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Aaron. Mansur R. Mogadam

B.B.A, Tehran University, . I980 "

THESIS SUBMITTED IN PARTIAL FULFILLMENT OF

THE REQUIREMENTS FOR THE DEGREE OF

MASTER OF SCIENCE

i n the'Department

of I

Mathematics & Statistics

@ Aaron. ~ a n s u r R. Mogadam 1987

SIMON FRASER UNZVERSITY

December. 1 987

r A l l rights reserved. This work may not be

reproduced in whole or in part, by photocopy - o r other heans, without permission of the author.

- .

Permission has been granted to the National Library of Canada to microfilm this thesis and to lend orasell +

copies of the film. b

3~

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~'autorisation a 6tb accordhe ' la ~ibliothbque nationale

du Canada -de microfilmer cette thhe et de 'prater ou de veadre dee exemglaires du' film.

L'auteur (titulaire du droit d'auteur) ee rhserve les autres .droits de publication; ni la th&se ni de longs extraits de cellei-ci ne doivent gtre imprimbs' ou aytrement reproduits sans son autoriaation 6crite.

*

Nme: Aaron M a n s u r R . Mogadam

Degree: Master of Science ' 7

Ti t l e , of thesis: ' MENSTRUAL 'CYCLE AND ENDURANCE TRAINING

- APPROVAL '

OVULATORY WOMEN

E x a m i n i n g Committee:

Chairman : Dr. G. Bojadziev . - -

Dr. D. Eaves Senior Supervisor

Dr. M. Stephkns Supervisor . . - --

c . - - V X

D r . T . Swartz- - "

Superviwr I I

1 , , , - D r . f . u r i o r External Examiner Department of Medicine University of British Colombia

Date Approved: November 24, 1987 *

my t hes i s , p r o j e c t o r extended essay . ( the t i t l e o f which i s shown b c i ~ w ) @

t o * u s e r s o f t he Simon Fraser U n j v e r s i t y L ib rary , and t o make pa r - f i a l o r /

s i n g e cop ies o n l y f c r such users o r i n response t o a ' reqbest from t h e

l i b r a r y of any o t h e r u n i v e r s i t y , o r o the r educat ional i n s t i t u t i o n , on

i t s own beha l f o r f o r one of i t s users. I f u r t h e r agree t h a t permiss ion -

f o r m u l t i p l e copy ing o f t h i s work . fo r scho la r l y purposes may be granted

by me o r ,the Dean o f Graduate Studies. I ndeistood t h a t cop; i ng 9

o r p u b l i d a t i o n % ? t h i s work f o r f i nanc ia sha l l not be a l lowed 1

w i thoutemy w r i t t e n permiss ion.

t \\

't i't l e o f Thesi s /Pro ject /Extended *Essay

f d a t e l

- - ABSTRACT - -- 7

% - - This project consists of analysis and model f itt,ing ;-of a

data set inchding menstrual cycle,hormonal, morphometric,

'& fitness, and endurance training variables. The objective was to - determine whether intense endurance training in sedentary

ovulatory women is associated with hormonal and menstrual cycle

changes. The forward\ selection procedure was employed to b investigate the existence of an association. Confidence regions

for the regression surfaces are also provided.

$1

B To my p a r e n t s , f o r their unfailing love & support.

" T h e t e a c h e r who w a l k s i n f h e 's h a d o v o f r h e f e m p l r . -

a m o n g h i s f o l i o w e r s , g i v e s nor o f h i s vi s d o m bur r a r bpi'

o f h i s f a i t h a n d h i s I o v i n g n e s . 2 3

I f h e i s i n d e e d w i s e h e d o e s nor br d y o u e n ! e r I he

b u t r a t h e r I pad.\ y o u r o I h r h o u s e o f h i s w i s d o m ,

i n d . " t h r e s h o l d o f y o u r own m

-- - Kahil Gibran

< ,

ACKNOWLEXEMENTS - C -- -

- -v -

4

- - -

I wish to thank all the staff, faculty, and fellow P

graduate students in the Mathematics . & statistics.

rtment.

In particular, I wlsh to .express my gratitude to my

Senior Supervisor Dr. David Eaves for his availabilit'y,

guidance, and willingness to, help. +

I wish also to acknowledge Dr. M. A . Stephens who, in

addition to serving on my graduate committep, also P, *

- 9 recommended he into the M. Sc. program7 which has changed my

future.

I w o u akso like to ;hank Dr. Jerilynn C. Prior and

Miss Yvettce Vigna for helping me to understand the medical

and the biological aspects of this project.

'. a -- ............ . Approval ..,...........,...'......,.. i . . . . . . . . . . ;..: i i

Abstract ................................................... i i i - - - . Dedication ................................................... i v - - 7 -

Acknowledgements ..............'.2................~,............ v 4

.................................................. List of ~ a b f e s v i i &'

.. ............................................. List of Figures v i i j

1 . The P r o b y ..............................,,........*...... 1

1 . 1 Introduction ........................................ 1 - .......... 1.2 Biological Interpretation :..........,.... 2

-

................................. 1.3 Scientific ~ e l i e f :. 4 +

- 2.1 The Goal of the Analysis .......................... 12 3. Regression Analysis ..................................... 15

C

...... 3.7 Model Fitting ......... ;(.... ,............... 15

3.2 Regression ~ n a l y s $ s frdm Phase A to B 20 - - .............

3.3 Rhgression Analysis from Phase A to € ............. 44 b

k

3.4 Statistical Critique, .............................. 62:.

.............................. . 3.5 Scientific Conclusion 64 b

.......................... Appendix A ........ ;............... - 6 6 '

Appendix B ................................................. 68 .................................................. Appendix C 69

BIBLIOGRAPHY ................................................ 8 5

Index . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 87 -

-

- * ,

Table *

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CHAPTER 1

- With - incr)asing numbers of women becoming involved in GX

intezse sport? cue'stions are being asked about the effects E9 \

t e - of this aclivi y on the reproductive function and pregnancy. I

The normal menstrual cycle seems straightforward enough:

I vaginal bleeding for a few days each month. In feality,-

though, the "period" is a very precisely regulated and4 "4p*-

I complex sequence of carefully timed events. More than seven .

hormones act iathe brain, to prepare the female for 'the

fertilization of an ovuin.(~ef. 1 , 2, and.3).

There are, however, phases of life when reproductibn, may -- 4

be decreased or temporarily stopped. Energies are sometimes

needed for even more basic functions, such as when intense P

labour is required toz respond to a natural disaster.

Anthropologists, for example, have documented the work- and

birth spacing of the ~ u n g San women of ~alalfari Desert in

Africa. These women use no birth control, yet they have

their children three to five years apart. The women,'are-food d

' gatherers, walking twenty to th'irty kilometers a day

- carrying heavy loads; it app2ars that the energy required by -

these women in food gathering decreases their fertility. y.

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- --

The largest increase in estrogen is obs~rved during the

Latter part of "he follicular Lphase, just prior to ..

ovulation. The -h-igh estrogen signal is received by the:

hypothalamus and pituitary gland and .leads to sudden * r

pituitary release of LH and (~e.f . , I page 36) FSH. his large

--LH surge preceded- by a smaller. FSH surge, triggers

ovulation.'

F

The second half of the cycle, referred to as the luteal P

phase, is ten to-sixteen days in duration. The luteal phase

begins after ovulation and lasts until the next flow starts.--

I t is the declining production of estrogen and progestero'ne

that causes menstruati-on at th'e end of the luteal pha'se.

(Ref. 1 page 3 3 ) -

'Pituitary gonadotropins are regulated from below as well as from above. L H and F S H release are under feedback control by the major gonadal steroids, estrogen, and progesterone. Estrogen, when at low levels, has a negative feedback effect and increases the synthesis and storage of FSH and L H . It does not appear to alter LH secretion but inhibits F S H secretion. During the middle of the cycle when the hormonal explosion takes place, estrogen maintains a high level which stimulates a sustained pulse of F S H and L H . Estrogen feedback h a s become positive rather than negative. Progesterone also controls an and F S H secretion. Progesterone-administration in normal and hypogonadal women pretested with estrogen is necessary for midcycle surge of normal intensity and duration (Ref. 4 page 6 8 ) .

e

1.3 ~cientikic Belief s.

Many factors besides exercise aye hypothesiskd to be

cause of me~strual cycle changes. These factors includr .

;eight loss in young women (Ref. 1 2 ) , psychological stress,' - -. - . - seasonal . light cycle (Ref. 1 3 1 , previous

' reproductive

history, and physical illness (Ref. 5 ) . These factors c a u s e

alterations in.the production of the hypothalamic, pituitary L

and ovar-ian hormones ieading to menstrual cycle var ia.t i o n .

Biologically' it is expected that an increase in the

intensity of exercisTg decreases percentage body fat ( w i t h Q

or without weighb loss). Weight or fat loss and intense P *

exercise decrease pituitary (LH) and bvarian ,(estrogen and

progesteronej hormones; i t is<this change in pituitary and *-,, -4 i

- ovarian hormones that causes menstrual cycle var%ation.

Other- very good medical research looking a'r the

I menstrual cycle changes with exercise h& been conf ined t~

descripc.iy.: statistics (see Bullen Ref. 15). The forward - i

. I - 1 ,

selection procedure used here would enable more astute

physiological assessment of the complex changes documented ,

only categorically.

CHAPTER 2

THE DATA

-- br.jerilynn C. Prior, ~ssistant Professor in the

Department of Medicine at the University of Bri~iskColurnbia s

(U.B.C.), presented data which dealt with menstrual cycle - - disorders from strenuous exercise in previously inactive ,

women. ,

Subjects were found through notices on bulletin boards

.on i i tness. centre& hospitals, universities, community .

centres, newspapers, etc. I t was required that the subjects 1

be between the ages of 20-40, healthy, sane, ovulatory, have

had no significant change in weight for over .six months,

have had no synthetic hormone use for six months, and have

had no regular aerobic exercise for six months. Based on

these elements twelve *omen were chosen among those who were

interviewed. After the selection -prdcedure the subjects were

observed dudv nonexercise (control) phase. This phase

consisred of two ovulatory menstrual cycies. All of the

testing was in The midluteal phase (days 18-21) as

?dent i fied through basal temperature records. \

After the initial controlphase, the subjects started on

a c a r e f u , l l y graded running exercise prografi ' while keeping

records of their exercise (time, distance), their basal - - .

' A gradual increase in running either-in distance or infensity is called a graded running exercise program.

'1 "

pulse' and we1 kly weight. t / -

,The phases of the study were:

Control or pre-exercise phase, consisting of .two months. .

~ a f l y exercise or aiter six weeks of exercise. I

Late exercise or after six months of exercise.

At the end of each of these three time periods A , B, and

C specific hormonal a n d temperature tests were performed t o

document percent body fat, fitness, hormonal and temperature

responses. Eight sets of variables (Morphometric, Fitness,

Menst rval Cycle, Temperature Testing, Stress, 0

Hormone-Baseline, Naloxone, GnRH, Hematology) were measured . < ,-

at each of the three times. Morphometric, fitness, running,

and hormone variables were- suspected. to be associated w i ti1

changes in menstrual- cycle variables.

A short summary of these variables and their biological -

definitions is as f~llows. i

P

Short Name - Set A ) ~orphometric Variables:

N

1 . Dry weight a DW

- weight of a subject in shorts and

T-shirt; determined by standing on a

balance beam scale.

2. Sum of skinfolds

' - measurements of the thickness of a -

double layer of skin and unde~lying

adipose (fat) tissue, but not _muscle. - -

The skinfold is raised_by 'pinching the 0 . *

skin between the thumb anh index finger.

The assessment of subcutaneous fa (2 measured at specific skinfold sites

using calipers. Measurements from each

- of the skinfold sites are added together

to obtaln Sem of Skinfolds (Ref.(6)).

Percen t ~ b d y Fa t /

- sum of s k i n f o l d t h i c k n e s s is f e d

i n t o a formula t o e s t i m a t e body d e n s i t y . 3

(BD). P e r c e n t f a t was computed from body

d e n s i t y acco rd ing t o t h e f o r m u l a , o f

4 . Underwater weight U W W (\

- weight o f a s u b j e c t submerged i n a

t ank of wate r a f t e r e x p e l l i n g a i r ou t o f

' h e r l u n g s .

5 . ~ e i c e n t B6dy Fa t

S e t B )

- a person with more bone and muscle

mass-for t h e same f o t a l body weight w i l l .

weigh more i n t h e w a t e r , have a h ighe r

body d e n p - t y and a lower pe rcen t age body

f a t than ?-person w i t h l e s s muscle mass. - A

P

~ i t n e s s Variable:

Trimps - a measure o f g e n e r a l TRPS \

f i t n e s s , i nvo lv ing r e s p i r a t o r y

e f f i c i e n c y a n d p u l s e r a t e . The re fo re i t

i s expec ted t h a t i n t e n s e e x e r c i s e

i n c r e a s e s t r i m p s .

B

%

Set C)

1 .

-

Medstrual ~ y c l k and Running variables:

Cycle Length - . t o t a l number of c y c l e =

days s t a r t i n g w i t h t h e f i r s t day of flow - \

and ending . the day befoi-e t h e next

per iod . begins. Normal c y c l e length i s

25-32 days.

F o l l i c u l a r -Length 4 .

- t h e f o l l i c u l a r phase extends from ,

t he f i r s t day ,of f1o.w u n t i l t h e time of

ovu la t ion . A normal f o l l i c u l a r l eng th i s . 10-20 days.

CYCL

FOLL '

-

Luteal Phase LUTL

- t he l u t e a l phase extends from - - *

ovula t ion u n t i l t he s t a r t of the next -

menstrual flow. The normal l u t e a l 14ength \

i s 10-16 days long. The l u t e a l phase i s 1

c h a r a c t e r i z e d by higher temperatures

than those recorded dur-irng . t h e 1

' f o l l i c u l a r p h a s e . This thermal s h i f t i s

caused by the a c t i o n of proges terone , a

gonadal hormone produced by t h e ovary i f

ovula t ion has occurred. I f ovula t ion 2

does not take p lace t h e r e will be no

progesterone product ion , and no inc rease \_J.

i n temperature. ,

- -- ---

~ l o w Length FLWL

- a normal flow length i s 3-5 days.

-

Mean Temperature MEANTP

- an a r i t h m e t i c mean of a l l d a i l y

temperatures f o r a given c y c l e .

Miles per Cycle WII, ( 'Y

- a l l t h e mi les run during a given

- - m n s t r u a l cyc le a r e simply added

L t oge the r and recorded a s miles/'cycle.

Miles per cyc le day d /

M I L/CD I =

"- cycle- length i s divided i n t o

mi les /cycle t o g ive an average of the 8

miles run fo r each c y c l e day.

- - Miles per r u n M I L ~ R N -

- number of days run i n a cyc le a r e ' . i

divided i n t o t h e mi les run during t h a t

c y c l e t o give an average rhn l eng th .

Miles per week

i- - s e l f -explanatorTa - 4 L

Number. of days run per cyc le

- s e l f -explanatory. q

'.

Set D) Hormones :

- -

- (Chemical subs tances produced by .7

endocrine glands ( s p e c i a l c e l l s ) , which , -

t r a v e l i n t h e bloodstream t o ' a - t a r g e t 0 .

L. , organ where t h e i r e f f e c t is produced.)

I d

1 . Tes tos terone . TEST -- -

- produced by the ova-ry and adrena l

gland in women.

2 . Estrogen , ESTR .

- -produced by t h e %ary and f a t

c e l l s of the body.

Progesterone f - produced by t h e ovary fol lowing

ovu la t ion . - P

FSH -

- f o l l i c l e s t imula t ing . hoimone

produced by t h e p i t u i t a r y gland. - ,'

LH

FSH f .

- l u t e i n i z i n g hormone produced by

the p i t u i t a r y g land,

5

TSH

- thyroid s t i m u l a t i n g hormone' G

produced by t h e p i t u i t a r y gland.

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Table 1 : 4 Subset of the Raw Data

YIL/W m / C f lES& ESTR PRUG FSH LH yyl

body f a t . - - - -.

CHAPTER 3 >-

REGRESS IOK: ANALYS I S 3

3.1 Model Fittinq a,

Linear regression models were employed to investigate

any association between the changes in the menstrual cycle

and hormonal and other vari.ables. The regression analysis of . i

the changes is dividedlinto two sections (phase A to B, and

_ A to C). ' In each section the cGnges' in morphometric and

a fitness v riables with rega,rd to running variables, the

changes in hormones with respect to running, .morphometric,

and fitness variables, and at last' the changes in menstrual

cycle variables, are studied. The following gives a general

idea of what was done for all of these sections, A more -

detailed explanation including g r @ ~ ~ and tables, is given

-in the corresponding sections.

T-tests on averages have been employed to test whether

- - -

averages of morphometric, fitness, hormonal, and, menstrual --

I

cycle variables have change-d over the given time spans. That \

;s to test:

-'1t is of scientmfic interest to compare the result ef early exercise (time W, and late exercise (time C), with control or pre-exercise phase (time A ) . The anaJysis for time B to C was not address2d because there were too few subjects for the variations to show any patterns.

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a

%

\ where the dopendent variable Yi is the value of the change --

in a morphometric, fitness, hormonal, or menstrual cycle

- variable over the given time span in the ith subject, P o and

0, are theoret'cal population parameters, xi is the value of ,l

the independent variable in the ith subject and sis are

modeled as inde.pendent3 errora terms having a normal

distribution with mean 0 and variance o2 where i ranges from -

1 to 7.

00 and 0, are un,known, so that suitable estimates b O an&

1-be sought to produce 'fitted' values: . A

1

which gives a fitting error

known as a residual, the discrepancy beatween observation I

and the co-rrespdnding outcome fitted by the model. The

estimates b o and - 6 , are found by the method of least . ?

squares. A brief discussion of the method of least squares

and its properties is given in ~ppendix B. b.

*

A source file consisting of MIDAS and MINITAB commands, , ,

. was written to run simple regressions of the dependent

- variables (i.e., changes in physiological variables) over

each of the two time spans. -. t

d

, I Here tests concerning D l are of interest, particularly

of the form: -- +

"?or the discussion of random sampling see Statisticai Critique, section 3.4.

I

W

UI

O

.rl

r

C,

. aJ

0,

m

Ll 0,

aJ L: c,

C

C,

HI:not both. equal 0,

F-test statistics were used. The t-est statistic denoted by F

is dibtributed as ~(2,n-3) when Ho holds. - - * -

C - .

The improvement (partial) F statistic .associated with b k

each remainin-g variable based on a regression equation

containing that variable and the variable initially selected

was calculated, - to test whether the second variable

contributes significantly to the model ,given .the first ,

variable _is already in the model. I t should be noted that

*, --. the improvement test was done twice: ', C

- ( 1 )!second variable given first in the model.

( 2 ) first variable given second in thg model. (Ref. 10 page

- In this ' way multiple regressions of Ahormones on

Afitness .and running, and also menstrual on Atitness, N

running and Ahormones variables were considered.

Departures from the model were studied by residual , ,

- - -

plots. I f the model is reasonable the residuals should be

v structureless; in particular, they should be unrelated to

. a c y other variable including the fitted and the response -- -

variable. Therefore plots of residuals versus the fitted -- -

values were studied.

k. \

A combined source f i l e on MIDAS and MINITAB was-- wri-tten . - - - rn perform a l l o f t , t h e ab-ove analyse 's . The s tepwise -.

r k g r e s s i o n procedures a v a i l a b l e on s t a t i s t i c a l packages were -

avoided . .There a r e s e v e r a l reasons f o r t h i s . ( a ) S ince t h e

procedures a u t o m a t i c a l l y " s n o o p " through many models t he .

model s e l e c t e d may f i t t h e - d a t a " t o o we l i " . That i s , t h e

procedures cam look a t many v a r i a b l e s and s e l e c t ones which,

by pure chance , g i v e a good f i t . ( b ) Automatic procedures

cannot t a k e i n t o account s p e c i a l . knowiedge t h a t t h e a n a l y s t

may have about h i s d a t a . ( f o r more s e e page 7 9 o f t he

MINITAB manual) .

3 . 2 Regress ion Ana lys i s from Phase - A t o B

3. 2 , J M o r p h o m e r r i c a n d / i t n e s s pararne~f erJ

Biologic ' a l ly i t i s + expected t h a t t h e change in

morphometric and f i t n e s s v a r i a b l e s i s a s s o c i a t e d wl t h the

running v a r i a b l e s . Based on t h i s b e l i e f s c a t t e r p l o t s of

(ADW, ASS, .... ) v s . (MIL/CY, MIL/CD, .... 1 were s t u d i e d L

c a r e f u l l y ; a few of t h e s e p l o t s ' a r e shown i n F i g u r e 3 . 2 5 .

The purpose of t h e s e p l o t s i s t o i n s p e c t whether or n o t ? 7 \.-

t h e exp lana to ry v a r i a b l e i s a s s o c i a t e d with t h e response

v a r i a b l e (ADW, ASS, &BF, W W W , AUWBBF, TRPSI, a n d i f , s G ,

then i n what s o r t o f way ( l i n e a r , q u a d r a t i c , a n d sc o n ) - - I t

1 seems tHat b inea r a s s o c i a t i o n would be an adequa te

assumption f o r m a n y of thege p l o t s , in view of t h e smal l

Figure 3.2a: Worphometric and Fitness variables vs. Runninq

sample size. For some 0% these plots (TRPS vs. MIL/CY 1 some - ---

positive assdciation have been detected, and there seems to

be no need to employ a model more sophist.icated than a

P

first-order regression with constant variance

(hom~scedasticity~.~ Some of the plots on Page 21 would nat

look significant i f a single point were removed (i.e subject

3).5

* T-tests on averages to dqtect changes ovek phase A to B

(without any independent- variable) in DW, SS, % B F , . . . , were

performed and no significant chLpges was observed , except

for TRPS. The results are shown in Table 1 of Appendix A .

For further analysis, linear regression was employed to

investigate whether the data reveals any association between

the morphometric variables and fitness variable change and

running variables. Each dependent variable (ADW, ASS,. A%BF, I

AUWW, AUW%BF, TRPS) was regressed on the running variables

:(MIL/CY, ML/CD, MIL/RN, MIL/W, NDRUN/CY) one variable at a

time. To test whether the dependent "variable is

significantlv associated with the corresponding independent

variable, the t-test for slope was utilised.

The following table contains significant regressions and

their significance levels. -k

4Homoscedastic scatter diagrams have oval-shaped residual plots. (i.e. regression estimates off by the same amounts all along regression line.

- =for more see section 3.4

Is

Dependen? Explanatory P-value - - - -

\-

ASS MI L/RUN 0 . 0 1 0

TRPS

n

I t seems that 'there js a strong association between the .pB

change in SS from phase A to B and MIL/RUN, and also the

increase in TRPS (which is a measure of exercise intensity)

is highly associated with MIL/CY, MIL/RN, and MIL/W.

Biologically it is believed that hormonal changes are

associated with the changes in morphometric variables, , a

fitness variable and running. /

To 'determine whether the data reveals any association, , -

'scatter plots of hormone changes (AESTR, APROG,' .... ) vs. running and the change in morphometric and ' fitness

variables, were studied.

Figure 3 . 2 b displays these plots. Studying the scatter

plots .reveals that there is a strong negative linear i

association between AESTR and A B W , and also between -APROG .-\ and ASS. I t is hard to detect any strong association between

I

1

running variables at this stage of'analysis.

T test on averages to detect changes over phase A to B

in ESTR, PROG, ..., indicate no significance changes;. the

Fiqure 3.2b: Hormone Chanqes vs. Running -

result is shown in Table 1 of Appendix A. . - ' --

For further investigation. simple regressions. of APROG,

OESTR, AFSH. ALH, and AT3 on running variables,'and change

i n morphometric and f i ~ n e s s variables, were examined..

Significant r e g r e s ~ o n s and their significance levels 'are

illustrated in the following table. \

5 J

Dependent -Explanatory P-va 1 ue - --

I .

U S T R ADW 0;013 B

APROG . -

ASS

AFSH ADW 0.040

> -

It can be concluded that- AESTR and AFSH are significaRtly - -

associated with ADW and APROG strongly associated with Y u

ASS, etc. No'significant regression was found,for ALH. , 5 C *

Next, regressions with. two'independent variables were

c2nsidered, where APROG, AESTR, ... are ' the dependent

,variables and ADW, ASS, .. . ,TRPS, and MIL/CY, MIL/CD, . . . a r e ',

the independent variables. Each dependent .variable is . d . =

regressed on. two independent variables, one from the

morphometric variables (including TRPS), and the - other one - a

from ruunig variable&. One- object is to test whether the

corresponding dependent variable is significantly explained

by . the two independent variables in the model., that is

testing:

vs.

The test statisti-c for the analysis of' variance 'approach is

denoted F. I t compares MSR ( ~ e a n Square ~egrkssion) and MSE

(Mean Square Error) in the' following fashion; * -

F=MSR/MSE ,

Under the null hypothesis F, has the ~ ( 2 ~ 4 ) distribution. I f

v the null hypothesis is rejected a t-ratio is used to test

whether the slope against one independent_ variable is

significantly, different than zero given thk; ;he other

independent variable is already in the model.

-The following table summarizes all of those regressions

. among those described which showed a significance level of

0.05 or smaller. In some cases (ALH, and A F S H ) , where no

significant regression was found, the regression with the 1

lowest significance level is shown. I-,

Dependent ~xplanatory P-level RSQ \

Signif F- -

-

4 C =

AESTR : A D W 0.02 81.8% 0.045 %

APROG : &SS 0.005 8 8 . 7 % 0.010

APROG : TRPS 0 . 0 1 82.8% 0 . 0 3 0

APROG : A%BF

MI L/RUN

AFSH ADW 0.19 6 6 . 5 % 0 . 1 1 0 0 .

ALH : A:EF 0 .15 5 4 . 8 % 0 . 2 0 0

MI L/CY a 0 .32 '

AT3: TRPS . 0 . 0 0 8 9 3 . 9 % 0 .003 -

It seems that AESTR is significantly associated with A D W ,

and MIL/CY is insignificant when DW' is already in the

model. And also the change in PROG seems to be highly -

- -- --

associated with the change in $BF ~~~'MIL)IIUN. T h e e is no I

significant association in ALH with ditness and running E

variables. AT3 is associated with ASS and ~IL/CD. -- - I

I .,

3 . 2 . 3 M e n s f r u a l C y c l e \ + b

1 t is known a priori that the change i~ the menstrual I

cycle variables is associated with the dunning variables

in6irectly through the inc&nediary effe'ct of the change in

hormones, fitness and morphometric variables. With this in

'mjnd, scatter plots of.ACYCL, AFOLL, ALUTL, and AFLWL vs &

AESTR APROG, ..., ADW, ASS, ..., ~ ~ ~ ' M I L / c Y ~ , MIL/CYD, ..., were studied careiully. Some of these. plots qre shown in

T

figures 3 . 2 ~ through 3.29. i %

i \

7' Car ful study-of these plots reveal that there is " a . '

strong non-zero. monotone association between ACY~? and TRPS. 'I i

ACYCL and ASS, and also between AFOLL and TRPS, \AFOLL and

ASS, AFOLL and APROG, and also AFOLL and AESTR. T is linear '\ \

pattern can dlso be seen between ALUTL and A%BF, bnd also \

ALUTL and Fgr the rest of the scatter pldts there I

seems to be no strong suggestion of any trend. Many \f these ',

plo- seem to depend strongly on the influence of jbst one

individual (individual 3 ) . & '\

b ', A simple t-test (without any independent variablk) of

\ the hypothesis of A=O vs At0 shows significancb. This l@oes

1

not necessarily suggest A=0; i t could also be attributed to i

I \ __---------------- I

6for more see section 3.4

Figure 3.2~: Scatter Plots of ACYCL 7

Figure 3 . 2 d : Sca t t e r P l o t s of MOLL

F i g u r e L f e s : S c a t t e r Plots of AFOLL d i, --

Fiqure 3.2f:.Scatte1r P l o t s of L U T L

' 2 . 5 +

Mlutl - 0. 0.

2.5.

Mlutl -

-

Figure 3.2g: Sca t t e r Plots of AFLWL

smallness of sample size, or to the fact that this'test does

not utilise error-reducing , in ormation contained in f ( available independent variables1.L~he results are shown in

As before, first-order regression was employed. Each

'menstrual variable ACXCL, AFOLL, ALUTL, and AFLWL was

regressed on Amorphometric, Afitness, running, L a -

variables, one, variable at a time.

and Ahormones

-

T h e f o l l o w i n g t a b l e c o n t a i n s a l l o f t h e r e l a t i v e l y --

s i g n i f i c a i ~ t simple r e g r e s s i o n s and t h e i r s i g n i f i c a n c e --

l e v e l s .

P - v a l u e /"

D e p e n d e n t E x p l a n a t o r y RSQ

ACYCL , -BSTR 0 . 0 6 0 53; 0 %

n APROG 0 . 0 8 0 4 8 . 0 % .

H , ASS 0 . 0 0 8 7 7 . 7 %

n TRPS 0 . 0 3 3 - 6 2 . 9 %

AFOLL APROG 0 . 0 0 8 7 8 . 0 %

I1 FSH 0 . 0 0 0 9 2 . 9 % '

PROL -

11 TRPS 0 . 0 2 0 6 8 . 5 % -

I1 AS s 0 . 0 0 0 I '

91 . 6 %

A J ~ ~ T L AESTR 0 . 0 1 7 7 0 . 7 %

n ALH 0 . 0 2 5 6 6 . 8 %

ADW 0 . 0 4 6

AESTR

AFSH 0 . 0 5 6

AT 3 0 . 0 1 4

A D W 0 :060

N e x t , r e g r e s s i o n s w i t h two i n d e p e n d e n t v a r i a b l e s a r e

I considered. One of the independent variables is one of those -

8

.above that was found significant by a t-test of regression

slope, and the other variable belongs to a different group .m d

that is believed" a priori to be associated to the

corresponding dependent variable. All t,he different - combinations were considered. To test whether the dependent

a variable is significantly associated with the the two

independent variables 'an ove'rall F-test was performed. A

regression F test is reported for those regressions that

showed a significant level. '2.

The following table contains the signlflcant x \*

regtessions. (i.e. Those that have .overall ~50.05) '. -

Dcpenden t Explanatory t-siq level .RSQ- Siqnif F

ACYCL: ' ASS

ALH ' -

< ACYCL: TRPS

ACYCL: - ASS

- APROG

The result indicates that

associated with the

0.040

0.280

the change '9

in CYCL is highly 5

variable ASS, and ALH is less ,

significant in ascociation with ACYCL when ASS is already in

' ~ h e search for the significant regressions was based on medicine literature and a priori belief (see sections 1.2 and 1 . 3 1 , therefore the reported p-levels can not be automatically attributed to a "search" effect

the model. Note that the correlation between ASS andALfI' is --

0.206 which indicates that collinearity is not a problem 8

here.

For the regression of ACYCL on A S S and L\LH: - - ACYCL=-0.62+0.626*bSS-0.04*ALH

the fitted values and their standard errors are presented in ,

*- - thg folLowing table. Working-~otelling confidence band for - ,

the regression plane is used to find the confidence regions.

~orkin~-~otelling 95% confidence P

reqion for the regression surface i , -

Individual Fitted Estimated S E , Lower bound Lpper bound

* 1 -3.613 0.574 -6.167 - 1 .060

2 - Q . 987 0.351 - 2 . 5 4 9 0 . 5 7 6

5 b

The confidence coefficient (0.95).indicates the percent of

time the estimating procedure wil_l yield a confidence region

in (ASS, AL&,-AcYcL) space which covers the entire true A

regression plane,. in a long ser'ies of ' samples in which the

ASS and ALH observations are kept at the same levels as in

the sample actually taken.

The following table contains the multiple regressions of

AJ?OLL with overall F50.05.

i

Dependent Explanatory P-level RSQ Si-gnif F

AFOLL : ASS 1

AESTR

AFOLL : T R P S /

MIL f w -

AFOLL: . MI L/RN

AFOLL; AS S

.. APROG J

-

. I AFOLL : AS 9

AFOLL : TRPS

APROG

The result ihdicates that the change in-FOLL 'is highly

associated with A%BF and MIL/RN, and none of the hormone

variab1,es AESTR, A P R O G , . ? . , seems f o be significant when A S S

is already in the model,

b

" The following table contains the fitted values and their

standard errors for the regression of) AFOLL on A%BF and

MI L/RN :

Ig and also working-~oteP1ing -95% confidence band for tHe- - -

a regression plane.

working-HoteLlinq 95% confidence 4

region for the regression surface L

Individual Fitted Estimated SE Lower bound Upper bound

, - 1 -3 .326 0.634 ,

" -6 .145 0 .506

2 -0 . 'go3 0.379 -2 .590 0 .704

3 4 . 9 7 4 . 0 .859 1 . 1 5 1 B.800

7 1 . 4-04 0.605 -1 .287 - 4 .095

The confidence coefficient ( 0 . 95 ) indicates the percent of

*the sime the estimating procedure will yield a confidence

region in (A%BF, MIL/RN, AFOLL) which covers the'entire true I

regression plane, in a long series of samples in which the

A%BF and MIL/RN obserFati'ons are kept at the same levelL$ as

in the sample actually taken. P I

he following table contains the multiple regressi~ns~of - -

- &

ALUTL with overall Ff0.05.

Dependent Explanatory P-level RSQ Siqnif F

ALUTL : ADW

ALUTL : A%BF 0.020 8 3 . 1 % 0.020

ALUTL': A%BF

AFSH

ALUTL : AESTR

2 The results i~dicate that ALUTL is significantly associated

\ with. A E S T R , and that running and fitness variables are not

significant. when AESTR is already in the model.

The following table contains the fitted values andtheir 2

. - standard errors for the regression of ALUTL on AESTR:

and also working-~otelli'ng 95% .confidence band for the

regression line.

Working-Hotelling 95% confidence -- - ---

band for qression line -

~ndividual Fitted - Estimate,d SE Lower bound Upper bound

The following table contains the multiple regressions of

AFLWL with overall F10.05.

Dependent Explanatory P-level RSQ Signif F

AFLWL : aDW 0.280 80.8% 0.030

AFLWL :- AT3 ' 0.010 8 3 . 9 % 0.025

AFLWL is siggificantly assoc.iated with AT3 and A % B F . That is

A%BF has an extra association with AFLWL even when AT3 is /

already in the model. Collinearity could be a problem since

r=-0.62, which may result in the estimated regression

coefficients having large sampl i ng var iabi 1 i ty..

~ulticoilinearity is usually not a problem ,when the purpose

of the regression analysis is to make inferences on the

response function or predictions of new observations,

- - provided that these inferences are made within the range of

* 9 observations.

The following table contains the'fitted values and their

standard errors for'the regression of AFLWL on A%BF and'AT3:

AFLWL=-0.25-0.5*A%BF-0.03*AT3

hnd also Working-Hotelling 95% confidence region for the

regression PLANE.

workinq-Hotelling 95% confidence

reqion for the reqression reqion

Individual Fitted Estimated SE Lower bound Upper bound

3.3 egression Analysis from Phase A tQ C P

3.3. 1 M o r p h o m e t r i c and f i t n e s s p a r a m e t e r s

The same steps as A to B have been taken for .this phase.

Scatter ,plots of (NW. ASS. .... and TRPS.) vs. ( M I L / C Y ,

MIL/CD, .... ) were studied carefully; a few of these plots

are shown in Figures 3.3a.

There seems to be no strong suggestion of ally trend

which could not be reasonably approximated by a first-order

. model. Many of the plots shown on Page 45 seem t o depend

strongly fluence of just on individual (individual

4 ) . 8 On the--! - --

T-tests on averages for ADW, ASS, A%BF, UWW, and UW%BF,

i.e., without any independent variables, except for ATRPS,

C fail to reveal signi•’icant diffqrences, . t h e results a r e - y.

shown i'n Table 2 of Appendix A .

First-order regression was. employed to formally quanti6y

the extent to which the data ~eveals an association between

the change in morphometric, fitness variable and the running

variables. Eac'h dependent variable (ADW, ASS, A % B F , AUWW, --

-I AUW%BF, TRPS) was regressed on running variables ( M I L / C Y , " .

ML/CD, MIL/RN, MI~/W. NDRUN/CY) one variable at a t i rnei To f

test whether the dependent variable is significantly

associated with the'corresponding independent~variable, the

.' ------------------ sfor more see section 3.4

F'iqure 3.3a: PMorphometric and ~itness'variables vs. Running 1

Was -

5 0.

0. o*

h

T-test for the slope coefficient (which is equivalent to

regression F-test) was utilised.

The following table contains significant. regressions

their significance levels.

Dependent Explanatory P-value

TRPS . MIL/RN 0 . 0 0

I t seems that there is a strong association between

change (increase) in TRPS

also A%BF and ASS are,

3 . 3 . 2 H o r m o n e s , , .

Scatter p1ot.s w

and

the

from phase A to C and M I L / R N , and 4

significantly associated with -F

ere aga~in used to see whether the data

reveals any association of hormone chanqes (AESTR, APROG, 3

.... ) vs. change in the running and fitness variables.

Figure 3 .3b displays these plots. These do not revesl

any strong association between AESTR and APROG and the rest 2 - +

of the var.iabes, except for an apparently strong association

between APFOl and M I L / R N .

The result of the \-test on AESTR, APROG, . . . are shown r ' ,

in Table 2 of Appendix A . I t can be seen that the.re is '

/ '

Fiqure 3.3b: Scatter P l o t s of AHormones

insufficient evidence to reject the null hypothesis ( e x c e p t --

%

for TSH).

f. For furt er inve'stigation, simple regressions of APROG,

.ESTR, &SH, A?H, and AT3 on running variables and the ? I

change in morphometric and fitness variables were examined.

For each of the hormone variables regressions with the

lowest p-value a r e given in the following table. b

Dependent Explanatory P-value RSQ -

AESTR ADW 0 . 16 3 4 . 7 %

, APROG ADW

' AFSH

AT 3 TRPS 0.02

ALH

ATSH T W S 0.26 23.8%

No adsoc iat ions between hormones and the other relevant - variables were deiected except for AT3 which is

significantly associated with TRPS. In spite of the above

results, regressions with two independent variables are '

considered, where APROG, AESTR, ... are the dependent and

ADW, 'ASS, ..., and MIL/CY, MIL/CD, ... are the independent variables. Each dependent &variable is regressed on two"

< %

independent variables, consist'ing of morghometric (including

TRPS) variables, and a running variable. An'overall F test

is performed for a31 of the regressions, and for those with

a small p-value ( 1 0 . 0 5 ) , an improvement F test is, used to

test i f the fiut independent variable is signifiently

different than zero given that the second independent

variable is already in the model. Another improvement F test

is done for the second independent variable to find its

significance l?vel given that the first independent is L-

already in the model.

- - - - - - - - - - - -__---__ ' 1 t can be shown that F,,,=(T ) 2 . ~herefors significance levels are obtained from a T tabie. fn this particular case the improvement F test statistjc has one degree of freedom on the numerator and four degree of freedom on the denominator, which is qua1 to (T,)~.

I

The following table shows the multipre regressions of - --

hormones with the lowest overall F. 7

Dependent Explanatory P-level RSQ Signif F

AESTR : ADW 0.30 37.9% C.38'

MI L/'CD 0.66 i

x APROG : ADW 0.16 43.9% 0.32

NDRUN/CY 0.28

AFSH ADW I

ALH : A%BF 0'. 17 4 1 . 8 % 0 . 3 3

AT3: TRPS

APRQL : TRPS

' d MI L/RN 0.0 1

I t seems that there is no significant of . A P R O G ,

AESTR, ALH, and AFSH- with any such pairs of independent

variables. The change in AT3 seems to be associated w i t h

TRPS, and APROL is significantly associated with TRPS and

* 3 . 3 : 3 M e n s r r u a l C y c l e

Scatter plots of ACYCL, MOLL, ALUTL, and AF'LWL vs AESTR 0

APROG, ..., ADW, ASS, ..., and MIL/CYC, MIL/CYD, ..., were

studied carefully. Some of these plots are shown in Figures "

3 . 3 ~ through 3.3f.

Studies of these plots reveal: that there is a -s'trong'

association between K Y C L and MIL/CD, and also between AFOLL

and ATSH and ALUTL and ATSH. E L W L and MIL/W seems to be

associated linearly as well. For the rest of the scatter 1

plots there seems to be no strong suggestion of any trend.

. A S before t-tests on averages were performed, i.e

without any independent variable. The results are

illustrated in Table 2 of Appendix A . For further analysis,

linerr regqession was employed. Each menstrual variable

ACYCL, AFOLL, ALUTL, and AFLWL is regressed on D

~mor~hometr'ic, Af itness, running and the Ahormones

variables, one variable at .a time. For each of the menstrual

variables the following table contains the regressions with

the p-value53.05 for the slope coefgicient. -.

Dependent Explanafory P-value RSQ -

J F O L L ATSH 0.030 63.7%

ALUTL ATSH 0.01

MI L/W 0.02

The results indicate that there is a significant change in

'3

Figure 3 . 3 ~ : Sca t t e r Plots of ACYCL

Figure 3.3d: Scatter Plots of AFOLL . a

Figure 3.3e: Scat te r P J o t s cf KUTH

Mlutl - 0. 0.

- & 5 *

Mlutl -

Figure 3 . 3 f % : Sca t t e r Plo t s of AFLWL-

CYCL and it is associated with MIL/CD, and qlso AFOLL and -

ALUTL are both highly associated with ATSH, and AFLWL is

associated with M I L / W . It seems that the change i n menstrual

cycle variables are not associated with the morphometric,

fitnes's, and other hormone variables this time span. P

Next, regressions with two independent variables are

considered. Here, one of the independent variables has been

found significant by a t-test on the slope coefficient, and .

the other variable belongs to a different group believed to

,be associated with . u the corresponding dependent variable. All

of the different combinations wePe considered. To test

whether the ,change in the dependent variable is

significantly associated with the two independent variables en

an overall F-test was performed.Improvement F tests were 4

utilized for those regressions that show a significant F ,---

statistics.

The following table contains the multiple regressions

for the menstrual cycle variables with an overall F10.05. 'L

-. Dependent Explanatory P-level RSQ Signif F

ACYCL : MI L/CD

LH

ACYCL: .MI L/w .

ass -

ACYCL: MI L / C D

ACYCL: MI L,/CD

FSH

The results indicate

associated with MIL/CD

-

0 .00 93.9% 0 . 0 0 3 ail

0 .04 r that the change in CYCL is strongly

and .the level of the hormone LH at

. time C (the correlation between MIL/CD and

rather than with.ALH. I t ca7n be seen from the table

45 that there is no significant change in LH regarding

fitness and running variables. But from the above table it

cafi be seen that the level of the hormones at time C

together with' running variables are important in explaninig

the change in CYCL over this time s@an.

The following table contains the fitted values and their .

standard * errors for the regression of ACYCL on MIL/CD and

working-~otellin-g 95% ~onfidence~region for the regression

line is also presented.

Workinq-Hotelling 95% confidence

reqibn for the reqression surface \ - -

In*dividual Fitted E S ~ imated SE Lower bound Upper bound

1 -4 .566 0 .173 -5 .337 '. -3 .780

2 - 1 . 3 6 5 0 .138 - 1 . 980 - 0 . 7 5 1 P

3 0 . 0 9 0 0 .180 -0 713 C

0 . 8 9 3

4 -2 .240 0 .237 - 3 . 2 9 5 - 1 . 1 8 0

T h e following table contains the multipye regressions of

AFOLL with overall F significance level 1 0 . 0 5 .

Dependent Explanatory 'P-level RSQ., Signif F

-- AFOLL : TSH 0 . 0 2 7 8 . 8 % 0 . 0 4

MIL/CY 0 .02

AFOLL : ATSH 0 . 0 1 8 6 . 5 % 0 . 0 1

MI L/CD 0 . 0 6

AFOLL : ATSH 0.03 85 .4% 0 .02

'The'results ihdicate that the change in FOLL is associated Y

with MIL/CY and TSH level at C . Thetother two- fitted

models indicate that the-change in P O L L is significantly

associated with ATSH, and the running and fitness varia6les

are hot significant when ATSH is already ih the model.

The following table contain? the fitted values and their --

q

standard errors for the regression of dFOLL on MIL/CY and

TSH :

A F O L L = ~ . ~ ~ - ~ ~ . ~ * T S H + ~ . ~ ~ ~ ~ M I L / C Y '

working-Hotelling 95% confidence region.for the regression

surface is also presented:

Workinq-Hotelling 95% con•’ d ence reqion for the regression surface

I

Individual Fitted Estimated SE Lower bound Upper bound

, The following table contains the multiple-regressions of -- -

ALUTL with overall F significance level 20.05.

Dependent Explanatory P-level RSQ Signif F

ALUTL : ATSH 0.0 1 ; 88 .4% 0.01

ASS 0.15

ALUTL : ATSH 0.01 ( 82,5% 0.03,

It seems that ALUTL is significantly associated with ATSH

and the other variables (fitness and running variables) are e

t significant when ATSH is already in the model.

The following table contains the fitted values and t h e i r

standard errors of ALUTL on ATSH:

working-Hotelling 95% confidence band for the regression

line is also presented.

Workinq-Hotelling 95% confidence

band for the reqression line. -

Individual ~i tted Estimated SE Lower bound Upper bound

The following table contains the multiple regression of -

t AFLWL with overall F 1 0 . 0 5 ,

Dependent Explanatory P-level RSQ Signif F

AFLWL : A%BF 0 . 1 5 79 .7% 0 . 0 4 ,

MI L/CD 0 . 0 5 I

AFLWL : 4LH 0 . 0 4 7 87.7% 0 , 0 1 5

MI L/CD 0 . 0 0 8

AFLWL :- AFSH 0 . 0 0 5 96.3% 0 .001

- MI L/W 0 . 0 0 0

A F L W L * is significantly associated with AFSH and MIL/W

ir=0.29) . That is AFSH has an extra effect on AFLWL when

M!L/W is already in the model.

The following table contains tlie fitted values ,and their

standard errors for the regression of AFLWL on AFSH and

\i AFLWL=2.2~7+0.12A*FSH-0.2*MIL/W 1

WorkingHotelling 95% confidence region for the regression

p:ane is also shown.

\ I

workinq-Hotelling 95% confidence - -

region for the regression surface -

Indiqidual ~itted. Estimated SE Lower bound Upper bound

* 3.4 Statistical Critique

This was an exercise 'in data modelling. I t produced

regression coefficients, F-ratios, significance levels, etc.

Any value -these summary statistics might have for predicting C )

I outcomes (for example: menopausal cycle changes) in subjects

in general, depends upon what "subjects in general" means,

and upon whether the data analysed can be considered as

representative or typical of subjects in general, and upon

general knowledge or opinion about the detected patterns,

which were already held prior to this datadanalysis.

1 2 social sciences, the relati~nshi~sebetween t w ~ t

variables are usually observational. ~s;ociat ion does not

mean causation. I f the experimenter can control independent

variables then association can suggest a causation (Ref 1 2 ) . '1

I t should be emphasized that searching among many

independent variables may tend to fit a well-fitting model 6

by chance, somewhat obscuring the scientific meaning of

significance levels (see discussion in BMDP manual program

P ~ R ) . On the other hand "knowledgable" search- does not .6\

necessarily entail this d8hger. I t is the investigator's

task to. strike a subjective balance.

$

For future experiments, it is recommended that fewer

variables should be studied, that is those that have. the

same nature (MIL/CY, MIL/W, MIL/CD, .... ould be combined. )7 And also it would be a good idea for a statistician to be

consulted before the sampling procedure, so that the sample

can be as representative as gossible.

it is a l s ~ recommended that i f possible, more

observations should be taken; so that more detailed

statistical analyses . like regression models wiah

interactions could be studied.

I t should be noted that individual 3's response to (ASS,

TRPS, ACYCL, and AFOLL) from phase A to B, and individual

4's respopse to (ASS, A%$F, and AUW%BF) from phase A to C

were extremely different than the others. Their extreme

response could be due to many factors, for example it could

be due to the fact that both subjects had the highest MIL/CY

compared to the others ( at phase B for.individua1 3 and at

phase C for individual 4 ) . The inclusion of ' t h s two

subjects has a - definite influence on some of the reported

p-values (e.g. from phase A to B no significant regressions *

of morphometric and fitness variables on running were found,

when subject 3 was removed and also from phase'^ to C no V

significant regressions of morphometric variqbles on running

were found, when subject 4 was removed). Since there were

only 7 ;ubjects, i t did not s"eem reasonable to ,remove these

subjects from the list of data. However further

investigation regarding the nature of the extreme responses i

of these two subjects is recommended.

3.5 Scientific Conclusion {7 (6 / I .

h he most compelling associations for each time period is as

follows :

Phase A to B:

It seems that ACYCL is associated with ASS and ALH (see

page 37); where ASS is significantly associated with MIL/RN

(see page 231, no significant change in LH with regard to

morphometric, fitness, and running'variables was found (see

page 2 6 ) . AFOLL is associated with A%BF -and MIL/RN (see

391, no significant change in %BF with regard to running

variables was found (see page 23). ALUTL is associated with

AESTR (see page 41 1 , and ~ E S T R is assxiated with ADW (see

page 2 8 ) , no significant change in DW with regard to running

variables- was found (see page 23). AFLWL is associated with

AT3 and C%BF (see page 421, where AT3 is associated with A S

and MIL/CD (see page 2 8 ) . I

*

Phase A to C:

i

I t seems that N Y C L is associated w-ith LH and MIL/CD

, (See page 56), AFOLL is associated with TSH and MIL/CY (see

page 5 8 ) , ALUTL is associated-with ATSH (see page 60), and

AFLWL is associated with FSH and MIL/W (see page. 61).

I t looks like that the change in the menstrual cycle b

variables from time A to B is associated with change in

morphometric and hormone variables, where the change from

phase A ts C is associated with the level of h,ormones at

time C and running variables. 3 The implications of Dr. J. Prior's work are:

This study explores complex and interrelated variables-which

subsequently. affect menstrual cycle characterstics. The

running variable as primary acts through changes in

morphometric (nutrition) and fitness (see pages 23 and 46)

and directly to effect changes in hormones (see pages 28 and

5 Q ) . The hormone changes then alter interv,als, phase lengths

and flow characteristics (see sections 3.2.3 and 3.3.3).

The luteal phase shortening confirms the' previously

reported changes. his change i$ of biological and medical

significance. The association with AESTR and ATSH may be

helpful in other investigations (see tables on page 42 and

bO and also Ref. 16)

APPENDIX A

-:

-? T t e s t s o n a v e r a g e c h a n g e for / f t n e s s , h o r m o n e s .s " a n d

F

m e n s t r u a l c y c l e v a r r a b l e s

Phase A to B:

Variable Name Average T statistics P - v a l u e

T R P S BB

Variable Name Average T statistics P-val ue

A E S T R 6 . 3 0 0 . 3 5 0 . 7 3

APROG 1 . O O 0 . 6 4 0 . 5 4

A F S H - 0 . 2 9 0 . 3 1 0 . 7 6

ALH

AT 3

Variable Name ~ v e r a g e T s t a t i s t . i c s p-value

ACYCL -0 .29 - 0 . 3 0

A F O L L

ALUTL

+ - -

Phase A t o C:

Var iab l e Name Average T s t a t i s t i c s .P-value

3

ASS - 0 . 1 1 -0 .05 0.96

. V a r i a b l e Name Average T statistics P - v a l u e

AESTR - 8 . 0 0 - 0 . 1 9 0 . 8 5 . _ APROG - 2 . 5 7 - 1 . O O 0.34,

ALH ' - 5 . 8 6 - 1 . 5 0 0 . 1 6

Var i a b l e Name A v e r a g e T statistics p-va lue

ACYCL - 2 . 2 9 - 2 . 8 9 - 0 . 0 2

5FOLL - - 0 . 3 3 - 0 . 2 3 0 . 8 2

ALUTL - 2 . 3 2 - 2 . 4 0 0 . 0 5

AFLWL - 0 . 2 6 - 0 . 9 1 0 . 3 9

a,,

Met h o d of Least Squac P S

To find "good" estimators of the regression parameters d o

$and P I I method of least squares is employed. For each sample \ observation ( X i , Y l ) , the method of least squares considers

the deviation o f Y i from its expected value:

In particular, the method of least squares requires that we

consider th; sum o f the n squared deliations, denoted by Q: n - 7 '@

Q = ~ ( Y ~ -0 0 - P 1 1 A. i i L - '

~ccording to the method of least squares, the estimators of

Po and 0, are those values b 0 and b , respectively w h i r h

minimize Q.'

------------------ ' For more'on the mathematical operations and I and b , formulas p lease see ( ~ e f ; 5 Page 3 8 ) .

0

APPEND I X

Figure 4: Scatterplot Source File from Phase A to B

W T Y U-TOP OK WTY - T OK ELPW -P OK RUN = M u

PLOT Cl8 C3 PLOT C18 U PLOT C18 CS PLOT C18 C6 PLOT C1 C12

.PLOT ~l! C13 PLOT C18 C14 PLOT C18 C16 PLOT Cl9 C1

PLOT C1 PLOT C19 C?j PLOT C19 C6 PLOT 1 ROT E&3f PLOT Cl9 14 PLOT C19 Et5 PLOT C20 C1 PLOT uo C2 PLOT C20 C3 ' PLOT C20 u PLOT C20 C5 PLOT n o PLOT CTO p PLOT UO 13 PLOT C20 C14 PLOT C20 C16 PLOT C21 C1 nor c21 c2 PLOT C21 C3 PLOT Ul C4

F:f g;: g PLOT C21 C12 PLOT C21 C13 PLOT CZI C14 PLOT C21 C1Z

F:;: 8E E: PLOT C22 C3 PLOT C22 U

R8: P PLOT C22 12

2:; % El: 2:; E! E? PLOT C23 U PLOT C23 C3 PLOT C23 U PLOT C23 C5 PLOT C23 C6 PLOT C23 C12 PLOT C23 13 PLOT C23 814 PLOT C23 C15 PLOT C24 Ck, PLOT C24 C2

I

Figure 4 , continued,

Figure' 5: Minitab Regression Run from Phase A to B

'r-

B i%rF REGRC7 RECA C7 m m n REW C7 REmn RE6RC7 REGRC7 REmm REGR C7 ROW C7 REQR C7 REGR C7 REGR C7 REBR C7 REm C7

REER RECiR C7 REGR c7 mm C7 RECJT C7 REGP C7 REER C7 REQR C7 Rim C7 REB( C7 mC7 REWC7 REGR C7 R m ? C7 RELiR C7 REm C7 mC7

m of: C16 C17

Ei8 C20 C2 1 c22 C23

U 7 C28 C29 C30 C3 1

1 ti C6 C11 C12 C13 C14 C15 C18 C1 Cl8 C2 C18 C3 C18 u Ei! E a 8 C23 C3 C23 U

Figure 5 , continued.

Figure 5 , continued.

In f o l l l-th VS.

I c Y

I I .

' Figure 5, continued.

: ' trdjlge i n flor l m Q t h v 'mange i n f l o r lengtn vs

's cnrngc in normes m g e in a l l vars'

Fiqure 5, continued.

REGR C9 2 13 M 9 REGR C9 2 El3 C30 REGR C9 2 C13 C31k v

Figure 6: Sca t te rp lo t Source F i l e from Phase A t o C 8

WPI 22-TOP OK EwlY -1 01. ElPn -P M Elpry -S OK m 'YID1S READ INT FI.DATS:HPCDHIID WALL WlTE FI--T V-504-608.530-539 Crl6-21 FO-(16F10 4) WRITE F 1 - 9 V361-668 261-268 C=lS-21 FO= .6F10 4) WITE FI=-S V-230,236~240 C.16-21 FO-(~FI& 4) MTS

RUn W N I T I B SPRINT-22-TOP NOECHO OUTWT wpm IS 60 HIM IS o Ffs ,:;, E&Ci81 \

READ '-S' C32-C38

PLOT C1 C36 PLOT C1 C37 PLOT 1 C38 PLOT b C34 PLOT C2 C35 PLOT M C36 PLOT C2 C37 ROT c2 W8 PLOT C3 W4 PLOT C3 C35 PLOT C3 C36 PLOT.C3 C37 PLOT 3 U8 PLOT L C34 PLOT U C 5 PLOT U c g 3'; 3 3 8

%T 8 Eg PLOT C6 C35

PLOT :::; Fi'B PLOT C6 C37 PLOT C6 C38 &attar lots of cl-mge I n Mr- vs ctunge rn .srQlt 6 ruonJng PLOT C17 E l

PLOT 19 C1 PLOT Em 2 PLOT C19&

PLOT C19 37 PLOT 18 i 3 8 PLOT $20 C1 PLOT CZO C2 PLOT C2O C3 PLOT CZO C1 PLOT 20 C5 PLOT E20 C6 PLOT C2O C34 PLOT 20 C36 PLOT 820 c36 PLOT C20 C37 PLOT C2O C38

PLOT C22 C4

E?; f2 gj

Figure 6, continued.

:ycIe var v

Fiqure 7: ~initab Reqression Run from Phase A to C

:Y :35 : 36 :37 . :a :12 13 : 14 16

3 4 138 a . :37 :38 16 Of 'chPnga in Ill C2 C3 c4

C12 C13 c14 C 16 C32 C33 C34 C35 C36 C37 C3B C 1 C2

E3 C5 C6 C12 C13 C14 C I 6 C32 a

c33 C34 C36 C36 C37 C38 C I C2 C3 c4 C6 C6 C12 C13 c i r C15 C32 ,

running 6 cmnw i

Figure 7 , continued. 1

Figure 7 , continued.

'cmppc ~ r , f e l l Imgtn vs 1n a l l vars

1 C

;! 1 I 1

j 1 1

1 I ( I t ( 1 ( I l l I 1 I I l l I l l I l l )11 ) 1 I )11 ) I ' 11 11 11 11 11 1 1 1 1 I f 1 1 1 1 11 1 1 1 1 1 1 1 1 1 1 ; ! 2 2 2 2 2

$ !2

i$ !2 8 12 U 23 23

~ i g n r & 7 , continued.

REGR c23 1 C3

REGR REGR C23 C23 1 1 C4 CS

" C2 ; 2;; R E m R E W ~ 1 3 I C32 R€GR c23 I C33 REGR C23 1 C34 REGR C23 1 C35 REGR C23 1 C36 REGR C23 1 C37 REGR C23 1 C3E

SS lbns of 3 1 C 1 6 3 ! C17 3 1 C 1 8 3 1 C 1 9 3 1 C 2 0 3 1 C21 .) 1 C22

3 1 C 2 3 4 1 C24 3 1 C 2 5 3 1 C 2 6 I 1 C27 9 1 C 2 8 ' 1 C 2 9 J 1 C 3 0 1 1 C31 I 1 C32

I 1 C 1 1 C 2

1 C 3 1 C4 1 C5 1 C 6 1 C l l 1 C12 1 C 1 3 1 C l 4 I C 1 5 1 C 3 3 1 C Y 1 C 3 5 1 C 3 6 1 C 3 7 1 U 8

' 2 C l d C l 2 C I S C2 2 C 1 8 C 3 2 C 1 8 W 2 c l a C5 ? C 1 8 C 6 2 c 1 a C34 2 C 1 8 C35 2 C 1 8 C3B

Figure 7 , continued.

c.34.

E4 c 3 7

!?! C13 C14 2 16 :34 ;35 -38 :37 :3a lots o f , is of C l C2 C 3 w M CB C l Z C 1 3 C14 c15

8% c 3 4 C 3 5 636 C 3 7 c349 C 1 ; C5 C6 C 1 2 C 1 3 c14 C I 5

% % EB C 3 8 C l c 2 C 3 C4 c5 C6 C12 C 1 3 C 14 C I S

CMnW In w ~ g h t d runninp chanpl I n w i p n t h r u n n r n g - .

Figure 7 , continued,.

E&Es I EB C 1 0 1 C 2 2

REGR C 1 0 1 C 2 9 RLGR C l O 1 C 3 0 REGR C1O I C 3 1 REGR C:O I MZ

C 1 0 I C5 R E C ~ cio I ce REGR C 1 0 1 C l 1 REW C l O 1 C 1 2

REGR C 1 0 2 C 3 C1B REGR C t O 2 C 3 C 1 9 REGR C I O 2 C 3 C 2 0

C1Q 2 C 3 C 2 3 REGR C l O 2 C 3 C24

BIBLIOGRAPHY

'b Prior, J. and Vigna, Y. "Reproductive Responses to

Endurance Exercise- in Women", Canadian Women studies volume 4,number 3,spring 1983.

Abraham, G.E. "The normal menstrual ,cyclen In J.R. Givens (Ed.), Endocrine causes of menstrual disorders. Chlcago: Pear Book, 1978.

Vollman, R.F. "The menstrual cycle" In E.A. @rieeman (Ed.), Major problems- in obstetrics & gynecology. Toronto: W.B. Saunders, 1977.

Prior, J. and -Vigna, Y. "Hormonal mechanisms of Reproductive- Function and Hypothalamic Adaptation to- Endurance TrainingW,~he- Menstrua1 cycle and Physical ~ctivity, Puhl, J. and Brown, H. Human ~inetics ~ublishers, Inc. PP.63-73, 1986.

Woolf , P.D. etc. "Transient Hypogonadctropic Hypogonadism Caused By Critical Illness", Journal of Clinical,Endocrinology and Metabolism, 1985.

Durnin J.V. and Womersley J , "Body fat from total body density and its estimation from 'skinfold thickness: Measurements on 481 men and women aged from 16 to 72 years", Brit J Nutrition, 1974, 32:77-106.

Brozek J, Grande R, Anderson JT and Keys A "densitometric analysis of body composition: revision of some quantitative assumptions", Annals of New York Academy of Sciences, 1963, 110:113-.114.

Dixon, W.J. ' (Chief Editor,) BMDP Statistical.Sgftware, 1985 printing. Berkely, California: university of

Neter, John, and Wasserman, Will'iam. Applied Linear Statistical Models. 2nd ed Illinois: ~ichard D. Irwin Inc., 1985.

10 . Klzinbaum/Kupper, Anplied Regression Ana-l~sis and other Multivariable Methods. Massachusetts: Duxbury Press, 1978.

1 1 P o J. "Luteal phase d e f q s and anovulati'on: adaptive alterations occur-ing with conditioning

. L exercisen, Seminars jn Reproductive Endocrinology 31, February 1985.

'12. Jonathan ~erkowitz, "Lecture five of math 10lW, 22, . Janua ry 1985. \ --

d

13. McArthur, J."Endocine Studies Durlng the Refeeding of C

Young Women with Nutritional Amenorrhea and infertility", Clinical Practice 51. 1976 PP 607.

' 14. Ronkainen, H. Pakarinen, A . Kirkinen, P. and Kauppila, A "Physical Exerc ise-Induced Changes and Season Associated Differences in the Pituitary-Ovarian function of runners and joggers", Journal of Clinical Endocrinology and Metabolism. Vol. 60, PP 3. 1985.

15. Bullen, B. etc. "Induction of menstrual cycle disorders by strenuous exercise in untrained women", N. Engl. J. Med 1985; 312 :1349 ;

16. Prior, 3.C. Conversation 16 October 1 9 8 7 .

Abstract, iir Acknowledgements, v Appendix A, 66 Appendix B, 68 Appendix C, 69 BIBLXOGRAPHY, 85 Biological Interpretation, 2 Dedication, iv Hormones, 23, 46 Introduction, 1 Menstrual Cycle, 29, 51 Model Fitting, 15 Morphometric and fitness parameters, 20, 44 Regression! Analysis, 15 Regression Analysis from phase A to B, 20 Regression Analysis from Phase A to C, 44 Scientific Belief, 4 Scientific Conclusion, 64 Statistical Critique, 62 The Data, 5 The Goal of the Analysis, 12 The Problem, 1