Equivalency between the shock index and subtracting the systolic blood pressure from the heart rate: an observational cohort study

The shock index (SI) is an indicator of the severity of hypovolemic shock and is calculated by dividing the heart rate (HR) by systolic blood pressure (SBP) [1]. It serves to predict the mortality, need for blood transfusion, or necessity of intensive care unit admission among patients with trauma [2‐7], postpartum haemorrhage [8, 9], acute myocardial infarction [10, 11], stroke [12, 13], sepsis [14, 15], and other critical conditions [16, 17]. Numerous previous studies have demonstrated that the SI demonstrates superior prediction for mortality to traditional vital signs, although it has some limitations, including its low sensitivity especially for the elderly or obstetric patients [2‐17]. However, in clinical practice, calculating the SI for all patients is difficult. An SI value > 0.9 is generally accepted as a cut-off point for an increased risk of mortality [16], but it is sometimes difficult to quickly calculate whether the patient meets this cut-off when the value of the quotient (particularly when considering the second decimal place) is extremely close to 0.9 (e.g. When a patient has an HR of 103 beats per minute and SBP of 114 mmHg, the quotient is approximately 0.904 and it technically meets the cut-off but it is exceedingly difficult to calculate promptly without a calculator). Having a confusing cut-off value, the SI needs to be interpreted from several variables to identify patients with a critical status but stable HR and SBP making it an impractical indicator that is rarely used in scoring systems assessing emergencies. Furthermore, despite its utility, there is no established consensus on when and where to utilize SI in emergency departments (EDs) [18]. Recent studies have attempted to validate revised SI measurements meant to improve its ability to predict mortality [19‐22]; however, such calculations are more complicated and tend to be avoided by clinicians. If the calculation of the SI can be made simpler, it would lead to rapid progress in terms of the clinical research using SI.

Considering that SI is used to represent the different dynamics of HR and SBP [23, 24], it is possible that simply subtracting the SBP from the HR may provide a useful substitute for SI, improving the availability of a calculated value as it is easier to mentally subtract integers than to divide them.

In this study, we identify the proposed new index the simple shock index (sSI) and investigated whether the sSI predicted SI equivalently among patients transported to hospitals via ambulance.

The Pearson’s product-moment correlation coefficient between the SI and sSI was 0.917 (95% CI 0.912–0.921, P < .001), indicating an extremely high correlation. The log SI/sSI correlation plot represented a proportional relationship (Fig. 2) and the regression equation was estimated as sSI = 258.55 log SI using the least-squares method with logarithmic transformation. According to this equation, an sSI value of − 12 was found to correspond to the SI value of 0.9.

Next, an equivalence test with TOST was performed for comparisons between SI and the estimated value of SI derived by sSI. The estimated value of SI was calculated as 10^sSI/258.55 according to the regression equation mentioned above. Equivalence margin was determined as ±0.052, since it was 0.25 of the standardized effect size of SI. The TOST revealed an equivalency between the SI and sSI (mean difference, 0.004; 90% CI, 0.003 to 0.005; statistical power, 100.00%). Similar consequences were also derived from subgroup analyses except for severe hypertension (Table 2, Fig. 3). The statistical power for all analyses of each subgroup and all subjects were over 97.29%.

In the sensitivity analysis, the robustness of equivalency was validated using 3629 cases (66.8%) that did not lack any data of ED (mean difference was 0.006, 90% CI 0.004 to 0.007, statistical power 100.00%).

In this study, we revealed that the sSI, which was derived by subtracting the SBP from the HR, strongly correlated with the SI among the patients transported via ambulance. Meanwhile, an sSI value of > − 12 was observed to correspond to the known SI cut-off value of > 0.9, which is the most common optimized cut-off point, as has been previously described [16]. However, as positive numbers are more easily calculated and interpreted, instead of calculating the sSI cut-off using HR − SBP > − 12 as we have done in the present study, we recommend using either SBP − HR < 12 or HR + 12 > SBP instead, which can be considered to be equivalent to an SI > 0.9.

This finding confirms the utility of using the sSI for more rapid assessment of the condition of patients admitted for emergency care than the more complicated SI. Assuming that a calculator is not available, judging whether the SI is more than 1.0 is quite easy because the hypothesis is true when the value of HR is greater than that of SBP. However, when the SI cut-off value is 0.9, the judgement becomes difficult. As calculating HR/SBP mentally can cause confusion, we often calculate SBP times 0.9 mentally and then compare it with HR. For example, when an HR of 103 and SBP of 114 are known, we calculate 114 × 0.9 = 102.6 and then compare it with 103. Thus, we can judge SI to be > 0.9 because 103 > 102.6. Obviously, this procedure is complicated and tends to lead to miscalculation. On the other hand, an alternative criterion of sSI > − 12 makes the procedure much simpler. For example, using the same values of HR of 103 and SBP of 114, calculating HR plus 12 is the first step to solve the hypothesis. When the sum (e.g. 103 + 12 = 115) is compared with SBP, we are able to judge that sSI is > − 12 because 115 > 114. Since this addition is quite easy, mental calculation can be performed at a glance.

While attempts have been made to improve the predictive ability of SI for mortality or other outcomes, these endeavours have made the process more complicated. Examples of such previously proposed predictors include an index called ‘age shock index’ derived by multiplying the SI with the patient’s age, or another referred to as the ‘modified shock index’ obtained by dividing the HR by the mean blood pressure [19, 20]. Other complicated predictors were also proposed such as ‘respiratory adjusted shock index’ calculated by multiplying the SI with the respiratory rate/10 and ‘reverse shock index multiplied by Glasgow Coma Scale score’ derived by dividing the Glasgow Coma Scale by the SI [21, 22]. To the best of our knowledge, this is the first study aimed at simplifying the calculation using subtraction, as no previous groups have proposed the idea of subtracting the SBP from the HR for purposes of estimating the SI.

The sSI was shown to be equivalent to SI in most subgroups by TOST and only significantly underestimated SI in the severe hypertension subgroup. However, we believe this finding will have minimal on the utility of sSI in clinical practice mainly because SI was mainly developed to identify patients who were in a critical state despite their vital signs being within normal range [16, 31]. Another reason is that very low SI values should not be ignored as they can often pose risks to patients contrary to what is expected. Several studies have reported a J-shaped relationship between SI and mortality [4, 13], that is mortality increases when the SI value is under 0.5. Therefore, our new indicator sSI would not be utilized on patients with severe hypertension who would typically require close monitoring as their SI values tend to be very low.

Regarding the moderate number of missing values, when comparing analysis using values generated from the imputation method and from using only cases without missing values our results indicated good concordance between the measures examined and indicated that sSI is a useful and precise tool.

This study has several limitations. We were unable to investigate patients of different ethnicities because this study was conducted in a single geographic area. Moreover, there is a dearth of a theoretical framework to support the sSI, given that this study was intended as merely a proposal of a pragmatic alternative to the SI. Additionally, although the SI is used to predict mortality, necessity of blood transfusion, or necessity for intensive care unit admission, our study did not address these outcomes; we tested only the correlation between the SI and sSI here. Moreover, we could not prove that the assessed patients were clinically in shock or not since this diagnosis is determined using various factors such as cardiac output, lactate level, urine output, blood gas analyses, and mental status. Furthermore, there is certainly a possibility of multiplicity in the subgroup analyses, although this possibility was estimated to be sufficiently low. These issues should be addressed in future studies intended to clarify the scientific underpinnings of sSI, to further validate sSI as an accurate substitute calculation for SI, or to justify the clinical utility of sSI.

The sSI was demonstrated to highly correlate with the SI among patients transported to hospitals in our study via ambulance, though further studies are needed to validate its clinical utility. Given that the sSI is easier to calculate and use for performing evaluations, it can be a useful and highly precise alternative to the SI.