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7252700_Statistics_and_Probability_revised_assignment[1] correction2.ppt
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Microchimerism: a blessing in

disguise?

Cell transfer happens through the umbilical cord during gestation

period in both ways. Some of the transferred cells survive in the

host body, and...
Microchimerism: a blessing in

disguise?

Cell transfer happens through the umbilical cord during gestation

period in both ways. Some of the transferred cells survive in the

host body, and proliferate. This is called Microchimerism. When fetal

cells survive in mothers body, its fetal microchimereism.

Microchimerism has been shown to provide protective effect in

Breast Cancer in a previous paper:

Gadi VK, Malone KE, Guthrie KA, Porter PL, Nelson JL (2008) Case-Control Study of

Fetal Microchimerism and Breast Cancer. PLoS ONE 3(3): e1706.

doi:10.1371/journal.pone.0001706.

Since this most probably to happen through some secondary

immunological mechanism, and Breast Cancer susceptibility and

surface antigens vary with genotype, we can do this study for a

specific ethnic group, for example Asians.

This study is of course practicable but will involve a lot of effort for

data collection.

The scientific hypothesis

The null hypothesis we have here is that level of fetal

microchimerism (FMc) has no effect on being affected

with Breast Cancer, i.e. FMc does not provide a

protective role in Breast Cancer.

When a woman bears a male child, some cells with XYchromosome survive in FMc in the mothers body. We

can quantify the amount of FMc by amount of fetal cells,

which is measured by the relative quantity of Ychromosome specific marker in the sample, and will be

measured by Quantitiative PCR.

Experimental design - 1

Analysis will be done on blood samples obtained from

parous Asian women who have borne at least one

male child.

Samples can be collected from Breast Cancer patients

in the corresponding ward of a public health center, as

well as maternity wards.

Ethical permission has to be obtained from the

corresponding authority, each patient has to be filled

up with a pre-tested questionnaire and their identity

must be kept confidential.

Sterilized environment and instruments, and

competent work-force has to be used for safety

reasons.

Data measurement and

recording

Breast cancer affected status is a 0/1 variable.

Level of FMc can be obtained from checking a Ychromosome specific marker, say DYS14 in the

blood sample.

Data has to be collected for some confounders

that include age, contraceptive use, age of onset

of menarche, male children borne, smoking status,

history of breastfeeding, miscarriage and abortion.

Since the level of FMc is very less in the host

body, we need to amplify the amount of Y

chromosomes to detect it in the sample. For

simultaneous multiplication and detection,

quantitative PCR is used.

Experimental Design - 2

Case samples have to be collected from Asian

women who come to the Cancer ward of a public

hospital / health establishment.

Control samples are women with no history of

malignancy. An easy way to get these samples is

from general section of maternity ward.

For case and control samples, 5 and 3

quantifications in the quantitative PCR will be

done.

Since Breast cancer patients are not that frequent

to come by, the data collection phase will take

considerable time. It is best to continue analyzing

samples simultaneously with data collection.

Summarization of results

We take presence of FMc defined as whether

the amount of FMc in sample is above/below

a certain threshold.

A 2-by-2 contingency table can be obtained

by considering Breast cancer affected/not

affected status and presence/absence of

FMc.

Different regressions have to be performed

and the p-values for significance of

regressions have to be found out for other

variables, taking case/control status as

dependent variable to ensure no bias is there

among the two groups.

Graphical representation

A plot of levels of FMc in the samples, with the index of a data

point in x-axis and case/control status highlighted in different

colors will give an idea about the effect, if any, of FMc across

the two groups. The plot for the original paper is given below.

Statistical tests used

Odds ratio can be obtained from the

contingency table and then it will be

checked that if it is significant. A

significantly more/less value will suggest

that Breast cancer happens more with

presence/absence of FMc.

For multiple regression of other

explanatory variables on case/control

status, overall F-tests and individual t-tests

have to be done.

Overall F test

In multiple linear regression this is used to test whether

the regression is significant or not as a whole.

The null hypothesis is that the vector of regression

coefficients has all elements equal to zero.

When we have n samples, each of dimension p, and

we assume that samples are i.i.d. multivariate normal,

then the test statistic F = MSreg/MSres follows an F

distribution with parameters p and n p. So we reject

the null hypothesis at 95% confidence level if the value

of the test statistic exceeds the 0.05-tail of the

corresponding distribution.

Individual t test

In multiple linear regression this test is used to determine

whether a certain independent variable is significant in the

regression.

The null hypothesis is that the corresponding regression

coefficient is zero.

When we have n samples, each of dimension p, and we assume

that samples are i.i.d. multivariate normal, then the test statistic t

= sqrt(n p)* bi/s where bi is the estimate for the i-th regression

coefficient (were testing significance of the i-the variable), and s

is the estimate of error variance. Under the assumption of

normality of samples as before, this follows a t distribution with

degrees of freedom n p.

So we reject the null hypothesis at 95% confidence level if the

absolute value of t exceeds the 0.025 tail of the corresponding t

distribution.

Table

case

control

FMc level (/10^6

maternal cells

1

2

3

4

0

0

0

0

0

1.3

2.51

12.6

5

0

0

6

0

3.11

7

0

0

8

0

0

9

0

9.21

10

0

2

11

1

2.45

12

13

1

1

0

32.54

14

1

21.22

15

16

1

1

3.43

0

17

1

9.76

18

1

3.47

19

1

65.3

20

1

234.56

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