This study was approved by the Institutional Ethics Committee of Shanghai Pulmonary Hospital affiliated to Shanghai Tongji University (K21-317), and the requirements for written informed consent were waived for the retrospective study. Data was collected from July 2019 to May 2021, and inclusion criteria included the availability of histopathology results with defined benign or malignant pulmonary nodules, primarily in T1/T2 stage. PET/CT data was collected from 1068 patients for modeling and further analysis. Prior to the PET/CT examination, patients were instructed to fast for at least 6 hours and serum glucose levels were monitored to ensure levels were less than 110 mg/dl before administration of ¹⁸F-FDG. PET images were obtained using a hybrid PET/CT scanner (Biograph mCT 64, Siemens, Germany) approximately 1 hour after intravenous injection of 3.7MBq/kg of ¹⁸F-FDG. CT scan parameters included a tube voltage of 120kV, automatic tube current modulation, pitch of 0.8, collimation of 16 * 1.2 mm, rotation time of 0.5 seconds, and reconstruction thickness of 5.0 mm. PET scans were performed using a three-dimensional model from the skull base to the middle of the thigh, with a scan time of 1.2 minutes. PET images were reconstructed using the TrueX+TOF (ultraHD-PET) method, with a reconstructed layer thickness of 5.0 mm and interval of 3.0 mm, and were corrected for CT attenuation. All collected data were processed using Syngo via Siemens Medical Systems for post-processing to reconstruct PET, CT, and PET/CT fusion images.

The modules of machine-learning method in this study were illustrated in Figure 1 . Prior to model training, preprocessing was implemented on raw data to ensure structural expression and exclude outliers, as previously reported (14). Afterwards, a cohort of feature data was carried out for model training. Python 3.9 software (Python Software Foundation) was used to construct and test the model. Sixteen factors comprising clinical information and PET/CT factors were selected as candidate key factors, including age, gender, smoking history, maximum diameter, lobulation, spike, calcification, hole, GGO status, upper lobe location of the PNs, SUV_max, SUV_mean, MTV (20%), MTV (40%), TLG (20%), and TLG (40%). Orthogonal partial least squares discrimination analysis (OPLS-DA) was used to discriminate between malignant and benign groups, and variable importance for the projection (VIP) scores were utilized to select key factors (15).

The logistic regression algorithm was applied in the study, which is suitable for modeling the probability of a certain class or event existing (16) and predicting disease risk based on several clinical characteristics (17, 18). The algorithm was trained on a dataset containing 190 benign and 187 NSCLC samples retrospectively. Mathematically, the logistic regression algorithm is represented by a standard logistic function, which is a sigmoid function that takes any real input t and outputs a value between zero and one (16). It takes log-odds as input and gives probability as output in terms of logit. The standard logistic function is expressed as

where exp represents the powers of nature logarithm. It is assumed that t is a linear function with a set of variables

  x 1 ,   x 2 ,   … ,   x n then t can be defined as

where β 0 ,     β 1 ,     β 2 ,   … ,   β n   represent the linear coefficients. The general logistic function can be written as

In the logistic model, p(x) is indicated as the probability of positive case. By implementing the gradient descent algorithm on the training data, an optimal solution was obtained, which led to the development of the predictive model represented by Eq. 4. The result of risky score was a probability between zero and one, thus diagnosis decision could be given.

Twelve key factors were finally enrolled, including gender, age, smoking history, nodule diameter, GGO status, spike, lobulation, calcification (19, 20), SUV_max, SUV_mean, TLG (20%), MTV (40%). For setting principles of parameters and structuring the input data, factor of age represented sample’s age in years and that of nodule diameter was the pulmonary nodules maximal diameters in millimeters. Parameters for smoking history, spike, lobulation, and calcification were assigned a value of 1 if present and 0 if absent. Gender was assigned a value of 0.6 for female samples and 0 for male samples. GGO status was assigned a value of 1 for nodule size ≥3 cm, 0 for solid nodules, and -1 for other types (e.g., ground glass, ground glass opacity, and mixed ground glass opacity). The raw data of biochemical indications including SUV_max, SUV_mean, TLG (20%), MTV (40%) were substituted in calculation. Coefficients of twelve key features for Eq. 4 is listed.

The machine-learning-based model was tested using a dataset collected between July 2020 to December 2020, which consisted of 378 lung cancer and 84 benign samples. Equations 4-5 were used to generate diagnosis results. A validation group, comprising 147 malignant and 82 benign samples, collected between December 2020 to May 2021, was used to further evaluate the model’s performance. Fourfold tables, receiver operating characteristic curves (21) and AUC were used to evaluate the model’s performance.

Python 3.9 and MetaboAnalyst 5.0 were used for statistical analysis and plot drawing. MetaboAnalyst 5.0, developed by members of the Wishart Research Group at the University of Alberta, is a free online tool for metabolomic data analysis. P<0.05 was considered statistically significant.

The study enrolled a total of 1068 patients, with the stage classification of malignant samples depicted in Figure 2 . The majority of patients were diagnosed with early-stage lung cancer, with 78% classified as T₁N₀M₀ and 17.1% classified as T₂N₀M₀. The patients were grouped chronologically into three sets: a retrospective training group consisting of 377 patients (35.3% of all), a testing group with 462 patients (43.3% of all), and a validation group with 229 patients (21.4% of all).

The statistical characteristics of the samples are presented in Table 1 , which indicates no significant differences in basic clinical information between malignant and benign groups. Morphological characteristics, the average maximal diameter of PNs was also in similar ranges. However, the samples clinically diagnosed as lung cancer exhibited distinct CT features, such as GGO status, spike, calcification, lobulation, and upper lobe. In terms of biochemical characteristics, malignant PNs had higher mean values of SUV_max, SUV_mean, TLG (20%), and TLG (40%) but lower mean values of MTV (20%) and MTV (40%) than the benign ones.

To build a model that comprehensively reflected the influence of PET/CT parameters on lung cancer diagnosis, the parameters were evaluated synthetically. The OPLS-DA analysis showed a potential classification between the benign and non-small cell lung cancer (NSCLC) groups in the projection plot shown in Figure 3A . Based on the VIP score ranking in Figure 3B , lobulation, spike, GGO status, calcification, and the maximum diameter of PNs were considered important CT factors, while the PET indicators SUV_mean, TLG (20%), and MTV (40%) were also included. The final predictive model, described by Eq. 4, comprised 12 key factors. The coefficients of the model indicated that spike, lobulation, SUV_mean, and GGO status were the main contributors to lung cancer diagnosis, while calcification and SUV_max were more associated with benign PNs. The model achieved a sensitivity of 90.4% and specificity of 74.7% in the training cohort.

Based on the model, the factor of SUV had higher VIP scores than smoking history and nodule diameter factors, and had much lower deviations than other biochemical factors ( Figure 3B ; Table 1 ), indicating its significant influence and good independence, and having expected advantages for early-stage lung cancer diagnosis. However, the commonly set threshold of SUV_max at around 2.5 to distinguish lung cancer from benign [if a patient had SUV_max higher than 2.5, it was prone to get a malignant diagnosis in clinical experience (22, 23)] was found to be insufficient, as the boxplot of benign samples showed a high probability of SUV_max values occurring within the range of 0 to 5 (with mean and median value of 3.4 and 2.6 shown in Table 1 and Figure 4 ). This suggests a high risk of misdiagnosis, particularly for benign cases, if a one-size-fits-all approach is taken. Therefore, a multivariate modeling approach that takes advantage of all the biochemical factors is more appropriate for accurate diagnosis. In comparison, the PET/CT model had an AUC of 0.89, while the CT model that was trained without any biochemical factor had an AUC of 0.83, as demonstrated in Figure 5 . These findings highlight the potential of SUV as an important biochemical factor for early-stage lung cancer diagnosis, and emphasize the importance of a multivariate modeling approach in improving the accuracy of diagnosis.

The present study evaluated the diagnostic performance of an automatic diagnostic model for early-stage lung cancer using a testing and validation group approach. The model’s accuracy in both groups was 82.0% and 82.1%, respectively, at the cutoff value of 0.5 ( Table 2 ). Despite different ratios of malignant and benign nodule samples, the results of the model were similar to previous studies and comparable (24). The testing group provided a less biased evaluation of the model in clinical diagnosis, and together with the validation group, ensured the reliability of the results, which are important for future large-scale clinical studies.

Upon statistical observation of the classifications, the testing and validation groups exhibited a pathological diagnosis of malignancy in the majority of GGO status samples. Specifically, out of 147 samples in the GGO status (GGO = -1 in the dataset), around 94.6% or 139 samples were diagnosed as malignant. Conversely, solid pulmonary nodules (SPN) samples (GGO = 0 or 1 in the dataset) had a relatively uncertain diagnostic result, with 70.8% or 386 malignancies in 545 SPN cases ( Table 3 ). This trend reflects the clinical cases where patients with GGO status have a higher risk and a greater chance of being diagnosed as positive. In contrast, the SPN status introduces more ambiguity in the diagnosis (25, 26). It is notable that the conventional visual assessment of SPN on CT has a diagnostic accuracy of around 60% in distinguishing benign SPNs from malignant cases (27). Based on the data distribution and clinical difficulty, the classification of SPN warrants attention.

The study involved a testing and validation group comprising 545 cases of SPN. The diagnostic model demonstrated a positive predictive value (PPV) of 87.2% and an accuracy of 79.1%, which was notably superior to the PPV of 70.8% obtained from surgical outcome ( Table 3 ). The decline in PPV between the overall and SPN cohorts was evaluated, revealing that the surgical results exhibited a greater decline of 6.8% (from 76.0% to 70.8%) compared to the model, which only declined by 2.6% (from 89.5% to 87.2%), as shown in Tables 2 , 3 .

Through mathematical computations, it has been observed that the varying maximum diameters of SPNs exhibit slight differences in their AUC values, with AUCs of 0.82, 0.87, and 0.89 for SPNs with maximum diameters of less than 15 mm, 16 to 30 mm, and greater than 30 mm, respectively. As the SPN diameter increases, the PPV and AUC values also increase, ranging from 78.1% to 89.7%, as presented in Table 3 . It remains a great challenge to accurate discrimination of malignant and benign SPNs, especially in small-sized cases. In this investigation, for nodule size ≤ 15 mm, the proposed model was able to accurately diagnose 57 malignant and 53 benign nodule cases, resulting in a PPV of 78.1%. In contrast, clinical surgical findings revealed 56.9% PPV, defined 91 malignant and 69 benign cases (as shown in Table 3 ). The encouraging result of improving diagnosis PPV by 37.3% demonstrated a potential clinical applicability of this diagnosis model.