Some very cautionary statistics
by Dr Gavin Hitchcock
This article was sent to all Zimbabwean schools receiving Zimaths. We are still awaiting their response on this possibly contreversial article. The contreversy not being the article itself but the fact that a mathematics magazine had somehow decided to tell people facts that few others seemed to be mentioning. Your comments will also be appreciated.
Here are some statistical figures which are vitally relevant to everyone
---
and some ideas for discussing them critically, and deducing consequences
from them, which should bring every classroom to vibrant life. For what
follows is, quite simply and bluntly, about matters of life and death.
Statistics can be boring --- these are not! Statistics can be meaningless,
misleading, or downright deceitful. We have taken care to select and cite
our
references; that does not mean we think they're crystal-clear or
infallible, nor do we
endorse them, but we have chosen reasonably trustworthy sources. Graphs,
charts and histograms can be abused, for alarmist or cover-up
motives; we would
encourage you to make diagrams to help understand what the figures really do
mean. We urge our readers to be critical --- don't swallow anything based
on statistics without careful scrutiny:
Are they well-referenced? Are the
cited references reputable? Do the different sources agree within limits of
error? Are these limits specified? Do they supply dates? Are they
taken out of context? Have they been correctly reported? Watch
for vagueness, ambiguities, apparent contradictions...the watchword with all
such figures is: "Statistics change daily and should never be assumed
to be up-to-date or complete."
With all that, we suggest that the overall message of the statistics we are
about to quote is inescapable and urgent. We believe it is our duty and the
duty of school and government authorities to bring these figures and their
possible implications to the attention of all Zimbabweans.
- Trouble brewing in Africa
- Report on quality control of condoms: "In the year 1992 to 1993 the
laboratory tested 304 batches; 141 batches failed, 163 batches passed. The
condoms tested were from all over the world."
The conclusion: "More condom testing laboratories should be set up in
the developing countries to enable them to check the quality of the condoms
imported into their countries. This would help in the fight against HIV
infection." (Paper by I.Matondo of the Zimbabwe Regional Drug Control
Laboratory, Harare,in the Xth International Conference on AIDS, in 1994
in Japan)
[Ed: Can we assume that the quality has substantially
improved since then? Do you know the current statistics? Surely it is even
more important to set up the necessary
communications programmes so that young people are made aware of the past
and current statistics, and become aware of just how unsafe so-called
"safe" sex really is?]
- "Sexually transmitted diseases (STD's) besides HIV are a major
cause of disease..., particularly in young adults in the developing
world\ldots. In
contrast to the traditional clinical approach to STD control which focuses
on the treatment of self-presenting patients with an STD at specialized
clinics, the new strategy emphasizes the promotion of safer sexual
behaviour, condom provision, and appropriate health-care-seeking
behaviour ..." (Report in the same 1994 conference, by World
Health Organisation (WHO) Global Programme on AIDS)
- Report on the impact of HIV on population growth in rural
Rakai District, Uganda, during 1990-1991 : "HIV prevalence in
district adults was projected to be 12,6% in 1990 \ldots the annual rate of
natural population increase in the presence of HIV infection remained at
17,6 per 1000 in the district. It is estimated that in the absence of HIV
infection the rate of natural increase would be 25,3 per 1000.
(Paper in the same 1994 conference by researchers
Sewankankambo NK, Wawer MJ, Gray RH, of the Rakai Project)
- Zimbabwe now in big trouble
- "Harare has
experienced a sharp increase in TB
(tuberculosis) and STD's ... .
Of the 10~021 death records in the capital between January and September
1997, 10% were Aids-related, with the 25-44 year-age group accounting for
62,6% of the deaths ... . Aids has become the biggest killer disease,
with over 600 deaths attributable to the disease every week. A total of
51~360 STD's were treated in the city clinics from January to September 1997
compared to 64 069 cases covering the same period in 1996. Over 18,7% of
these cases were from Mbare." (The Herald, 8 Jan.1998. The Herald is Zimbabwe's leading daily. It is state sponsored. Mbare is a high density suburb of the capital Harare.)
- "About 30% of pregnant women are HIV positive and 50% of children
born to
HIV women die within two to three years, a chief medical technologist with
the UZ School of Medicine said in Harare last night, ... [He] said the
rate of HIV infection had increased from 18% in 1990 to 30% in
1996.... In Zimbabwe about 7,2% of pregnant women, 17% of males and
18%
of females are infected with HIV-2 which is prevalent in West Africa. Mr
Mashu described the situation as frightening ... About 68% of people who
have once suffered from STD are highly vulnerable to HIV infection."
(The Herald, 14 Jan.1998 )
- "Zimbabwe's HIV-prevalence rate for the 15-50 age group in rural
areas could be as high as 50%, and within the next 10 years life expectancy
is expected to drop from 55,3 years to 30,4 years for males, and from 58,6
to 31,7 years for females .... It is projected that HIV-1 prevalence will
peak at around 25% among adults in the 15-49 age group in the late 1990's,
with the peak occuring slightly earlier among men (1996) than among women
(2001). After reaching its peak, HIV-1 prevalence is expected to remain more
or less constant."
"Overall, the chances of survival from age 20 to 50 are liable to fall from
over 80% to 20%. As a result, much higher proportions of children will be
orphaned. If fertility continues to decline, negative population growth is a
real possibility, although the rate of reduction would be slow... However,
the age and sex composition of the population will change. There will be
less young children but higher numbers of teenagers and young adults. The
working age population of 18-60 will become younger on average. Men may form
the majority in the younger age-groups, but be under-represented at older
ages."
(Both extracts from the Zimbabwe Standard 25-31 May
1997, write-up on a joint Report: The Early Socio-demographic Impact of
the HIV-1 Epidemic in Rural Zimbabwe, by the Blair Research Institute,
Harare, and the Centre for the Epidemiology of Infectious Disease, Dept. of
Zoology, University of Oxford.)
- A major epidemic of STD in the USA
- "A major
epidemic
of STD has developed [in the USA]
during
the last 30 years.This and the next two items quoted from
pamphlet "The Facts About STD Epidemic" (by the Medical Institute for Sexual
Health, PO Box 4919, Austin, TX 78765-4919, USA, undated --- approx.
1995-1997).
In the 60's syphilis and gonorrhea, both easily treated
with penicillin, were the only important STD's. Today there are over 20
significantly prevalent diseases with 12 million newly-infected persons each
year. (Facts in Brief, New York: The Alan Guttmacher Institute, 1993).
It is estimated that 1 in 5 Americans is now infected with a viral
STD. (Ibid.) This does not include the bacterial diseases such
as
chlamydia, syphilis, and gonorrhea which are at very high
levels.
Tragically, 63% of these infections occur in persons under age
25. (Ibid. )
- "What caused this dramatic change in a period of just 30 years? The
answer
is simple: increased sexual mixing of the population. As more and more
people change sex partners, the inevitable result is an acceleration in the
spread of STD. The problem is compounded by the fact that 80% of those
infected experience no noticeable symptomsMoscicki,B., et al,
"The Use and Limitations of Endocervical Gram Stains and Mucopurulent
Cervicitis as Predictors for Chlamydia trachomatis in Female Adolescents,"
(American Journal of Obstetrics and Gynaecology, 157:1, July, 1987.
and therefore cannot know that they are infecting others.)
- "Adolescents have a higher degree of susceptibility than do older
people...
Researchers have estimated that a sexually active 15 year old has a 1 in 8
chance of developing pelvic inflammatory disease (PID), but that by
age
24
the probability has decreased to 1 in 80.Westrom, I. and March,
P., (Pelvic Inflammatory Disease, New York: McGraw Hill, 1992.) PID is
the most rapidly increasing cause of infertility in the US and is a primary
reason for the 600% increase in ectopic pregnancies since
1970AMA News, Feb 13, 1995. ...
Human papillomavirus [HPV] ...infects
over 40% of some groups (Bauer. H., et al, "Genital Human
Papillomavirus Infection in Female University Students as Determined by a
PCR-Based Method," Journal of the American Medical Association, 265:4,
Jan 1991) and ... is the precipitating agent for the vast majority of
cancers of the cervix, vulva, vagina and penis."
- (Based on the Video SEX 1996 by Pam Stenzel,
Creative Youth
Resources, 7670 South Vaughn Court, Englewood, CO 80112, USA. Information
about the Video available from Worth the Wait Zimbabwe, PO Box MP
700, Mt Pleasant, Harare, Zimbabwe.) In 24 hours, 55~000 people (including 12~000
teenagers)
[in the USA] contract an STD. For young people, there is a four times
greater chance of contracting an STD than of getting pregnant. In the 1950's
there were 5 known STD's, in 1996 over 50, of which 25 are significantly
prevalent among teens, and at least 8 of these are incurable.
Chlamydia, like syphilis and gonorrhea, is bacterial, so easily
cured, but the trouble is it has no symptoms (only internal scar tissue),
and furthermore it may cause infertility: infected once, a female has a 25%
chance of becoming sterile; infected twice, she has a 50% chance. Human
papillomavirus (street name genital warts) is the fastest growing STD
among 16-24 year olds. The American College of Obstetrics and Gynaecology
estimates that 46% of sexually active singles are already infected with
this virus. No condom can protect from it because it can infect the whole
genital region. It's the number one cause of cervical cancer in women ---
also can cause cancer of the uterus, vulva and penis. More women died in
the US in 1985 of cancer due to this disease than of AIDS.
- "Between 650~000 and 900~000 people in the US are currently either
HIV-positive or have developed full-blown Aids, a US epidemiologist said
here on Monday."Kevin de Kock of the Atlanta-based Centre for
Disease Control, reported in The Herald 4 Feb.1998.
- What about a cure?
- The most common self-justification of those who do not allow such
statistics to influence their behaviour, is "It's not going to happen to me
--- anyway, even if it does get me in the end, by that time there will be a
cure." [This is in the USA; African excuses may be quite different.] The
answer to this is: That's what thousands of young people said 10 years ago,
who are now dead, and thousands more who are now sterile or have cancer.
NEVER IN THE HISTORY OF THE WORLD HAVE WE CURED A VIRUS.
(Pam Stenzel, Ibid.)
- "A cure, or vaccine, for
herpes has been rumoured for years, but has not yet been produced. A
cure for the highly complex HIV virus is probably many years away at
best." Anyway: "While medical science has made great advances, it is
clearly not the solution to the STD epidemic. The development of a cure does
not guarantee an end to the problem. Syphilis is easily cured in its
early stages, but the number of people with syphilis in our country
[USA] is at much higher levels than at the end of World War II.
Chlamydia and gonorrhea can be `cured' with antibiotics, but can
leave scars which often require future treatment and may cause
infertility." (Both quotes from The Facts, Medical Institute
for Sexual Health, ibid.)
- What about condoms?
- (The Facts, ibid.) "Although touted by many as the
solution to the problem of STD and
unwanted pregnancy, condoms definitely are not. They have a poor record for
prevention of pregnancy, with failure rates of up to 13%
(Jones, E.F., and Forrest, J.D., "Contraceptive Failure in the United States:
Revised Estimates from the National Survey of Family Growth," in Family
Planning Perspectives, 21:3, May/June, 1989) or more per year.
The preponderance of scientific evidence demonstrates that condoms are
equally poor in preventing the transmission of STD. They do not
significantly reduce tubal infections or the infertility which may be the
result of those infections. (Cramer, D.W., et all, "The
Relationship of Tubal Infertility to Barrier Method and Oral Contraceptive
Use," in Journal of the American Medical Assoc., 257:18, May 8, 1987).
...In vivo studies by Dr.
Susan Weller suggest a 69% reduction in risk, or a 31% failure rate in
preventing HIV transmission. (Weller, Susan, "A Meta-Analysis of
Condom Effectiveness in Reducing Sexually Transmitted HIV," in Social
Science and Medicine, 36:12, 1993). This led her to state that "it is a
disservice to encourage the belief that condoms will prevent sexual
transmission of HIV."
- Based on Pam Stenzel, (Ibid). How can we estimate the
failure
rate
of condoms in preventing STD? Nobody knows directly --- estimates vary
between 2% and 50%! We only have the technology for testing antibodies
present some time after infection. A negative test only means it may not
have shown up yet --- and it may take as long as 3 years to show up.
Meanwhile the infected person is ignorantly infecting others.
But we do know much more about condom failure rates in preventing pregnancy.
It takes 10-14 days to test and be sure. It is generally agreed that the
failure rate of condoms here is 10%--30%. One fifth of teenagers [in USA]
regularly having sex using condoms will be pregnant in 18 months.
Now, what do you think happens to these statistics when we ask about STD and
HIV, in the light of the following?
- you can only get pregnant about 3 days (some sources say 10) a month; you can get infected
any day;
- only 50% of people can get pregnant; 100% can catch STD;
- the sperm cell is 450 times larger than the HIV virus in size --- 300
million of these viruses can fit on one `full-stop' like this. Only one
virus is needed to kill you.
- "Disadvantages [of condoms] ... Of 100 women who use condoms,
between 11 and 14 will become pregnant. Success rates are higher if vaginal
contraceptives are used at the same time.... Ideally, spermicides should be
used with condoms for extra protection....Spermicides used alone, although
not as effective as condoms used consistently, provide some protection and
are under a woman's control. Other barrier methods, including the
diaphragm, cervical cap, and female condom, generally prevent pregnancy
somewhat more effectively than spermicides and also protect against STD's
to a degree." (Extracts from Draft Trainer's Manual of the
Zimbabwe
National Family Planning Council Nov.1996)
- Is there any way of ensuring I am safe?
"Postponing sexual activity until marriage with an uninfected mate is the
only way for adolescents to be 100% sure of avoiding STD infection and
pregnancy. Most of them can accomplish this if properly instructed and
encouraged....Likewise, single adults, including those with previous sexual
experience, would be wise to save sex for a mutually monogamous lifetime
partner. It is unrealistic to expect people to use condoms
consistently and correctly with every act of intercourse for a long period
of time. Delaying sex until marriage is the most medically sound advice we
can give people in today's environment." (The Facts About STD
Epidemic, Medical Institute for Sexual Health, ibid.)
Questions:
[Assume populations in millions: Zimbabwe 12, Harare 2, USA
250]
- Can you see any ambiguities or apparent contradictions in the first
Herald report (item 1 of section 2) on
death statistics? How might they be explained? Assuming the weekly
AIDS related deaths are
correctly reported for January 1998, and that it doesn't get better or
worse, how old will you be when 1 million people have died of Aids in
Harare? Will you still be alive?
- How many STD's are mentioned in the text above? Which are viral,
so untreatable by antibiotics? Which was (at the time of reporting) the
major
cause of infertility among young people in the USA? Which was the
fastest growing? Which was a major cause of cancer? Which is not protected
against by condoms at all? Are these statements likely to be transferable
to 1998 and to Zimbabwe?
- What is the definition of `failure-rate'? Could the 13% in item
1 of section 5 mean (and why are we left to guess?!):
- 13 out of every 100 sexual encounters with new condoms fail to
prevent conception, or
- 13 out of 100 women regularly (whatever that means!) using new
condoms will eventually get pregnant, or
- 13 out of 100 women regularly using new condoms will get
pregnant in one year, or
- other....
- What does `most rapidly increasing cause' mean (in item 3 of section
3)?
- How do the Zimbabwe statistics (for HIV prevalence, STD prevalence,
condom failure etc.) compare with those from other countries at
similar times (Uganda, USA)?
- Do the statistics quoted in items 1 and 4 of section 3 correlate
well? If not, what possible reasons are there? [Look at the difference in
estimated numbers of people in the USA contracting an STD per year, over
the period separating the two dated references.]
- If the population of USA was 240 million in 1993, how many under
25's in the USA in 1993 were likely to be infected with a viral STD? How
many were likely to be ignorant of the fact? What are the figures likely to
be now?
- How many under 25's in the US are HIV positive or have AIDS? [Use the
estimates given in item 5 of section 3, and assume that the age
distribution is similar to that for STD's reported in item 1 of section 3.]
Compare the figure you get with your estimate in question 7, and draw some
possible conclusions for Zimbabwe.
- If the probability is f of catching a virus in each
sexual encounter, then the probability of doing so in 2 encounters is 1 minus the probability of 2 successes =
1-(1-f)^2, in 3 encounters is 1-(1-f)^3 , and in n encounters is
1-(1-f)^n. If f=1/1000, how many people out of 100 will contract the
virus over a year? [Assume 50 encounters.] How many in the (very) long
run? [Let n run to infinity.]
- Suppose that 13% of women (using new condoms regularly) fall
pregnant every year, and that the fertile period for a woman is 3
days per month --- or approximately 10% of the time. Suppose also that
HIV prevalence rate for men is 25%.
What estimate can we make of the percentage of women (using new condoms
regularly) who will contract the virus in the next year? [You need to make
a similar assumption to that for the previous question, but it turns out
that the number of encounters does not matter very much!] How does your
answer compare with the figure given in item 1 of section 5?
- What does "safe'' mean in such widely advertised statements as `No
condom --- no sex. Play safe --- use a condom.' Is safety from financial,
social, moral, emotional, psychological or spiritual dangers (or `scars')
included? What do you think of such statements in the light of the
statistics?
- Is it possible to be 100% physically safe? Is it worth it?
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