Document ID: EPA-HQ-ORD-2015-0588-0019
Agency: epa
Document Type: Supporting & Related Material
Title: 
Posted Date: 2015-12-15T05:00Z

The  primary  objective  of  the  data analysis is to estimate the overall (or `mean') level of bite protection and associated 95% confidence  interval  for  different  `treatments'  (i.e.,  different  combinations  of  fabric  type, number of washes, and mosquito species).  The statistical validity of the design and analysis after reviewing the statistical design, analysis methods and submitted SAS code are given below: 
The numbers of blood-fed and total female mosquitoes found with treated and control fabric for each subject was analyzed as binomial distributed data in a generalized linear model using SAS GENMOD procedure using a log link.  Use of the log link makes it possible to obtain an estimate and confidence interval  for  the  ratio  of  the  treatment  and  control  bite-through  rates. 
However, the subject term was treated as a fixed effect in the GENMOD model to adjust for subject-subject differences. If this treatment of fixed subjects is a valid assumption then the presented analysis is appropriate. 
However, if the fixed subject treatment is not appropriate and the subjects used in this study should be treated as a random effect then the SAS procedure GLIMMIX is a better approach over GENMOD to accommodate mixed effects (both fixed and random effect).   

Please see the SAS output below: (SAS GLIMMIX when treating subjects as RANDOM)

      Examination of T and GLiM CIs with 8 Subjects  - Using SAS GLIMMIX
             Subject-Subject Background Variation (Logit SD) = 0.3
              Subject-Subject Protection Variation (Logit SD) = 0
                        NrSims = 5000, Seed = 98135183

                                                             Overall
Bkg
Rate,%
                                                                   True
% Prot
                                                                 Mean
% Prot
T
                                                                HalfWidth
T CI
                                                                 Coverage
T CI
                                                              Mean
% Prot
GLiM
                                                             HalfWidth
GLiM CI
                                                              Coverage
GLiM CI
                                                                             10
                                                                             70
                                                                           68.3
                                                                           12.3
                                                                             95
                                                                           69.6
                                                                           14.0
                                                                             99

                                                                             85
                                                                           84.2
                                                                            8.2
                                                                             95
                                                                           84.7
                                                                            8.7
                                                                             98

                                                                             95
                                                                           94.8
                                                                            4.3
                                                                             94
                                                                           94.9
                                                                            4.6
                                                                             99

                                                                             98
                                                                           97.9
                                                                            4.2
                                                                             93
                                                                           97.9
                                                                            3.3
                                                                             98

                                                             Overall
Bkg
Rate,%
                                                                   True
% Prot
                                                                 Mean
% Prot
T
                                                                HalfWidth
T CI
                                                                 Coverage
T CI
                                                              Mean
% Prot
GLiM
                                                             HalfWidth
GLiM CI
                                                              Coverage
GLiM CI
                                                                             25
                                                                             70
                                                                           69.5
                                                                            7.0
                                                                             94
                                                                           69.8
                                                                            9.6
                                                                             99

                                                                             85
                                                                           84.7
                                                                            4.8
                                                                             95
                                                                           84.8
                                                                            5.8
                                                                             99

                                                                             95
                                                                           94.9
                                                                            2.7
                                                                             94
                                                                           94.9
                                                                            2.9
                                                                             99

                                                                             98
                                                                           98.0
                                                                            1.6
                                                                             94
                                                                           98.0
                                                                            1.8
                                                                             98

                                                             Overall
Bkg
Rate,%
                                                                   True
% Prot
                                                                 Mean
% Prot
T
                                                                HalfWidth
T CI
                                                                 Coverage
T CI
                                                              Mean
% Prot
GLiM
                                                             HalfWidth
GLiM CI
                                                              Coverage
GLiM CI
                                                                             50
                                                                             70
                                                                           69.9
                                                                            4.5
                                                                             95
                                                                           70.0
                                                                            6.3
                                                                            100

                                                                             85
                                                                           84.9
                                                                            3.2
                                                                             95
                                                                           84.9
                                                                            3.8
                                                                             99

                                                                             95
                                                                           95.0
                                                                            1.8
                                                                             95
                                                                           95.0
                                                                            1.9
                                                                             98

                                                                             98
                                                                           98.0
                                                                            1.2
                                                                             94
                                                                           98.0
                                                                            1.2
                                                                             98

                                                             Overall
Bkg
Rate,%
                                                                   True
% Prot
                                                                 Mean
% Prot
T
                                                                HalfWidth
T CI
                                                                 Coverage
T CI
                                                              Mean
% Prot
GLiM
                                                             HalfWidth
GLiM CI
                                                              Coverage
GLiM CI
                                                                             75
                                                                             70
                                                                           69.9
                                                                            3.4
                                                                             96
                                                                           70.0
                                                                            4.1
                                                                             99

                                                                             85
                                                                           85.0
                                                                            2.5
                                                                             95
                                                                           85.0
                                                                            2.7
                                                                             98

                                                                             95
                                                                           95.0
                                                                            1.5
                                                                             95
                                                                           95.0
                                                                            1.4
                                                                             98

                                                                             98
                                                                           98.0
                                                                            0.9
                                                                             94
                                                                           98.0
                                                                            0.9
                                                                             97