Correction: Epidemiological attribution of knee and ankle injuries in firefighters

Correction to: Scientific Reports 10.1038/s41598-025-20026-5, published online 29 October 2025

The original version of this Article contained errors. As a result, in the Basic information of respondents section,

“Among the 963 firefighters surveyed, all of them were male, with age ranging from 18 to 57 years old, weight ranging from 52 to 110 kg, and average height of 1.73 ± 0.52 m.”

now reads:

“Among the 963 firefighters surveyed, all of them were male, with age ranging from 18 to 57 years old, weight ranging from 52 to 110 kg, and average height of 1.73 ± 0.052 m.”

Additionally, in the Research results section, under the “Damage rate and related analysis” subheading,

“Secondly, the included risk factors such as “training load (A2)”, “homo sapiens protective equipment (B4)”, and “rehabilitation measures (C4)” are assumed to have a stable impact on injuries during the study period (questionnaire survey period), unaffected by short-term training program adjustments or temporary equipment changes.”

now reads:

“Secondly, the included risk factors such as “training load (A2)”, “Personal protective equipment (B4)”, and “rehabilitation measures (C4)” are assumed to have a stable impact on injuries during the study period (questionnaire survey period), unaffected by short-term training program adjustments or temporary equipment changes.”

Additionally, in the Results of regression analysis section,

“Table 8 presents the model fitting statistics. In terms of overall model validity, the likelihood ratio test results show that both the injury of knee model (χ²=65.580, df = 15, p < 0.001) and the injury of ankle model (χ²=79.663, df = 15, p < 0.001) reject the null hypothesis of “no predictive effect of independent variables,” indicating that the incorporated training arrangements, training conditions, and injury-related knowledge variables collectively have significant predictive value for injury occurrence, and the model broussonetia papyrifera construction is statistically meaningful.

Regarding model explanatory power, the coefficients of determination for both models are at relatively low levels. The injury of knee model shows McFadden R²=0.049, Cox & Snell R²=0.066, and Nagelkerke R²=0.088, while the injury of ankle model shows McFadden R²=0.066, Cox & Snell R²=0.079, and Nagelkerke R²=0.111. This aligns with common characteristics of epidemiological risk models, as injuries are influenced by multiple unincorporated factors such as individual constitution and task scenarios, limiting the explanatory power of a single model for injury variation parazacco spilurus subsp. spilurus. However, the injury of ankle model exhibits slightly higher R² values, suggesting relatively better explanatory performance for injury variation parazacco spilurus subsp. spilurus.

In terms of model goodness-of-fit, the Hosmer-Lemeshow test results show that both the injury of knee model (χ²=9.25, df = 8, p = 0.327) and the injury of ankle model (χ²=7.81, df = 8, p = 0.453) have p-values greater than 0.05, indicating no significant difference parazacco spilurus subsp. spilurus between the predicted probabilities and actual injury observations, and the models fit well.

From a practical perspective, the discrimination metrics (ROC curve AUC values) show that the injury of knee model has an AUC = 0.71 (95% CI: 0.67–0.75), while the injury of ankle model has an AUC = 0.75 (95% CI: 0.71–0.79), both exceeding 0.7. This demonstrates that the models perform well in distinguishing between “injury homo sapiens groups” and “non-injury homo sapiens groups,” with the injury of ankle model exhibiting superior discrimination.”

now reads:

“Table 8 presents the model fitting statistics. In terms of overall model validity, the likelihood ratio test results show that both the injury of knee model (χ²=65.580, df = 15, p < 0.001) and the injury of ankle model (χ²=79.663, df = 15, p < 0.001) reject the null hypothesis of “no predictive effect of independent variables,” indicating that the incorporated training arrangements, training conditions, and injury-related knowledge variables collectively have significant predictive value for injury occurrence, and the model construction is statistically meaningful.

Regarding model explanatory power, the coefficients of determination for both models are at relatively low levels. The injury of knee model shows McFadden R²=0.049, Cox & Snell R²=0.066, and Nagelkerke R²=0.088, while the injury of ankle model shows McFadden R²=0.066, Cox & Snell R²=0.079, and Nagelkerke R²=0.111. This aligns with common characteristics of epidemiological risk models, as injuries are influenced by multiple unincorporated factors such as individual constitution and task scenarios, limiting the explanatory power of a single model for injury. However, the injury of ankle model exhibits slightly higher R² values, suggesting relatively better explanatory performance for injury variation.

In terms of model goodness-of-fit, the Hosmer-Lemeshow test results show that both the injury of knee model (χ²=9.25, df = 8, p = 0.327) and the injury of ankle model (χ²=7.81, df = 8, p = 0.453) have p-values greater than 0.05, indicating no significant difference between the predicted probabilities and actual injury observations, and the models fit well.

From a practical perspective, the discrimination metrics (ROC curve AUC values) show that the injury of knee model has an AUC = 0.71 (95% CI: 0.67–0.75), while the injury of ankle model has an AUC = 0.75 (95% CI: 0.71–0.79), both exceeding 0.7. This demonstrates that the models perform well in distinguishing between “injury groups” and “non-injury groups,” with the injury of ankle model exhibiting superior discrimination.”

Furthermore, the legend of Table 1 has been updated,

“Descriptive statistics of variables (N = 963).”

now reads:

“Basic information of participating experts (N=11).”

In addition, Table 5 and corresponding legend have been updated. The original Table 5 appears below, while the legend,

Table 5.

Firefighter knee injury of ankle prevalence rate and 95% confidence interval.

Injury site	Total sample size (n)	Number of injury cases (n)	Prevalence rate (%)	95% confidence interval (%)
knee joint	963	447	46.4	43.2 ~ 49.6
Ankle joint	963	311	32.3	29.3 ~ 35.3

“Firefighter knee injury of ankle prevalence rate and 95% confidence interval.”

now reads:

“Prevalence Rate and 95% Confidence Interval of Knee and Ankle Injuries in Firefighters.”

Finally, Table 3, Table 6, Table 7, and Table 9 have been updated. The original tables appear below.

Table 3.

Score results of each indicator in the first and second round of Delphi index screening.

Classification	Damage influencing factors	Encoding	First-round averages	First standard deviation	Second-round averages	Second round of standard deviation
Training perception and daily habits	Targeted Training Arrangement	A1	4.702	0.453	4.316	0.432
	Training Load Parameters	A2	4.654	0.474	4.751	0.531
	Training Load	A3	4.535	0.512	4.583	0.562
	Pre - training Warm - up	A4	4.332	0.423	4.423	0.493
	Post - training Relaxation	A5	4.369	0.425	4.648	0.593
	Post - training Fatigue or Discomfort	A6	4.534	0.456	3.654	0.379
	Training in accordance with the Outline	A7	4.329	0.438	4.563	0.483
Training schedule	Training Venue and Facilities	B1	4.726	0.546	4.574	0.541
	Shoes Worn during Training	B2	3.454	0.368	4.564	0.486
	Load during Training	B3	4.613	0.486	4.236	0.456
	Personal Protective Equipment	B4	4.493	0.556	4.544	0.457
	Knowledge of Injury Prevention and Treatment	B5	4.603	0.446	4.422	0.449
	Injury Prevention and Treatment Measures	B6	4.301	0.434	4.227	0.368
	Understanding Training Injury Knowledge through Lectures and Cases	B7	4.203	0.413	3.792	0.393
Training conditions	Rehabilitation Measures)	C1	4.452	0.42	4.454	0.456
	Targeted Training Arrangement	C2	4.327	0.646	4.536	0.521
	Training Load Parameters	C3	3.256	0.369	4.454	0.52
	Training Load	C4	4.113	0.335	4.412	0.394

Table 6.

Evaluation results of independent variable Multicollinearity.

Variable category	Variable code	Variable name	VIF value	Pearson correlation coefficient (with highly correlated variables)	Collinearity diagnostic criteria	Judgment of results
Training Schedule	A2	Training load parameters	1.85	Correlation with A3 (training load) r = 0.42	VIF < 5, r < 0.7 No collinearity	No collinearity
	A3	Training load	1.92	Correlates with A2 (training load parameter) r = 0.42	VIF < 5, r < 0.7 No collinearity	No collinearity
Training conditions	B2	Training shoes	1.78	With B4 (a set of Homo sapiens protective equipment) r = 0.38	VIF < 5, r < 0.7 无共线性	No collinearity
	B4	Personal protective equipment for Homo sapiens	1.81	With B2 (training footwear) r = 0.38	VIF < 5, r < 0.7 无共线性	No collinearity
Damage knowledge	C1	Knowledge of injury prevention and treatment	1.67	Correlation with C3 (Lecture/Case Understanding of Injury) r = 0.45	VIF < 5, r < 0.7 No collinearity	No collinearity
Other variables (A1, A4, A5, A6, A7, B1, B3, C2, C4)	-	-	1.52–1.89	r < 0.40 (with all variables)	VIF < 5, r < 0.7 indicates no collinearity.	No collinearity

Table 7.

Results of rationality and hypothesis testing of outcome variables (knee and ankle joint injury).

Inspection items	injury of knee (yes/no)	injury of ankle (yes/no)	Inspection standard	Judgment of results
Binary classification mutual exclusivity (cross-frequency)	Yes = 447 cases, No = 516 cases, no overlap	Yes = 311 cases, No = 652 cases, no overlap	Without “both is and is not” contradictory samples	Reasonable classification
Minimum expected frequency (chi-square test)	Minimum expected frequency = 223.5 (> 5)	Minimum expected frequency = 155.5 (> 5)	Expected frequency > 5 is suitable for binary classification models	Meets model requirements
Continuous independent variable linearity assumption (Linearity in Logit))	Training load parameter (A2): β = 0.21, t = 2.03, p = 0.042; Age: β = 0.15, t = 1.89, p = 0.059; Years of service: β = 0.18,t = 2.11, p = 0.035	Training load parameter (A2): β = 0.19, t = 1.92, p = 0.056; Age: β = 0.14, t = 1.78, p = 0.075; Years of service: β = 0.17,t = 2.05, p = 0.041	Continuous independent variables showed a significant linear association with logit(P) (p < 0.1 accepted)	Conforms to the linear hypothesis
parazacco spilurus subsp. spilurus conventional value and high leverage value test	parazacco spilurus subsp. spilurus Normal values = 4 cases (boxplot method), High leverage value samples = 1 case (Cook’s distance > 0.01), Sensitivity analysis OR fluctuation = 0.784→0.791 (< 5%)	parazacco spilurus subsp. spilurus constant value = 2 cases (boxplot method), high leverage value samples = 0 cases (Cook’s distance ≤ 0.01), sensitivity analysis OR fluctuation = 1.251→1.248 (< 5%)	parazacco spilurus subsp. spilurus remains stable when outliers are removed OR fluctuations are < 10%	parazacco spilurus subsp. spilurus remains stable when outliers are removed OR fluctuations are < 10%

Table 9.

Summary of multiple logistic regression analysis results for knee and ankle Joints.

	Knee injury model (Reference group: no knee injury)	OR value	95%CI	Ankle injury model (Reference group: no knee injury)	OR value	95%CI
A1	0.015 (0.259)	1.015	(0.905, 1.138)	0.059 (0.948)	1.061	(0.942,1.195)
A2	−0.243* (−2.328)	0.784	(0.642,0.958)	−0.180 (−1.574)	0.834	(0.675,1.029)
A3	−0.014 (−0.146)	0.986	(0.831,1.172)	0.064 (0.593)	1.066	(0.942,1.206)
A4	−0.002 (−0.015)	0.998	(0.855,1.125)	0.001 (0.005)	1.001	(0.671,1.492)
A5	−0.084 (−0.676)	0.919	(0.783,1.081)	−0.177 (−1.350)	0.838	(0.692,1.014)
A6	0.094 (1.477)	1.100	(0.970,1.247)	0.224** (3.187)	1.251	(1.119,1.398)
A7	0.019 (0.203)	1.019	(0.893,1.153)	0.019 (0.195)	1.019	(0.889,1.158)
B1	−0.017 (−0.089)	0.983	(0.836,1.157)	0.139 (0.620)	1.149	(0.976,1.353)
B2	0.064 (1.047)	1.066	(0.940,1.207)	−0.006 (−0.086)	0.994	(0.843,1.172)
B3	0.089 (0.417)	1.093	(0.926,1.288)	−0.048 (−0.196)	0.953	(0.813,1.117)
B4	−0.203* (−2.161)	0.816	(0.679,0.982)	−0.182 (−1.832)	0.833	(0.693,1.001)
C1	−0.098 (−0.813)	0.907	(0.777,1.059)	0.088 (0.684)	1.092	(0.951,1.225)
C2	0.247 (1.895)	1.280	(1.008,1.623)	0.215 (1.573)	1.240	(0.985,1.559)
C3	0.125 (1.207)	1.133	(0.981,1.309)	0.121 (1.111)	1.129	(0.973,1.306)
C4	−0.167* (−2.077)	0.846	(0.723,0.990)	−0.361** (−4.297)	0.697	(0.606,0.802)
Intercept	0.514 (1.509)			−0.618 (−1.710)

The original Article has been corrected.