Evaluation of orthodontic relapse using the cubic spline function.

A sample of 72 orthodontically treated patients was reexamined many years out of retention. They had been treated either by the extraction of four premolars or without extractions. The average number of years between the end of treatment and the taking of follow-up records was 20, with a range of 12 to 35 years. Some conventional measurements were studied such as intertooth widths, arch perimeter, and incisor irregularity. In addition, a new method for comparison of arch form at different stages of treatment, which uses the cubic spline function, was used. Cases were grouped into extraction and nonextraction, and statistics were used to test the differences between the two groups. Correlations between the spline variables and conventional variables were computed, and multiple regression analysis was carried out using the spline variables as dependent variables. Some treatment and relapse changes were independent of whether the case was treated with extractions or not, whereas other trends were unique to one treatment group. The correlation analysis revealed strong relationships between variables that measured changes during the same treatment stage. There were also moderate correlations between some of the spline variables and the traditional measurements. Multiple regression analysis was used to account for changes in some spline variables, however, the usefulness of the model as a predictor is limited.