Fisher’s discriminant model based on LASSO logistic regression for CT imaging diagnosis of pelvic rhabdomyosarcoma in children


Clinical data and pathological findings were obtained from patients’ medical records. Imaging data was extracted from our image archiving and communication system.

Study subjects

A total of 121 pediatric patients who underwent abdominal CT scans with contrast and were diagnosed with pelvic tumors from January 2013 to January 2021 were included in this study. According to the pathological findings, these patients were divided into RMS and non-RMS groups. The RMS group included 36 patients (14 males, 22 females) aged 1 month to 16 years, and the non-RMS group included 85 patients (24 males, 61 females) aged 1 month to 15 years. Those in the non-RMS group suffered from various malignancies, including 19 patients with yolk sac tumors, 18 patients with malignant teratoma, 13 patients with neuroblastoma, 9 patients with lymphoma, 5 patients with Ewing’s sarcoma, and 21 patients with other types of reproductive malignancies.

CT imaging and feature extraction

All pediatric patients in our study underwent plain and contrasted pelvic CT examinations on a 256-slice spiral CT system (Philips Brilliance iCT, Philips, The Netherlands) with a low tube voltage of 80–100 kV, a low 100–200 mA tube current (current varied during scan and child weight), 0.4 s rotation time, 0.925 pitch, 128*0.625 mm collimation , a section thickness of 5.0 mm and a reconstruction layer thickness of 1 millimeter. To obtain images with arterial and venous phase contrast, dynamic dual-phase CT with contrast was performed at 30 and 65 s, respectively, after intravenous injection of the contrast agent (Omnipaque, 350 mg/mL, Amersham Healthcare , Shanghai, China). The contrast agent was administered at a dose of 2 ml/kg body weight, with a maximum of 80 ml.

During routine radiological diagnosis, for tumor lesions, attention should be paid above all to their morphology, density, margin, mode of enhancement and metastases. Therefore, our study mainly selected image features of these five aspects to explore the differences between the two groups (RMS group and non-group). According to previous literature and diagnostic experience. The following CT characteristics of the tumors were assessed: (a) morphology (multinodular/lobulated/round/orbicular fusion); (b) density (lower or higher than normal muscle density/calcification/hemorrhage/necrosis); (c) margin (light or unlight); (d) modes of contrast enhancement (surrounding blood vessels/smooth progressive centripetal enhancement/ring enhancement/grape cluster enhancement); (e) metastasis (lymphatic metastasis/bone erosion). The evaluation criteria for the above relatively special CT features are as follows: (1) multinodular fusion: in the CT images, several nodules of different sizes were observed in the pelvic cavity. Some of the nodules were fused and fused into a lobulated mass21; (2) surrounding blood vessels: multiple band-like and punctate vascular shadows can be seen in the mass on enhanced CT images21; (3) homogeneous progressive centripetal enhancement: on dynamic contrast-enhanced CT images, the mass can be seen with peripheral annular inhomogeneous enhancement in the arterial phase, and progressively centripetal inhomogeneous enhancement in the venous and delayed phase21; (4) Reinforcement of the bunch of grapes: when the mass is in a hollow structure (vaginal or bladder, etc.), a mass like a bunch of grapes will appear on the CT image22; (5) lymph node metastases: cervical lymph nodes I, II and inguinal lymph nodes with a short diameter ≥ 1.5 cm, other cervical lymph nodes with a short diameter ≥ 1 cm, or the degree of enhancement was significantly greater than muscle tissue23.

Prospective evaluation of CT images for each patient was performed independently by two abdominal radiologists with 10 to 20 years of experience. Abdominal radiologists were blinded to patient characteristics and histological findings and assessed tumor morphology, density, margin, enhancement patterns, and metastasis. In case of disagreement between the two radiologists, a consensus was found with a third senior abdominal radiologist and two other abdominal radiologists.

statistical analyzes

Patients were divided into an RMS group and a non-RMS group based on pathological findings. For quantitative variables, continuous variables that followed a normal distribution are described as the mean and standard deviation (SD), and a parametric t-test was used to determine statistical significance between the two groups. Otherwise, variables are described as medians and interquartile ranges (IQRs), and a nonparametric Mann-Whitney U test was used for comparisons between the two groups. The categorical variables are expressed in number of patients and as a respective percentage, and the χ2 Fisher’s exact test or test was used to compare rates.

LASSO logistic regression was used to select the optimal features for the diagnosis of RMS from the baseline morphological and CT characteristics of the patients. The penalty parameter λ was optimized and the resulting nonzero coefficient variables in the model were selected as diagnostic variables. Based on these findings, FDA was established as a quantitative diagnostic model for pediatric pelvic RMS. The diagnostic ability of this model was evaluated by the receiver operating characteristic (ROC) curve. In addition, the cumulative diagnostic ability of features was analyzed.

A two-sided P

Establishing the model

FDA is a classic approach to identify a linear function of variables to distinguish samples from different groups as much as possible13. In our study, patients with RMS and without RMS were divided into two groups: ({G}_{1}) (RMS group) and ({G}_{2}) (non-RMS group). A total of 6 CT functions (({x}_{i})) were used as diagnostic variables to establish a linear discriminant function:

$${G}_{i}={sum }_{j=1}^{6}{c}_{j}{x}_{ij} begin{array}{c}i=mathrm {1,2}end{array}$$

Using the discriminant rule, the examination result was found to belong to ({G}_{1}) Where ({G}_{2}).

(1) Raw data matrix: Two matrices (({W}^{1},{W}^{2})) were built for ({G}_{1}) and, ({G}_{2})with CT features as column vectors and pediatric patients as row vectors.

Data matrix of ({G}_{1}):

$${W}^{1}=left[begin{array}{cccc}{1}& {1}& text{…}& {1} {2}& {0}& text{…}& {1} text{…}& text{…}& text{…}& text{…} {36}& {1}& text{…}& {0}end{array}right]$$

Data matrix of ({G}_{2}):

$${W}^{2}=left[begin{array}{cccc}{37}& {0}& text{…}& {1} {51}& {1}& text{…}& {0} text{…}& text{…}& text{…}& text{…} {121}& {0}& text{…}& {1}end{array}right]$$

(2) The mean distributions of the columns of the matrices O1 and O2 are the following:

$$overline{{{x}_{j}}^{1}}=frac{1}{36}{sum }_{i=1}^{36}{{X}_{ij} }^{1} begin{array}{c}j=mathrm{1,2}cdots ,6end{array}$$

$$overline{{{x}_{j}}^{2}}=frac{1}{85}{sum }_{i=1}^{85}{{X}_{ij} }^{2} begin{array}{c}j=mathrm{1,2}cdots ,6end{array}$$

(3) Coefficients ({this}) were calculated using the differential calculus method.

(4) The discriminant function is defined as follows:

$${G}_{i}={c}_{1}{x}_{1}+{c}_{2}{x}_{2}+{c}_{3}{x} _{3}+{c}_{4}{x}_{4}+{c}_{5}{x}_{5}+{c}_{6}{x}_{6}$ $

(5) The discriminant values ​​represented by ({G}_{1}) and ({G}_{2}) have been calculated.

$$overline{{G}_{1}}={sum }_{i=1}^{36}{c}_{i}overline{{x}_{i}^{1}} $$

$$overline{{G}_{2}}={sum }_{i=1}^{85}{c}_{i}overline{{x}_{i}^{2}} $$

(6) The value of the Fisher discrimination function at the centroids was obtained as follows:

$${G}_{0}=frac{36overline{{G}_{1}}+85overline{{G}_{2} }}{121}$$

(7) The above calculation was performed using SPSS software with the following discriminant rule: If (overline{{G}_{1}})>({G}_{0})the sample of (G) belongs to ({G}_{1}), which means that the sample belongs to the RMS group. Otherwise, the sample belongs to ({G}_{2}); that is, the sample belongs to the non-RMS group.

(8) The resulting discriminant functions for classification were also calculated using SPSS.

$${G}_{1}={c}_{11}{x}_{1}+{c}_{21}{x}_{2}+{c}_{31}{x} _{3}+{c}_{41}{x}_{4}+{c}_{51}{x}_{5}+{c}_{61}{x}_{6}( mathrm{RMS group})$$

$${G}_{2}={c}_{12}{x}_{1}+{c}_{22}{x}_{2}+{c}_{32}{x} _{3}+{c}_{42}{x}_{4}+{c}_{52}{x}_{5}+{c}_{62}{x}_{6} ( mathrm{no}-mathrm{RMS group})$$

The values ​​of ({G}_{1}) and ({G}_{2}) were calculated by substituting the CT features into the function. By comparing the ({G}_{1}) and ({G}_{2}) values, the subjects were classified according to the following principle: if ({G}_{1}) > ({G}_{2}), the subjects were classified in the RMS group; if ({G}_{1})({G}_{2})subjects were categorized into the non-RMS group.


({G}_{i}): disease population, (I=1, 2);

({W}^{i}): data matrix of ({G}_{i});

({this}): coefficients of the Fisher discriminant function, (i=0, 1, 2,cdots , 6);

({G}_{0}): values ​​of the Fisher discrimination function at the centroids;

({x}_{ij}): content of the (j) CT function in the (I) patient.

Model Validation

Cross-validation without one, in which each respective case is classified using all cases other than that case to derive the classification formula, was used to validate the accuracy of the model. In addition, ROC curves were used to validate the accuracy of the model, where an area under the ROC curve (AUC) between 0.5 and 0.7 represented a low diagnostic value, that between 0.7 and 0.9 represented an average diagnostic value, and that greater than 0.9 represented a high diagnostic value24.

Ethics statement

The study was conducted in accordance with the Declaration of Helsinki (as revised in 2013). The study was approved by the Institutional Ethics Committee of Children’s Hospital Affiliated with Chongqing Medical University and individual consent for this retrospective analysis was revoked.

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