Consensus building and measurement

Five authors(JJM, KHS, KML, and MSP, who are orthopedic surgeons with 2, 16, 17, and 19 years of experience, respectively, and S-SK, a statistician) agreed on the indices to be measured in the radiographs. Previous studies were reviewed [7, 11–15], and one of the authors(JJM) pooled seven indices relevant to the PV and hallux valgus(HV) that have been established with convergent and discriminant validities and intra, inter-rater reliabilities [12]: naviculocuboid(NC) overlap, AP talonavicular(TN) coverage angle, AP and lateral talo-1^stMT angles, AP talo-2^ndMT angles, HV angle, and intermetatarsal angle. In our study, NC overlap and AP TN coverage angle were excluded due to incomplete ossification of the navicular bones in younger patients, making evaluation of indices that include the navicular bone difficult. We have also noted that not only does PV progress over time, but HV also progressed in CP patients, which may disturb the talo-1^stMT angle. Therefore, we introduced the talo-2^ndMT angle as a main index in our evaluation.

Consequently, the AP and lateral talo-1^stMT, AP talo-2^ndMT, and HV angles were the four indices chosen. We used AP and lateral talo-1^stMT angles and AP talo-2^ndMT angle as surrogate indices for the progression of PV and the HV angle as surrogate for the progression of HV.

The AP talo-1^st and talo-2^ndMT angles are the angles between a line bisecting longitudinal axis of first and second metatarsal bones, respectively, and the line bisecting the longitudinal axis of the talus on standing AP plain foot radiograph [12] (Fig. 2). The lateral talo-1^stMT angle is the angle between the line bisecting the longitudinal axis of the first metatarsal bone and the line bisecting the longitudinal axis of the talus in standing lateral foot radiograph [12] (Fig. 3). The HV angle is the angle between longitudinal axis of the first proximal phalanx and first metatarsus [12, 16] (Fig. 2).

a The anteroposterior talo-first metatarsal angle is the angle between the line bisecting the longitudinal axis of the first metatarsal bone and the line bisecting the longitudinal axis of the talus on standing anteroposterior plain foot radiograph. b The anteroposterior talo-second metatarsal angle is the angle between the line bisecting the longitudinal axis of the second metatarsal bone and the line bisecting the longitudinal axis of the talus on standing anteroposterior plain foot radiograph. c The hallux valgus angle is the angle between the longitudinal axis of the first proximal phalanx and the longitudinal axis of the first metatarsus

The lateral talo-first metatarsal angle is the angle between the line bisecting the longitudinal axis of the first metatarsal bone and the line bisecting the longitudinal axis of the talus on the standing lateral plain foot radiograph

After consensus building, reliability test was conducted before primary measurements. Sample size estimation showed that a minimum of 36 feet (18 left and 18 right) radiographs should be assessed. Three authors(JJM, KHS, and MSP) with 2, 16, and 19 years of orthopedic experience determined the interobserver reliability using intraclass correlation coefficients(ICCs), and independently measured the radiographs in a blinded fashion. Four weeks after the primary measurements, intra-observer reliability was assessed by one of the authors(JJM) who repeated the radiographic measurements.

Following reliability testing, two authors(JJM and MSP) measured indices in all the radiographs. Patient’s age, sex, GMFCS level, involvement(unilateral/bilateral), history of tendo-Achilles lengthening(TAL) or gastrocnemius recession(Strayer), laterality of the feet, and the date the radiographs were also included.