Hi,
my
name
is
Michael
Crotty.
I'm
a
statistical
writer
with
the
Stat
Documentation
Team
at
JMP,
and
today,
I'm
going
to
talk
about
an
introduction
to
censored
data
analysis
in
JMP
and
JMP
Pro.
To
start,
we've
got
three
common
types
of
censoring.
Just
to
back
up
a
bit,
censored
data
occur
when
you
don't
have
an
exact
measurement
for
an
observation,
but
you
do
know
a
range
for
the
observation,
so
you
know
not
the
exact
value,
but
you
do
know
something
about
where
the
value
might
be.
What
we
want
to
do
by
using
censoring
in
our
analyzes
is
to
use
that
information
that
we
have,
even
if
it's
not
exact.
The
three
types
of
censoring
that
we'll
talk
about
today
are
right
censoring,
left
censoring,
and
interval
censoring.
Right
censoring
is
probably
the
most
common
form
of
censoring.
It
occurs
when
the
event
of
interest
just
doesn't
have
time
to
occur
yet
by
the
end
of
the
study.
In
a
reliability
test,
you
might
have
a
bunch
of
light
bulbs
under test
and
at
the
end
of
the
test
period,
some
of
them
have
failed.
Those
are
exact
observations,
but
then
some
haven't
failed
yet.
You
know
they're
going
to
fail,
but
your
study
has
ended,
so
it's
censored
at
that
point.
Same
thing
in
survival
models
where
a
patient
survives
to
the
end
of
the
study.
One
thing
to
note
is
that
right
censoring
is
the
only
type
that
in
JMP,
supports
a
single
response
column
alongside
of
a
binary
censor
column.
The
next
type
is
left
censoring.
That's
where
the
event
of
interest
occurs
before
the
observation
starts.
A
common
example
of
that
would
be
where
you
put
a
bunch
of
units
under
test
and
at
the
time
that
you
do
the
first
inspection,
some
of
them
have
already
failed.
You
know
that
they
started
without
a
failure,
but
by
the
time
you
measured
them,
you
checked
on
them,
they
had
failed.
So
they
failed
sometime
before
that
point.
Another
example
of
that
is
limited
detection
where
you
have
a
measurement
tool
that
can't
measure
below
a
certain
threshold.
The
last
type
we'll
talk
about
today
is
interval
censoring.
This
is
where
your
event
of
interest
happens
between
observation
time.
If
you
have
a
periodic
inspection
schedule
instead
of
continuous
observation,
you
might
see
that
something
fails
or
something
happens
between
time
two
and
three.
It
didn't
happen
at
time
two
and
it
didn't
happen
at
time
three,
but
it
was
somewhere
in
that
interval.
Take
a
quick
look
at
what
this
looks
like
in
JMP.
Here's
an
example
of
the
right
censoring
with
a
response
column
and
a
censor
column.
In
the
platforms
that
support
censoring,
you
always
see
this
censor
role,
that's
for
that
binary
censoring
column.
This
is
the
way
that
you
can
do,
you
can
specify
censoring
more
generally,
which
is
with
two
response
columns.
Basically,
it's
like
a
start
time
and
an
end
time.
For
left
censoring,
we
don't
know
when
it
happened,
so
the
start
time
is
missing,
but
the
end
time,
we
know
it
happened
before
time
50,
so
somewhere
before
that.
Reversed
that
for
right
censoring,
we
know
that
at
time
25,
it
hadn't
happened
yet,
but
it
happened
sometime
after
that.
Then
with
interval,
both
the
start
and
endpoints
are
non-missing,
but
we
don't
know
when
the
event
happened
in
this
case
between
80
and
150.
It's
not
shown
in
the
table
up
here,
but
down
here,
we've
got
somewhere
there's
exact
censoring.
To
specify
that,
you
just
use
the
same
value
in
both
columns.
That
means
essentially
it's
like
an
interval
with
zero
width.
It
happened
at
that
exact
time.
Next,
we're
going
to
talk
about
two
examples
of
censoring.
The
first
is
if
you
have
censoring
in
your
data,
but
maybe
you
don't
know
how
to
handle
it,
and
so
you
just
think,
"I'll
just
ignore
it."
We're
going
to
look
at
what
can
possibly
happen
when
you
do
that.
In
this
example,
we've
got
simulated
data
from
a
lognormal
distribution
and
the
observed
data
that
we'll
use
for
analysis
in
our
different
cases
is
where
all
the
values
from
the
true
data
that
are
over
1,900,
we
set
them
to
1,900,
as that's
the
censoring
time
for
it's
right
censoring.
There
are
a
few
possible
things
you
could
do
if
you're
trying
to
estimate
this
mean
failure
time.
You
could
do
nothing.
You
could
just
use
this
observed
data
with
a
whole
bunch
of
values
set
to
1,900,
act
like
that's
when
it
happened.
You
could
treat
those
as
missing
values,
just
drop
them
from
your
data,
or
you
could
use
the
censoring
information
that
you
have
in
your
analysis.
For
right
censoring,
these
first
two
approaches
are
going
to
tend
to
underestimate
the
mean
failure
time
because
you're
dropping
information
from
the
data
at
that
far
end.
Looking
more
closely
at
this,
because
this
is
simulated
data,
we
have
the
true
distribution
here
in
this
first
column.
That's
just
for
comparison,
but
in
general,
you
wouldn't
have
that
because
you'd
have
that
all
values
above
1,900.
You
don't
know
where
these
fall.
In
our
observed
Y,
this
is
where
we
just
use
all
the
1,900s
as
values
of
1,900.
We
have
no
missing
values,
but
a
big
point
mass
at
the
top
of
our
distribution
here.
You
can
see
that
the
mean
is
a
lot
smaller
than
the
true
mean.
In
this
missing
Y
column,
this
is
where
instead
of
treating
them
as
1,900,
we
drop
them.
We
set
them
to
missing
and
analyze
the
distribution
without
them.
Here
you
can
see
that
now
our
maximum
of
the
non-missing
values
is
less
than
1,900,
which
really
doesn't
make
any
sense
because
we
know
that
a
bunch
of
them,
21
observations,
in
fact,
are
some
value
greater
than
1,900.
So this
underestimates
the
mean
even
more.
Then
on
the
right
here,
we've
got
an
analysis
in
life
distribution
in
JMP.
This
is
where
we're
using
the
observed
Y
column.
It's
got
those
1,900s,
but
we're
also
using
a
censoring
column
alongside
it.
For
the
rows
where
observed
Y
is
1,900,
our
censor
column
is
going
to
say
that
it's
a
censored
observation.
Here
we
can
see
that
our
mean,
it
actually
ends
up
being
a
little
higher
than
the
true
mean,
but
our
lognormal
parameter
estimates
are
much
closer
to
the
true
values
and
we're
incorporating
all
the
information
that
we
have.
For
our
next
example,
we're
going
to
look
at
detection
limits.
This
is
a
limit
of
detection
problem
where
we
have
data
on
the
yield
of
a
pesticide
called
Metacrate that's
based
on
levels
of
some
other
regression
variables.
In
this
situation,
the
measurement
system
that
we
have
has
a
lower
limit
of
detection
where
it
can't
measure
any
yields
that
are
less
than
1
%.
So
in
the
data,
they're
just
coded
as
zeros,
but
it
really
just
means
it's
some
yield
below
1
%.
There
are
two
ways
you
could
analyze
this
incorporating
that
information
in
JMP.
The
first,
you
could
treat
it
as
left
censoring,
use
two
response
columns
with
the
first
the
left
column
has
a
missing
value,
and
the
right
column
would
be
a
one,
or
you
can
use
the
detection
limits
column
property
that's
new
in
JMP
and
JMP
Pro.
We'll
take
a
look
at
this.
Here's
a
subset
of
the
data.
This
Metacrate
Reading
column
is
the
same
as
the
original
reading
column,
but
it's
got
a
detection
limits
column
property.
Because
this
is
a
lower
detection
limit
where
we
can't
measure
any
lower
than
that
limit,
we're
going
to
set
the
lower
detection
limit
to
one.
The
other
way
you
could
do
this
is
with
the
two
columns.
In
this
case,
we
know
that
it's
left
censoring,
so
the
left
side
is
missing
and
the
upper
side
of
that
is
one,
just
means
that
the
value
is
somewhere
less
than
one.
That's
all
we
know.
But
as
you
can
see
from
the
column
information
window
down
here,
the
detection
limits
column
property
is
recognized
by
the
distribution
and
generalized
regression
platform.
So
this
is
a
regression
problem.
We'll
use
generalized
regression
in
JMP
Pro.
Here
we
fit
a
lognormal
response
distribution,
and
it's
able
to
do
that
on
this
Metacrate
reading
column,
even
with
the
zeros
in
there,
because
GenReg's
not
treating
those
observations
as
zeros,
it's
treating
them
as
values
censored
at
one.
Now,
we
were
able
to
use
all
the
information
and
get
a
regression
model.
In
conclusion,
probably,
the
most
important
thing
is
when
you
have
censoring
information,
it's
better
to
use
it
in
your
analysis
than
to
ignore
it.
Censoring
can
occur
a
lot
of
times
for
time
responses,
but
it
can
also
occur
for
other
responses.
A
good
example
of
that
is
these
limited
detection
problems.
Finally,
you
can
use
the
following
approaches
to
specify
censoring
in
JMP.
There's
the
two-column
approach
that's
probably
the
most
flexible
because
that
allows
you
to
do
right
censoring,
left
censoring,
interval
censoring,
as
well
as
a
mix
of
all
three
of
those.
For
right
censoring,
you
can
use
the
one
column
response
paired
with
a
binary
indicator
column
for
censoring.
There's
also
this
new
column
property
in
JMP
for
detection
limits
where
you
can
set
a
limit
of
detection
either
on
the
low
side
or
the
high
side.
We've
got
a
few
references
here
if
you're
interested
in
more
information.
One
of
those
is
a
Discovery
talk
I
did
in
2017
that's
got
more
of
the
background
of
how
the
censoring
information
is
used
in
the
calculations
of
these
analyzes.
That's
it.
Thank
you.
