Introductory Statistics for Laboratorians dealing with High Throughput Data sets Centers for Disease Control

Light Scattering Measurements for Detection of Precancerous Conditions of the Cervix. Objective: To examine the utility of in vivo elastic light scattering measurements to diagnose high grade squamous interepithelial lesions (HSIL) of the cervix. Methods: A newly developed fiber optic probe was used to measure light transport in the cervical epithelium of 36 patients undergoing standard colposcopy. Both unpolarized and polarized light transport were measured in the visible and near-infrared.

Groups: Three groups of women were identified using histopathology of the measured sites: – Group 1: Women with HSIL – Group 2: Women with low-grade lesions and – Group 3: Women with normal tissue Dependent Measures: Three spectroscopic parameters: – SP1 – SP2 – SP3

Analysis with ANOVA ANOVA: – Three groups – 1 outcome/dependent variable We have 3 Dependent Measures Could do 3 ANOVA’s But get 3 times the error rate ANOVA for SP1 Scores Group 1 HSIL Group 2 Low-Grade Lesions Group 3 Normal Tissue SP1 score

ANOVA for SP2 Scores Group 1 HSIL Group 2 Low-Grade Lesions Group 3 Normal Tissue SP2 score ANOVA for SP3 Scores Group 1 HSIL Group 2 Low-Grade Lesions Group 3 Normal Tissue SP3 score

MANOVA Provides one overall test for all the dependent measures combined Creates a linear combination of the dependent measures and tests the significance of the combined variable Treats the combined variable as a single dependent variable and does something similar to ANOVA on it.

MANOVA LAYOUT Group 1 HSIL Group 2 Low-Grade Lesions Group 2 Low-Grade Lesions SP1- Scores SP2- Scores SP3 - Scores SP1- Scores SP2- Scores SP3 - Scores SP1- Scores SP2- Scores SP3 - Scores X1X1 X2X2 X3X3 X1X1 X2X2 X3X3 X1X1 X2X2 X3X3 X1X1 X2X2 X3X3 X1X1 X2X2 X3X3 X1X1 X2X2 X3X3 X1X1 X2X2 X3X3 X1X1 X2X2 X3X3 X1X1 X2X2 X3X3 X1X1 X2X2 X3X3 X1X1 X2X2 X3X3 X1X1 X2X2 X3X3 X1X1 X2X2 X3X3 X1X1 X2X2 X3X3 X1X1 X2X2 X3X3 X1X1 X2X2 X3X3 X1X1 X2X2 X3X3 X1X1 X2X2 X3X3 X1X1 X2X2 X3X3 X1X1 X2X2 X3X3 X1X1 X2X2 X3X3 X1X1 X2X2 X3X3 X1X1 X2X2 X3X3 X1X1 X2X2 X3X3 X1X1 X2X2 X3X3 X1X1 X2X2 X3X3 X1X1 X2X2 X3X3 X1X1 X2X2 X3X3 X1X1 X2X2 X3X3 X1X1 X2X2 X3X3

Computation of Combined Variable W Group 1 HSIL Group 2 Low-Grade Lesions Group 2 Low-Grade Lesions SP1- Scores SP2- Scores SP3 - Scores W’s Gp 1SP1- Scores SP2- Scores SP3 - Scores W’s Gp 2SP1- Scores SP2- Scores SP3 - Scores W’s Gp 3 X1X1 X2X2 X3X3 WX1X1 X2X2 X3X3 WX1X1 X2X2 X3X3 W X1X1 X2X2 X3X3 WX1X1 X2X2 X3X3 WX1X1 X2X2 X3X3 W X1X1 X2X2 X3X3 WX1X1 X2X2 X3X3 WX1X1 X2X2 X3X3 W X1X1 X2X2 X3X3 WX1X1 X2X2 X3X3 WX1X1 X2X2 X3X3 W X1X1 X2X2 X3X3 WX1X1 X2X2 X3X3 WX1X1 X2X2 X3X3 W X1X1 X2X2 X3X3 WX1X1 X2X2 X3X3 WX1X1 X2X2 X3X3 W X1X1 X2X2 X3X3 WX1X1 X2X2 X3X3 WX1X1 X2X2 X3X3 W X1X1 X2X2 X3X3 WX1X1 X2X2 X3X3 WX1X1 X2X2 X3X3 W X1X1 X2X2 X3X3 WX1X1 X2X2 X3X3 WX1X1 X2X2 X3X3 W X1X1 X2X2 X3X3 WX1X1 X2X2 X3X3 WX1X1 X2X2 X3X3 W

MANOVA The MANOVA tests the significance of the difference between the means of the W’s Computer selects the b’s that make the difference between the means as large as possible If it still isn’t significant you know none of the X’s are doing anything ANOVA for SP1 Scores Group 1 HSIL Group 2 Low-Grade Lesions Group 3 Normal Tissue WWW WWW WWW WWW WWW WWW WWW WWW Mean W for Group 1 Mean W for Group 2 Mean W for Group 3

MANOVA Provides an overall test of the differences among the means of the groups on the combined variable. Provides tests of the significance of each of the b’s. If the b for a particular X variable is not significantly different from zero, that X variable isn’t doing anything Provides the equation for the optimal combination of the variables. May lead to the discovery of emergent variables. Provides post hoc tests comparing the means of the groups on each variable

Results and Conclusions Results: Three spectroscopic parameters are statistically different for HSIL compared with low- grade lesions and normal tissue. Conclusions. : Reflectance measurements of elastically scattered light show promise as a non- invasive, real-time method to discriminate HSIL from other abnormalities and normal tissue. These results compare favorably with those obtained by fluorescence alone and by fluorescence combined with light scattering.