Original article Biomath 1 (2012), 1209031, 1–7

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Exploring Family Relations between
International Patent Applications

Peter Hingley
European Patent Office

Erhardtstrasse 27, Munich, Germany
Email: phingley@epo.org

Received: 12 July 2012, accepted: 3 September 2012, published: 10 October 2012

Abstract—In the international system for granting
patents for inventions, first patent filings can be followed
by subsequent filings at other patent offices within one
year. Each such group of related filings constitutes a patent
family. Tests are developed as to whether the observed
number of first filings that leads to subsequent filings (r)
is in agreement with a random process of assignment of the
hits from the subsequent filings. An exact expression for
the random distribution can be used for small sized data
sets. Its behaviour and also the behaviour of an asymptotic
Poisson approximation as well as a censored binomial
distribution for r are assessed. The approach is stimulated
by the Fisher-Wright model in population genetics and
possible parallel applications to other biological processes
are sought, such as transformations of stem cells and
cancer.

Keywords-censored binomial; genetics; patents; random
assignment

I. INTRODUCTION

Usually an inventor starts a quest for intellectual
property protection by making a first patent filing at
the local national patent office. Then, within one year,
subsequent filings quoting the priority of that first filing
can be made at any patent office. These are termed
subsequent filings. Unlike most national patent offices,
the applications that are received at the European Patent
Office (EPO) are mostly subsequent filings, due to its
supranational character as an umbrella Office for the
European Patent convention contracting states (EPC),
which also have their own national offices to which
applications can be made [1].

To aid the statistical description of the flows of
such (provisional) patent rights, the concept of patent
families is useful. These are explained in II. The PRI
database is a patent families file that is extracted from
a worldwide patent database at EPO called DOCDB,
that itself contains data on patent publications from all
the main offices around the world [2]. A subset of the
documents in DOCDB represents published patent filings
that can be identified as representing either first filings
or subsequent filings, depending on whether or not they
contain priority references to earlier first filings. In PRI
the data are re-ordered and compacted so that each record
is indexed by a priority reference. Information is also
given on the activities of subsequent filings that quote
that priority, such as the major geographical blocs in
which subsequent filings took place.

Studying the international spread of patent filings
combines concepts from several streams. Mainly since
the 1960s there have been studies of patent economics
and statistics, starting with examples of the patenting
process as motivators for econometric models, but later
on centring more on elements of the system itself that
has become an important economic driver [3]. In parallel
the subjects bibliometrics and scientometrics have been
developed. Network theory can also be relevant [4]
because the relationship of subsequent filings to first
filings is not one-to-one, even when considering just a
single first filing office / subsequent filing office pair.
That is, one first filing can be quoted as a priority in
more than one subsequent filing, and a subsequent filing
can quote several first filings as priorities.

Citation: P. Hingley, Exploring Family Relations between International Patent Applications, Biomath 1 (2012),
1209031, http://dx.doi.org/10.11145/j.biomath.2012.09.031

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P. Hingley, Exploring Family Relations between International Patent Applications

Fig. 1. Structure of patenting in terms of a generation of first filings,
followed by subsequent filings up to one year later.

Here some probabilistic aspects will be considered,
concentrating on subsequent filing activities at the EPO.
The concepts to be explored are inspired by tests for
random mating in population genetics. Patent family
populations do not directly exhibit so many directly
analogous characteristics to biological populations, but
nevertheless it is interesting to study the parallels and
differences. It will be suggested that the methods might
have some as yet unrecognised ability to model cellular
processes in biology, or at least be able to give fresh
insight into experiments and models that could be tried
out.

II. THE STRUCTURE OF PATENTING AND PATENT
FAMILIES

First patent filings (FFs) lead on to subsequent filings
(SFs) in other countries up to one year later. Imagine two
generations as set up in Fig. 1, rather like the Fisher-
Wright model in population genetics [5]. The FFs are
the F0 generation and the SFs are the F1 generation.
The members of F0 do not all reproduce, but some do
to give one or more offspring in F1. Each member of F1
however must have at least one parent in F0.

The parallels with biology do not go much further
than this in any strict sense, because after F1 the patents
are examined and granted if considered worthy, then
maintained against the payment of appropriate fees for
up to 20 years before they lapse. This means that no
further reproduction of this cohort can normally take
place. The generational pair of populations F0 and F1
can be said to be renewed over and over again every
year. (This could be paralleled perhaps in population
genetics by a model for pets.) Beyond the limited set-up
considered here however, the population of inventors and

Fig. 2. Single priority patent families arising from first filings in
2006 (2005 in brackets), indicating first filings and flows, which are
the counts of first filings referenced as priorities in subsequent filings
in other blocs. From [7].

firms that make patent applications persists over time as
well as with dynamic entries and departures each year
[6]. The act of filing for patents can be considered as
a possible survival tactic in a competitive world. There
are no genes or DNA in patent families, although there
are technical classification systems to describe the areas
covered by a patent that play some kind of analogous
role.

There are various types of patent families according to
different definitions. For single priority families, which
will be used here, each family constitutes one FF to-
gether with all the SFs that lead from it. Thus each FF
from which a priority filing emanates can initiate one
family only. But the SFs in F1, that are the offspring of
the FFs, can belong to more than one family.

More extensive definitions of patent families are possi-
ble, that include for instance composite patent families,
where each family consists of a complete interconnected
network of FFs and SFs. This has the advantage of
making every family unique, because no patent publica-
tion can belong to more than one family. However this
may not be such an important consideration. In a study
involving the whole population of recorded publications
with earliest priorities in the period from 1991 to 1999, it
was found that the nine most common family structures
relate to a single priority and make up more than 77 per
cent of patent families [8]. Also, 29 per cent of families
consisted of only a pair of one FF with one SF.

Single priority families can be used to describe patent

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P. Hingley, Exploring Family Relations between International Patent Applications

Fig. 3. Random hits model.

filings flows between countries (Fig. 2), although the
subtleties of multiple assignments between FFs and SFs
should also be taken into account to give a complete
description. In order to do this, the concept of links is
important. That is, each priority reference from a SF
forms a link to the FF that is referenced. In a set of p
FFs and y SFs emanating from those FFs, involving in
each case filings at one or more patent offices, let there
be L links. Say that the average number of SFs that are
linked to a FF is φ, while the average number of FFs
that are linked to a SF is θ. These averages relate to L
as follows [2].

L = p.φ = y.θ

III. RANDOM HITS MODEL FOR PRIORITIES

Fig. 3 shows that the setup of p priority filings in
the F0 generation with L links to y SFs in the F1
generation can be represented by a surjective directed
graph. For the idealised model to be considered here,
the occasional groupings of several members of L into
sets that represent SFs with several priority references
will be ignored.

Let r be the number of members of p that are hit by
the L links. If p and L are considered to be fixed, r can
be modelled by a random process of hits on p by L.

A. Exact Distribution

Feller [9] developed the following formula for
the discrete probability distribution of r, under the
hypothesis of a process of independent random hits.

P r(r) = 1
pL

( p
p−r

) ∑r
ν=0 (−1)

ν ( rν )(r − ν)L

This is valid for any values of L and p that are positive
integers. No explicit expression is given for the moments
of this distribution. Feller’s examples concentrate on the
case L > p, such as where r is the number of days in
a year when there is at least one birthday in a village
of 2000 people (L = 2000, p = 365). In our case here
L < p, because only a proportion of FFs lead to SFs.

For the following calculations, routines were written
in R. P r(r) is easily computable only when r is small.
Fig. 4 shows P r(r) for the case p = 30 and L = 20.
Direct evaluation gives a mean of 14.77 and a standard
deviation (square root of variance) of 1.49. The distrib-
ution was checked by constructing the r values obtained
in one million simulated sets of data, where each set
was formed by sampling randomly with replacement
the first p integers L times. The resulting histogram is
indistinguishable visually from Fig. 4, with a mean of
14.76 and a standard deviation of 1.50. This shows good
agreement with the exact distribution.

B. Poisson approximation

Feller [9] argues for a Poisson approximation for
P r(r) as p and L −→ ∞. Say t is the number of
members of p that do not lead to subsequent filings. He
asserts that, if λ = pe−

L

p remains bounded,

P r(t) −→ e−λ. λ
t

t!
| [0 < t < ∞]

The support of this distribution is not bounded above. In
fact p is finite and we are interested in P r(r = p − t).
This can be approximated by a transform of the Poisson
distribution, bounded above at p but unbounded below 0.

P r(r) ≈ e−λ. λ
(p−r)

(p−r)! | [−∞ < r ≤ p]

Fig. 5 shows P r(r) for the case p = 30 and L = 20,
and can be compared to the exact distribution in Fig.
4. Direct evaluation gives a mean of 14.61 and the
quantity p − λ is 14.60, showing good agreement with
the mean according to Feller’s argument, and not too far
from the exact distribution mean of 14.76. However the
standard deviation is 3.92, which is more than twice as
high as 1.49 for the exact distribution. The shape is also
different, and is essentially censored at the upper limit
of 20, where r = L.

C. Censored Binomial Approximation

Since the Poisson approximation does not work well
at this sample size, other approximations can be tried. A
censored binomial distribution is in some way equivalent

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P. Hingley, Exploring Family Relations between International Patent Applications

Fig. 4. Exact distribution with p = 30 and L = 20.

to Feller’s exact distribution, except that the hit probabil-
ities are all considered independent and equivalent, and
dependency due to the conditional probability chain is
ignored.

Say that s is the number of hits from L to a
member of p. This can be represented approximately as
Binomial(s, L, 1

p
), meaning the binomial probability

of s successful outcomes when there are L independent
trials, each with probability 1

p
of success.

P r(s) ≈ L!
s!(L−s)! (

1
p
)s

(
1 − ( 1

p
)
)(L−s)

=
Binomial(s, L, 1

p
)

Under an assumption of independence, the probability
that a particular member of p is hit is then as follows.

1 − Binomial(0, L, 1
p
) = 1 − (1 − 1

p
)L

r is the number of distinct members of p that are hit.
If L ≥ p, as in the birthdays example in IIIA,

P r(r) ≈
Binomial(r,p,1−(1− 1

p
)L)

[1−Binom(0,p,1−(1− 1
p
)L)]

This is a censored binomial that removes the zero class,
because at least one member of p must be hit (P r(0) =
0).

But in the patent families case, where L < p, the
response range is restricted to r in (1, ..., L), so there
is also censorship to remove all classes between and
including L + 1 and p.

P r(r) ≈
Binomial(r,p,1−(1− 1

p
)L)

[1−Binom(0,p,1−(1− 1
p
)L)−

Pp
j=L+1 Binomial(j,p,1−(1−

1
p
)L]

Fig. 5. Poisson approximation with p = 30 and L = 20.

Fig. 6 shows P r(r) for the case p = 30 and L = 20, to
compare with Fig.s 4 and 5. The R routine in this case
calculates the probabilities using the normal approxima-
tion to the binomial distribution. It was checked that this
makes minimal difference to usage of the exact binomial
expressions, even at this small population size.

Direct evaluation gives a mean of 14.63, again fairly
close to the exact distribution mean of 14.76. This time
the standard deviation is 2.64, which is closer than
the Poisson approximation to the 1.49 for the exact
distribution. The shape is however still quite different
to the exact distribution, although not as far away as the
Poisson was.

IV. RANDOM HITS MODEL FOR PATENT FAMILIES
DATA

The distributions in III can be scaled up to give tests
of random hits to patent families with SFs at EPO. In the
following examples, FFs at EPO were ignored because
they were already hit in a sense at the time of first filing.
It should also be recognised that FFs and SFs at EPO do
not represent all the patenting activity in Europe, because
of the alternative possibility to file at the national patent
offices in each EPC contracting state. Note also that the
analysis will be monospecific, in that it is only the flows
to EPO that are considered, and not the spread of flows
to all offices, as was considered in [8].

In order to scale up to the case of an annual data set
of first filings (F0 generation) and the subsequent filings
that quote them as priorities (F1 generation), consider
p =1 052 420 worldwide first filings in the year 2002
and L =135 439 references to these priorities that were
made in SFs to EPO, mainly in the year 2003. The subset

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P. Hingley, Exploring Family Relations between International Patent Applications

Fig. 6. Censored binomial approximation with p = 30 and L = 20.

of p that were referenced was of size r =120 701. How
near was this to a random process of hits of L on p?

Feller’s exact distribution is not calculated in this
case because it is no longer straightforward to do so
with large numbers (the practical upper limit for the R
routine is about p = 60). Simulations are also more time
consuming, but it is possible to make enough of these
to get a good idea of the shape of P r(r). Fig. 7 shows
a first estimate of the distribution that was made with
1000 simulated data sets. What is being emulated here
is presumably a unimodal discrete distribution like Fig.
4, but due to a lack of binning we see a discretised ap-
proximation (P r(r) = 0.001 equivalent to one simulated
outcome, P r(r) = 0.002 equivalent to two simulated
outcomes, etc.). The mean is estimated as 127 079 and
the standard deviation is 84. While these parameters are
obviously not determined with great accuracy, due to
the small number of simulations carried out, the shape
of the distribution indicates that the observed value r =
120 701 is significantly lower than its expectation under
the random hits model.

The simulation results in Fig. 7 lie in a very tight
range around their mean, compared to the support. Under
a normal approximation, 95 per cent of the simulated r
values are expected to be between 126 911 and 127 247.

The distributions P r(r) according to Feller’s Poisson
formula and the censored binomial approximation are
shown in Fig.s 8a and 8b respectively. They are both
centered close to the mean of the simulations, and p−λ
from the Poisson approximation is 127 086, which is
also close to the mean of the simulations. But the spreads
of both distributions are again too large, with standard
deviation according to the Poisson distribution at 962
and for the censored binomial formula at 334. However

Fig. 7. Simulated distribution of r, based on 1 000 simulated data
sets with p = 1 052 420 and L = 135 439.

it can be seen in this figure that the observed value of r
is still significantly too low to be entirely random, even
for the Poisson formula.

So it seems that the number r of worldwide priorities
in 2002 that were hit by EPO SFs was lower than
expected under a random hits model. The test was also
carried out on priorities after separation into the main
geographical blocs of origin (EPC, Japan, US, Others)
and over five priority years (2002 to 2006 inclusive). See
Figs. 9a to 9d. The expected values under the random
hits model are represented in these diagrams by values
of p − λ (triangles).

The results are fairly consistent over the years that
were studied. There are less hits than expected for
priority references to US first filings, but more hits than
expected for priority references to EPC, which is the
European home area for EPO operations. This suggests
that there is only a subset of US FFs that somehow
qualify for filings as SFs later on at EPO, which is
reasonable for a large country with some of its own
specific internal markets that are not relevant abroad.
For Europe, the contrary result means that priorities are
better sampled than expected and rarely lead to multiple
EPO SFs. The results show r conforming more or less
to its expectation under random hits for Others origin
and Japan origin priorities (in the case of Japan at least
for the years 2004 to 2006). The values of L

p
(average

number of links to priorities overall) differ between blocs
(EPC 35 per cent, Japan 8 per cent, US 20 per cent,
Others 2 per cent, for priorities in 2002). It is interesting
that in Japan and Others this was far less than in the
other two blocs. Perhaps the fact that the probability of
a hit was lower has led to a better fit of the Poisson

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P. Hingley, Exploring Family Relations between International Patent Applications

Fig. 8. a) Poisson approximation; b) Censored binomial approxi-
mation; with p = 1 052 420 and L = 135 439.

approximation or to the random hits model in general.

V. POSSIBLE APPLICATIONS IN BIOLOGY

In II it was suggested that temporal F0/F1 generations
with annual replacement represents only a special case
in population genetics. The schema lacks the attractive
equilibrium properties that are interesting when making
theoretical predictions about population dynamics and
evolution over many generations.

But there may be possibilities for applications of such
models to special cases in biology. Consider for example
the transformation of an undifferentiated bank of stem
cells into tissues and/or organs, such as the development
of clones of immune cell against specific antigens [10].
How many of the stem cells will differentiate and into
what tissue, if there are indeed different possible stem
cell fates in development? In III and IV an unexpected
tightness of the distribution P r(r) was found around
its mean. This suggests that the number of stem cells
committing to become certain organs under a random
differentiation model may be almost constant, even if
random. Aberrations in the process could perhaps occur
in cancer.

It may be useful to study competition between tissues
as sinks for stem cells. In the patent world this is
analogous to studying the fates of first filings in terms
of priority references from subsequent filings in several
other offices. For example such counts appear in [7] in
terms of trilateral (EPO, Japan, US) and Four Office
(EPC, Japan, Korea, US) family subsets.

Another extension to the present model that can be
beneficial to consider in both biological and patent
regimes is the case where there are several conversions
of the original entity via a sequence of transforming hits
taking place in a temporal series. In the patent world
there is the sequence of transformations of the priority

forming first filing into a subsequent filing, followed by
the possible grant of the patent and its eventual expiry,
not to mention the collection of a cumulative set of fees
at the patent office in lieu of these various steps. In
biology there are sequences of cellular development that
lead down limited paths of development under certain
restrictions, such as colon crypt cell growth. This is a
special case to which population genetics theory can be
adapted, and brings us back towards schemes such as in
Fig. 1 [11].

VI. CONCLUSIONS

The development started with a description of the fam-
ily relations of groups of patents in terms of population
genetic parameters, and then continued by developing
specific tests of random assignment of subsequent filings
to priorities via distributions of hits. It turned out that
the distributions are so tight that the outcomes almost
appear to be fixed, even though the underlying process
is random. There was a brief consideration of how
biological models for certain special phenomena may be
able to make use of the method.

The exact formula in IIIA gives the best representation
of the effects of random hits, but it is not easily calcu-
lable when constructing a null distribution for large data
sets. Feller’s argument for a limiting Poisson distribution
does not apply well for the case that L < p, because
its variance is too large. However the quantity p − λ
is a good approximation for the mean. A censored
binomial distribution is also well centered and has a
lower variance than the Poisson, but is still too disperse.
A closer approximation to the exact distribution should
be established, that can work with larger numbers and
stays as close to the original formula as possible.

For patent families that involve subsequent filings at
EPO, the observed number of priorities is less than that
predicted by the random hits model. This is mainly due
to less hits than expected from applicants in US, although
there are more hits than expected from Europe. To model
these situations more explicilty, it may be beneficial to
develop a weighted version of the exact formula, where
combinations with fewer hits have higher weights (US
case) or lower weights (EPC case) than combinations
having a greater number of hits.

Apart from the possible extensions that were men-
tioned in V, it will also be interesting to develop more
intricate models of the international patenting system.
This could include an extension of the model presented
here to test independence of hits to a common set of
first filings when subsequent filings are made to several

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P. Hingley, Exploring Family Relations between International Patent Applications

Fig. 9. The results for apparent randomness of r depend on blocs
of origin of the patent families. Reading clockwise from top left: a)
EPC, b) Japan, c) Others, d) US. L: dotted line; r: boxes; p − λ:
triangles.

other patent offices. Models could also be developed to
consider the effects of having several priority references
to different first filings from some of the subsequent
filings.

ACKNOWLEDGMENT

The author would like to thank colleagues for supply-
ing and maintaining the PRI data file, and Marc Nicolas
for useful discussions on the methods.

REFERENCES

[1] P. Hingley, and M. Nicolas, (eds), Forecasting Innovations,
methods for predicting numbers of patent filings, Springe, 2006.

[2] P. Hingley, Patent families defined as priority forming filings and
their descendents,
http://forums.epo.org/students-2-students/topic720.html (2010).

[3] Z. Griliches, Patent statistics as economic indicators: a survey,
Journal of Economic Literature 28, 1661–1707 (1990).

[4] J.C. Vivar, and D. Banks, Models for networks: a cross-
disciplinary science, WIREs Comp. Stat. 4, 13–27 (2012).
http://dx.doi.org/10.1002/wics.184

[5] J. Ewens, Mathematical population genetics, Vol. 1, 2nd edition,
Springer, 2004.
http://dx.doi.org/10.1007/978-0-387-21822-9

[6] P. Hingley, and S. Bas, Numbers and sizes of applicants at the
European Patent Office, World Patent Information 31, 285–298
(2009).

[7] European Patent Office, Japan Patent Office, Korean Intellectual
Property Office, United States Patent and Trademark Office. Four
Office Statistics Report, 2010 edition,
http://www.trilateral.net/statistics/tsr/fosr2010.html (2011).

[8] C. Martinez, Insight into different types of patent families,
http://www.oecd.org/dataoecd/21/32/44604939.pdf (2010).

[9] W. Feller, An introduction to probability theory and its applica-
tions, Vol. 1, Wiley, 1968.

[10] D. Wodarz, Killer cell dynamics, Springer, 2007.
http://dx.doi.org/10.1007/978-0-387-68733-9

[11] M.A. Nowak, Evolutionary dynamics, Belknap Harvard, 2006.

Biomath 1 (2012), 1209031, http://dx.doi.org/10.11145/j.biomath.2012.09.031 Page 7 of 7

http://forums.epo.org/students-2-students/topic720.html
http://dx.doi.org/10.1002/wics.184
http://dx.doi.org/10.1007/978-0-387-21822-9
http://www.trilateral.net/statistics/tsr/fosr2010.html
http://www.oecd.org/dataoecd/21/32/44604939.pdf
http://dx.doi.org/10.1007/978-0-387-68733-9
http://dx.doi.org/10.11145/j.biomath.2012.09.031

	Introduction
	The Structure of Patenting and Patent Families
	Random Hits Model for Priorities
	Exact Distribution
	Poisson approximation
	Censored Binomial Approximation

	Random Hits Model for Patent Families Data
	Possible Applications in Biology
	Conclusions
	References