Prognostic role of Ki-67 in colorectal carcinoma: Development and evaluation of machine learning prediction models

Abstract

BACKGROUND

Ki-67 is a routine test item in clinical pathology departments. However, its prognostic value requires further investigation, especially in the context of research using machine learning (ML), which remains relatively underdeveloped.

AIM

To investigate the prognostic value of Ki-67 in cases of colorectal carcinoma (CRC) and explore the potential application of ML algorithms to predict the Ki-67 index.

METHODS

Case data and pathological sections from two centers were systematically collected. To analyze the prognostic value of the Ki-67 index in CRC, multiple cutoff values were established. Meanwhile, by virtue of the histological features presented in the hematoxylin and eosin-stained CRC images, three mainstream ML algorithms, support vector machine (SVM), random forest (RF), and eXtreme gradient boosting (XGBoost) were employed to construct prediction models. Subsequently, the potential of these algorithms to classify and predict the Ki-67 index was explored.

RESULTS

Non-parametric tests revealed that Ki-67 ≥ 40% correlated with a high histological grade (P = 0.017), deficient mismatch repair protein status associated with ≥ 50%-90% cutoffs (all P ≤ 0.028), and ≥ 80% linked to lymph node metastasis (P = 0.006). Kaplan-Meier analysis showed that Ki-67 ≥ 50% predicted higher survival (log-rank P = 0.0299, hazard ratio = 2.142), with no differences for other cutoffs. COX regression identified the Ki-67 positive rate as a significant predictor (P = 0.027, hazard ratio = 2.583), while other variables had no association. In algorithmic model predictions, the SVM, RF, and XGBoost models achieved training area under the curve (AUC) values of 0.851, 0.948, and 0.872, respectively, with corresponding test set AUC values of 0.795, 0.755, and 0.750, respectively. During external validation, their AUC values for predicting Ki-67 status reached 0.757, 0.749, and 0.783, respectively.

CONCLUSION

In algorithmic model predictions, the SVM, RF, and XGBoost models achieved training AUC values of 0.851, 0.948, and 0.872, respectively, with corresponding test set AUC values of 0.795, 0.755, and 0.750, respectively. During external validation, their AUC values for predicting Ki-67 status reached 0.757, 0.749, and 0.783, respectively.

Key Words: Machine learning; Colorectal carcinoma; Ki-67; Prognosis; Prediction

Core Tip: This study pioneers the application of machine learning to predict Ki-67 status in colorectal carcinoma directly from hematoxylin and eosin-stained images. By analyzing data, 50% was identified as the optimal Ki-67 cutoff, with high-expression being linked to improved survival rates and low-expression being associated with advanced tumor stage and lymph node metastasis. Predictive models were developed using the support vector machine, random forest, and eXtreme gradient boosting algorithms, achieving area under the curve values (0.851-0.948 in training and 0.750-0.795 in the external validation group). This innovative approach highlights the potential of machine learning to enhance prognostic accuracy.

INTRODUCTION

Colorectal carcinoma (CRC) is one of the most prevalent and lethal cancers globally[1,2]. In the past three decades, a contrasting trend has been observed in the incidence and mortality rates of CRC between the United States and China. While the United States has experienced a decline in these rates, China has seen a consistent increase[3]. Additionally, the proportion of young individuals (< 50 years old) diagnosed with CRC is increasing annually, the disease is more prevalent in the distal colorectum, such as rectal and left-sided colon cancers[4]. Given these circumstances, the exploration of early diagnostic methods, accurate prognostic assessment, and personalized treatment strategies for CRC is of utmost clinical significance.

Numerous studies have identified Ki-67 as a key biomarker in the prognosis of various tumors[5]. As early as 1999, Palmqvist et al[6] discovered that in Duke’s B stage CRC, a low Ki-67 index at the invasive tumor margin was associated with a poor prognosis[6]. On the one hand, some studies have proposed that high Ki-67 expression in CRC is linked to favorable clinical outcomes[7,8]. On the other hand, additional investigations have revealed that high-expression levels of Ki-67 are negatively correlated with the maturation of tertiary lymphoid structures. Intriguingly, the degree of tertiary lymphoid structure maturation is positively associated with patient survival rates, indicating that the role of Ki-67 in the CRC tumor microenvironment might be intricately intertwined with immune responses[9].

Furthermore, high Ki-67 expression has been identified as an adverse indicator of invasiveness in colorectal adenomas and as a risk factor for the development of CRC[10]. Combining the expression levels of Ki-67 with other biomarkers, such as p53 and RNF135, has shown the potential to provide a more precise prediction of patient survival rates and disease progression[11,12]. These collective findings strongly underscore the clinical utility of Ki-67 as an independent prognostic biomarker for CRC. Nevertheless, due to the inconsistent cutoff values of Ki-67 applied across different studies, substantial variations in patient prognoses have been observed. Consequently, future research should focus on determining the optimal prognostic-related cutoff value of Ki-67, which is essential for enhancing the accuracy of clinical interpretation and patient management.

In the realm of detecting Ki-67 expression in tumor tissues to determine post-treatment tumor cell proliferation activity, immunohistochemistry (IHC) is a conventional and reliable method[13]. However, the inherent heterogeneity of tumor cells and the subjectivity of observers invariably give rise to discrepancies during the interpretation of Ki-67 expression rates. The hematoxylin and eosin (HE) stain has stood the test of time as the standard stain for histologic examination of human tissues. This simple dye combination can highlight the fine structures of cells and tissues[14].

In the analysis of HE-stained images using machine learning (ML), domain-agnostic features enable a more effective characterization of image features across diverse diseases and tissue types[15]. Given the assumption that the differences between Ki-67-positive and -negative cells in IHC-stained sections correlate with the histological features of the corresponding region in HE-stained images, there is a need to establish a connection between the cellular feature information in HE images and the IHC staining status. Identifying and inferring such information from HE-stained sections via ML techniques would substantially boost interpretation efficiency and alleviate subjective bias. Moreover, this approach could potentially eliminate the need for IHC staining, thus conserving both economic and human resources.

ML, a pivotal branch of artificial intelligence (AI) technology, extracts features by harnessing domain knowledge, enabling computers to learn and make decisions and predictions regarding real-world events[16]. This process unearths latent information within the experimental data. With the widespread application of computer-aided diagnostic technologies in medical image processing, the practice of pathological diagnosis has undergone a remarkable transformation. Novel tools, such as digital imaging, advanced AI algorithms, and computer-aided diagnostic techniques, increasingly facilitate and augment computational pathology and AI-based diagnostics[17].

The digitization of pathological images not only enables seamless transmission of rich pathological data across remote locations, but can be widely adopted in digital diagnostics, teleconsultations, education, and research[18,19]. The efficacy of computer-assisted digital whole-slide imaging (WSI) algorithms for cancer diagnosis has approached the level of experienced pathologists[20,21]. Additionally, certain algorithms can predict molecular marker statuses[22,23], detect cancer-associated gene mutations[24,25], assess treatment efficacy[26,27], and estimate patient survival rates[28,29]. These investigations reveal the promising potential of AI in extracting comprehensive and detailed information from standard pathological images. Satisfactory outcomes have occurred in numerous cancers, including CRC. However, to date, no applications of AI technology for predicting Ki-67 status from HE images of CRC have emerged.

This study aims to explore the optimal cutoff value of the Ki-67 index in CRC regarding its prognostic value and to construct algorithmic models for Ki-67 classification prediction by leveraging HE image features and ML. The overarching goal is to reduce or even eliminate subjective bias among pathologists through AI-assisted means, enhance work efficiency, reduce medical costs, and achieve a more accurate and standardized prediction of CRC patient prognosis.

MATERIALS AND METHODS

The technical workflow of this study is illustrated in Figure 1.

Figure 1 Technical workflow for colorectal carcinoma Ki-67 predictive classification integrating case cohort assembly, whole-slide imaging, deep feature engineering, and machine learning modeling. CRC: Colorectal carcinoma; AI: Artificial intelligence; WSI: Whole-slide imaging.

Study population

This retrospective study gathered data from 872 patients diagnosed with primary CRC. Among them, 664 patients had undergone surgical resection at the First Affiliated Hospital of Guangxi Medical University between April 2019 and April 2021, and 208 patients at the Yulin Red Cross Hospital from April 2020 to March 2021. The inclusion criteria consisted of the following: (1) Pathological confirmation of CRC; (2) Radical surgical specimens; (3) Complete clinical and pathological data; and (4) Availability of IHC results for Ki-67 protein. The exclusion criteria encompassed: (1) CRC other than carcinoma or metastatic cancer; (2) Treatment limited to biopsy, submucosal dissection, or simple tumor resection; (3) Incomplete clinical and pathological data; and (4) Absence of IHC results for Ki-67 protein.

Ki-67 grouping strategy and statistical analysis

Ki-67 expression was evaluated using nine pre-specified cutoff values (10%, 20%, 30%, 40%, 50%, 60%, 70%, 80% and 90%). However, cutoffs of 10%, 20%, and 30% were excluded due to excessively small sample sizes in the lower-expression groups (Table 1), which posed risks of bias and insufficient statistical power. The final analysis included six cutoff values: 40%, 50%, 60%, 70%, 80%, and 90%, with patients stratified into two groups for each cutoff: < cutoff value and ≥ cutoff value.

Table 1 Distribution of cases by Ki-67 cutoffs.

Cutoff	< cutoff (n)	≥ cutoff (n)	Total (n)	Exclusion reason
10%	3	869	872	< 1% in < cutoff group
20%	9	863	872	1% in < cutoff group
30%	15	857	872	< 2% in ≥ cutoff group
40%	82	790	872	Retained
50%	200	672	872	Retained
60%	301	571	872	Retained
70%	437	435	872	Retained
80%	578	294	872	Retained
90%	728	144	872	Retained

Normality of clinical pathological parameters - gender, age, tumor stage, tumor location, number of lesions, histological type, histological grade, vascular invasion, nerve invasion, lymph node metastasis, and mismatch repair (MMR) protein status - was assessed using the Shapiro-Wilk test. Since all parameters failed to meet the normal distribution assumption, non-parametric tests were employed. The Mann-Whitney U test (equivalent to the Wilcoxon rank-sum test) was used to compare differences between the two groups (< cutoff vs ≥ cutoff) for each continuous or ordinal variable. The Wilcoxon W statistic, a value derived from the Mann-Whitney U test, and the standardized Z score were reported. Statistical significance was defined as a two-tailed P value < 0.05. All analyses were performed using the SPSS software (Version 26.0, IBM).

Survival analysis

A total of 208 CRC patients from the Yulin Red Cross Hospital were included in this survival analysis. The patients were initially stratified into seven Ki-67 expression cutoff groups: 20%, 30%, 40%, 50%, 60%, 70%, and 80%. Groups with < 3% of cases in the lower cutoff category (i.e., < 20%, < 30%, and ≥ 80%) were excluded due to increased risk of bias and insufficient statistical power (Table 2). The remaining four cutoffs (40%, 50%, 60%, and 70%) were used for Kaplan-Meier survival analysis. Survival curves were compared using the log-rank test hazard ratios (HRs) with 95% confidence intervals were calculated to assess the associations between Ki-67 expression and patient survival. Statistical significance was defined as P < 0.05. All the analyses mentioned above were conducted using GraphPad Prism (Version 8.0). To comprehensively assess the influence of Ki-67 expression and other potential confounding factors - gender, age, tumor budding, pathological grade, clinical stage, mismatch repair function, and lymph node invasion - on patient survival, a COX proportional-hazards regression analysis was conducted using SPSS software (Version 26.0, IBM).

Table 2 Distribution of patients by Ki-67 cutoff and exclusion criteria.

Cutoff	< cutoff (n)	≥ cutoff (n)	Total (n)	Exclusion reason
20%	2	206	208	< 1% in < cutoff group
30%	6	202	208	< 3% in < cutoff group
40%	54	154	208	Retained
50%	117	91	208	Retained
60%	165	43	208	Retained
70%	190	18	208	Retained
80%	204	4	208	< 2% in ≥ cutoff group
20%	2	206	208	< 1% in < cutoff group
30%	6	202	208	< 3% in < cutoff group

Pathological section processing

Pathologists with over five years of experience screened all HE-stained sections from the included cases based on pathological results and reviewed them under a microscope to ensure accuracy. The selection criteria demanded complete tissue within the HE-stained section, clear and uniform staining, good contrast, and absence of wrinkles and impurities. A digital pathology slide scanner (model: KF-PRO-020) scanned the HE-stained sections. Operators correctly set all scanner parameters, and precisely scanned the images at a magnification of 400 ×, then saved them as high-resolution WSIs in tagged image file format.

Region of interest selection

Based on previous studies on Ki-67 cutoff values[30], we selected the most frequently reported 50% as the threshold for the ML-based predictive grouping of Ki-67 expression. When the proportion of positively stained CRC cell nuclei reaches or exceeds 50%, it indicates high expression; otherwise, it indicates low expression. To mitigate the impact of the non-uniform distribution of Ki-67 hotspots caused by tumor heterogeneity, two senior pathologists first identified regions with Ki-67 positivity rates closest to those reported in pathological diagnoses on IHC sections of CRC, with consensus reached through joint evaluation. Subsequently, corresponding tumor regions were localized in the WSI of HE-stained sections from the same tissue samples to facilitate targeted image acquisition. Figure 2 displays representative cases across the low, moderate, and high Ki-67 expression ranges.

Figure 2 Morpho-proliferative characterization of colorectal carcinoma specimens. A: Ki-67 immunohistochemistry (IHC), Ki-67 proliferation indices (positive cells/total): 10%; B: Ki-67 IHC, Ki-67 proliferation indices (positive cells/total): 30%; C: Ki-67 IHC, Ki-67 proliferation indices (positive cells/total): 50%; D: Ki-67 IHC, Ki-67 proliferation indices (positive cells/total): 90%; E: Hematoxylin and eosin (HE) histology at 400 × microscopic resolution, Ki-67 proliferation indices (positive cells/total): 10%; F: HE histology at 400 × microscopic resolution, Ki-67 proliferation indices (positive cells/total): 30%; G: HE histology at 400 × microscopic resolution, Ki-67 proliferation indices (positive cells/total): 50%; H: HE histology at 400 × microscopic resolution, Ki-67 proliferation indices (positive cells/total): 90%.

Quantitative image feature selection and model construction

Leveraging image characteristics, we employed the open-source software Cellprofiler 4.2.5 to extract 350 quantitative image features, such as “area shape”, “intensity”, “location”, “radial distribution”, and “texture”. After eliminating non-valid image features, we selected 225 quantitative image features that demonstrated statistically significant differences between the high and low Ki-67 expression groups for subsequent analysis. We trained a random forest (RF) model using these feature datasets and computed feature importance to identify the 31 most crucial image features in the dataset (Supplementary Table 1). We averaged the target image features and utilized SPSS 26.0 for data analysis, organizing the data in Microsoft Excel (combining data from both groups and excluding features without significant differences). To achieve a higher level of statistical significance, we consistently chose feature values with P < 0.01. The correlation between the selected 31 features (such as “Texture_SumVariance-Hematoylin”) and Ki-67 expression was tested using the Spearman rank test (P < 0.01), combined with RF feature importance analysis, and biological significance features related to nuclear morphology and staining intensity were prioritized for preservation.

During the training phase of the cases, we predefined the computational parameters of the support vector machine (SVM), RF, and eXtreme gradient boosting (XGBoost) algorithms and furnished the computer with image feature data for recognition. Based on these recognition results, we classified the images into either high or low Ki-67 expression groups, thus constructing a preliminary AI prediction model for CRC Ki-67 classification. We evaluated the performance of the model by generating receiver operating characteristic (ROC) curves and calculating the area under the curve (AUC). We partitioned the samples from the model development cohort into training and testing datasets in a 7:3 ratio with a random seed of 6588. We then optimized the initial parameters of the model using the training dataset and then evaluated the model’s generalization ability on the testing dataset.

Additionally, we selected quantitative image features from the external validation group, the same as those from the model construction group, for external validation of the SVM, RF, and XGBoost algorithms. The goal was to prove the universal applicability of the three models in predicting Ki-67 expression classification in colorectal cancer under different conditions. We appraised the diagnostic performance of the models through ROC curves and AUC, further analyzed algorithm parameters, and ultimately constructed an AI prediction model for CRC Ki-67 classification. The SVM model used the radial basis function as the kernel function, which has good classification performance in nonlinear feature space and is suitable for processing high-dimensional image feature data. GridSearchCV was used to optimize SVM and RF model hyperparameters, and the Python package “optuna” was used to optimize XGBoost model hyperparameters to avoid model overfitting. We implemented the algorithms SVM, RF, and XGBoost algorithms using Python (version 3.11).

RESULTS

Association between Ki-67 expression and clinicopathological features

Table 3 summarizes the results of the non-parametric tests for six Ki-67 cutoffs (40%-90%). Most parameters showed no significant association with Ki-67 expression at the P < 0.05 threshold. Notable findings included: (1) Histological grade (40% cutoff): Patients with Ki-67 ≥ 40% had a significant association with a high histological grade (Mann-Whitney U = 28922.000, Z = -2.383, P = 0.017), indicating that higher Ki-67 expression was linked to more aggressive tumor differentiation; (2) MMR status (50%, 60%, 70%, 80%, 90% cutoffs): Deficient MMR (dMMR) was significantly associated with Ki-67 ≥ 50% (P = 0.028), ≥ 60% (P = 0.005), ≥ 70% (P < 0.001), ≥ 80% (P < 0.001), and ≥ 90% (P < 0.001). This suggests that dMMR tumors are more likely to exhibit higher Ki-67 expression across these cutoffs; and (3) Lymph node metastasis (80% cutoff): A significant association was observed between Ki-67 ≥ 80% and lymph node metastasis (Mann-Whitney U = 76857.000, Z = -2.744, P = 0.006), indicating that patients with higher Ki-67 expression (≥ 80%) had a greater likelihood of lymphatic spread. No significant associations were found for gender, age, tumor stage, location, lesion number, vascular invasion, or nerve invasion across any of the analyzed cutoffs (all P > 0.05).

Table 3 Clinicopathological correlations with Ki-67 expression groups.

Ki-67 expression groups	Clinicopathological indicators	Mann-Whitney U value	Wilcoxon W value	Z value	Asymptotic significance (two-tailed) P value
< 40 vs ≥ 40	Gender (male, female)	31612.000	344057.000	-0.425	0.671
	Age (> 50, ≤ 50)	28845.000	341290.000	-2.655	0.008
	Stage (I and II, III and IV)	29815.000	33218.000	-1.370	0.171
	Tumor location (right colon, left colon, rectum)	30872.500	34275.500	-0.746	0.455
	Number of lesions (1, > 1)	31917.000	344362.000	-0.679	0.497
	Histological type (non-specific type, specific type)	32110.000	35513.000	-0.294	0.769
	Histological grade (low-grade, high-grade)	28922.000	341367.000	-2.383	0.017
	Vascular invasion (no, yes)	30354.000	33757.000	-1.413	0.158
	Nerve invasion (no, yes)	30897.000	343342.000	-1.039	0.299
	Lymph node metastasis (no, yes)	31463.000	34866.000	-0.508	0.611
	MMR (pMMR, dMMR)	27290.000	30140.000	-1.563	0.118
< 50 vs ≥ 50	Gender (male, female)	66972.000	293100.000	-0.086	0.931
	Age (> 50, ≤ 50)	63892.000	290020.000	-1.720	0.085
	Stage (I and II, III and IV)	65120.000	85220.000	-0.768	0.442
	Tumor location (right colon, left colon, rectum)	64225.000	84325.000	-1.016	0.310
	Number of lesions (1, > 1)	66812.000	292940.000	-0.387	0.699
	Histological type (non-specific type, specific type)	65788.000	291916.000	-1.030	0.303
	Histological grade (low-grade, high-grade)	64452.000	290580.000	-1.311	0.190
	Vascular invasion (no, yes)	66860.000	86960.000	-0.164	0.870
	Nerve invasion (no, yes)	64780.000	84880.000	-1.169	0.242
	Lymph node metastasis (no, yes)	66728.000	292856.000	-0.180	0.857
	MMR (pMMR, dMMR)	63276.000	83376.000	-2.191	0.028
< 60 vs ≥ 60	Gender (male, female)	85356.000	130807.500	-0.194	0.846
	Age (> 50, ≤ 50)	83525.000	246831.000	-1.109	0.268
	Stage (I and II, III and IV)	84560.000	130011.000	-0.449	0.653
	Tumor location (right colon, left colon, rectum)	84505.500	247811.500	-0.432	0.666
	Number of lesions (1, > 1)	85805.000	249111.000	-0.115	0.908
	Histological type (non-specific type, specific type)	85373.500	248679.500	-0.363	0.717
	Histological grade (low-grade, high-grade)	84727.500	248033.500	-0.510	0.610
	Vascular invasion (no, yes)	85433.500	248739.500	-0.214	0.831
	Nerve invasion (no, yes)	82664.000	128115.000	-1.397	0.162
	Lymph node metastasis (no, yes)	82995.000	246301.000	-0.989	0.322
	MMR (pMMR, dMMR)	80296.000	125747.000	-2.806	0.005
< 70 vs ≥ 70	Gender (male, female)	94780.000	190483.500	-0.085	0.932
	Age (> 50, ≤ 50)	92855.000	187415.000	-1.077	0.282
	Stage (I and II, III and IV)	92867.000	187697.000	-0.677	0.498
	Tumor location (right colon, left colon, rectum)	94707.500	189537.500	-0.098	0.922
	Number of lesions (1, > 1)	93942.000	189645.000	-0.927	0.354
	Histological type (non-specific type, specific type)	93333.500	188163.500	-1.051	0.293
	Histological grade (low-grade, high-grade)	94255.500	189085.500	-0.318	0.751
	Vascular invasion (no, yes)	94253.500	189083.500	-0.322	0.748
	Nerve invasion (no, yes)	94907.000	189737.000	-0.057	0.955
	Lymph node metastasis (no, yes)	91071.000	185901.000	-1.272	0.203
	MMR (pMMR, dMMR)	87145.000	182848.500	-3.724	0.000
< 80 vs ≥ 80	Gender (male, female)	84512.000	127877.000	-0.153	0.878
	Age (> 50, ≤ 50)	82565.000	125930.000	-1.110	0.267
	Stage (I and II, III and IV)	81625.000	124990.000	-1.097	0.273
	Tumor location (right colon, left colon, rectum)	84876.000	128241.000	-0.027	0.978
	Number of lesions (1, > 1)	84769.000	128134.000	-0.175	0.861
	Histological type (non-specific type, specific type)	83122.000	126487.000	-1.196	0.232
	Histological grade (low-grade, high-grade)	84070.000	251401.000	-0.380	0.704
	Vascular invasion (no, yes)	84270.000	127635.000	-0.298	0.766
	Nerve invasion (no, yes)	84853.000	128218.000	-0.049	0.961
	Lymph node metastasis (no, yes)	76857.000	120222.000	-2.744	0.006
	MMR (pMMR, dMMR)	76568.000	243899.000	-4.220	0.000
< 90 vs ≥ 90	Gender (male, female)	52336.000	62776.000	-0.034	0973
	Age (> 50, ≤ 50)	50368.000	60808.000	-1.206	0.228
	Stage (I and II, III and IV)	51616.000	62056.000	-0.335	0.738
	Tumor location (right colon, left colon, rectum)	50731.000	61171.000	-0.652	0.515
	Number of lesions (1, > 1)	51928.000	62368.000	-0.551	0.582
	Histological type (non-specific type, specific type)	51584.000	62024.000	-0.687	0.492
	Histological grade (low-grade, high-grade)	49548.000	314904.000	-1.549	0.121
	Vascular invasion (no, yes)	50776.000	61216.000	-0.895	0.371
	Nerve invasion (no, yes)	49540.000	59980.000	-1.573	0.116
	Lymph node metastasis (no, yes)	49948.000	60388.000	-1.063	0.288
	MMR (pMMR, dMMR)	45368.000	310724.000	-4.473	0.000

MMR: MisMatch repair; pMMR: Proficient MisMatch repair; dMMR: Deficient MisMatch repair.

Survival analysis with Ki-67 expression groups

After excluding groups with inadequate sample sizes (20%, 30%, 80% cutoffs, where the lower-expression groups comprised < 3% of cases), four valid cutoff groups were retained: 40%, 50%, 60%, and 70%. Patients with Ki-67 ≥ 50% exhibited a higher survival rate compared to those with Ki-67 < 50% (log-rank P = 0.0299, HR = 2.142). No significant differences was observed for the 40% (P = 0.3490; Figure 3A). Kaplan-Meier analysis revealed that only the 50% cutoff demonstrated statistical significance (Figure 3B). There were also no significant differences observed for the 60% (P = 0.4259; Figure 3C), or 70% (P = 0.2614; Figure 3D) cutoffs, where survival curves overlapped substantially and HRs lacked statistical significance.

Figure 3 Kaplan-Meier survival curves for colorectal carcinoma patients stratified by Ki-67 40%, 50%, 60%, and 70%. Data from the external validation dataset (208 colorectal carcinoma patients from the Yulin Red Cross Hospital). A: Ki-67 < 40% vs Ki-67 ≥ 40% Kaplan-Meier analysis with log-rank test: P = 0.3490, hazard ratio (HR) = 1.451; B: Ki-67 < 50% vs Ki-67 ≥ 50% Kaplan-Meier analysis with log-rank test: P = 0.0299, HR = 2.142; C: Ki-67 < 60% vs Ki-67 ≥ 60% Kaplan-Meier analysis with log-rank test: P = 0.4259, HR = 1.400; D: Ki-67 < 70% vs Ki-67 ≥ 70% Kaplan-Meier analysis with log-rank test: P = 0.2614, HR = 2.026. HR: Hazard ratio.

Results of the COX analysis

Overall model test: The Omnibus test of the model coefficients showed that the significance values of the overall model and each change part (0.144 and 0.139, respectively) were both greater than 0.05. This indicates that when combined the independent variables included in the model, when combined, had no statistically significant impact on the dependent variable, suggesting limited explanatory power of the overall model.

Variable analysis: Ki67 positive rate: The significance level of 0.027 (< 0.05) was statistically significant. The regression coefficient (B) was 0.949, and the HR Exp(B) was 2.583. That is, for every one-unit increase in the Ki67 positive rate, the risk was approximately 2.583 times the original. The 95% confidence interval (1.114-5.990) did not include 1. Other variables: Variables such as gender, age, tumor budding, clinical stage, mismatch repair function, pathological grade, and lymph node invasion all had significance values greater than 0.05, showing no statistical significance and having no clear association with risk.

CRC Ki-67 grouping and tile cutting

Based on IHC test results, we divided patients in the model construction group into high-expression (581 cases) and low-expression (83 cases) groups. Given the significant difference in the number of cases between the two groups, to prevent overfitting, we cut an average of three tiles per sample in the high-expression group, amounting to a total of 1743 tiles, and an average of 20 tiles per sample in the low-expression group, resulting in a total of 1660 tiles. We divided the external validation group into high-expression (91 cases, with an average of three tiles per sample, amounting to 273 tiles) and low-expression (117 cases, with an average of three tiles per sample, resulting in 351 tiles) groups according to the same criteria.

Performance of SVM, RF, and XGBoost models in predicting Ki-67 status in the model construction group

Based on the cellular characteristics in tumor images, a Ki-67 classification prediction model for CRC was constructed using 664 CRC samples from the First Affiliated Hospital of Guangxi Medical University. The findings revealed that the AUC values for the SVM, RF, and XGBoost models in the training dataset reached 0.851 (accuracy = 0.771, sensitivity = 0.795 and specificity = 0.746), 0.948 (accuracy = 0.862, sensitivity = 0.847 and specificity = 0.876), and 0.872 (accuracy = 0.797, sensitivity = 0.826 and specificity = 0.766), respectively. In contrast, the AUC values of the SVM, RF, and XGBoost models in the test dataset attained 0.795 (accuracy = 0.724, sensitivity = 0.735 and specificity = 0.712), 0.755 (accuracy = 0.690, sensitivity = 0.689 and specificity = 0.690), and 0.750 (accuracy = 0.750, sensitivity = 0.722 and specificity = 0.669), respectively (Figure 4). The performance comparison of each model is shown in the confusion matrix and precision recall curve in Figure 5. The accuracy of the 5-fold cross-validation of the SVM, RF, and XGBoost models is 0.51, 0.65, and 0.66, respectively. GridSearchCV and Python package “optuna” were used to avoid model overfitting. Exceptional proficiency in classification prediction was demonstrated by each of the three models.

Figure 4 Comparative predictive performance of Ki-67 classification models. A: Support vector machine with receiver operating characteristic (ROC) curves; B: Random forest with ROC curves; C: The eXtreme gradient boosting with ROC curves. ROC: Receiver operating characteristic; SVM: Support vector machine; XGBoost: eXtreme gradient boosting.

Figure 5 Confusion matrixes and precision-recall curves of Ki-67 classification models. A: Support vector machine in the train set and test set; B: Random forest in the train set and test set; C: The eXtreme gradient boosting in the train set and test set. SVM: Support vector machine; XGBoost: eXtreme gradient boosting; PR: Precision recall.

Valuation of the effectiveness of SVM, RF, and XGBoost models in forecasting Ki-67 expression within the external validation cohort

An external validation model for predicting Ki-67 classification in CRC was developed using the SVM, RF, and XGBoost algorithms. A dataset consisting of 208 CRC samples from Yulin Red Cross Hospital was utilized. ROC curves were generated from the testing results to evaluate the efficacy of the models (Figure 6). The AUC values of the respective models were 0.757 (accuracy = 0.677, sensitivity = 0.660, specificity = 0.696), 0.749 (accuracy = 0.686, sensitivity = 0.647, specificity = 0.728), and 0.783 (accuracy = 0.686, sensitivity = 0.677, specificity = 0.705), respectively. The performance comparison of these models on the validation set is shown in the confusion matrix and precision recall curve in Figure 7. These results indicated that the models possessed excellent classification capabilities and demonstrated good generalizability and stability during the external validation process.

Figure 6 Comparative receiver operating characteristic analysis of prediction models in the external validation set. A: Support vector machine; B: Random forest; C: The eXtreme gradient boosting. ROC: Receiver operating characteristic; SVM: Support vector machine; XGBoost: eXtreme gradient boosting.

Figure 7 Confusion matrixes and precision-recall curves of Ki-67 classification models. A: Support vector machine in the external validation set; B: Random forest in the external validation set; C: The eXtreme gradient boosting in the external validation set. SVM: Support vector machine; XGBoost: eXtreme gradient boosting.

Feature weight analysis of the XGBoost model

Based on the XGBoost model, we achieved the highest external validation AUC. We used the “SHAP” package to rank the features of the model and analyze its interpretability. After comparing the data, the top five features included the following: “AreaShape_MaxFeretDiameter”; “Intensity_IntegratedIntensityEdge_Hematoxylin”; “Texture_SumAverage_Hematoxylin_3_02_256”; “Texture_SumAverage_Hematoxylin_3_03_256”; “Texture_SumAverage_Hematoxylin_3_00_256” (Figure 8). “AreaShape_MaxFeretDiameter” represents the largest distance between two parallel lines tangent on either side of the object. “Intensity_StdIntensityEdge” represents standard deviation of the edge pixel intensities of an object. “Texture_SumVariance” represents the average of the normalized grayscale image in the spatial domain.

Figure 8 SHapley Additive exPlanation score of Ki-67 classification eXtreme gradient boosting models. SHAP: SHapley Additive exPlanation.

DISCUSSION

Ki-67 expression and clinicopathological correlations

This study explored the association between Ki-67 expression and clinicopathological features across multiple cutoffs (40%-90%), revealing distinct patterns. A key finding was the significant link between high Ki-67 expression (≥ 40%) and high histological grade, consistent with Ki-67’s role as a marker of cellular proliferation and tumor aggressiveness. This is consistent with prior research indicating that increased proliferative activity, as measured by Ki-67, correlates with poorer differentiation and more aggressive tumor behavior[9,31,32].

Notably, dMMR status showed a strong association with higher Ki-67 cutoffs (50%-90%), suggesting that dMMR tumors, characterized by high tumor mutational burden and microsatellite instability, exhibit heightened proliferative activity. This may reflect oncogenic stress and replicative demand in hypermutated tumors, driving elevated cell cycle progression. Conversely, lymph node metastasis was only significantly associated with the highest cutoff (≥ 80%), implying that extremely high proliferative activity may be a critical threshold for lymphatic invasion. This finding could inform risk stratification for patients with aggressive diseases.

Survival analysis and cutoff selection

Survival analysis highlighted the 50% cutoff as the only significant threshold, where patients with Ki-67 ≥ 50% exhibited a higher survival rate (HR = 2.142, P = 0.0299). This finding appears to align with the results from some previous studies. For instance, Li et al[33] established a cutoff value of 50% for Ki-67 and discovered that patients with stage III CRC exhibiting high Ki-67 expression had superior three-year disease-free survival and overall survival rates. Furthermore, among stage IV CRC patients, a significant enhancement in three-year progression-free survival was observed.

Similarly, Fodor et al[34] adopted the median value as the cutoff for Ki-67 and reported an improved five-year overall survival rate in the high Ki-67 subgroup within Dukes C stage patients, who also appeared to derive greater benefits from chemotherapy[34]. However, we believe this finding warrants cautious interpretation. This may reflect selection bias due to excluded small sample groups (e.g., 80% cutoff) or interactions with other biological pathways, such as immune cell infiltration in high-proliferation tumors, which is known to correlate with improved outcomes in CRC[35]. The lack of significance in other cutoffs underscores the importance of validating optimal Ki-67 thresholds in larger heterogeneous cohorts.

ML models for Ki-67 prediction

With the aid of deep learning technology, Liu et al[36] managed to estimate the number of Ki-67-positive cells in HE-stained images[36]. Their study no longer relied on IHC-stained images. There have been studies using AI technology to identify and predict the Ki-67 index in pathology images of breast cancer[37], brain tumors[38], and gastrointestinal neuroendocrine tumors[39]. This study aimed to develop a Ki-67 classification prediction model for CRC by leveraging three algorithms: SVM, RF, and XGBoost. To the best of our current knowledge, this might be among the early attempts to construct such a model using these specific algorithms for CRC globally. The analysis of the training dataset demonstrated that the AUC values for the SVM, RF, and XGBoost models were 0.851, 0.948, and 0.872, respectively. In the test dataset, the corresponding AUC values decreased to 0.795, 0.755, and 0.750, respectively. These results suggest that the models have a certain level of predictive ability for Ki-67 classification. However, the performance decline from the training to the test dataset may indicate potential overfitting issues, which require further investigation.

During external validation, the SVM, RF, and XGBoost models yielded AUC values of 0.757, 0.749, and 0.783, respectively - performance metrics that approached the reported inter pathologist agreement levels for Ki-67 interpretation in the literature[40]. These findings suggest that the models demonstrate reasonable generalizability across external datasets. Nevertheless, the generalizability and reliability of the models cannot be firmly established at this stage, as the external validation results could be influenced by various factors such as differences in patient characteristics, data collection protocols, and histological assessment criteria between the external dataset and the training and test datasets.

Based on the SHAP score, we sorted the data to identify the top five features that contribute the most to the model. One “AreaShape_MaxFeretDiameter”, one “Intensity_IntegratedIntensityEdge”, and two “Texture_SumAverage”. Based on these features, to some extent, they reflect the size, staining depth, and texture of the cell nucleus. The importance of the “AreaShape_MaxFeretDiameter” indicated that the expression of Ki-67 was positively correlated with the shape change of the nucleus. This is consistent with the known function of Ki-67, which is closely related to mitosis[41]. “Intensity_IntegratedIntensityEdge” shows that the expression levels of Ki-67 may have had a correlation with the intensity. The intensity of the nucleus is related to the degree of nuclear staining. The deep staining of the nucleus also reflects the malignant degree of the tumor, which is consistent with the way the high expression of Ki-67 can reflect the malignant degree of CRC. Although the importance of the feature “Texture” indicates that the Ki-67 Level may be related to the nuclear texture, to our knowledge, there is no relevant study. We hope to validate this result in future research. The reliability of our ML model was explained to some degree by the confirmed correlations between Ki-67 and pathomics features. The unproven correlation would be the goal of our next step. Tumor nuclei from high-risk tiles tended to exhibit increased size, more distorted shapes, and anomalous textures.

Limitations and future directions

Several limitations merit consideration. First, the survival analysis excluded cutoffs with small sample sizes, potentially limiting the generalizability of threshold-specific outcomes. Second, traditional IHC may have differences in readings due to differences between slide producers and readers. Therefore, Ki-67 cannot become an important biomarker for CRC prognosis in traditional IHC and can be applied in clinical practice. Our ML models may be able to avoid these errors caused by humans, making Ki-67 a better indicator for CRC prognosis. Third, while the ML models demonstrated promise, their reliance on manually curated tiles and single-institution training data may affect scalability. Prospective studies with multi-center datasets and the integration of genomic/transcriptomic data could further refine these models. Additionally, exploring the mechanistic link between dMMR status and Ki-67 expression - e.g., via pathways like mismatch repair deficiency–induced replicative stress - would deepen our understanding of tumor biology.

CONCLUSION

This study identified clinically relevant associations between Ki-67 expression and histopathological features, particularly highlighting dMMR status as a key correlate of high proliferative activity. The development of robust ML models for Ki-67 prediction represents a step toward automated, precision pathology, with the potential to enhance diagnostic consistency and guide personalized treatment strategies in CRC.