea was not found to be associated with any of our pain measures in our falsification testing, decreasing the possibility that the previous results are erroneous or solely due to chance.


Case study

We will first discuss our unexpected results and then discuss the general issue of counterintuitive data. Our results that increasing levels of patient-reported pain severity post-CABG surgery are associated with better clinical outcomes were not consistent with our initial hypothesis that better outcomes correlate with better pain control as per the reported literature. In fact, prior studies have found increased levels of pain in the hospital to be associated with increased mortality.15

The difference in the study cohort between our study and others may explain some of the discordance. Our initial analysis was limited to ‘fast-tracked’ patients who did not have intra-operative complications and were extubated early in their ICU course. These patients made up 44% of the database patients. Studies that have reported worse clinical outcomes associated with postoperative pain did not select for a relatively healthy sub-cohort of patients. Why would patients with higher levels of pain have better outcomes? It is well documented that an increased inflammatory reaction is associated with increased pain. Pro-inflammatory cytokines such as interleukin-1 beta, interleukin-6 and tumour necrosis factor-alpha have been directly implicated in the physiology of pain.16 17 These cytokines have also been found to be directly involved in wound healing through the stimulation of processes such as keratinocyte and fibroblast proliferation and synthesis and breakdown of extracellular matrix proteins.18 We speculate that those patients who demonstrated better outcomes mounted a more robust inflammatory response leading to more pain, but also to increased healing ability.

Another possibility is that higher perceived pain levels represent a proxy for a generally better state of health, including superior physiological function of the cardiovascular, respiratory, renal and hepatic systems. In tandem, these systems act to metabolise and eliminate anaesthetic and analgesic drugs so that the net pharmacokinetic result would likely be increased susceptibility to pain due to less administered agent remaining at active sites. Furthermore, patients with better cardiovascular function would likely have better cerebral perfusion with improved central neurological function, and thereby have a pharmacodynamic reason for perceiving more pain. Also patients who are generally in better overall condition would be expected to manifest better outcomes. These thoughts are admittedly speculative and additional research is needed to explore these possibilities.

It is important to point out that the goal of clinicians should not be in any way to maximise pain to optimise outcomes. Conventional approaches that aim to control pain adequately should be employed. Our observation is just that - an observation of an association and conjectures of possible linking mechanisms but is not intended in any way to drive pain management policy in the direction of tolerating undertreated pain.

We performed sensitivity analyses, one including all patients regardless of postoperative ventilation duration and another excluding patients who died during hospitalisation and reached similar conclusions. When excluding in-hospital deaths, we discovered the 30 day mortality rate had a similar OR, but was no longer statistically significant. This is most likely due to the low mortality rate after hospital discharge following CABG, making it difficult to detect a statistically significant effect.

We believe that researcher bias is a non-issue as these findings were not expected, but rather, the opposite. Sampling bias was also minimal. Our inclusion criteria were predefined prior to database sampling and only 28 patients needed to be excluded due to missing data. We performed multiple sensitivity analyses to determine if those that were excluded would have influenced our results. However, the study has several limitations inherent in any retrospective data analysis. We acknowledge that correlation does not equal causation and further research is needed to determine the underlying physiological mechanism for the results seen. Due to the self-reported nature of the pain scores, reporting bias is a concern. Some patients may have over-reported and others under-reported their pain. We also recognise that analgesic administration is a confounder and were unable to completely control for this due to lack of information regarding oral analgesics in the database. However, with respect to intravenous analgesics, we attempted to limit this potential confounder by excluding those with prolonged intubations who would inherently have received and required greater doses of sedatives and analgesics. We also compared the amount of narcotics that patients were receiving and did not observe any significant differences among the various pain groups. Despite measures taken to guarantee internal validity, we anticipate appropriate scepticism with regard to generalisability of the findings. This, of course, is of genuine concern given the current state-of-affairs where clinicians are already inundated with conflicting studies of questionable quality. We therefore invite other investigators to replicate (and expand) our analysis in other databases.

Counterintuitive results and examples

As noted, our findings were contrary to clinical expectations and to most published works which associate increased pain with worse outcomes.15 19 20 Encountering counterintuitive results is not unique to retrospective data analysis. Clinicians encounter unexpected, possibly aberrant, values in situations such as the evaluation of laboratory and monitor data. When a possibly spurious lab result is obtained, the usual response is to repeat the test. When the second test comes back with a more acceptable value, we generally then ignore the unexpected value. But what if the repeat value is also aberrant? Do we repeat it again or do we begin to believe that the value is ‘real’ and start to formulate a response to a clinical problem? In this case, it is the consistency and reproducibility of the counterintuitive value that drives its possible validity. The details of this process are determined by the overall clinical risks involved. The consistency we found in the pain score values drove us to consider the possibility that the values were ‘real’ even though they were counterintuitive in terms of our expectations.

Another issue in evaluating to counterintuitive values is whether they are possible. Impossible values would include a potassium of 64.5, one incompatible with life. But a potassium of 7.3 is a possible value. The pain values associated with better outcomes were unexpected, but not so high that they were impossible in the observed context.

One question that would arise with a potassium of 7.3 would be that of continuity - did the value occur suddenly or gradually in a stream of normal values? Were surrounding values similarly abnormal? In the context of persistently abnormal values, for example, untreated uraemia, a normal value would be counterintuitive. So that while most counterintuitive values will tend to be out of the ‘normal range’, they will not necessarily be so. In the context of increasing values, it might simply be the first one that was not only out of the normal range, but that crossed the line into a critical range.

The fundamental question is whether counterintuitive results are actually false results or does the problem lie in our perception of what should be. Table 3 displays a categorisation of error types that could result in faulty data. We are not able to attribute the counterintuitive data we observed to any of these factors, however.

Table 3

Putative causes of truly faulty data

How can counterintuitive results be approached in secondary data analyses? Table 4 displays characteristics that may distinguish reliable (but counterintuitive) from truly faulty data. With consideration of these factors, the first investigative step is to retrace the process and work flow involved in data entry so far as possible. Our data was obtained at the institution of several of the authors where nurses are trained to assess pain on a standard scale from 0 to 10. There are several potential faults to this method. The nursing staff could neglect to regularly assess pain or neglect to enter the information into the medical record generating the database. While this may alter a few data points, it is unlikely to systematically affect all data unless there was an obvious glaring institutional issue affecting every nurse and every data entry.

Table 4

Criteria to establish possible validity of counterintuitive data

After determining that the data source is valid, additional statistical tests can be run on the patient cohort. Tests such as the falsification hypothesis testing we used, add validity to the results as they show that the cohort follows other generally known principles. In our study, falsification analysis provided support for our findings.

Concurrent contextual data can also help to confirm the veracity of data - for example, one could examine ECGs if hyperkalaemia was being analysed. We examined concomitant vital signs during the time of pain measurements. We expected to observe significant increases with higher pain levels, but did not: With the combination of analgesics, residual anaesthetics and the concurrent use of drugs that directly affect vital signs such as beta-blockers, the lack of correlation is probably not surprising. In fact, we learnt that in this setting, it appears to be inadvisable to use vital sign changes as a proxy for the presence of unvoiced pain. Finally, one can attempt to physiologically explain the disparity between the observed and expected results as we did above for the case of post - CABG pain.

The use of lower thresholds for blood transfusions in the ICU is an example of a counterintuitive finding. ICU target haemoglobin levels were historically set at greater than 10 g/dL, theoretically to ensure adequate oxygen delivery.21 This led to increased transmission of blood borne diseases, unnecessary healthcare expenditures and actually worse outcomes.22 Later research showed that this rule was not necessary for most patients, but only for selected patients such as those with acute coronary syndrome actively experiencing chest pain. The initially counterintuitive findings that lower haemoglobin levels were not only acceptable but preferable in most cases, served as research triggers to more fully elucidate optimal clinical practice. Our case may serve as an analogous research trigger in terms of optimally managing postoperative pain. Outcomes such as mortality and LOS are complex phenomena driven by many factors - to observe a clear and robust statistical effect such as we did is strongly suggestive that something ‘real’ is occurring even if the data were counterintuitive.

The final step when dealing with counterintuitive data is to look for additional evidence that confirms the reliability of the results (perhaps this could be termed ‘confirmatory metadata’). With respect to our CABG case, the analysis should be rerun on additional databases and in different settings. Just as clinicians continued to manage intensive care unit anaemia as they always had until more definitive results were reported, our results should not impact the analgesic care of patients at this point. However, we hope that we have raised the issue in the appropriate minds that outcomes may benefit from approaches slightly different from usual. After all, one can easily eliminate all pain from postoperative patients, but they would have to remain sedated and ventilated for an indefinite period of time to do so and after they are extubated, pain management should not be so aggressive that it leads to apnoea and respiratory arrest. In other words, there may be a detectable level of tolerable pain that leads patients to their best outcomes and no honest clinician will guarantee a patient that they will have no pain at all after a procedure like a sternal-disrupting CABG.


Contrary to our expectations, we observed, in a retrospective analysis of electronic health records, that post-CABG fast-track patients with higher pain scores had better outcomes. The increasing use of electronic health records for secondary analysis will likely lead to an increasing incidence of such apparently counterintuitive results. While the first step in this situation is to attempt to confirm the reliability of both the analytical process and the data itself, such findings that prove to be robust may lead to further ideas and subsequent research that drive future clinical care. On the other hand, clinicians must be careful in terms of modifying their practices until the implications of such counterintuitive (or any) data have been thoroughly vetted and confirmed in diverse database contexts and via the peer review process.


We would like to thank J Michael Jaeger, MD, PhD of the University of Virginia School of Medicine, for his assistance with background information r



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  • Contributors ED was responsible for the data extraction, the initial statistical analysis and writing and editing the manuscript. NM was involved in validating the statistical models and participated in editing the manuscript. DS was responsible for assisting with background information and editing the manuscript. LC was the project supervisor, responsible for project conception and manuscript editing.

  • Funding Leo Anthony Celi receives extramural funding from the National Institute of Health.

  • Competing interests None declared.

  • Provenance and peer review Not commissioned; externally peer reviewed.

  • Data sharing statement The datasets generated for the current study were derived from the MIMIC-III Database available at The data subsets and statistical code used in this project can be found at

  • Patient consent for publication Not required.

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