1. Background

Patient safety research is concerned with finding means for avoiding accidental and unplanned events (incidents) that either cause harm or have the potential to do so. A fundamental tenet of some safety research is that measures taken to reduce the incidence of ‘no harm’ or ‘near miss’ incidents inevitably reduce the number of major incidents in which patients are harmed. This was a view originally championed by a safety expert, Herbert W. Heinrich,[1] whose work gave rise to the principle of the Heinrich ratio. Studying insurance claims forms for industrial accidents in the 1920s, Heinrich developed a three-way categorization of incidents, depending on their outcome. He classified them as ‘no-injury accidents’, ‘minor injuries’ and ‘major injuries’, and suggested that the relative frequency of these events is comparatively constant. This gives a rationale for a belief held by some in safety science that reducing the incidence of minor or no-harm incidents will lead to a proportionate reduction in harm. It has been suggested that the Heinrich ratio can be used in quantitative terms and that the overall effects of new safety measures can be estimated by monitoring minor incidents and then inferring the reduction in major incidents by pro rata scaling.[2–4] Whilst much of the early work in this area has been carried out in industry, the principle of a fixed Heinrich ratio is increasingly referred to in the emerging field of patient safety research.[5–7]

Calculating a Heinrich ratio is simply a matter of deriving the relative ratios of three numbers. It is thus undoubtedly true that such ratios exist. This paper is more concerned with the scientific principle espoused by Heinrich that such ratios are constant.

Here, our aim is to establish whether the principle of a fixed Heinrich ratio is sound.

2. Research Methodology

Some may find our research methods unusual in that we use deductive, rather than inductive inference. Inductive inference is by far the most common form of investigation used in healthcare research. However, it is not the only valid scientific method. In deductive inference, the focus is on generating new knowledge by examining the logical consequences of a given set of facts.[8] There are many ways this might be done and the world of deductive science is nowhere near as formulaic as that of inductive science. Deduction, often using mathematics or formal logic, can take many forms. These include the use of the ‘thought experiment’ (Gedankenexperiment), which has a long tradition dating back to 1812, perhaps most notably in the work of Einstein. Note that it may only take one case to establish that a principle is unsound. For example, the statement, “All swans are white.” can be refuted by the discovery of a single black swan.

Our research has been sequential, using a range of methods and approaches in a sequence of studies, each providing different grounds for refuting the principle of a fixed Heinrich ratio.

2.1 ‘Thought Experiments’

First, we explored the logic of the Heinrich ratio via thought experimentation, using deductive reasoning and mathematical modelling to fashion a series of vignettes to establish whether there were logical flaws in the notion of a fixed Heinrich ratio.

2.2 Empirical Data

2.2.1 Selection of Empiricial Data

We next reviewed the medical literature to find studies that reported numbers of incidents classified in three categories of harm. First, we examined a well documented example of medical harm, concerning outcomes for patients attending an accident and emergency department based on electronic case records of hospital discharges, emergency department records and death certificates.[9]

We then considered our own particular research area of medication errors. We conducted a literature review to find all original studies that reported the incidence of medication errors in the hospital setting by actual or potential outcome in at least three categories (minor, moderate and severe). The medication-error literature is particularly sensitive to methodological variation, so we only included studies that had sufficient detail regarding their methodology, including data collection methods and data analysis, to judge the quality of the study. Studies had to report the definition of the medication error, the exact method of data collection, a description of how the medication-error rate was calculated and a description of how the severity of the medication errors were determined. Studies were excluded if the results could not be recategorized. Studies were also excluded if data came from (spontaneous) incident reporting as this method is known to be associated with underreporting and possibly a bias towards reporting more serious errors.[10]

Finally, we searched for examples from outside the medical literature. We used data from road traffic accidents in Great Britain reported on an annual basis between 1993 and 2003.[11] Meticulous records are kept of every road traffic injury accident that is reported to the police. Great pains are taken to ensure that data are complete and a standardized data collection form is used, which provides little scope for non-uniformity in what is recorded in different centres.

2.2.2 Analysis of Empirical Data with a Triangle Plot

A graphical technique called the lstriangle plot’ has been devised for displaying three relative proportions of the data from these studies as a point within an equilateral triangle. A point at the centre (technically the centroid) of the triangle corresponds to the case where the relative proportions are all equal. The further a point is from a vertex, the smaller the relative proportion is corresponding to the category associated with that vertex.

In principle, the results of several studies that categorize incidence into three severity categories can be displayed using a three-dimensional scatter plot, where the three coordinate axes correspond to the different severity categories and the results of a single study are represented by a point with coordinates that are the relative proportions of cases in each of the three categories.

This can be difficult to visualize. However, for each point, the three proportions sum to unity and, as a consequence, the scatter of points lies in a plane. Furthermore, since all the proportions are non-negative, a symmetry argument can be used to show that the scatter of points all lie on an equilateral triangle whose vertices correspond to the points where the plane meets three axes. These three points are at unit distance from origin. In view of this, subject to a certain amount of coordinate transformation, the scatter plot can equally well be represented as a two-dimensional scatter of points within an equilateral triangle. This is what we refer to as the triangle plot.

Standard methods exist for estimating confidence intervals for relative proportions when cases are assigned to one of two categories.[12] These have been extended so that within the triangle plot, an approximate 95% confidence region can be plotted, generally taking the form of a hexagon surrounding the point concerned.

2.3 Nomenclature

Medication errors and industrial accidents are incidents that take place in entirely different contexts. The harm associated with an industrial accident is usually apparent with harmful outcomes that can be observed. In medicine, however, one would classify many incidents as ‘harmful’, even though the patient might not perceive them as such, for example administering the wrong dose of a drug might reduce the clotting time of blood, but this would often not be noticed by the patient (although there are circumstances where there could be fatal consequences). In view of this, medication-error studies often rely on devising means for categorizing incidents in terms of the degree of potential harm. Even so, it is common to use a three-way classification of incidents. We shall refer to incidents as ‘minor’, ‘moderate’ or ‘severe’ in terms of the degree of harm or potential harm associated with them.

3. Findings

3.1 Thought Experiments

During the course of the study, thought experimentation was used to devise vignettes that illustrate the logical inconsistency of the notion of a fixed Heinrich ratio. Several were identified; the two most informative are summarized here.

3.1.1 Vignette 1

A version of Russian roulette is played with a revolver that has six chambers. One is loaded with a live cartridge, two are loaded with blank cartridges and the other three are left empty. The chambers are spun several times, the player places the gun against his head and pulls the trigger. Analysis of outcomes from this dangerous game show a remarkably consistent pattern. The relative frequencies of deaths, powder burn injuries and no injuries were in the ratio 1 : 2 : 3. In an effort to make the game safer (equivalent to a patient safety intervention), a new loading pattern was adopted with one live cartridge, one blank and four chambers left empty. This halved the proportion of powder burn injuries, but had no affect on the proportion of deaths, in contravention of a fixed Heinrich ratio.

3.1.2 Vignette 2

Consider a hypothetical study aiming to establish the proportion of newborn babies judged to be underweight. Using a continuous measure such as birth weight as a proxy for ‘harm’ allows us to address the question of how one should determine what is abnormal. In the context of the Heinrich ratio, suppose that one wishes to categorize babies as ‘normal’, ‘underweight’ or ‘grossly underweight’. Such a categorization relies on determining two threshold weights that define three weight bands. Clearly the ratio of numbers of babies assigned to each band relies on the choice of thresholds. Less obvious, but easy to establish mathematically, is that any set of relative ratios could be achieved by judicious choice of threshold values. Indeed, this does not depend on the distribution of weights being Gaussian, and it is sufficient that the cumulative probability distribution is continuous.

This shows that in cases where there is no natural three-way categorization of the harm associated with incidents, the rule chosen for stratification can have a major impact on the resulting Heinrich ratio. It does not support the notion that the ratio is constant.

3.2 Analysis of Empirical Data

The triangle plot shown in figure 1 summarizes the distribution of outcomes for accident and emergency department attendance, dependent on the type of accident. The closer a point is to a vertex of the triangle, the more frequent the corresponding outcome is in the data, starkly demonstrated by the point representing self-inflicted gunshot wounds that, unsurprisingly, are shown as having a high death toll. What is clear is that there is considerable heterogeneity of outcomes, which provides no support for a stable Heinrich ratio in this context.

Fig.1
figure 1

A triangle plot illustrating the relative proportions of three different outcomes for patients attending an accident and emergency department. ‘No admission’ corresponds to patients treated within the unit.[9]

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Figure 2 summarizes the data from medication-error studies.[13–22] Again there is no support for a stable Heinrich ratio. The hexagonal 95% confidence regions for the grand mean of data shown in this plot did not overlap with those for any of the constituent datapoints shown. They are not shown since they clutter the diagram.

Fig.2
figure 2

A triangle plot showing the relative proportions of different severities of medication errors in 11 different studies.[13–22] Different symbols correspond to studies concerning different types of error.

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The triangle plot (figure 3) of road traffic data shows a tight cluster of points so, at first, seems suggestive that there might be some homeostatic mechanism at play. However examining the triangle plot more closely revealed a very systematic year-on-year evolution of the relative proportions of accident types, as shown in the expanded section of figure 3. The proportion of death accidents remains relatively constant. However there has been a steady shift to the left, whereby the proportion of serious accidents diminishes while the proportion of minor accidents increases. This is contrary to what would be expected if there were a constant Heinrich ratio; indeed this exhibits the same behaviour as the Russian roulette thought experiment described above. Here, given the large sample size, 95% confidence regions are so small that they are comparable in size to the symbols used to represent the data.

Fig.3
figure 3

A triangle plot showing relative proportions of road traffic accidents categorized according to their severity reported for Great Britain between 1993 and 2003.[11] Numbers indicate date order of plotted points.

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4. Interpretation

At first sight, a potential criticism of our analysis of clinical incidents is that perhaps different studies use different criteria to categorize them in terms of outcomes. This may well be the case. However, this is akin to the problem identified in our second thought experiment (vignette 2). The Heinrich ratio is indeed likely to vary depending on the criteria used to categorize incidents, thus de facto, is not constant. In addition, the road safety data use well established and objectively defined criteria for the incidents and still do not support the Heinrich ratio.

There is currently considerable pressure to improve safety in relation to healthcare, and much needs to be done in terms of research.[23] One of the problems faced is that major incidents occur relatively infrequently and are thus difficult to study. On the other hand, minor incidents abound. In view of this, the notion of some form of fixed ratio between the two is appealing since, if this were the case, it would mean that the overall effects of new safety initiatives could be evaluated by focussing on minor incidents. Our work suggests that such reasoning is fallacious.

As we have shown, there may be circumstances in which remedial measures that reduce the frequency of minor incidents would have no effect whatsoever on the relative frequency of severe incidents; indeed it is not hard to imagine circumstances where the reverse might be the case. Introducing measures that reduce the incidence of minor surgical errors may, on the face of it, seem to be an admirable goal. However, an inadvertent effect might be that surgical trainees, having less exposure to what an experienced surgeon does when things go wrong, do not develop these skills themselves. Thus, later in the trainees’ careers, when minor errors do occur, they might be much more likely to result in death.

It may be that the assumption of a fixed Heinrich ratio is reasonable in the patient safety field under special circumstances, in which the minor and severe errors both have the same cause. But the authors’ experience is otherwise, and we have only found evidence of such ‘common cause’ analysis in one safety study related to the railway industry.[24]

Our findings also suggest that much of the effort spent on the analysis of data from minor incidents (e.g. as part of ‘near miss reporting schemes’) may be wasted, unless it can be established that minor incidents share a common cause with severe incidents. In our view, a substantial research initiative is needed to better understand the complex relationships between incidents and harm. If predictive relationships can be found, it will improve the choice of interventions and make their evaluation more feasible.

5. Conclusion

This paper raises serious doubts about the validity of assuming a constant Heinrich ratio linking the frequency of occurrence of safety incidents of different severities. It does not support the use of the Heinrich ratio as the basis of policy for the collection of safety data, for designing interventions or for evaluating them.