burns 41 (2015) 85–90
Available online at www.sciencedirect.com
ScienceDirect journal homepage: www.elsevier.com/locate/burns
A nomogram for calculation of the Revised Baux Score D.J. Williams a, J.D. Walker b,* a
Department of Anaesthetics, Welsh Centre for Burns, Abertawe Bro Morgannwg University NHS Trust, Swansea, UK b Department of Anaesthetics, Betsi Cadwaladr University Health Board, Ysbyty Gwynedd, Bangor, UK
article info
abstract
Article history:
Since its original publication, the revised Baux score for mortality prediction in burns
Accepted 1 May 2014
patients has been widely adopted. It uses readily available measures, and it is based on
Keywords:
sary calculations are too complex to perform with anything other than a scientific calculator
Baux score
or dedicated software, which may create issues in a clinical setting where access to
Prediction of mortality
electronic devices may be limited.
regression analysis from actual data rather than a theoretical model. However, the neces-
We designed a nomogram capable of performing the calculation to a high degree of
Nomogram
accuracy, and evaluated its performance on a set of randomly generated patient data to ensure that the nomogram gives accurate and repeatable results. The nomogram has a bias of
0.003 percentage points, with limits of agreement
0.3619 to 0.3550 and a repeatability
coefficient of 0.29 percentage points. We feel that the nomogram’s accuracy, low cost, speed and ease of use would make it a very useful adjunct during the initial assessment of burns patients. It could also realistically be used to crosscheck calculations made by other methods. # 2014 Elsevier Ltd and ISBI. All rights reserved.
1.
Introduction
1.1.
Accurate prediction of mortality
Objective probability estimates for the predicted mortality of patients with burns provide clinicians with information to aid decision making regarding clinical management, resource allocation and efficacy of treatment. An ideal mortality scoring system must have good predictive value (accuracy), repeatability, and generalizability to a wide range of institutions and patient demographic groups. For practical purposes, it must require relatively few and readily measurable input variables; which are combined through a simple calculation or algorithm * Corresponding author. Tel.: +44 1248 384177. E-mail address: [email protected] (J.D. Walker). http://dx.doi.org/10.1016/j.burns.2014.05.001 0305-4179/# 2014 Elsevier Ltd and ISBI. All rights reserved.
to provide an output estimate of mortality (P) as a continuous variable on a percentage scale, rather than as a percentage range or categorical variable. The main predictor variables which determine mortality (%) following burn are: age (years), total body surface area burned (TBSA, %), and inhalation injury [1–3]. These have been used as the basis for a number of scoring systems [4–7]. The Revised Baux Score described by Osler et al. [5] has been widely adopted as it uses the above predictor variables to produce outcome estimates on a continuous scale, and is based on linear regression analysis of real patient data rather than a theoretical model. However the necessary logistic regression calculations are too complex to perform by mental calculation, and even with the aid of an electronic device
86
burns 41 (2015) 85–90
(calculator, computer or dedicated smart phone app), data entry errors may occur. Osler et al. describe a graphic conversion scale to facilitate calculation, however their method still requires the user to perform part of the calculations by other means. We have therefore developed and evaluated a more comprehensive nomogram to rapidly calculate the Revised Baux Score, and provide a permanent record of the whole calculation which may be filed in the patients’ records.
equations would require the axes to be of infinite length to accommodate predicted mortality scores in the range 0–100%. Axes were therefore truncated to ranges of 1–99%. Principles of graphic and typographic design were applied to maximise legibility and ease of use. These include the use of a specialist typeface, Tall Man lettering, written instructions, icons to aid identification of the axes, and a thumbnail diagram illustrating method of use [9,10]. The nomogram was printed onto A4 paper in portrait format (Fig. 2).
2.2.
2.
Method
2.1.
Nomogram development
Routine techniques of analytic geometry [8] were used to convert each of the algebraic formulae for the Revised Baux Nomogram (Fig. 1a and b) into Standard Algebraic form; whereby the formulae are expressed as the sum or product of a series of functions which are equal to zero (Fig. 1c and d). These were then converted into Matrix Determinant (‘‘Design Determinant’’) form (Fig. 1e and f); and multiplied by transformational matrices to adjust the size and proportions of the axes to produce the Constructional Determinant matrices. Each row of the Constructional Determinant Matrices represents a variable from the original algebraic formula (age, TBSA, mortality); and an axis in the resulting nomogram. The first and second columns define the relationship between the x and y Cartesian coordinates of the tick marks on the nomogram scales. This procedure resulted in a pair of three axis parallel scale nomograms: one for ‘‘Inhalation Injury’’ and one for ‘‘No Inhalation Injury’’. A two-dimensional nomogram cannot normally accommodate more than three variables. Further transformation matrices were therefore applied to make the two nomograms congruent, so that they could be combined in a single three-axis nomogram with shared axes and a central axis for TBSA which was calibrated for both ‘‘Inhalation Injury’’ and ‘‘No Inhalation Injury’’. Graphic software (PyNomo, open-source software available from http://www.pynomo.org; RhinocerosTM, McNeel North America, Seattle, Washington, USA; IllustratorTM, Adobe Systems, San Jose, CA, USA) was used to aid transformation and plotting of the resulting nomogram. The regression
Method of use
A straight line (isopleth) connecting the appropriate scale values for Age and TBSA (with or without inhalation injury) will indicate predicted mortality (%) at its point of intersection with the third axis. Measurements falling between scale marks of the nomogram are interpolated as appropriate for the scale graduations.
2.3.
Evaluation
Although the mathematical construction of the nomogram was sound, the authors elected to evaluate its practical utility by comparison against spreadsheet calculations using simulated clinical data. A spreadsheet (ExcelTM, Microsoft, Redmond, Washington, USA) was used to randomly generate 100 sets of simulated patient values for age (range 1–100 years), TBSA (range 1–99%), and presence or absence of inhalation injury. The predicted mortality (%) was then calculated independently by the authors in each case using the nomogram. Bland–Altman analysis was used to assess the accuracy and repeatability of the results [11]. No conscious bias was exercised in performing the calculations, and the authors were blinded to the results calculated by each other and by the spreadsheet until analysis was completed. It was decided a priori that the results calculated by the first author would be used for accuracy calculations, while the results calculated by the second author would be used for repeatability calculations.
3.
Results
No difficulties were encountered in using the nomogram.
Fig. 1 – Mathematical functions used to construct the Revised Baux Score nomogram.
burns 41 (2015) 85–90
87
Fig. 2 – Nomogram for the Revised Baux Score for mortality following burns.
Bland–Altman analysis [11] demonstrated a close degree of agreement between nomogram and spreadsheet (Fig. 3a) and repeatability of results by the two authors (Fig. 3b). For the evaluation of accuracy, bias was 0.003, SD 0.18, and limits of agreement 0.3619 to 0.3550. The assessment of repeatability demonstrated bias 0.08 and SD (repeatability coefficient) 0.29. (All values are percentage points.) Inaccuracies were more frequent and of larger magnitude around mortality values near 50%, while accuracy increased at the extremes of the range. This is a consequence of the underlying mathematical formula, which causes clustering of values in the middle of the mortality range.
4.
Discussion
The Baux score [12] is frequently misquoted as ‘‘age + TBSA = % mortality’’; however the original description
of the formula was: age + TBSA = the Baux score; where a Baux score >75 indicates ‘‘almost certain’’ probability of death, P. It has been subsequently shown that a Baux score of >95 indicates P > 50% [13]. The role of Age, TBSA and Inhalation injury as the three main determinants of mortality from burns is well established [4–6]. The Abbreviated Burn Severity Index [14] uses the above parameters with the two additional predictor variables of Full Thickness Burn (%) and gender. However the probability estimate is provided as a categorical variable, which is less useful than a continuous variable [15]. The Belgium score [7] is simple to use and employs the same three variables broken up into ranges, each of which generates a score which must be added together, in much the same way that the Glasgow Coma Scale is calculated for head injuries. However in contrast to the Glasgow Coma scale where the scores correlate with clearly defined clinical signs (e.g. eyes open to voice or pain), the category boundaries for the Belgium scores occur at seemingly
88
burns 41 (2015) 85–90
Fig. 3 – Bland–Altman plots for 100 sets of randomly generated patient data to evaluate (a) Accuracy: mean mortality rate versus difference in mortality rate (nomogram versus spreadsheet). (b) Repeatability: Bland–Altman plot for repeatability of mortality rate (nomogram) versus mortality rate (nomogram). Mean difference (Bias) (black); limits of agreement (95% CI = Bias W 1.96 SD) (black, dashed); regression line (red); line of equality (difference = 0) (blue). (For interpretation of the references to color in figure legend, the reader is referred to the web version of the article.)
arbitrary points (e.g. age 50–64, age 65–79), which are difficult to remember. This may explain why the Belgium score is not more widely used. The revised Baux Score has its limitations, and these must be borne in mind when using it clinically. It does not take into account many factors including: race, incidence of escharotomy and tracheostomy, co-morbidity pre- and post burn, pneumonia, carbon monoxide levels, mechanism of burn (e.g. scald/contact/electrical/chemical burn), and serological markers which may also influence outcome [14,16–19]. There may indeed be other variables, as yet uninvestigated, which may affect mortality. However, increasing the number of input variables does not guarantee a better model. More variables result in a more complex model with greater risk of errors due to variable interdependence; or for some variables to be unavailable for a given patient, causing the problem of how to account for this in practice. Probit analysis, discriminant analysis, logistic risk function analysis all enable greater predictive accuracy from the input
variables, but at the expense of increased complexity of calculation [13,20]. Artificial neural networks may be a means of weighting these additional factors to more closely predict outcome [21], however the underlying emergent models are extremely complex and remain ‘hidden’, and further work remains to be done in this area. Many models are based on relatively small sample sizes and data from a specific population treated at a single institution. It is therefore difficult to generalise conclusions drawn from such studies. More complex models do not necessarily result in greater predictive accuracy; and they require multiple variables and are more complex to calculate, which may render them impractical. By applying logistic regression analysis, Osler et al. have greatly improved the predictive accuracy of the original Baux score. Although the model requires only three input variables (age, TBSA (%) and presence or absence of inhalation injury), the results compare favourably with those of the more complex methods described above [13]. The Revised Baux
burns 41 (2015) 85–90
89
Fig. 4 – 3D surface plots of the Revised Baux Score formulae (Fig. 1a and b), showing the relationship between age, TBSA and mortality where: (a) inhalation injury present and (b) no inhalation injury present.
Score is therefore well suited as a practical tool for use in the clinical environment; however the logistic regression equations are too complex to be performed manually or using mental calculation. Nomograms have been traditionally accepted on face value on the grounds that provided that the correct methods of construction have been applied, the nomogram will accurately perform the calculation. However we wanted to evaluate both the accuracy and repeatability of our device. The precision of a nomogram is typically limited to three significant digits due to practical restrictions of scale size, however this is generally adequate for most clinical applications. Burns mortality scoring systems based on the three predictor variables age, TBSA and presence or absence of inhalation injury may be visualised as a pair of 3D surface plots (Fig. 4a and b) to facilitate a qualitative understanding of the relationships between the parameters [19]; however this method is not sufficiently accurate to allow calculation of predicted mortality. Our nomogram allows users to explore qualitative relationships between these variables, and also to perform quantitative calculations to a high degree of accuracy and repeatability. The bias of our nomogram was 0.003 percentage points. This is trivial compared to reported variation of 20% in estimation of TBSA [22]. User errors in reading the nomogram may occur due to: incorrect use, poor visual acuity, parallax error, and incorrect interpolation of non-linear scales. However both the incidence and magnitude of error when nomograms are used to perform comparable clinical calculations have been shown to be much smaller than those which occur when electronic devices are used [23]. Our repeatability coefficient was 0.29 percentage points. This would lead us to expect that in 95% of cases two different users would calculate the same mortality to within 0.58 of a percent of each other. Our assessment of the nomogram used a relatively small number of calculations and was potentially susceptible to unconscious bias. We therefore plan to perform future studies
using the nomogram in the clinical environment with a range of users to better assess its accuracy and practical utility.
5.
Conclusion
Our nomogram provides a simple low cost means of simultaneously visualising, calculating, and recording predicted mortality using the Revised Baux Score; and is sufficiently accurate to be used as the primary method of calculation or as a means of cross-checking the results derived by other means (e.g. electronic devices).
references
[1] Mahar P, Wasiak J, Bailey M, Cleland H. Clinical factors affecting mortality in elderly burns patients admitted to a burns service. Burns 2008;34:629–36. [2] O’Keefe GE, Hunt JL, Purdue GF. An evaluation of risk factors for mortality after burn trauma and the identification of gender-dependent differences in outcomes. J Am Coll Surg 2001;192:153–60. [3] Smith D, Cairns B, Ramadan F, Dalston J, Fakhry S, Rutledge R, et al. Effect of inhalation injury, burn size, and age on mortality: a study of 1447 consecutive burn patients. J Trauma 1994;37:655–9. [4] Clark C, Reid W, Gilmour W, Campbell D. Mortality probability in victims of fire trauma: revised equation to include inhalation injury. Br Med J 1986;292: 1303–5. [5] Osler T, Glance L, Hosmer D. Simplified estimates of death after burn injuries: extending and updating the Baux Score. J. Trauma 2010;68:690–7. [6] Ryan C, Schoenfeld D, Thorpe W, Sheridan R, Cassem E, Tompkins R. Objective estimates of the probability of death from burn injuries. N Engl J Med 1998;362–6. [7] The Belgian outcome in burn injury development and validation of a model for prediction of mortality in patients with burn, injury. Br J Surg 2009;96:111–7.
90
burns 41 (2015) 85–90
[8] Allcock H, Jones J, Michel J. Nomograms of the fourth and higher classes. The nomogram: the theory and practical construction of computation charts. London: Pitman; 1950: 122–88. [9] Connecting for Health. Final report for use of TallMan lettering to minimise selection errors of medicine names in computer prescribing and dispensing systems; 2009. [10] Weinger M, Wiklund M. Handbook of human factors in medical device design. Boca Raton, FL: CRC Press; 2011. [11] Bland JM, Altman DG. Statistical methods for assessing agreement between two methods of clinical measurement. Lancet 1986;307–10. [12] Baux S. Contribution a l’etude du traitement local des brulures thermiques etendues. Paris; 1961. [13] Stern M, Waisbren BA. Comparison of methods of predicting burn mortality. Burns 1979;6:119–23. [14] Tobiasen J, Hiebert JM, Edlich RF. The abbreviated burn severity index. Ann Emerg Med 1982;11:260–2. [15] Knaus WA, Wagner DP, Lynn J. Short-term mortality predictions for critically ill hospitalized adults: science and ethics. Science 1991;254:389–94. [16] Baux S, Mimoun M, Saade H, Lioret N, Esteve M, Nolland X, et al. Burns in the elderly. Burns 1989;15:239–40.
[17] Berry CC, Wachtel TL, Frank HA. An analysis of factors which predict mortality in hospitalized burn patients. Burns 1982;9:38–45. [18] McGwin GJ, George RL, Cross JM, Rue LW. Improving the ability to predict mortality among burn patients. Burns 2007;34:320–7. [19] Shirani KZ, Pruitt BA, Mason AD. The influence of inhalation injury and pneumonia on burn mortality. Ann Surg 1987;205:82–7. [20] Bowser BH, Caldwell FT, Baker JA, Walls RC. Statistical methods to predict morbidity and mortality: self assessment techniques for burn units. Burns 1983;9:318–26. [21] Estahbanati HK, Bouduhi N. Role of artificial neural networks in prediction of survival of burn patients – a new approach. Burns 2002;28:579–86. [22] Collis N, Smith G, Fenton O. Accuracy of burn size estimation and subsequent fluid resuscitation prior to arrival at the Yorkshire regional burns unit: a three year retrospective study. Burns 1999;25. [23] Bodger O, Theron A, Williams D. Comparison of three techniques for calculation of the Parkland formula to aid fluid resuscitation in paediatric burns. Eur J Anaesthesiol 2013;30.
Available online at www.sciencedirect.com
ScienceDirect journal homepage: www.elsevier.com/locate/burns
A nomogram for calculation of the Revised Baux Score D.J. Williams a, J.D. Walker b,* a
Department of Anaesthetics, Welsh Centre for Burns, Abertawe Bro Morgannwg University NHS Trust, Swansea, UK b Department of Anaesthetics, Betsi Cadwaladr University Health Board, Ysbyty Gwynedd, Bangor, UK
article info
abstract
Article history:
Since its original publication, the revised Baux score for mortality prediction in burns
Accepted 1 May 2014
patients has been widely adopted. It uses readily available measures, and it is based on
Keywords:
sary calculations are too complex to perform with anything other than a scientific calculator
Baux score
or dedicated software, which may create issues in a clinical setting where access to
Prediction of mortality
electronic devices may be limited.
regression analysis from actual data rather than a theoretical model. However, the neces-
We designed a nomogram capable of performing the calculation to a high degree of
Nomogram
accuracy, and evaluated its performance on a set of randomly generated patient data to ensure that the nomogram gives accurate and repeatable results. The nomogram has a bias of
0.003 percentage points, with limits of agreement
0.3619 to 0.3550 and a repeatability
coefficient of 0.29 percentage points. We feel that the nomogram’s accuracy, low cost, speed and ease of use would make it a very useful adjunct during the initial assessment of burns patients. It could also realistically be used to crosscheck calculations made by other methods. # 2014 Elsevier Ltd and ISBI. All rights reserved.
1.
Introduction
1.1.
Accurate prediction of mortality
Objective probability estimates for the predicted mortality of patients with burns provide clinicians with information to aid decision making regarding clinical management, resource allocation and efficacy of treatment. An ideal mortality scoring system must have good predictive value (accuracy), repeatability, and generalizability to a wide range of institutions and patient demographic groups. For practical purposes, it must require relatively few and readily measurable input variables; which are combined through a simple calculation or algorithm * Corresponding author. Tel.: +44 1248 384177. E-mail address: [email protected] (J.D. Walker). http://dx.doi.org/10.1016/j.burns.2014.05.001 0305-4179/# 2014 Elsevier Ltd and ISBI. All rights reserved.
to provide an output estimate of mortality (P) as a continuous variable on a percentage scale, rather than as a percentage range or categorical variable. The main predictor variables which determine mortality (%) following burn are: age (years), total body surface area burned (TBSA, %), and inhalation injury [1–3]. These have been used as the basis for a number of scoring systems [4–7]. The Revised Baux Score described by Osler et al. [5] has been widely adopted as it uses the above predictor variables to produce outcome estimates on a continuous scale, and is based on linear regression analysis of real patient data rather than a theoretical model. However the necessary logistic regression calculations are too complex to perform by mental calculation, and even with the aid of an electronic device
86
burns 41 (2015) 85–90
(calculator, computer or dedicated smart phone app), data entry errors may occur. Osler et al. describe a graphic conversion scale to facilitate calculation, however their method still requires the user to perform part of the calculations by other means. We have therefore developed and evaluated a more comprehensive nomogram to rapidly calculate the Revised Baux Score, and provide a permanent record of the whole calculation which may be filed in the patients’ records.
equations would require the axes to be of infinite length to accommodate predicted mortality scores in the range 0–100%. Axes were therefore truncated to ranges of 1–99%. Principles of graphic and typographic design were applied to maximise legibility and ease of use. These include the use of a specialist typeface, Tall Man lettering, written instructions, icons to aid identification of the axes, and a thumbnail diagram illustrating method of use [9,10]. The nomogram was printed onto A4 paper in portrait format (Fig. 2).
2.2.
2.
Method
2.1.
Nomogram development
Routine techniques of analytic geometry [8] were used to convert each of the algebraic formulae for the Revised Baux Nomogram (Fig. 1a and b) into Standard Algebraic form; whereby the formulae are expressed as the sum or product of a series of functions which are equal to zero (Fig. 1c and d). These were then converted into Matrix Determinant (‘‘Design Determinant’’) form (Fig. 1e and f); and multiplied by transformational matrices to adjust the size and proportions of the axes to produce the Constructional Determinant matrices. Each row of the Constructional Determinant Matrices represents a variable from the original algebraic formula (age, TBSA, mortality); and an axis in the resulting nomogram. The first and second columns define the relationship between the x and y Cartesian coordinates of the tick marks on the nomogram scales. This procedure resulted in a pair of three axis parallel scale nomograms: one for ‘‘Inhalation Injury’’ and one for ‘‘No Inhalation Injury’’. A two-dimensional nomogram cannot normally accommodate more than three variables. Further transformation matrices were therefore applied to make the two nomograms congruent, so that they could be combined in a single three-axis nomogram with shared axes and a central axis for TBSA which was calibrated for both ‘‘Inhalation Injury’’ and ‘‘No Inhalation Injury’’. Graphic software (PyNomo, open-source software available from http://www.pynomo.org; RhinocerosTM, McNeel North America, Seattle, Washington, USA; IllustratorTM, Adobe Systems, San Jose, CA, USA) was used to aid transformation and plotting of the resulting nomogram. The regression
Method of use
A straight line (isopleth) connecting the appropriate scale values for Age and TBSA (with or without inhalation injury) will indicate predicted mortality (%) at its point of intersection with the third axis. Measurements falling between scale marks of the nomogram are interpolated as appropriate for the scale graduations.
2.3.
Evaluation
Although the mathematical construction of the nomogram was sound, the authors elected to evaluate its practical utility by comparison against spreadsheet calculations using simulated clinical data. A spreadsheet (ExcelTM, Microsoft, Redmond, Washington, USA) was used to randomly generate 100 sets of simulated patient values for age (range 1–100 years), TBSA (range 1–99%), and presence or absence of inhalation injury. The predicted mortality (%) was then calculated independently by the authors in each case using the nomogram. Bland–Altman analysis was used to assess the accuracy and repeatability of the results [11]. No conscious bias was exercised in performing the calculations, and the authors were blinded to the results calculated by each other and by the spreadsheet until analysis was completed. It was decided a priori that the results calculated by the first author would be used for accuracy calculations, while the results calculated by the second author would be used for repeatability calculations.
3.
Results
No difficulties were encountered in using the nomogram.
Fig. 1 – Mathematical functions used to construct the Revised Baux Score nomogram.
burns 41 (2015) 85–90
87
Fig. 2 – Nomogram for the Revised Baux Score for mortality following burns.
Bland–Altman analysis [11] demonstrated a close degree of agreement between nomogram and spreadsheet (Fig. 3a) and repeatability of results by the two authors (Fig. 3b). For the evaluation of accuracy, bias was 0.003, SD 0.18, and limits of agreement 0.3619 to 0.3550. The assessment of repeatability demonstrated bias 0.08 and SD (repeatability coefficient) 0.29. (All values are percentage points.) Inaccuracies were more frequent and of larger magnitude around mortality values near 50%, while accuracy increased at the extremes of the range. This is a consequence of the underlying mathematical formula, which causes clustering of values in the middle of the mortality range.
4.
Discussion
The Baux score [12] is frequently misquoted as ‘‘age + TBSA = % mortality’’; however the original description
of the formula was: age + TBSA = the Baux score; where a Baux score >75 indicates ‘‘almost certain’’ probability of death, P. It has been subsequently shown that a Baux score of >95 indicates P > 50% [13]. The role of Age, TBSA and Inhalation injury as the three main determinants of mortality from burns is well established [4–6]. The Abbreviated Burn Severity Index [14] uses the above parameters with the two additional predictor variables of Full Thickness Burn (%) and gender. However the probability estimate is provided as a categorical variable, which is less useful than a continuous variable [15]. The Belgium score [7] is simple to use and employs the same three variables broken up into ranges, each of which generates a score which must be added together, in much the same way that the Glasgow Coma Scale is calculated for head injuries. However in contrast to the Glasgow Coma scale where the scores correlate with clearly defined clinical signs (e.g. eyes open to voice or pain), the category boundaries for the Belgium scores occur at seemingly
88
burns 41 (2015) 85–90
Fig. 3 – Bland–Altman plots for 100 sets of randomly generated patient data to evaluate (a) Accuracy: mean mortality rate versus difference in mortality rate (nomogram versus spreadsheet). (b) Repeatability: Bland–Altman plot for repeatability of mortality rate (nomogram) versus mortality rate (nomogram). Mean difference (Bias) (black); limits of agreement (95% CI = Bias W 1.96 SD) (black, dashed); regression line (red); line of equality (difference = 0) (blue). (For interpretation of the references to color in figure legend, the reader is referred to the web version of the article.)
arbitrary points (e.g. age 50–64, age 65–79), which are difficult to remember. This may explain why the Belgium score is not more widely used. The revised Baux Score has its limitations, and these must be borne in mind when using it clinically. It does not take into account many factors including: race, incidence of escharotomy and tracheostomy, co-morbidity pre- and post burn, pneumonia, carbon monoxide levels, mechanism of burn (e.g. scald/contact/electrical/chemical burn), and serological markers which may also influence outcome [14,16–19]. There may indeed be other variables, as yet uninvestigated, which may affect mortality. However, increasing the number of input variables does not guarantee a better model. More variables result in a more complex model with greater risk of errors due to variable interdependence; or for some variables to be unavailable for a given patient, causing the problem of how to account for this in practice. Probit analysis, discriminant analysis, logistic risk function analysis all enable greater predictive accuracy from the input
variables, but at the expense of increased complexity of calculation [13,20]. Artificial neural networks may be a means of weighting these additional factors to more closely predict outcome [21], however the underlying emergent models are extremely complex and remain ‘hidden’, and further work remains to be done in this area. Many models are based on relatively small sample sizes and data from a specific population treated at a single institution. It is therefore difficult to generalise conclusions drawn from such studies. More complex models do not necessarily result in greater predictive accuracy; and they require multiple variables and are more complex to calculate, which may render them impractical. By applying logistic regression analysis, Osler et al. have greatly improved the predictive accuracy of the original Baux score. Although the model requires only three input variables (age, TBSA (%) and presence or absence of inhalation injury), the results compare favourably with those of the more complex methods described above [13]. The Revised Baux
burns 41 (2015) 85–90
89
Fig. 4 – 3D surface plots of the Revised Baux Score formulae (Fig. 1a and b), showing the relationship between age, TBSA and mortality where: (a) inhalation injury present and (b) no inhalation injury present.
Score is therefore well suited as a practical tool for use in the clinical environment; however the logistic regression equations are too complex to be performed manually or using mental calculation. Nomograms have been traditionally accepted on face value on the grounds that provided that the correct methods of construction have been applied, the nomogram will accurately perform the calculation. However we wanted to evaluate both the accuracy and repeatability of our device. The precision of a nomogram is typically limited to three significant digits due to practical restrictions of scale size, however this is generally adequate for most clinical applications. Burns mortality scoring systems based on the three predictor variables age, TBSA and presence or absence of inhalation injury may be visualised as a pair of 3D surface plots (Fig. 4a and b) to facilitate a qualitative understanding of the relationships between the parameters [19]; however this method is not sufficiently accurate to allow calculation of predicted mortality. Our nomogram allows users to explore qualitative relationships between these variables, and also to perform quantitative calculations to a high degree of accuracy and repeatability. The bias of our nomogram was 0.003 percentage points. This is trivial compared to reported variation of 20% in estimation of TBSA [22]. User errors in reading the nomogram may occur due to: incorrect use, poor visual acuity, parallax error, and incorrect interpolation of non-linear scales. However both the incidence and magnitude of error when nomograms are used to perform comparable clinical calculations have been shown to be much smaller than those which occur when electronic devices are used [23]. Our repeatability coefficient was 0.29 percentage points. This would lead us to expect that in 95% of cases two different users would calculate the same mortality to within 0.58 of a percent of each other. Our assessment of the nomogram used a relatively small number of calculations and was potentially susceptible to unconscious bias. We therefore plan to perform future studies
using the nomogram in the clinical environment with a range of users to better assess its accuracy and practical utility.
5.
Conclusion
Our nomogram provides a simple low cost means of simultaneously visualising, calculating, and recording predicted mortality using the Revised Baux Score; and is sufficiently accurate to be used as the primary method of calculation or as a means of cross-checking the results derived by other means (e.g. electronic devices).
references
[1] Mahar P, Wasiak J, Bailey M, Cleland H. Clinical factors affecting mortality in elderly burns patients admitted to a burns service. Burns 2008;34:629–36. [2] O’Keefe GE, Hunt JL, Purdue GF. An evaluation of risk factors for mortality after burn trauma and the identification of gender-dependent differences in outcomes. J Am Coll Surg 2001;192:153–60. [3] Smith D, Cairns B, Ramadan F, Dalston J, Fakhry S, Rutledge R, et al. Effect of inhalation injury, burn size, and age on mortality: a study of 1447 consecutive burn patients. J Trauma 1994;37:655–9. [4] Clark C, Reid W, Gilmour W, Campbell D. Mortality probability in victims of fire trauma: revised equation to include inhalation injury. Br Med J 1986;292: 1303–5. [5] Osler T, Glance L, Hosmer D. Simplified estimates of death after burn injuries: extending and updating the Baux Score. J. Trauma 2010;68:690–7. [6] Ryan C, Schoenfeld D, Thorpe W, Sheridan R, Cassem E, Tompkins R. Objective estimates of the probability of death from burn injuries. N Engl J Med 1998;362–6. [7] The Belgian outcome in burn injury development and validation of a model for prediction of mortality in patients with burn, injury. Br J Surg 2009;96:111–7.
90
burns 41 (2015) 85–90
[8] Allcock H, Jones J, Michel J. Nomograms of the fourth and higher classes. The nomogram: the theory and practical construction of computation charts. London: Pitman; 1950: 122–88. [9] Connecting for Health. Final report for use of TallMan lettering to minimise selection errors of medicine names in computer prescribing and dispensing systems; 2009. [10] Weinger M, Wiklund M. Handbook of human factors in medical device design. Boca Raton, FL: CRC Press; 2011. [11] Bland JM, Altman DG. Statistical methods for assessing agreement between two methods of clinical measurement. Lancet 1986;307–10. [12] Baux S. Contribution a l’etude du traitement local des brulures thermiques etendues. Paris; 1961. [13] Stern M, Waisbren BA. Comparison of methods of predicting burn mortality. Burns 1979;6:119–23. [14] Tobiasen J, Hiebert JM, Edlich RF. The abbreviated burn severity index. Ann Emerg Med 1982;11:260–2. [15] Knaus WA, Wagner DP, Lynn J. Short-term mortality predictions for critically ill hospitalized adults: science and ethics. Science 1991;254:389–94. [16] Baux S, Mimoun M, Saade H, Lioret N, Esteve M, Nolland X, et al. Burns in the elderly. Burns 1989;15:239–40.
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