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_COMETS, CONTAGION AND CONTINGENCY
_

S.J. Senn, CIBA-Geigy AG, Medical Department, 4002 Basel, Switzerland

(Current affiliation: Department of Epidemiology and Public Health and
Department of Statistical Science, University College London)

_Presented to the International Society of Clinical Biostatistics,
Innsbruck 1988
_

Note: this paper was presented to ISCB 9 in Innsbruck and submitted to
_Statistics in_ _Medicine_ for publication in the proceedings of that
conference. The editors and referees requested revision but I chose
not to revise it and it was never published.

_COMETS, CONTAGION AND CONTINGENCY
_

_Summary
_

Two astronomers, F. Hoyle and C. Wickramasinghe, have collected data
on various epidemics in schools in an attempt to show that person to
person transmission alone is unable to explain the pattern of disease
and that outside contamination from a cometary source must therefore
be considered. It is explained here, with the help of an artificial
model, why their analysis is inadequate. It is shown that the problem
of deciding between the 'conventional' hypothesis and the 'cometary'
hypothesis is one of deciding between competing clustering processes,
that this is no easy task, and that data in the form in which Hoyle
and Wickramasinghe have collected them are unsuitable for this
purpose.

_ Introduction
_

_'The question arises here whether or not the comet Venus infested the
earth with vermin which it may have carried in its trailing atmosphere
in the form of larvae...' _

Immanuel Velikovsky1

'...it does not seem to be entirely out of the question that the eggs
and sperms of insects might once have been arrivals from space...'

Fred Hoyle2

In the preface to the paperback edition of his controversial best
selling work of cosmology, _Worlds in Collision1 , Immanuel
Velikovsky, reviewing the reaction to the first appearance of his
theories in 1950, had cause to refer to a British astronomer's
discussion of the evolution of scientific knowledge in the following
terms:_
__
In 1950 it was generally assumed that the fundamentals of science were
known and that only decimals were left to fill in. In the same year a
cosmologist, certainly not of a conservative bent of mind, Fred Hoyle,
wrote in the conclusion of his book,
The Nature of the Universe: '_Is it likely that any astonishing new
developments are lying in wait for us? Is it possible that the
cosmology of 500 years hence will extend as far beyond our present
beliefs as our cosmology goes beyond that of Newton?' And he
continued: 'I doubt whether this will be so. I am prepared to believe
that there will be many advances in detailed understanding of matters
that still baffle us ...But by and large I think that our present
picture will turn out to bear an approximate resemblance to the
cosmologies of the future'._

By a curious irony, which Immanuel Velikovsky could hardly have
foreseen, within a few years. Fred Hoyle himself, in association with
another astronomer and mathematician, Chandra Wickramasinghe, was to
publish a theory regarding the origins of life which was to attract
reactions similar in terms of hostility and incredulity to those which
had greeted the appearance of _Worlds in Collision_ a quarter of a
century before, and which, were it to be commonly accepted as true,
would require a similar cataclysmic revolution of accepted scientific
dogma2,3,4,5,6,.

Although Velikovsky and Hoyle and Wickramasinghe have mounted very
different attacks on accepted cosmology, in particular the inspiration
for the two theories (historical in the case of Velikovsky and
astronomical for Hoyle and Wickramasinghe) is quite different, the
theories have curious similarities. Both of these extraordinary
cosmologies attack accepted theories of evolution and palaeontology,
both accept the possibility of extra-terrestrial life (although this
has differing degrees of importance for the two theories), both have
led the authors to make successful predictions about other members of
the solar system (Venus, Jupiter and the moon in the case of
Velikovsky, Halley's comet in the case of Hoyle and Wickramasinghe),
and both sets of authors have found their predictions explained away
after they have been fulfilled7,8. A final irony, which would not,
however, surprise Immanuel Velikovsky, is that there is no reference
to his work in _Diseases from Space._

This article is concerned with the latter of these two theories or
more precisely with one particular aspect of it: Hoyle and
Wickramasinghe's contention that certain epidemics can only be
explained in terms of contamination from bacteria or viruses falling
through the earth's atmosphere and having their origin in comets. Two
important points need to be made before starting the examination of
this aspect. First that Hoyle and Wickramasinghe's theories deserve to
be taken seriously - if true they have enormous implications for every
scientific discipline including medicine and statistics, if false they
nevertheless serve to expose the extent to which many of the 'facts'
we take for granted are no more than a habit of thinking. Secondly
that although the course and pattern of epidemics is an important
element in the cometary hypothesis it is only one of many, and it is
possible that developments in other fields may render statistical
analysis an irrelevant means of examining the cometary theory.
Nevertheless if seeking to join this cosmological debate the medical
statistician can do no better than pose himself the question that
Immanuel Velikovsky advises all would be cosmologists to consider:
'Which part of the work is committed to us?'. It is the purpose of
this article to explain how at least in general qualitative terms a
number of the epidemics which Hoyle and Wickramasinghe have reported
can be explained in terms of conventional theories of person to person
transmission. If the reader is disappointed by the lack of a more
rigorous and mathematical element in what is to follow it will perhaps
serve as excuse to note that a theory may be adequately defended in
the terms in which it is attacked but also to remark that another
purpose of this review is to encourage other statisticians, more
suitably qualified for the task than the author, that this is a
general area worth investigating and debate worth joining.

If any further justification for the topic is required it is perhaps
worth remarking that a recent editorial in _The Lancet_ on the subject
of the common cold, whilst finding no space to discuss the cometary
hypothesis, nevertheless began as follows: 'Everyone knows what it is
like to catch a cold, yet we know surprisingly little about how it
happens. Years ago we thought we knew.'9 There are many puzzling
features of epidemics which do not at first sight accord well theories
of person to person transmission and the medical statistician might do
worse than to follow D.V. Lindley's advice regarding that prejudice
which Bayesians refer to as prior belief: 'so leave a little
probability for the moon being made of green cheese; it can be as
small as 1 in a million, but have it there since otherwise an army of
astronauts returning with samples of the said cheese will leave you
unmoved.'10 All that it is necessary to add to this is a warning to
the reader not to dismiss the cometary theory out of hand without
first reading what Hoyle and Wickramasinghe have to say about it; like
the theories of Immanuel Velikovsky it has subtleties which may
embarrass rash attempts to dismiss it.

_Mathematical Epidemiology
_
Mathematical epidemiology also conceals traps for the unwary and if
Hoyle and Wickramasinghe have had cause to complain that the range and
subtlety of their theories have been underestimated and their nature
misrepresented and misunderstood it may reasonably be said that they
have committed the same sin with regard to mathematical epidemiology.
In this context it is worth reviewing a number of important features
of epidemic models.

The first is that the distributions of numbers infected to which
epidemiological models give rise have large variances. One of the
simplest of contagious models leads to the negative binomial, a
distribution which, in any empirical investigation in which
extra-Poisson variation is discovered is often the first to be
considered. Even the negative binomial, however, frequently
understates the case as regards variability, and as a number of
authors have noted, given suitable parameter combinations, U shaped
distributions can be produced11,12.

The second feature is that very different models of disease may give
rise to identical distributions. An interesting paper of Neyman's
discusses the way in which a process corresponding to true contagion,
and a process with variable proneness corresponding to false
contagion, can give rise to multivariate distributions with identical
margins13. He also gives a varied list of phenomena to which a further
clustering model may be applied: the distribution of larvae in the
field, the clustering of galaxies, population theory, and, two
applications which are extremely interesting in the present context:
the theory of epidemics and the investigation of bombing by formations
of planes.

The third feature is the historical one that elaborate theories of
disease mechanism have, on occasion, been rendered superfluous by
suitable developments in mathematical modelling. One such is
Brownlee's theory of exponential decay in infectivity. A fascinating
account of the circumstances which led Brownlee to incorporate this
feature into his mathematical models is given in an excellent review
by Paul Fine14 (which in no way concerns itself with the theories of
Hoyle and Wickramasinghe). Brownlee's theory is now regarded as a
result of semantic and mathematical flaws but three points from Fine's
review may be of interest to defenders of the Hoyle- Wickramasinghe
hypothesis. The first is Fine's description of Brownlee as having the
misfortune, 'to have worked at a time when his subject was making the
radical shift from miasma to germ'. This is a shift which Hoyle and
Wickramasinghe are seeking (in some sense) to reverse and its
acceptance as fact should not of course be considered in any analysis
of their work. The second is Fine's interesting reference to William
Farr's successful predictions of the course of epidemics _despite
_believing in the miasma theory. The third is his discussion of a
particular problem for Brownlee's theory: the fact that epidemics
recur requires organisms to regain their infectivity if they also lose
it during the course of an epidemic. This is not a problem for Frost's
epidemic model which was the first to avoid Brownlee's mass-action
fallacy and is now part of mainstream mathematical epidemiology but
then it ought to be noted that it is not a problem for the
Hoyle-Wickramasinghe hypothesis either if the recurrence of epidemics
results from repeated encounters with a source of infectivity
maintained in historic condition by the environment of outer space.

The fourth point, related perhaps to the previous three, is that
naive reason is not a very safe guide when discussing the effects of
changes in conditions or assumptions in the field of mathematical
modelling and counter-intuitive results may obtain. For example,
recent work on the modelling of the spread of AIDS has led to the
discovery that under certain circumstances individuals of moderate
promiscuity may be at equal risk to those of high promiscuity15.
Similarly under certain circumstances an increase in rubella
vaccination may lead to a rise in the numbers of babies born with
rubella related syndrome16. Returning to AIDS again for a third
example it is not necessarily the case that the higher the proportion
of persons with HIV infection who go on to develop full blown AIDS the
greater will be the eventual number of deaths from this condition.
Bartlett's remark, 'that complex and certainly not obvious
consequences flow from even the simplest model,' is an appropriate
warning17.

Finally a fifth point of importance is that unlike other problems in
medical statistics, in mathematical epidemiology, probability is
affected by data order. Thus in chain binomial theories the sequence
in which cases occur carries information which is lost by a summary in
terms of totals affected and this is a striking difference from the
standard binomial.

A consequence of all these elements is that definitive identification
of underlying process using totals infected classified by location is
an extremely difficult task which requires very careful thought and
may in many cases prove impossible. An excellent review of attempts to
investigate the supposed phenomenon of leukaemia clustering by Smith18
makes clear just how difficult this task may be. In such a case,
however, the null hypothesis (that of no infection) at least makes
possible the calculation of the size of various tests even if the
power of such procedures is often unknown. In making their challenge
to conventional epidemiology, however, Hoyle and Wickramasinghe pose a
much more difficult problem and one whose nature they have
misunderstood: one of deciding between competing clustering processes.
If Neyman could find the same distribution applicable to infectious
disease and bombing patterns, the problem of deciding between person
to person transmission and infection as a result of bacterial rain is
no easy matter.

In fact, as Bates' solution to the false and true contagion problem
shows, progress can sometimes be made in deciding between epidemic
processes given adequate models and suitable data19. As will be shown
below, however, Hoyle and Wickramasinghe have neither.

_An Illustrative Model
_
Before proceeding to a discussion of Hoyle and Wickramasinghe's data
and methods, however, a simple model will be reviewed in order to be
able to illustrate a number of peculiar features of contingency tables
when these represent data from epidemics20. Lest there is any danger
of the purpose of this model being mistaken, it should be clearly
understood that it is not being proposed as a means of practical
investigation but simply because it is adequate for illustrating the
effect of clustering on contingency analysis.

Imagine a population of _n_ individuals arranged in a circle. Each
individual can infect either or both his neighbours. Imagine that a
disease appears in this community as a result of a single introduction
and that it is characterised by a fixed serial interval and a short
period of infectivity. If _X_ is the final number of cases infected
and
q is the probability that a currently infectious individual will
infect a given, adjacent, uninfected individual, then, given that an
epidemic has started we have,

P(X = x ) = xq x-1 (1-q )2,

x
£ n-1

= (n-1)
q n-1 (1-q ) + q n-1,

x = n

, Next suppose that we have an even number of individuals in the
population and that _n_/2 may be classified as type _A_ and _n_/2 as
type _B_. Suppose that the pattern of social contacts in such that the
individuals are arranged such that the _A_s are together and the _B_s
are together and there are two points of contact.

Let the random variable _Y_ represent the final number of infected
cases of type _A_. A simple geometric argument then shows that the
conditional distribution of _Y_ given _X_ is given by

P(Y=y IX=x) = 2/n ,

0 < y < x

= {n-2(x-1)}/(2n) ,

y = 0 or y = x

= 0,

elsewhere,

x
£ n/2

= 2/n ,

x - n/2 < y < n/2

= {n-2(n-x-1)}/(2n) ,

y = n/2 or y = x - n/2

= 0 ,

elsewhere,

x
³ n/2.

For ease of discussion this will be referred to as the _ring
_distribution.

Table 1

Contingency Table Associated

With Spatial Epidemic Model

A

B

Infected

y

x-y

x

Not-infected

n/2-y

n/2-x+y

(n-x)

n/2

n/2

n

Also note, however, that corresponding to this model is the
contingency table given by table 1. Now it is interesting to consider
what the consequence is of applying standard techniques of analysis
for contingency tables to such a model. Suppose we evaluate the
probability of every possible table having marginal totals _n_/2,
_n_/2, _x_ and _n - x_. Such tables may be indexed by the number of
infected individuals of type A, _Y_, and therefore the probability
distribution of the tables is that of _Y_ given _X_ above. The usual
test for such a table, however, is Fisher's exact test, which uses the
hypergeometric distribution. Figure 1 compares the probability plot
for the hypergeometric distribution (red) and the ring distribution
when _n _= 60 and _x _= 16 . The U shaped character of the ring
distribution is in stark contrast to the unimodal hypergeometric.

Clearly the usual tests of association cannot be applied to such a
table. The underlying assumptions of within-cell independence that
such methods (e.g. chi-square analysis) require are not valid. Of
course it may be argued that what has invalidated this test is the
underlying spatial clustering of the As and Bs. If these
characteristics themselves had been independently distributed across
the population, the chi-square test of association would be valid
whatever the underlying epidemic process. The simple model serves to
make a point, however, namely that for numbers infected, standard
tests are not _in general_ valid for the purpose of investigating
association with spatial factors. This point will be considered in
more detail below, but, for a recent example of an epidemic which was
incorrectly analysed because the investigators failed to appreciate
this feature, see Senn's discussion of Dupuis et al 21,22.

There is another important point which this model serves to raise,
however, namely, that even the appropriately calculated distribution
of usual test statistic (e.g. chi-square) under the null hypothesis is
not sufficient to provide an adequate test. For example, in this
particular case it is not at all clear, without further investigation,
what is an appropriate partition of the sample space for deciding
between good and bad model fit. In this particular instance, unlike
for standard contingency problems, high values of the chi-square might
be taken as an indication of good model fit.

Of course in general it is not possible to produce most powerful tests
without considering alternative hypotheses. The exact nature of the
appropriate alternative hypothesis, for example, has been one of the
problems in the search for possible infectious clusters of leukaemia,
already referred to12. For this particular problem, however, the
underlying null hypothesis at least (i.e that of no clustering) is
relatively simple and leads to unimodal (i.e _n-shaped_) distributions
for which standard measures of discrepancy (such as, e.g, squared
distance measures) may at least be presumed to be related (if
imperfectly) to that statistic which would be used for the most
powerful test were a characterisation of the alternative hypothesis
available. If the null hypothesis itself requires clustering, however,
no adequate test can be devised unless the alternative clustering
process associated with the alternative hypothesis can be modelled.

One final point can be made profitably using this model. Although, for
all the reasons given above, judgements as to whether or not the model
is tenable may be difficult to make using totals infected, the same
may not be the case if certain additional information becomes
available. For example, the observation that three persons had become
infected in a given period, or that there had been a period (longer
than the serial interval) with no new infections in the middle of the
epidemic, or that there was more than one epidemic chain, would each
be sufficient to invalidate the model in the strict form in which it
is defined above.

_Statistics from Space
_
Hoyle and Wickramsinghe have presented many different arguments in
favour of their theory over the last ten years. We are only concerned
with the statistical ones here, and the most relevant of all their
works in this context is _Diseases from Space5. The table below is
taken from that book and gives data from an epidemic at Howell's
school in 1978 and shows the distribution of infected cases amongst
two groups adjacent houses._

Table 2

Pupils at Howell's School

Classified by Location and Condition

House Grouping

Hazelwood & Taylor

Oaklands & Bryn Taff

Total

Infected

26

10

36

Not infected

25

39

64

51

49

100

Hoyle and Wickramsinghe present their analysis of the null hypothesis
of person to person transmission in the following terms ' So what was
the chance, if one were to make a random allotment of 36 apples into
two essentially equal boxes, of finding that 26 apples had gone into
one of the boxes and only 10 into the other box? ....And if one were
to include all the still more unequal possibilities, such as 27 apples
going into one box and only 9 into the other, 28 into one box and 8
into the other, and so on, the chance of any one of these unusual
distributions would be 1 in 100'.

This argument, of course, ignores some of the conditioning on the
table, but (if such a probability process were appropriate) could be
excused on two grounds. First that _Diseases from Space_ is addressed
as much to the general public as to fellow scientists, Hoyle and
Wickramasinghe feeling perhaps that the former may be capable of a
flexibility of thinking the latter are unlikely to develop. Secondly,
in many of the other epidemics presented in _Diseases from Space_, the
calculated significance level is so low as to render such refinements
of calculation as correctly conditioning on margins an irrelevancy.
(See, e.g., the
[1]Data they present on an epidemic at Eton College).

What is extraordinary (and revealing) about the argument is the
analogy made and the blatantly inappropriate assumption of
independence it implies. If the appropriate model is of some
blindfolded cosmic green grocer distributing cases of disease amongst
the houses it is unclear as to why this should have any more relevance
to an infectious process than to the cometary model, indeed it could
be regarded as being more relevant to the latter. A more telling
analogy, surely, would be to consider a crate full of apples some of
which have been found to be mouldy. Such analogy does not encourage
consideration of the binomial distribution.

This basic flaw in Hoyle and Wickramasinghe's reasoning was pointed
out in a article in _New Scientist_ in 198123 and it would not be
necessary to repeat it here if the authors of _Diseases from Space_
had shown any sign of developing their own thinking as a result of
it24,25. Instead they have made repeated references to the arguments
presented in that book as providing conclusive support for the
cometary hypothesis.

As an illustration of the dangers of drawing rash inferences from
contingency tables it is worth considering an epidemic at a boarding
school which was similar to those presented in _Diseases from_ _Space_
and reported in the columns of New Scientist by Jennison, Butt and
Byrom26,27. This concerns an outbreak of influenza in 1978 at the
King's School Canterbury. In nine houses on a given site, and having
an average of 51 pupils per house 61% of the pupils were infected
(attack rates ranged from 37% to 84%). In a tenth house on another
site with 59 pupils, none were infected. Jennison, Butt and Byrom had
this to say about the epidemic, 'our own calculations cannot account
for it by random chance.' What these calculations were is unclear
since they were not presented. What exactly 'random chance' is or
should be in this context and whether its definition can provide any
relevant link to a model of person to person transmission is also
uncertain. What can be conceded is that a very impressive chi-square
value can be calculated for these data. Nicoll, however, using chain
binomials for which the probability of infection between individuals
in the same house was allowed to be higher than the probability of
infection between individuals in different houses, was able to find
models for which nine was the commonest number of houses infected and
with average attack rates exceeding those reported in the King's
School epidemic and showing that apparently impressive contingency
tables were easily generated28.

In fairness it has to be noted that this required extremely high
ratios (e.g. 150 to 1) for within house to between house infection but
her models assumed, in the absence of more detailed information on
social geography, that every individual was capable of infecting each
other. Because of the nature of the chain binomial model (which is not
in fact a spatial process) equal values of infectivity would place an
individual at greater overall risk of catching the disease from
individuals in other houses than from those in the same house. The
models Nicoll used, in fact are extremely parsimonious. It would not
be unreasonable to consider infection between and within bedrooms and
between and within classrooms and include interactions for these
factors as well and since such a model must include the one she did
consider as a special case the fit that would result could not
possible be worse.

_Parsimony in Modelling
_
Parsimony is not to be found, however, in the Hoyle-Wickramsinghe
model itself. In fact for none of the epidemics reported in _Diseases
from Space_ do they perform any probability calculations on the
assumption that the cometary hypothesis is true, for the simple reason
that the model is insufficiently defined. Since they allow viral
in-fall to be patchy at any scale required, since they allow that
different buildings can offer different degrees of protection, since
they allow that chance events like opening a window at the wrong time
can affect the course of an epidemic, since viral particles from a
given passage of a comet may be allowed to fall to earth over a decade
if the data require this24, since comets may be of short or long
period, since the debris from them may be localised or not, there is
nothing that the theory cannot explain. One should hesitate a long
time before adopting such a theory since the task of finding
refutations will not be easy.

If clouds of viruses may be as heterogeneous as you please the same is
not true of human society, which is implicitly taken to be more
regular than an ideal gas by the authors of _Diseases from Space_. It
is interesting to contrast this attitude to human society with that of
Neyman who, having developed some clustering processes from simple
assumptions, delivers a warning about believing that these will be
adequate for the analysis of an actual epidemic because of the varied
locations, crowded or lonely in which infectious individuals may find
themselves at key moments. He ends with the observation that, 'those
statisticians who have a liking for applied problems of some delicacy
may enjoy trying their hand at theory of epidemics.'13
_

_Mixing and Analysis

It is worth considering carefully nevertheless whether there are any
possible conditions as regards the organisation of human society and
the nature of disease that could combine to make the analysis of Hoyle
and Wickramasinghe valid.

For example, perfect mixing (as perhaps approximated to at a party),
is a strong condition which would make the distribution of cases
across space random. This would not, however, validate the contingency
analysis because if individuals mix perfectly any classification of
them by location is arbitrary, and whilst this arbitrariness
guarantees random allocation under the null hypothesis it also has to
do so under any alternative hypothesis and makes identification of
process impossible.

A possible suitable combination would be a (presumed) highly
infectious disease in a prison in which prisoners spent most of the
time isolated in cells but came together for short periods of
exercise. Under such conditions the spatial classification by location
of cell might be considered arbitrary under the hypothesis of person
to person transmission but not under the cometary hypothesis if viral
in-fall may be assumed to be patchy at an adequate scale and it can be
hoped that there is a reasonable chance of the exercise areas and some
of the cells being missed. Despite their common reputation it is
doubtful as to whether such conditions are ideally replicated in
Britain's boarding schools and whether it is reasonable (one is
tempted to say fair) to shackle the conventional theory with so much
regularity whilst allowing so much liberty to the cometary hypothesis.
__

The Development of the Debate

For the cometary debate, at least regarding statistics of epidemics,
to develop further, a number of conditions would seem to be desirable.
The first would be for Hoyle and Wickramasinghe to recognise the
inappropriateness of their own analysis of the contingency tables
presented in _Diseases from_ _Space_ and to adopt some of the
stochastic models which epidemiologists had actually felt that
theories of person to person transmission required them to use in the
fifty or so years between McKendrick's pioneering work29 and the
appearance of _Diseases from Space5. This will have the further effect
of bringing them into contact with a considerable literature of
disease modelling whose successes they will have to explain. (There is
no space to begin to review these successes here but since the paper
has already been cited, Bartlett's work on measles periodicity may
perhaps be singled out17 ). Hoyle and Wickramasinghe may prosecute as
they wish and will no doubt make their own judgements but mathematical
epidemiology has to be permitted to make the defence. Secondly,
because, the problem is one of deciding between different clustering
mechanisms and because, therefore, it is unclear what sort of unusual
pattern gives more support for the cometary hypothesis than for the
conventional theory some explicit modelling is required for the
cometary hypothesis itself. Thirdly it will be necessary to collect
data which is richer in detail than that considered in Diseases from
Space and which may have include classification by time of infection
as well as by location and quite probably information on social
relationships as well. Fourthly it will be necessary for mathematical
epidemiologists to consider the cometary hypothesis seriously and this
they are unlikely to do until the proponents of the cometary
hypothesis give mathematical epidemiology the same respect._

Finally, there is always the possibility, that developments in other
sciences may make the statistical debate irrelevant, and decisive
evidence for the cometary hypothesis may be discovered. In that case
the statistical argument in _Diseases from Space_ may take its place
with Kepler's theory of the regular solids and Galileo's theory of the
tides as a false milestone on the road to true enlightenment.

_REFERENCES
_
1. Velikovsky, I. _Worlds in Collision_, Abacus, London, 1972.

2. Hoyle, F. _The Intelligent Universe_, Michael Joseph, London, 1983.

3. Hoyle, F and Wickramasinghe, C. 'Does Epidemic Disease Come From
Space? _New Scientist_', _76_, 402-404 (1977)

4. Hoyle, F and Wickramasinghe, C. _Lifecloud: origin of Life in the
Universe_, Dent, London, 1979.

5. Hoyle, F and Wickramasinghe, C. _Diseases from Space_, Dent,
London, 1979.

6. Hoyle, F and Wickramasinghe, C. _Living Comets_, University College
Cardiff Press, Cardiff, 1985.

7. Talbot, S (editor) _Velikovsky Reconsidered_, Abacus, London, 1978.

8. Maddox, J. 'When Reference means Deference'. Nature, _321_, 723,
(1986).

9. Lancet Editorial 'Splints Don't Stop Colds - Surprising!' _Lancet_,
Feb 6, 277-278, (1988).

10. Lindley, D.V. _Making Decisions_. Wiley, Chichester, 1985.

11. Whittle, P. 'The Outcome of a Stochastic Epidemic - a Note on
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12. Bailey, N.T.J. _The Mathematical Theory of Infectious Diseases and
its Applications_. Griffin, London, 1975

13. Neyman, J. 'Certain Chance Mechanisms Involving Discrete
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(proceedings) 4-14, 1963.

14. Fine, P. 'John Brownlee and the Measurement of Infectiousness: an
Historical Study in Epidemic Theory'. _Journal of the Royal
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15. Peto, J. 'Aids and Promiscuity' _Lancet_, Oct 25, 979 (1986).

16. Knox, E.G. 'Evolution of Rubella Policy for the UK'.
_International Journal of Epidemiology_, 16, 569-578, (1987).

17. Bartlett, M.S. (1957) Measles Periodicity and Community Size,
_Journal of the Royal Statistical_ _Society_ A, _120_, 48-71.

18. Smith, P.G. 'Spatial and Temporal Clustering' in _Cancer
Epidemiology and Prevention_, Schottenfeld, D and Fraumeni, J.F.
Editors, Saunders, Philadelphia, 1982.

19. Bates,G.E. and Neyman, J. 'Contributions to the Theory of Accident
Proneness II. True or False Contagion.' _University of California
Publications in Statistics_, _1_, 255-236 (1952).

20. Senn, S.J. 'Statistics from space'. Paper presented at the Young
Statisticians Conference, Dundee, (1987).

21. Dupuis, G., Petite, J., Peter, O. and Vouilloz, M. 'An Important
Outbreak of Human Q Fever in a Swiss Alpine Valley'. _International
Journal of Epidemiology_, _16_, 282-287, (1987).

22. Senn, S.J. 'A Note Concerning the Analysis of an Epidemic of Q
Fever.' _International Journal of_ _Epidemiology_, _17_,891-893(1988).

23. Senn, S.J. 'Can you really catch cold from a comet?' _New
Scientist_, _92_, 244-246, (1981.

24. Hoyle, F. and Wickramasinghe, C. 'Influenza viruses and comets',
_Nature_, _327_, 664 (1987).

25. Senn, S. J. 'Contingent Contagious Constraints', _Nature_, _329_,
22, (1987).

26. Jennison, R.C., Butt, R.V.J. and Byrom, H. 'Flu' _New Scientist_,
_92_, 697, (1981).

27. Senn, S.J. 'Infection Statistics' _New Scientist_, _93_, 258-259,
(1982).

28. Nicoll, P. A Statistical Investigation of Hoyle's Cometary
Hypothesis, Dundee College of Technology, Dundee, 1984.

29. McKendrick, A.G. 'Applications of Mathematics to Medical
Problems.' _Proceedings of the_ _Edinburgh Mathematical Society_ _14_,
98-130, (1926).

_________________________________________________________________

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References

1. http://www.panspermia.org/chandra.htm
2. http://www.panspermia.org/
3. http://www.ucl.ac.uk/~ucaksjs/