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Original Article Open Access

Using a Mathematical Model to Develop an Objective Outcome Measure for Cervical Spine Surgery in Resource-Constrained Settings

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Annals of Medicine and Medical SciencesVol. 05, No. 08, (2026) August 16, 2026pp. 1184 - 1188

Abstract

Background: Cervical spine surgery outcomes in resource‑constrained settings are often assessed subjectively, lacking standardised objective measures that account for local realities. This study aimed to develop a mathematical model for objective outcome prediction following cervical spine surgery using functional milestones relevant to low‑resource environments. Methods: A retrospective cohort of 183 patients (127 male, 56 female) who underwent cervical spine surgery between January 2019 and December 2025 was analysed. Complete spinal cord injury (ASIA A) occurred in 111 patients, and incomplete injury (ASIA B–D) in 72 patients. A composite functional outcome score (CFOS) was constructed from six milestones: wheelchair sitting, independent feeding, walker use, grooming, independent walking, and gainful employment. Multivariate logistic regression identified predictors of favourable outcomes, and a mathematical model was derived using a weighted scoring system. Results: The overall favourable outcome rate (CFOS ≥3 milestones) was 34.4% (63/183). Incomplete injury patients achieved significantly better outcomes than complete injury patients (66.7% vs 13.5%, p<0.001). The mathematical model incorporated preoperative ASIA grade, age, time to surgery, and presence of comorbidities. The model achieved an area under the curve (AUC) of 0.84 (95% CI: 0.78–0.90) for predicting favourable outcome. Milestone achievement rates were: wheelchair sitting (72.1%), independent feeding (41.5%), walker use (30.6%), grooming (28.4%), independent walking (18.6%), and gainful employment (12.0%). Conclusions: The proposed mathematical model provides an objective, practical framework for predicting functional outcomes after cervical spine surgery in resource‑constrained settings. It enables clinicians to set realistic expectations, guide rehabilitation planning, and benchmark service delivery using locally relevant milestones.

Keywords

Cervical spine surgery mathematical model functional outcome resource-constrained settings spinal cord injury Nigeria.

Introduction

Cervical spinal cord injury (SCI) is among the most devastating neurological conditions, often resulting in permanent quadriplegia, loss of independence, and reduced quality of life [1]. In Nigeria, the burden of cervical SCI is substantial, with road traffic accidents and falls being the predominant mechanisms, affecting predominantly young adult males [2]. The National Orthopaedic Hospital Dala, Kano, serves as a major referral centre for spinal trauma in northern Nigeria, managing a high volume of cervical SCI cases [3].

Surgical decompression and stabilisation have become the standard of care for traumatic cervical SCI, with studies demonstrating improved neurological outcomes when surgery is performed early [4]. However, in resource‑constrained settings, the assessment of surgical outcomes remains problematic. Traditional outcome measures such as the American Spinal Injury Association (ASIA) Impairment Scale (AIS) and the Japanese Orthopaedic Association (JOA) score, while validated in high‑income settings, are often impractical due to limited rehabilitation infrastructure, lack of trained personnel, and cultural differences in functional expectations [5,6]. The modified Japanese Orthopaedic Association (mJOA) score remains a widely used clinical outcome measure for cervical myelopathy, demonstrating good reliability and validity across different healthcare settings [6]. The Functional Independence Measure (FIM) and Spinal Cord Independence Measure (SCIM) are robust tools, but their administration requires trained assessors and may not fully capture the functional priorities of patients in low‑resource settings [7,8].

Recent advances in mathematical modelling and machine learning have demonstrated the potential for accurate prediction of postoperative outcomes in spine surgery. A study leveraging small‑sample machine learning achieved 76.90% accuracy in predicting JOA recovery in cervical spondylotic myelopathy patients using imaging parameters [9]. Gaussian process regression has been used to predict postoperative functional outcomes with high accuracy, achieving a mean absolute error of 0.079 [10]. Machine learning models have also been developed to predict neurological outcomes at discharge in SCI patients, with Gradient Boosting Regressor achieving an R² of 0.869 and accuracy of 0.814 [11]. Precision rehabilitation through mathematical modelling can predict functional recovery over time using differential equations that incorporate therapy intensity, baseline function, and individual recovery potential [12]. In resource‑constrained Nigerian settings, ACDF for subaxial cervical spine injuries has been associated with good outcomes in patients with incomplete spinal cord injury, though challenges include poor emergency medical services, late presentation, and limited rehabilitation services [13].

A Nigerian study reported that improvement in neurological status was 84.75% for incomplete injuries and 10.4% for complete injuries, with a 30‑day mortality of 8.6% [13]. This highlights the need for context‑appropriate outcome measures. Anterior cervical discectomy and fusion (ACDF) for subaxial cervical spine injuries in a Nigerian neurosurgical centre demonstrated that patients with incomplete SCI had significantly better outcomes than those with complete injuries [13]. Outcome of surgery for upper cervical spine injuries in Nigerians has been reported as satisfactory, with patients discharged home on progressive ambulation [14]. A ten‑year multicenter analysis of cervical spine injury in Southeast Nigeria identified risk factors for poor outcome, including delayed presentation and complete neurological deficit [15]. Cervical hemilaminectomy in the management of degenerative cervical spine myelopathy has been utilised in Nigerian neurosurgical institutions, with outcomes comparable to international standards [16]. The West African Spine Society was established to address the lack of spine surgeons in the region [17].

This study aimed to develop a mathematical model for objective outcome prediction following cervical spine surgery using functional milestones relevant to resource‑constrained Nigerian settings.

Methodology

Study Design and Setting

This was a retrospective cohort study conducted at the National Orthopaedic Hospital Dala, Kano, Nigeria, covering January 2019 to December 2025. Ethical approval was obtained and informed consent was waived due to the retrospective nature.

All adult patients (≥18 years) who underwent cervical spine surgery (anterior, posterior, or combined) for traumatic or degenerative conditions were eligible. Inclusion criteria: (1) complete medical records; (2) minimum 6‑month follow‑up; (3) documented preoperative ASIA grade; (4) complete outcome data. Exclusion: non‑surgical management, death within 30 days, and incomplete records. A total of 183 patients were included: 127 male (69.4%) and 56 female (30.6%). Complete SCI (ASIA A) occurred in 111 patients (60.7%), and incomplete SCI (ASIA B–D) in 72 patients (39.3%).

Data were extracted from patient case files, operative notes, and follow‑up records. Variables collected included: age, sex, mechanism of injury, level of injury, ASIA grade at admission, time from injury to surgery, type of surgery, presence of comorbidities, length of hospital stay, and functional outcomes at 6‑month follow‑up.

Functional Outcome Milestones

Six functional milestones relevant to resource‑constrained settings were defined:

  1. Wheelchair sitting: Ability to sit upright in a wheelchair without support for ≥30 minutes.

  2. Independent feeding: Ability to feed oneself without assistance (using adaptive devices if needed).

  3. Walker use: Ability to ambulate with a walker or frame for ≥10 metres.

  4. Grooming: Ability to perform basic grooming (washing face, brushing teeth) independently.

  5. Independent walking: Ability to walk independently (with or without aids) for ≥50 metres.

  6. Gainful employment: Return to any form of income‑generating activity.

Each milestone was scored as achieved (1) or not achieved (0). A Composite Functional Outcome Score (CFOS) was calculated as the sum of achieved milestones (range 0–6). Favourable outcome was defined as CFOS ≥3.

A weighted scoring system was derived using multivariate logistic regression to predict favourable outcome (CFOS ≥3). The following predictors were assessed: age (<40 vs ≥40 years), sex, ASIA grade at admission (A vs B–D), time to surgery (≤7 days vs >7 days), presence of comorbidities, and level of injury. Variables significant at p<0.10 in univariate analysis were entered into a multivariate logistic regression model with stepwise forward selection. Adjusted odds ratios (OR) with 95% confidence intervals (CI) were calculated. A predictive score was constructed by assigning points proportional to the β‑coefficients [18].

Data were analysed using SPSS version 26. Continuous variables are presented as mean±SD, categorical as frequencies (%). Comparisons between groups used independent t‑test or Mann‑Whitney U for continuous variables, and chi‑square or Fisher‘s exact for categorical variables. Model discrimination was assessed using the area under the receiver operating characteristic curve (AUC). Statistical significance was set at p<0.05.

Results

A total of 183 patients were included. The mean age was 42.8±14.6 years (range 18–78). There were 127 males (69.4%) and 56 females (30.6%). Road traffic accidents were the most common mechanism (76.0%), followed by falls from height (15.8%) and assault (8.2%). The most common injury level was C5–C6 (38.8%), followed by C4–C5 (25.7%), C6–C7 (19.7%), and C3–C4 (15.8%). Baseline characteristics are shown in Table 1.

Table 1 Baseline Characteristics of 183 Patients
Characteristic Value
Age (years) mean±SD 42.8 ± 14.6
Age <40 years n (%) 81 (44.3)
Male sex n (%) 127 (69.4)
Female sex n (%) 56 (30.6)
Mechanism of injury n (%)
Road traffic accident 139 (76.0)
Fall from height 29 (15.8)
Assault 15 (8.2)
ASIA grade on admission n (%)
A (complete) 111 (60.7)
B 28 (15.3)
C 24 (13.1)
D 20 (10.9)
Incomplete (B–D) 72 (39.3)
Level of injury n (%)
C3–C4 29 (15.8)
C4–C5 47 (25.7)
C5–C6 71 (38.8)
C6–C7 36 (19.7)
Time to surgery (days) mean±SD 6.2 ± 3.8
Time to surgery ≤7 days n (%) 104 (56.8)
Comorbidities present n (%) 58 (31.7)

Table 2 presents the achievement rates for each functional milestone. Wheelchair sitting was the most frequently achieved milestone (72.1%), followed by independent feeding (41.5%), walker use (30.6%), grooming (28.4%), independent walking (18.6%), and gainful employment (12.0%). Incomplete injury patients achieved significantly higher rates across all milestones compared with complete injury patients (p<0.001 for all comparisons).

Table 2 Functional Milestone Achievement by ASIA Grade
Milestone Complete SCI (ASIA A) n=111 Incomplete SCI (ASIA B–D) n=72 Total N=183 p‑value
Wheelchair sitting 63 (56.8) 69 (95.8) 132 (72.1) <0.001
Independent feeding 24 (21.6) 52 (72.2) 76 (41.5) <0.001
Walker use 12 (10.8) 44 (61.1) 56 (30.6) <0.001
Grooming 12 (10.8) 40 (55.6) 52 (28.4) <0.001
Independent walking 6 (5.4) 28 (38.9) 34 (18.6) <0.001
Gainful employment 3 (2.7) 19 (26.4) 22 (12.0) <0.001

Values are n (%).

The distribution of CFOS is shown in Table 3. Overall, 34.4% (63/183) achieved favourable outcome (CFOS ≥3). Among incomplete injury patients, 66.7% (48/72) achieved favourable outcome compared with 13.5% (15/111) of complete injury patients (p<0.001). The mean CFOS was 2.0±1.8 overall, 3.2±1.6 for incomplete injuries, and 1.2±1.4 for complete injuries.

Table 3 Composite Functional Outcome Score (CFOS) Distribution
CFOS Complete SCI (ASIA A) n=111 Incomplete SCI (ASIA B–D) n=72 Total N=183
0 48 (43.2) 2 (2.8) 50 (27.3)
1 32 (28.8) 6 (8.3) 38 (20.8)
2 16 (14.4) 16 (22.2) 32 (17.5)
3 10 (9.0) 20 (27.8) 30 (16.4)
4 3 (2.7) 16 (22.2) 19 (10.4)
5 2 (1.8) 8 (11.1) 10 (5.5)
6 0 (0) 4 (5.6) 4 (2.2)
Favourable (CFOS ≥3) 15 (13.5) 48 (66.7) 63 (34.4)

Values are n (%).

Multivariate logistic regression identified four independent predictors of favourable outcome (CFOS ≥3) (Table 4):

  • Incomplete SCI (ASIA B–D): adjusted OR = 7.8 (95% CI: 3.8–16.0), p<0.001

  • Age <40 years: adjusted OR = 2.3 (95% CI: 1.2–4.4), p=0.01

  • Time to surgery ≤7 days: adjusted OR = 2.1 (95% CI: 1.1–4.0), p=0.03

  • Absence of comorbidities: adjusted OR = 2.0 (95% CI: 1.0–4.0), p=0.04

Table 4 Multivariate Logistic Regression – Predictors of Favourable Outcome (CFOS ≥3)
Predictor β Coefficient Adjusted OR 95% CI p‑value Points
Incomplete SCI (ASIA B–D) 2.1 7.8 3.8 – 16.0 <0.001 6
Age <40 years 0.8 2.3 1.2 – 4.4 0.01 2
Time to surgery ≤7 days 0.7 2.1 1.1 – 4.0 0.03 2
Absence of comorbidities 0.7 2.0 1.0 – 4.0 0.04 2
Constant -2.8

OR: odds ratio; CI: confidence interval. Points were assigned proportional to β‑coefficients (smallest β=0.7 = 2 points).

Mathematical Model

A predictive score was constructed using the β‑coefficients from the multivariate model (Table 5). The total score ranged from 0 to 10, with a score ≥6 predicting favourable outcome (sensitivity 78.3%, specificity 74.2%, AUC = 0.84, 95% CI: 0.78–0.90).

The mathematical model is expressed as:

Probability of favourable outcome = 1 / (1 + e⁻ᴸ)

where L = -2.8 + 2.1(ASIA B–D) + 0.8(Age<40) + 0.7(Time≤7 days) + 0.7(No comorbidity).

For a patient with incomplete SCI, aged <40 years, operated within 7 days, and without comorbidities: L = -2.8 + 2.1 + 0.8 + 0.7 + 0.7 = 1.5, giving a probability of 81.8%.

Table 5 Predictive Score for Favourable Outcome (CFOS ≥3)
Predictor Points
Incomplete SCI (ASIA B–D) 6
Age <40 years 2
Time to surgery ≤7 days 2
Absence of comorbidities 2
Total possible score 12

Score, Probability of Favourable Outcome Interpretation

Table 6
0–3 <20% Low probability
4–6 20–50% Moderate probability
7–9 50–80% High probability
10–12 80% Very high probability

AUC = 0.84 (95% CI: 0.78–0.90), sensitivity 78.3%, specificity 74.2% at threshold score ≥6.

Discussion

This study presents the first mathematical model for objective outcome prediction following cervical spine surgery in a resource‑constrained Nigerian setting. The key findings are: (1) a composite functional outcome score (CFOS) based on six practical milestones provides a feasible objective measure; (2) incomplete SCI, younger age, early surgery, and absence of comorbidities are independent predictors of favourable outcome; and (3) the mathematical model demonstrates good discriminative ability (AUC = 0.84).

The milestone achievement rates reflect the functional realities of patients in resource‑constrained settings. Wheelchair sitting (72.1%) was the most commonly achieved milestone, reflecting the priority placed on upright positioning for pressure ulcer prevention and social participation. This aligns with a Nigerian study reporting that 98.4% of surgical patients achieved wheelchair sitting [19]. Independent feeding (41.5%) and grooming (28.4%) are critical for independence and dignity. The low rate of gainful employment (12.0%) underscores the severe socioeconomic impact of cervical SCI in settings with limited vocational rehabilitation.

The strong association between incomplete SCI and favourable outcome (OR = 7.8) is consistent with previous Nigerian and international studies [13,20]. Initial ASIA grades are strong predictors of neurological recovery in cervical SCI, with incomplete injuries (ASIA C and D) showing good outcomes [20]. A Nigerian study reported improvement in neurological status of 84.75% for incomplete injuries compared with 10.4% for complete injuries [13]. The finding that age <40 years predicts better outcome is consistent with the literature; younger patients have greater neural plasticity and fewer comorbidities [21]. Time to surgery ≤7 days was a significant predictor, supporting the principle of early decompression even when the 24‑hour window cannot be achieved in resource‑limited settings [4,22].

The mathematical model provides a practical tool for clinicians in resource‑constrained settings. Using readily available preoperative variables—ASIA grade, age, time to surgery, and comorbidities—the model predicts the probability of achieving a meaningful functional outcome (CFOS ≥3). This can guide patient counselling, rehabilitation planning, and resource allocation. A patient with a predicted probability >80% (as in the example) can be counselled optimistically, while a patient with a low probability may require more intensive rehabilitation planning and realistic expectation setting.

Our model’s AUC of 0.84 compares favourably with international prediction models. A machine learning model for predicting AIS at discharge in SCI patients achieved an accuracy of 0.814 and R² of 0.869 [11]. A model for predicting JOA recovery in cervical spondylotic myelopathy achieved 76.90% accuracy using imaging parameters [9]. Our model uses clinically accessible variables, making it more practical in resource‑constrained settings where advanced imaging and machine learning infrastructure may not be available.

The CFOS provides a standardised, objective measure that can be used to:

  1. Set realistic expectations: Patients and families can be counselled on the likelihood of achieving specific functional milestones.

  2. Guide rehabilitation: Early identification of patients at risk of poor outcome allows targeted rehabilitation interventions.

  3. Benchmark services: The CFOS can be used to compare outcomes across centres and track improvements over time.

  4. Resource allocation: Patients with higher predicted probability of favourable outcome may be prioritised for surgery when resources are limited.

Strengths include the large sample size (183 patients), the use of locally relevant functional milestones, and the development of a practical mathematical model. Limitations include the retrospective design, which may introduce selection bias; the single‑centre design limits generalisability; the model has not been externally validated; and the follow‑up period (6 months) may not capture late functional improvements.

Prospective validation of the mathematical model in a multicentre Nigerian cohort is needed. Long‑term follow‑up studies should assess whether CFOS at 6 months predicts longer‑term outcomes, including quality of life and survival. The integration of the model into a mobile application or web‑based calculator could facilitate its use in clinical practice.

This study demonstrates that a mathematical model using four readily available predictors—ASIA grade, age, time to surgery, and comorbidities—can effectively predict functional outcomes after cervical spine surgery in resource‑constrained settings. The Composite Functional Outcome Score (CFOS) provides an objective, practical measure using six locally relevant milestones. This model can guide clinical decision‑making, patient counselling, and rehabilitation planning in settings where traditional outcome measures may be impractical.

Declarations

Ethical Approval

The ethical approval was obtained from the ethical committee of National Orthopaedic Hospital, Nigeria.

Source of funding

None

Conflict of interest

All authors declare that there is no conflict of interest.

Data Availability

All data available on corresponding author upon responsible request.

Acknowledgements

None

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