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Statistical exploration of data from Dr. Natasha Olby's Chiari study

Jason A. Osborne, Dept. of Statistics, Feb 3, 2006
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To investigate potential associations between the list of
factors below and the presence/absence of neurological (NEURO)
signs and syringohydromylia (SHM) an exploratory analysis of
the data was undertaken.  For factors that are ordinal (O),
contingency tables were created and chisquare tests for
association were conducted.  For factors that are continuous(C),
t-tests were carried out to test the equality of the mean
of the factor across the presence/absence of NEURO or across
SHM.  The reason for the approach of taking factors as 
responses is the case-control aspect of the study design.
Dogs were recruited on the basis of their disease status,
as opposed to the case where dogs are followed with random
disease outcomes.  In case it can be argued that the
study was prospective and SHM and NEURO can be viewed as
random binary responses, some logistic regression models
were considered. 

Association between disease severities (GRADES) and
categorical factors were investigated using chisquare
tests.  Associations between severity and continuous 
factors were investigated using spearman correlation
coefficients.


Factors:
Age (O) 
Sex (O)
Herniation (C)
Compression (O)
Kinking (O)
FMSize (C)
Hyrocephalus (O)
Volume_ofCDFossa (C)
Ratio_ofCD/Total (C)

PV FM V (C)
PV FM D (C)
PV Disc V (C)
PV Disc D (C)

This exploratory approach indicating the following potentially
significant results:

Among dogs with NEURO signs, a chisquare test of no assocation 
between NEURO grade and compression yields a pvalue of 0.0406.
(The dog with the highest NEURO grade (4) also had the highest
compression (3).)


T-tests:
The mean VOLUME OF CD FOSSA for dogs,
w presence of NEURO signs: mean=12.3, sd=1.6, n=13
w absence of NEURO signs:  mean=13.2, sd=1.2, n=45
(pvalue=0.0344 w/ pooled variance, .093 with unequal variances)

F-tests:
RATIO OF CD/TOTAL  more variable 
in presence of NEURO signs: mean=13.6, sd=1.6, n=13
in absence of NEURO signs:  mean=14.5, sd=1.0, n=45
(pvalue=0.0931 for equality of means (unequal variances))
(pvalue=0.0065 for a test of equality of variances) 

in presence of SHM: mean=13.7, sd=1.6, n=16
in absence of SHM:  mean=14.2, sd=0.9, n=25
(pvalue=0.0241 for a test of equality of variances) 

FM_Size more variable
w presence of SHM: mean=1.62, sd=0.19, n=15
w absence of SHM:  mean=1.62, sd=0.12, n=25
(pvalue=0.0406 for a test of equality of variances) 

CSF Flow rates:
PV FM V more variable 
in presence of NEURO signs (mean=.65,s=.32,n=13)
in absence of NEURO signs  (mean=.63,s=.18,n=45)
(pvalue=0.0043 for a test of equality of variances) 

PV FM D higher and more variable 
in presence of SHM (mean=.49,s=.2,n=16)
in absence of SHM  (mean=.32,s=.1,n=20)
(pvalue=0.0054 for a test of equality of means) 
(pvalue=0.0114 for a test of equality of variances) 


PV Disc D lower and less variable
in presence of SHM (mean=.57,s=.14,n=12)
in absence of SHM  (mean=.72,s=.25,n=23)
(pvalue=0.0288 for a test of equality of means) 
(pvalue=0.0442 for a test of equality of variances) 

Alternatively, if the case-control aspect of the study
design is disregarded and presence/absence of disease
is taken to be a binary response, then a logistic
regression provides some evidence of association between
presence of NEURO signs and the factors 
VOLUME of CDFOSSA (p=0.0300,r2=0.076) and 
RATIO_CD/TOTAL (p=0.0204,0.0872).  
In both cases, the chance of having NEURO signs decreases
significantly as the factor increases.  A model with
both factors as predictors is not well-determined, 
probably due to their high collinearity (r=0.56) in
the dataset. 

Similarly, presence/absence of SHM is associated with 
and PV FM D (p=.0021, r2=0.19) and 
with PV Disc D (p=.0485, r2=0.087).  The model with
both of these CSF flow rates explains is highly significant
and explains half of the variability in presence/absence
of SHM (p<.0001, r2=0.48).

The only cases where there was evidence of associations
between severities (GRADES) and continuous factors were

NEURO_GRADE and volume of CD fossa (r=-0.25, p=0.06)
NEURO_GRADE and Ratio of CD/Total (r=-0.22, p=0.09)
SHM_GRADE and volume of PV Disc D(r=-0.35, p=0.0122)