The SINPHONI-2 trial is an open-label randomized trial (UMIN-CTR: UMIN000002730) that followed the Guidelines for Good Clinical Practice and adhered to the principles of the Declaration of Helsinki (2002) of the World Medical Association. The study protocol was approved by the Tohoku University Hospital Ethics Committee and the Institutional Ethics Committee of each participating institution. Written informed consent was obtained from all patients or their representatives. Details of the patients, definitions of iNPH, protocol compliance, and data collection (including data acquisition and management) have been described previously (16). The study protocol is described in the Supplementary material file. Briefly, 102 candidates diagnosed with possible iNPH according to the second edition of the Japanese iNPH guidelines (17) were recruited from 20 Japanese centers between March 2010 and October 2011. The inclusion criteria were as follows: age 60–85 years at the time of entry; presence of one or more NPH symptoms including gait disturbance, cognitive impairment, and urinary disturbance, assessed using the iNPH grading scale within 3 months before consent provision; ventriculomegaly with an Evans index >0.3; concurrent narrow sulci at high convexity; and an enlarged Sylvian fissure observed on computed tomography or magnetic resonance imaging. The exclusion criteria were as follows: the presence of secondary or congenital hydrocephalus or aqueductal stenosis, CSF pressure ≥20 cm H₂O, complications of severe disuse muscle atrophy, and psychiatric disorders or other neurological diseases. According to these criteria, 93 patients were registered and randomly assigned to the immediate surgery (IS) or 3-month postponed surgery (PS) groups (Figure 1A). Randomization (1:1 ratio) was performed using a permuted block design with a block size of four or six within each clinical center according to a randomized code generated by the trial statistician. All patients in the IS group underwent lumboperitoneal shunt surgery using the Codman-Hakim programmable valve with the SiphonGuard (Codman Neuro-DePuy Synthes, Raynham, MA, USA). In the PS group, all patients underwent lumboperitoneal shunt surgery 3 months after registration. During the 3 months, patients in the PS group were instructed to perform physical tasks.

In SINPHONI-2 (Study of Idiopathic Normal Pressure Hydrocephalus on Neurological Improvement-second trial), gait performance was assessed in seconds using a 3-m timed Up-and-Go (TUG) test (18), which measures the time to complete the following six components: standing up from a chair, walking 3 m, turning around 180°, walking back to the chair, turning around 180° again, and sitting back down on the chair. All tests were performed twice. Because patients with severe conditions occasionally experienced interruptions in the second performance, data from the first performance were used. Frontal lobe function was assessed using the screening test developed by Dubois et al. (10). It consists of six tasks assessing the following executive functions: (1) conceptualization (similarities), (2) verbal fluency (mental flexibility), (3) motor programming (Luria’s fist-edge-palm (FEP) sequence (19)), (4) conflicting instructions (go-no-go test), (5) inhibitory control, and (6) environmental autonomy (prehension behavior). A modification was made to the “verbal fluency” task: the prompt “Say as many words as you can beginning with the letter ‘S’” was changed to “Say as many words as you can beginning with the letter ‘A’” because words starting with “S” are uncommon in Japanese (17).

Among the 102 potential patients, nine were eliminated owing to deviations from the inclusion criteria. Among the 93 patients included in this study, 83 completed the 12-month follow-up (45 in the IS group and 38 in the PS group). In the PS group, data obtained 3 months after registration were considered as the preoperative data. To examine the association between gait, assessed by TUG, and frontal lobe function, assessed by FAB, we selected patients with available preoperative and 12-month postoperative TUG and FAB data. In the IS group, three and seven patients were excluded due to the unavailability of preoperative and 12-month postoperative data, respectively. In the PS group, one and three patients were excluded due to the unavailability of preoperative and 12 months postoperative data, respectively. Consequently, 69 patients were enrolled in this study, 35 in the IS group and 34 in the PS group. Among them, one participant lacked 3-month postoperative data, and four lacked 6-month postoperative data (Figure 1B).

Among the SINPHONI-2 variables, age, sex, years of education, TUG test time (s), modified Rankin scale (mRS) scores (0–6), iNPH grading scale (0–4), and FAB total score were evaluated. The age and TUG test time were considered continuous variables. The FAB total score was considered a continuous variable based on the original work (10). The FAB task scores, as well as the mRS and iNPH grading scales, were treated as ordinal variables. These data were assessed at four different time points (preoperatively and at 3, 6, and 12 months postoperatively). In this dataset, there were one missing data point at 3 months and four at 6 months. We included these data for statistical analyses without imputation. All statistical analyses were performed using R software (20). Statistical significance was set at p < 0.05. For continuous variables, the mean and standard error were compared using parametric t-tests, following confirmation of normality with the Q-Q plots. Categorical data were analyzed using Fisher’s exact test because some categorical data had small sample sizes. Continuous data were plotted with means and standard errors using the “gggplot2” package (21). Categorical data, including ordinal data, were plotted as stacked bar plots. A multivariable linear model was applied with TUG test times as the dependent variable and FAB total scores as the independent variable, adjusting for age and years of education (both continuous covariates).

In contrast, FAB task scores were considered ordinal. Smoothing of the ordinal variables of the tasks was implemented using the “ordSmooth” function in the “ordPens” package (22), applying the smoothing penalty for adjacent dummy coefficients. The smoothed data were then analyzed with the GAM, using the “gam” function in the “mgcv” R package (14). Because the main interest was the relationship between TUG time and each FAB task, the GAM was applied to the respective tasks with age and years of education as covariates. GAM has the advantage of making inferences about associations between continuous outcomes and ordinal independent variables without placing parametric restrictions on the association (14). The p-values for ordinal data were reported only in cases of second-order penalties (13). The effective degrees of freedom (EDF) estimated from the GAM were used as proxies for the degree of nonlinearity in the relationships between the dependent and independent variables. An EDF of one is equivalent to a linear relationship. An EDF > 1 and ≤2 indicates a weak nonlinear relationship, while an EDF > 2 indicates a highly nonlinear relationship (23). Missing data, especially regarding years of education, were excluded from the multivariable linear regression and GAM.

Demographic data are listed in Table 1. In the IS group, data were obtained at registration and at 3, 6, and 12 months postoperatively. Data at the time of registration were considered preoperative data. In the PS group, preoperative data were collected 3 months after registration, just before the shunt surgery. The PS group showed lower mRS scores 3 months after registration compared to those at registration, but the difference was not statistically significant. Postoperative data were obtained in the IS group. Except for sex, preoperative differences in variables between the IS and PS groups were not statistically significant. Because our interest was focused on shunt effectiveness for possible iNPH, data from the IS and PS groups were combined for statistical analysis. Shunt responders (improvement by one or more points on the iNPH grading scale) were observed in 60.9, 53.6, and 55.1% of the cases, respectively, in gait, cognition, and urination. Sequential changes in the frequency of grades of general activity and NPH symptoms, assessed using the mRS and iNPH grading scales, respectively, are shown in Figure 2. Fisher’s exact test revealed that all parameters showed significant improvements in the postoperative state compared to the preoperative state. In this study, major co-morbidities were hypertension, hyperlipidemia, and diabetes. Their frequencies were 59.4, 33.3 and 26.01%, respectively. Correlation coefficients (r) with improvement on mRS at 1 year after surgery were 0.42, 0.08, and −0.03, respectively. For calculating the sample size of TUG time and FAB total, a power of 90% and a 2-sided alpha level of 0.05 were set for the analysis. Then, 55 patients were necessary for the TUG time, but 148 patients for the FAB total.

A statistically significant decrease was observed in TUG at 3 months postoperatively, and its improvement continued at 6 and 12 months (Figure 3A). In contrast, the total FAB score increased after surgery; however, statistical significance was observed only at 6 months (Figure 3B). Multivariable linear regression analysis (Figure 3C) was performed with TUG test time as the dependent variable and FAB total score, with covariates of age and years of education as independent variables, all of which were continuous. No association was observed between TUG time and preoperative FAB total score. In contrast, statistically significant associations between them were observed at 3, 6, and 12 months after surgery.

Sequential changes in the frequency of the respective FAB task scores are shown in Figures 4A–F. Preoperative–postoperative comparison using Fisher’s exact test revealed that the “conceptualization,” “inhibitory control,” and “environmental autonomy” tasks (A, E, F) showed no statistical significance at 3, 6, and 12 months postoperatively. Conversely, the “verbal fluency” and “motor programming” tasks (B, C) showed statistically significant differences at 6 and 12 months postoperatively. The “conflicting instructions” task (D) showed statistical significance only at 12 months postoperatively. Only a few patients scored the highest score (3 points) on the “conceptualization” task (A) both preoperatively and postoperatively. This finding suggests that this procedure is difficult for elderly patients to perform. In addition, relatively few patients scored high scores (2 or 3 points) on the “inhibitory control” task (E). In contrast, most of the patients scored the highest for the “environmental autonomy” task (F) both preoperatively and postoperatively. This finding suggests that this procedure is easy for elderly patients to perform.

The association between TUG time and FAB task scores was examined for the six FAB tasks using the GAM. The sequential changes in the mean and standard errors are shown in Figures 5A–C, 6D–F. The y-axis shows the fitted coefficients of the respective task scores with the TUG time, and the x-axis shows the FAB scores. Because TUG time is inversely related to gait speed, lower coefficients for higher scores indicate a positive relationship between gait and frontal lobe function. The GAM results for this association are shown in Table 2. In the model, the responder was the TUG test time (continuous variable), and the predictors were the FAB task scores (ordinal variable), age (continuous variable), and years of education (continuous variable). Preoperatively, no statistically significant association was observed between the TUG test time and the six FAB task scores. At 3 months postoperatively, a statistically significant association was observed between both “motor programming” (C) and “conflicting instructions” (D) with gait. At 6 months postoperatively, a significant association was observed between “environmental autonomy” (F) and the TUG time, in addition to the previous two tasks. Twelve months postoperatively, “verbal fluency” (B) was statistically significant in addition to the previous three tasks. Therefore, a significant association was observed between both “motor programming” (C) and “conflicting instructions” (D) and TUG time at 3, 6, and 12 months postoperatively. The “environmental autonomy” (F) was statistically significant at 6 and 12 months postoperatively. The “verbal fluency” (B) was statistically significant only at 12 months postoperatively. Among the continuous predictors, only age at 3 months was significantly associated with the TUG time.

Table 3 was extracted from Table 2 to summarize the sequential changes in the statistical significance of the ordinal predictors (A, B, C, D, E, and F). Statistically significant associations (gray cells) between the FAB tasks and TUG test time gradually increased after surgery. There was no significant association with the “conceptualization” (A) and “inhibitory control” (E) tasks. Although most of the EDFs for ordinal (non-linear) predictors were 1 or close to 1, three analyses (conflicting instructions at 3 months and environmental autonomy at 3 and 6 months) showed an EDF > 2, which indicated nonlinear relationships between them.