bright
Azim
den
1
Bhamani
2
Heuvel ,
, Julie
Francis
1
Horrocks ,
3
Tekpetey ,
Marianne van
B. Anne
4
Croy
Funding provided by: CHRP
1Mathematics
2Biomedical
& Statistics, University of Guelph,
Sciences,
3
University of Guelph, Obstetrics and Gynecology, University of Western
4
Ontario, Anatomy & Cell Biology, Queen’s University
Introduction
• Diagnosis and treatment of infertility is
expensive, hence, methods for prediction of
successful treatment are needed.
• Van den Heuvel et al. have shown that a
particular type of human blood cell, a
bright
CD56
lymphocyte, exhibits enhanced in
vitro capacity to adhere to decidual vascular
endothelium from pregnant mice during the
peri-ovulatory period of the menstrual cycle.
Introduction cont’d.
• A subsequent study by Van den Heuvel et al.
examines data from 18 infertile women
undergoing hormonal stimulation for in vitro
fertilization treatment.
• The data came from the study performed by
physicians in the Reproductive
Endocrinology and Infertility Program at the
London Health Sciences Centre.
• 7 of the 18 women became pregnant as a
result of the treatment.
Materials and Methods
• 8.5 ml of blood was drawn from the
participants every other day.
• Blood lymphocyte cells were applied to 12
micron sections of mouse uterine tissue.
bright
• The number of adherent CD56
cells were
counted in 25 high power fields per slide by
two independent and blinded researchers.
Graphs of Adhesion Data
Graphs of Adhesion Data
Method #1: Mixed Linear Model
• The mixed linear model for the log adhesion
data is:
log(adhesionij) = β1 + β2*dayj + u1i + u2i*dayj + εij,
εij ~ N(0,
2
σ)
u1i ~ N(0, σ1
2)
u2i ~ N(0, σ2
2)
where i indexes individual (i=1,…,18), and j
indexes measurement day (j=-6,…,1).
Method #1: Mixed Linear Model
• The following SAS code uses the mixed
model to predict the means for each
measurement day:
proc mixed data=adlongIVF(where=(mday>=-6 & mday<=1))
method=ml;
class outcome id;
model ladhes=mday|outcome mday0P /s chisq htype=3
outpm=residsIVF;
repeated /type=cs subject=id ;
title "Final Model IVF";
run;
Results
Type 3 Tests of Fixed Effects
Num
Den
DF
DF
Chi-Square
F Value
mday
1
85
3.30
3.30
0.0694
0.0729
outcome
1
16
11.89
11.89
0.0006
0.0033
mday*outcome 1
85
3.53
3.53
Effect
mday0P
1
85
16.14
16.14
Pr > ChiSq Pr > F
0.0604 0.0639
<.0001
0.0001
Predicted Adhesion
Pr e d i c t e d
Me a n
1. 7
1. 6
1. 5
1. 4
1. 3
1. 2
1. 1
1. 0
0. 9
0. 8
- 6
- 5
- 4
- 3
- 2
md a y
o u t c o me 2
Pr e g
x No t
- 1
0
1
Method #2: Discriminant Analysis
• It is used to classify observations into two or
more groups.
• In our case, the two groups are pregnant and
non-pregnant.
Method #2: Discriminant Analysis
• The following SAS code uses discriminant
analysis to classify observations into the two
groups:
proc discrim data=imputeddata
list crossvalidate outstat=output
outcross=outpcrss;
class outcome;
id id;
var avget_6 avget_5 avget_4 avget_3 avget_2 avget_1 avget
avgtest1;
run;
Method #2: Discriminant Analysis
• The results are based on Fisher’s linear rule.
• The coefficients for the linear rule are
a1 =
-1
S ū
and
a
=
1
2
-1
S ū
2
and
c1 =
T
-½ū 1 a1
and c2 =
T
-½ū 2 a2
• An observation is classified into the pregnant
group if
(a2 – a1
T
)u
≤ (c1 – c2)
Results
• Here we focus on the cross-validation
results.
• This method removes each observation,
produces a discriminant rule without it, then
classifies the observation that was removed.
• As a result, we obtain an unbiased estimate
of the errors of misclassification
• The mixed linear model (shown earlier) is
used to impute any missing values in the
predictors.
Results
Number of Observations and Percent Classified into outcome
From
outcome
Preg
xNot
Total
Preg
5
71.43
2
28.57
7
100.00
xNot
1
9.09
10
90.91
11
100.00
Total
6
33.33
12
66.67
18
100.00
Priors
0.5
0.5
Conclusions
• The mixed linear model provides predictions
of log adhesion for a specific measurement
day.
• Discriminant analysis is used to classify an
observation into the pregnant or the nonpregnant group.
• Future work includes exploring other
imputation techniques and comparing the
results.
References
1. M Van Den Heuvel, J Horrocks, S Bashar, S Taylor, S Burke, K Hatta,
JE Lewis, A Croy. (Submitted). Menstrual Cycle Hormones Induce
Changes in Functional Interactions Between Lymphocytes and
Endothelial Cells
2. M Van Den Heuvel, J Horrocks, K Hatta, S Burke, S Bashar, ME Junkins,
SS Evans, BA Croy, FR Tekpetey. (Submitted). Peri-ovulatory Increases
in Tissue Homing Potential of Circulating CD56bright Cells Are
Associated With Fertile Menstrual Cycles
®
OnlineDoc ,
3. SAS
Institute Inc.
Version 8. February 2000. Copyright ©2000, SAS
4. Carter, E.M. (2004). Methods for analyzing Multivariate Data,
University of Guelph Campus Bookstore.
Questions?