Bayesian statistics interpret data based on prior knowledge (or likelihood) and assume that the individual risk for an event reflects that of the population as a whole. In other words, the probability that an event will occur is based on prior knowledge of conditions that might be related to the event (Supplementary Fig. 1). Bayesian statistics are most correct when based on pre-existing assumptions that have been validated time and time again. They are useful for laboratory testing where the norms are well known. They are also useful for studying heart disease in women as thirty years of research have established that in relation to acute heart syndrome, women and men do indeed differ (the Yentl syndrome). So, if the risk of missing a myocardial infarction is related to the female sex, Bayes’ theorem will assess the risk of a missed myocardial infarction for an individual while taking into consideration that they are female rather than male.

However, contrary to early assumptions focusing on inequality alone, it has turned out that the reasons for male–female differences in heart disease are diverse. Heart disease manifests differently in women and men [1,2,3,4], there are specific challenges to achieving adherence to treatment and recommendations in women [5, 6], there was insufficient research on the effects of drugs and intervention on women [7,8,9] and more. And yes, at times, inequalities in care have also been discovered [6, 7].

The proportion of male admissions to intensive care is consistently higher than that of males in the population in general and in the elderly population specifically. In their nationwide retrospective study performed over 5 years on 450,948 adults in Switzerland, with 17.3% admissions to intensive care unit (ICU), Todorov et al. [10] attempt to elicit the reasons for this. Using two large databases, the authors sought gender differences in the provision of care to critically ill patients with cardiological or neurovascular diseases. They found that women were less likely to be admitted to an ICU than men despite being more severely ill, in particular younger women aged less than 45 years. Also, per each unit of increase in SAPS II, the odds of death were significantly higher among women than among men.

We salute the authors for their effort to adjust for the available variables in their analysis, as gender is, in general, a confounder but not when it is the focus of the analysis, like in the paper of Todorov et al. In addition, although they chose a Bayesian approach for analyzing the probability of ICU admission, analysis was conducted using non-informative priors, thus taking into consideration that prior data on differential treatment for men and women in relation to ICU admission is lacking. This improves the likelihood of reaching data-driven rather than bias-driven results. Sensitivity analysis to confirm the assumption that the non-informative priors have no influence on the results because of the size of the dataset, for example a frequentist model similar to the one performed on the secondary objective of death, was not performed even if it would likely have yielded similar results. However, concluding from the data presented that women may have less access to intensive care requires a (great) leap of faith. As stated by Jose Saramago: “Not everything is as it seems, and not everything that seems is. Between being and seeming there is always a point of agreement as if being and seeming were two inclined planes that converge and become one”. Much more data is required to elicit the reasons for the findings highlighted by the authors before the flag of inequality is raised.

Contrary to heart disease, thirty years of intensive care research has yielded little literature showing differential treatment given to women. Critically ill men and women probably differ from each other in many ways [6]. Although differential access to intensive care for men and women has been described, it has not been shown in European countries [11]. Women have longer life expectancies than men which probably explains why female ICU patients were older and had higher SAPS II than did men. But if women are admitted to ICUs despite less favorable baseline characteristics, there is no reason to assume that men and women do not have equal access to ICU. Similarly, there is no reason to manage men and women differently when they are critically ill [12]. So why did the adjusted analysis suggest a lower probability of admission and poorer outcome for females when compared to males?

First, retrospective database analyses are always limited to the data they contain, therefore “silent” (unreported) variables are always a potential source of bias. The larger the dataset and the smaller the number of variables adjusted for—the larger the potential effect of such bias if it does exist. The information regarding hospital admissions was extracted from two very large databases (the Swiss Federal Office of Statistics and the Minimal Dataset for MDSi—ICU Registry) [13]. Both the Swiss ICU-Registry and Swiss Federal Office of Statistics have a limited set of variables, as do many databases. The analysis presented included a very small number of variables in relation to the number of cases, therefore underfitting may be an issue despite the best efforts of the authors.

Second, important clinical variables which should ideally have been included in the model were not available in either database (Table 1). Examples include comorbidities and chronic diseases prior to hospital admission. Lacking adjustment for these variables, gender effect, which may be only a confounder, may be misinterpreted as the cause for the differences observed. The prevalence of quite a few chronic conditions is higher among males than among females, and particularly among females of similar age. For example, the authors informed us that 7% of individuals aged > 50 years in Switzerland suffer from cardiovascular disease and that it is more prevalent in men than in women (source: National Health Report 2015, Swiss Health Observatory). Other chronic conditions may be more prevalent in women. Without adjusting for all of these components separately and elucidating the interaction between them, it is difficult to know what may have affected the outcome.

Table 1 Gender differences in characteristics that may have confounded the analysis of Todorov et al. [10]
Full size table

Third, with regards to the use of the SAPS II score; this score was also only available for ICU patients. In addition, only three previous health conditions are included in the SAPS II—whether the patient had metastatic carcinoma, hematological malignancies or AIDS. Therefore, adjusting the mortality prediction model to the SAPS II is no substitute adjustment to chronic conditions and their severity. The SAPS II includes 12 physiological variables that reflect patient acuity. However, the score was also included in the model as a whole, rather than with its separate components. Adjustment for pooled data essentially eliminates the possibility of identifying important individual factors.

Finally, the model also includes the nine equivalents of nursing manpower use (NEMS) score which measures the burden of nursing care. While it is true that mechanical ventilation, continuous renal replacement therapy and the use of vasoactive drugs are all used in patients that are more sick, these interventions are only surrogates for patient acuity.

Seeking inequality is the first step in combating inequality. Yet when inequality is sought in places where it is not obvious, the search is often initially accompanied by derision. Todorov et al. [10] have drawn our attention to the possibility, remote as it seems, of unequal access to intensive care among men and women in Europe. Several methodological aspects of their study raise hope that their findings may yet turn out to be a false alarm. However, these authors have thrown a stone into the pond of intensive care. Further research must be conducted to elicit the reasons for their findings if we are to determine that the ripples they have created can easily be stilled.