A critical evaluation of the statistical methods used in heroin comparison

Most powder samples collected from crime scenes or from the streets are illicit drugs such as heroin, which are difficult to identify visually. The technique of using gas chromatography (GC) and mass spectrometry (MS) along with a range of chemometric methods to identify, quantify, and compare trace compounds in heroin samples seizure was studied. Following GC-MS analysis (n=25) of street samples of heroin seized by Cambridgeshire Constabulary, assumptions related to the validity of the statistical methods were tested and applied to profiling the heroin samples. Even though much work has been done on heroin profiling, evaluating the validity of statistical analyses applied to heroin to link samples by chemical profiling has not been reported.

GC-MS confirmatory test became necessary following the low reliability of presumptive colour tests based on Mandelin and Marquis Reagents. The underlying assumptions for the following chemometric methods: parametric methods such as normality test, Pearson Correlation Coefficient (PCC), t-test (Test statistic) and Euclidean and Manhattan distance methods, unsupervised techniques (principal component analysis (PCA), hierarchical clustering analysis (HCA), and K-means clustering, and supervised techniques (LDA and PSL-DA) were tested.

The results on tests for normality by the Shapiro-Wilk (S-W) test show that the concentration of Papaverine (PAP), Caffeine and Diamorphine (DAM) in the first batch of heroin samples are normally distributed whilst Acetylcodeine (AC) in second batch only DAM was normally distributed, others fail the normality test. As the underlying assumption for normal distribution is not satisfied for some drugs the Euclidean, Manhattan distance methods and Square Cosine Function cannot be applied for the pairs. In PCC, the component pairs are as follows: DAM/PAP (0.895), AC/PAP (0.845), AC/DAM (0.946), Caffeine/PAP (-0.095), Caffeine/DAM (-0.415), and Caffeine/AC (-0.427), while the significance of the correlation based on t-test follows the order AC/DAM > DAM/PAP > AC/PAP.

The lack of correlation for some pairs is due to deviation from normal distribution as confirmed by S-W test with a p-value less than critical value of 0.05. Due to outliers the heroin samples used in this research do not meet the assumptions surrounding distance methods application. Thus, the underlying assumptions make PCA and HCA appropriate.