Employing Multivariate Statistics and Latent Variable Models to Identify and Quantify Complex Relationships in Typical Compression Studies

The effect of storage condition (% RH) on flufenamic acid:nicotinamide (FFA:NIC) cocrystal compressibility, compactibility, and tabletability profiles was not observed after visual evaluation or linear regression analysis. However, multivariate statistical analysis showed that storage condition had a significant effect on each compressional profile. Shapiro and Heckel equations were used to determine the compression parameters: porosity, Shapiro’s compression parameter ( f ), densification factor (Da), plastic yield pressure (YPpl), and elastic yield pressure (YPel). Latent variable models such as exploratory factor analysis, principal component analysis, and principal component regression were employed to decode complex hidden main, interaction, and quadratic effects of % RH and the compression parameters on FFA:NIC tablet mechanical strength (TMS). Statistically significant correlations between f and Da, f and YPpl, and Da and YPel supported the idea that both rearrangement and fragmentation, and plastic deformation are important to FFA:NIC TMS . To the authors knowledge, this is the first time that simultaneously operating dual mechanisms of fragmentation and plastic deformation in low and midrange compression, and midrange plastic deformation have been identified and reported. A quantitative PCR model showed that f , Da, and YPel had statistically significant main effects along with a significant antagonist storage condition–porosity “conditional interaction effect”. f exhibited a 2.35 times greater impact on TMS compared to Da . The model root-mean-square error at calibration and prediction stages were 0.04 MPa and 0.08 MPa, respectively. The R 2 values at the calibration stage and at the prediction stage were 0.9005 and 0.7539, respectively. This research demonstrated the need for caution when interpreting the results of bivariate compression data because complex latent inter-relationships may be hidden from visual assessment and linear regression analysis, and result in false data interpretation as illustrated in this report.