The Braden scale was developed by Bergstrom et al. to evaluate pressure injury risk in 1987 [33,34]. It is also the most commonly used pressure injury assessment scale in the United States and has been translated into many languages [34]. The five risk factors of the scale are sensory perception (C${}_{\mathrm{1}}$), mobility (C${}_{\mathrm{2}}$), nutrition (C${}_{\mathrm{3}}$), moisture (C${}_{\mathrm{5}}$), and activity (C${}_{\mathrm{6}}$). The score ranges of these risk factors are 1 to 4, which are the lowest and highest scores, respectively. Additionally, the score ranges of friction and shear (C${}_{\mathrm{4}}$) are 1 to 3. The six risk factors’ scores are added to obtain the final Braden risk score, which ranges from 6 to 23. The Braden risk score is converted into the corresponding risk level through a standard, such as severe risk (score: less than or equal to 9), high risk (score: 10-12), moderate risk (score: 13-14), mild risk (score: 15-18), and no risk (score: greater than 18).

The six risk factors in the Braden scale are specific factors (called the condition attributes) that may develop into pressure injuries. The Braden risk score’s risk level indicates the level of pressure injury risk (called the decision attribute). The Braden scale is shown in Table 1.

This study was approved by the study hospital’s Institutional Review Board (approval number: K20201234). Recruitment was conducted after permission was obtained from the study hospital. This study’s subjects were elderly male inpatients (over 65 years old) from a medical centre in Zhejiang province, China. Braden data were obtained from the hospital’s nursing electronic medical record system. We used a set of hospital nursing clinical data sets from 27 October 2019 to 1 November 2020. In the case hospital, the total observation data (frequency) of male elderly inpatients was 13,851. The observation data (frequency) of each risk level were as follows: 49 cases of severe risk, 649 cases of high risk, 338 cases of medium risk, 1749 cases of mild risk, and 11066 cases of no risk.

The difference in the amount of observation data for each risk level was too large, which could have easily affected the prediction model’s quality. Therefore, the amount of observation data at all levels was set to 49 (based on severe risk values). The other four risk levels were randomly selected from the original observation data. For example, for medium risk, 49 observation data points were randomly selected from 338 observation data points. Finally, a group of 245 observation data points was obtained as input data for this study. The demographic characteristics of the study participants are shown in Table 2.

Pawlak invented the rough set theory in 1982 [28]. This method uses the classical set theory and equivalence relation as the basis of data space partition. The method then establishes the upper and lower approximation sets to approximate the classification boundary region for the objective through known information [35]. This approximation method can effectively deal with the potential fuzziness or uncertainty of the observation data’s classification boundaries. The rough set theory can effectively establish the behavioural relationship between condition attributes and decision attributes and use the decision rule form as information expression. Nowadays, rough set theory has been applied to many different topics [36-38].

This method does not require any prior information (such as membership function and distribution form) and can objectively deal with and describe uncertain phenomena in observed data [29-32]. Nurses can easily understand different risk levels of pressure injury among elderly male patients and provide corresponding nursing measures. A brief description of the calculation for rough set theory is as follows [28,38,39].

The first step: the information

The observation data of the Braden scale can be defined as an information system $S$, which includes four main elements: (1) a non-empty and finite set of Braden clinical behaviours for male elderly inpatients $U$; (2) a non-empty set of finite attributes $A=C\cup D$, that is, items $C$ and risk level $D$ in the Braden scale; (3) the domain value of the attributes $V$; and (4) an information description function (representing all correspondence) $f$. The information system can be defined by Eqn. 1.

(1)$$S=(U,A,V,f)$$

The second step: the indiscernibility relation

If the objects contain the same information on the same attribute, it will cause an indiscernibility relationship. The two objects are equivalent and belong to the intersection of the same classification. If the attribute set $D$ is a non-empty subset of the attribute set $A$, the indiscernible relationship between the objects $x_1$ and $x_2$ can be defined by Eqn. 2.

(2)$$(x_1,x_2)\in I_D\iff f(x_1,a_d)=f(x_2,a_d),\forall a_d\in D$$

The third step: the upper and lower approximate sets

The approximate space is composed of the equivalent relation between the universal set with $n$ objects and the attribute set. In the equivalence relation of an attribute set, the equivalence class forms elementary sets. The rough set is the following two sets of lower and upper approximations that represent the data’s uncertainty, as shown in Eqns. 3 and 5.

(3)$$\underset{¯}{D}(X)=\{x\in U:I_D(x)\subseteq X\}\cup \{Y\in U\mid D:Y\subseteq X\}$$

(4)$$\overline{D}\left(X\right)=\{x\in U:I_D\left(x\right)\cap X\ne \mathrm{\varnothing }\}\cup \{Y\in U\mid D:Y\cap X\ne \mathrm{\varnothing }\}$$

(5)$$B{N}_D(X)=\overline{D}(X)-\underset{¯}{D}(X)$$

Moreover, the boundary region $B{N}_D$ refers to the objects in the boundary region, which cannot be classified as belonging or not belonging to the set $X$ under the current information.

If the elements of the universal $U$ can completely determine the elements belonging to the set $X$, it is called a positive field $po{s}_D$. On the contrary, if it is uncertain, it is called a negative field $ne{g}_D$. These fields are expressed in Eqns. 6 and 7, respectively:

(6)$${\text{???}}_D(X)=\underset{¯}{D}(X)$$

(7)$${\text{???}}_D(X)=U-\overline{D}(X)$$

The fourth step: the classification accuracy and dependency degree between attributes

The condition attribute set $C$ corresponds to the degree of interpretation of the classification target, which can be defined by the ratio of the upper approximation set to the lower approximation set, as shown in Eqn. 8.

(8)$${\gamma }_D(C)=\frac{\sum \text{????}\underset{¯}{D}\left(X_i\right)}{\text{????}U}=\frac{{\text{???}}_D(C)}{|U|}$$

where dependency degree ${\gamma }_D\left(C\right)$ means that under the equivalent relation information of the attribute set $D$, the objects of the universal set $U$ can be correctly divided into a condition attribute set $C$.

The fifth step: the importance

According to the degree of dependency ${\gamma }_D\left(C\right)$ between attributes, the dependency degree change is further observed by deleting each condition attribute. The condition attribute $C_1$ is an example, and its strength is given by Eqn. 9.

(9X)${\sigma }_{(C,D)}\left(C_1\right)={\displaystyle \frac{\left({\gamma }_D(C)-{\gamma }_D\left(C-\left\{C_1\right\}\right)\right)}{{\gamma }_D(C)}}$ ${\sigma }_{(C,D)}\left(C_1\right)$ $={\displaystyle \frac{\left({\gamma }_D(C)-{\gamma }_D\left(C-\left\{C_1\right\}\right)\right)}{{\gamma }_D(C)}}$ (9Xa)$=1-{\displaystyle \frac{{\gamma }_D\left(C-\left\{C_1\right\}\right)}{{\gamma }_D(C)}}$ $=1-{\displaystyle \frac{{\gamma }_D\left(C-\left\{C_1\right\}\right)}{{\gamma }_D(C)}}$

where $\sigma$(C${}_{\mathrm{1}}$) is between 0 and 1, with a higher value indicating that condition attribute C${}_{\mathrm{1}}$ has a higher level of importance.

The seventh step: the decision rules and their corresponding strength

According to the degree of dependence between attributes, decision rules can be derived from the information system. This rule is also called the minimum coverage rule, and its expression is given by Eqn. 10.

(10)$$\text{A decision rule:}\mathrm{\Theta }\to \mathrm{\Gamma }\text{and it also read if}\mathrm{\Theta }\text{then}\mathrm{\Gamma }$$

where $\mathrm{\Theta }$ and $\mathrm{\Gamma }$ represent the condition attributes and decision attributes of the rules, respectively. The decision rules are ‘if-then’ statements related to the conditions and decision categories. It also expresses the relationship between condition attributes and decision attributes. The strength of the decision rules is given by Eqn. 11.

(11)$${\eta }_s(\mathrm{\Theta },\mathrm{\Gamma })=\frac{{sup}_s(\mathrm{\Theta },\mathrm{\Gamma })}{\text{????}(U)}$$

where ${sup}_s(\mathrm{\Theta },\mathrm{\Gamma })$ is the support of decision rule $\mathrm{\Theta }\to \mathrm{\Gamma }$ in $S\cdot \text{????}(U)$. is the cardinality of $U$.

For detailed calculation steps and the introduction of rough sets, please refer to Pawlak’s studies [28,40]. This study’s rough sets were calculated using the Rough Set Data Explorer (Rose2) software [41].

First, a prediction model is established using rough set theory. Then, after each risk factor is excluded one by one, the prediction model’s reduced accuracy is considered to be the importance degree of these factors. The results showed that the order of importance of all risk factors from high to low was: sensory perception (C${}_{\mathrm{1}}$), nutrition (C${}_{\mathrm{3}}$), activity (C${}_{\mathrm{6}}$), friction and shear (C${}_{\mathrm{4}}$), moisture (C${}_{\mathrm{5}}$), and mobility (C${}_{\mathrm{2}}$). Sensory perception (C${}_{\mathrm{1}}$) and nutrition (C${}_{\mathrm{3}}$) were the most prominent risk factors for elderly male patients. The degree of importance is obtained using Eqn. 9 in Step 5 of the rough set theory. The results for all the risk factors are shown in Table 3.

The rough set theory can further reveal the relationship between risk factors and risk levels in the original data and help in making decision rules through a minimum coverage rate. A total of 45 decision rules were derived from 245 observation data in this study through rough set theory. These rules include five rules for severe risk and 12 rules for high risk. Furthermore, 11 rules apply to moderate risk, 11 rules to mild risk, and six rules to no risk. To effectively understand each risk level’s main behaviours, only the top three main rules are displayed for each risk level. They are also the main behavioural patterns representing this risk level. The top rule in the severe risk level is taken as an example. In male elderly patients with severe risk of pressure injury, 42% of the observation data showed that their condition was characterized by ‘(Sensory perception (C${}_{\mathrm{1}}$) = 1) & (Nutrition (C${}_{\mathrm{3}}$) = 2) & (Friction and shear (C${}_{\mathrm{4}}$) = 1) & (Activity (C${}_{\mathrm{6}}$) = 1)’. Moreover, when a male elderly inpatient meets this rule, he has a 42% possibility of serious risk of pressure injury. The result of each risk level’s decision rules is obtained by Eqns. 10 and 11 in Step 6 of the rough set theory. The results of the top three main rules for all risk levels are presented in Table 4.

The rough set theory results come from actual clinical data, which reveal the behaviour rules of different risk levels of pressure injury among elderly male patients in the case hospital. To determine these decision rules’ robustness, we carried out a 5-fold cross-validation on the same data set through several well-known data-mining analysis methods from previous studies. These include random forest, backpropagation artificial neural network, and support vector machine [25,42].

All data-mining analysis methods cross-validated the same dataset based on a 5-fold cross-validation sampling method to ensure that each observation appears at least once in the training and test data. First, the entire dataset is divided into five datasets using the average method, of which four are the training data set, and the rest are the testing data set. The training dataset was used as the basis for establishing the prediction model. Further, the test dataset was used as the source to verify the accuracy of the model. Then, all methods built prediction models based on these datasets and obtained the correct classification rates. This operation was performed five times. Finally, all processes got the correct classification rate and average rate, as shown in Table 5. The results in Table 5 show that the average accurate classification rates for all methods: rough set theory (90.61%), random forest (89.55%), backpropagation artificial neural network (88.98%), and support vector machine (91.02%).

From the importance perspective (as shown in Table 3), ‘Sensory perception (C${}_{\mathrm{1}}$)’ and ‘Nutrition (C${}_{\mathrm{3}}$)’ are the most significant risk factors for identifying the risk of pressure injuries in the elderly male population, and they are also the critical risk factors for preventive measures. The main reason for this is that the self-protection and mobility of elderly male patients are reduced or lost due to the disease itself or physiological function decline. This decreases the skin’s sensitivity to destructive compression and causes excessive long-term compression of the skin in some parts of the body, thus leading to the occurrence of pressure injuries. Clinically, patients are often in a coma or bedridden state due to complete loss of perception and mobility. Therefore, patients do not feel pain stimulation caused by excessive compression. Further, they do not eat autonomously, which leads to insufficient nutrition intake. Often showing a state of inadequate nutrition or even gradual emaciation, the local bone protuberance pressure increases significantly, leading to a significant increase in pressure injury risk levels. Furthermore, elderly patients often remain in passive positions due to reduced or complete loss of self-protection and mobility caused by the disease itself or by physiological hypofunction. This may cause their skin to become sensitive to damaging compression decreases, which can cause excessive long-term compression of the skin on some parts of the body, thus leading to pressure injury.

From the perspective of decision rules (as shown in Table 4), nurses can further understand the possible clinical conditions (i.e., clinical behaviour rules) of male elderly inpatients at each risk level. Then, according to different clinical conditions, nurses can provide the corresponding nursing measures. A mild risk level is taken as an example. The mild risk level is common in some elderly male inpatients after surgery, and their mobility is slightly limited, such as in inpatients after orthopaedic hip replacement. Nursing measures for elderly male patients with mild risks include urging and assisting them in turning over frequently to minimise local pressure. If the patient needs to use a wheelchair, it can be matched with chair surface decompression equipment. The clinical descriptions and corresponding nursing measures are summarised in Tables 6 and 7, respectively.

From the 5-fold cross-validation results, the average classification accuracy of the four models was found to be between 88.98% and 91.02% (as shown in Table 5). The results showed no significant difference in classification accuracy among the four methods based on the same data. Therefore, these models have good prediction reliability. However, the advantage of rough set theory is that it can further explain the model using condition attributes (i.e., risk factors) and decision attributes (i.e., risk levels) through rule expression (i.e., IF-THEN). This expression can help nurses understand the behaviour pattern (i.e., occurrence characteristics) of each pressure injury risk level and take nursing measures accordingly. Three well-known methods (i.e., random forest, backpropagation artificial neural network, and support vector machine methods) have been applied to pressure injury studies [24,42]. However, these methods belong to the category of the black-box algorithms [43]. They cannot provide further information on decision-making rules for clinical nurses. Therefore, compared with previous related studies (Table 8), this study’s rough set theory can further highlight the importance of each risk factor and the decision rules for different risk levels. Simultaneously, it also makes up for the research gap caused by using the Braden scale in a data-driven decision-making environment.

Several limitations should be considered when interpreting the results of this study. First, we evaluated only some units, who might have characteristics that differ from those of the general population; that is, the generalisation and external validity of the results should be discussed further. Second, since the results of this study are based on Braden scale observation data (frequency) of 245 male elderly hospitalised patients in the hospital in the past year and do not consider other relevant clinical or physical factors of the patients themselves, the findings of this study are limited. In particular, the limitations of patient data collection and unidentified variables that lead to pressure injuries may have been missed in this analysis. Finally, this study only included subjects from one hospital in China as the target population. The results of this study should not be extrapolated to hospitals in other regions of China. Additionally, the rough set theory is based on set theory and is a formal modelling method. It has limitations similar to those of most data-mining methods. For example, owning and using correct data is a necessary prerequisite. However, compared with the black-box algorithms (e.g., random forest, backpropagation artificial neural network, and support vector machine), it is more sensitive to the results [44]. For example, the amount of data will affect the number of decision rules. The levels of attributes will affect the scope of decision rule coverage, and the lack of attributes and data will also limit the technology.

Future studies can include other relevant clinical data of patients themselves, physical health records, and family members’ attitudes and knowledge, thus providing more accurate and personalised comprehensive nursing measures. This study uses the rough set theory to identify the critical risk factors and decision rules for each risk level. In the future, the dominance-based set rough set method, fuzzy rough set method, and other data-mining methods can also be used to determine the predictive factors of pressure injury. Moreover, the research object can also consider the Braden Scale data of pressure injury patients from different departments.