A total of 156 patients with CA were included in the study. There were 84 cases (53.8%) in the recurrence group and 72 cases (46.2%) in the non-recurrence group. T-test and Chi-square test showed that gender, age, marital status, education, smoking and drinking had no effect on the recurrence of CA (P > 0.05), stay up late increases the recurrence of CA (P < 0.05, Table 1).

Sexual partner infection with HPV, condom use, number of warts, comorbid genitourinary disorders and other diseases with HPV infection had an effect on the recurrence of CA (P < 0.05). There were no significant differences between the two groups in the position of the warts of CA and the HPV typing (P ≥ 0.05, Table 2).

In summary, the univariate analysis showed that HPV type and location of age, sex, marriage, education, smoking, alcoholism and warts were not clinical factors associated with CA recurrence. Stay up late, sexual partners with HPV infection, condom use, genitourinary disorders, other diseases of HPV infection, and the number of warts were clinical factors associated with CA recurrence.

Univariate logistic regression analysis showed that sexual partners with HPV infection, the number of warts, the use of condoms, genitourinary diseases and other diseases with HPV infection were the risk factors of CA recurrence (P < 0.05, Table 3).

Multivariate logistic regression analysis showed that the HPV infection status of sexual partners (OR = 4.848), the number of CA warts in patients (OR = 1.212), condom use (OR = 0.166), and concomitant urogenital disorders (OR = 3.179) were the independent influencing factors for CA recurrence (P < 0.05, Table 4). It could be assumed that when a CA patient had a large number of warts, accompanied by genitourinary diseases, and sexual partners with HPV infection, the possibility of CA recurrence was greater. The correct use of condoms could prevent the recurrence of CA.

The results of multivariate logistic regression analysis showed that sexual partners with HPV infection, the number of warts and condom use can be used as independent influencing factors in predicting CA recurrence. According to the results of multivariate logistic regression analysis, the following predictive model could be derived. The equation is expressed as follows:

$$}\left( P \right)\, = \, - .0\, + \,.*}\, + \,\,0.*}\, + \,\left( .*}} \right)\, + \,\,.*}$$

where Logit (P) was equal to ln (p/(1-p)), and P was the probability of recurrence. P = elogit (P)/(1 + elogit (P)), e represented the base of natural logarithm, and the value was about 2.718. Significance of assignment: the entry value of sexual partner with HPV infection was 1, and the entry value of sexual partner without HPV infection was 0; The input value was taken as 1 when the condom was used correctly, and 0 when the condom was not used correctly; The substitution value for patients with genitourinary diseases was 1, and the substitution value for patients without genitourinary diseases was 0.

According to the results of multivariate logistic regression analysis, the ROC curve was drawn for the recurrence probability of each CA patient (Fig. 1), and the AUC was 0.867 (95% CI 0.812–0.923). According to the maximum value of Youden index, the corresponding specificity was 73.6% and the sensitivity was 84.5%. Include the prediction equation Logit (P) = 0.437.

The ROC curve developed for CA recurrence prediction model. The AUC of prediction model was 0.867 (95% CI: 0.812–0.923)

According to the prediction model equation and Logit (P) value, the following discriminant equation could be obtained:

$$}\, = \, - .0\, + \,.*}\, + \,\,0.*}\, + \,\,\left( .*}} \right)\, + \,\,.*}\,\, + \,\,0.$$

The significance of clinical variable assignment was the same as above. F was the criterion. The calculated value of F could determine whether CA patients have recurrence. When f value ≥ 0, it was judged as recurrence; when f < 0, it was judged as non-recurrence.

The internal validation was performed with stratified sampling, about 50% of the original cases were included in the above discriminant equation for verification. The results showed that the sensitivity was 80.5% and the specificity was 75.0% (Table 5).

From June 2020 to May 2021, 53 CA patients who met the inclusion criteria at the department of dermatological, the First Affiliated Hospital of Harbin Medical University were included in the above discriminant for verification, including 24 cases in the non-recurrence group and 29 cases in the recurrence group, the sensitivity was 75.9% and the specificity was 70.5% (Table 6).

According to the above results, this model had high stability and predictive value, and the clinical application was simpler. Therefore, this model could be used to predict the probability of CA recurrence in other independent samples.