The Early Detection of Disease

1
The Early Detection of Disease Statistical
Challenges

• Marvin Zelen
• Harvard University
• The R.A. Fisher Memorial Lecture
• August 1, 2007
• Joint Statistical Meetings
• Salt Lake City, Utah

2
Outline

• Background and Motivation
• Statistical Challenges
• The Early Detection Process
• Applications
• Breast Cancer Screening with mammography
• Do women under 50 benefit?
  --Controversial
• Public Health Programs U.S., U.K.
  and Nordic countries have
  different recommendations ---- tradeoffs?
• Prostate Cancer Probability of Over
  Diagnosis

3
Background and Rationale

• Screening Programs Special exams to diagnose
  disease when it is asymptomatic.
• Motivation Diagnosing and treating the disease
  early, before signs/symptoms appear, may result
  in more cures and lower mortality.

4
Examples of Screening Programs

• Tuberculosis Hypertension
• Diabetes Coronary Artery Disease
• Cancer Thyroid Disease
• Breast Cancer Osteoporosis
• Cervical Cancer HIV
• Colorectal Cancer
• Lung Cancer
• Prostate Cancer

5
Scientific Evidence of Screening Benefit

• Diagnosing disease early does not necessarily
  result in benefit e.g. diagnosing a primary
  cancer earlier may not be of benefit if the
  disease has already metastasized.
• A necessary condition for benefit by early
  detection requires that the disease tends to be
  diagnosed in an earlier stage
• If an effective treatment does not exist, there
  is no benefit in diagnosing disease early.
• The general consensus is that randomized
  clinical trials are the only way to evaluate
  screening programs for potential benefit.

6
Some Statistical Challenges

• Planning early detection clinical trials
• Early detection clinical trials are different
  from therapeutic trials. Power depends on number
  of exams and time between exams. There exists an
  optimum time for follow up and analysis.
• Public Health Programs Recommendations
• Initial age to begin screening, intervals
  between exams, high risk individuals.
  Recommendations should be made by risk status.
  --- Costs may be an important consideration.
• Over diagnosis
• Disease may be diagnosed early, but may never
  evolve clinically in a persons lifetime.
  Important to estimate probability of over
  diagnosis?

7
Early Detection Randomized Clinical Trials

• Typical trial consists of two groups . One
  group (control) receives usual care the other
  group (study group) receives invitation to have
  a finite number of special examinations.
• Follow up for disease occurrence and death
  continues after the last exam.
• Endpoint is death from disease.
• Randomization may be carried out on an
  individual basis or by cluster randomization
• e. g. geographical region, physician practice.

8
Early Detection vs. Therapeutic Trials

Statistical Problem Design of Early Detection
Clinical Trials. -- How many subjects, exams,
exam spacing, follow up and optimal analysis
time, etc.
9
Early Detection Clinical Trials

• Only subjects who are diagnosed with disease
  carry information about benefit.
• Trials need very large number of subjects
• Relatively low incidence is characteristic of
  many chronic diseases e.g. female breast cancer
  incidence is about 80-100 per 100,000 women per
  year depending on age.
• Typical trial will require 10-20 years. During
  this time the technology for diagnosing disease
  may have changed.
• Conclusions may be of limited interest.
• Statistical challenge Is it possible to carry
  out an early analysis, with limited follow up
  time?

10
Public Health Programs

• Screening Program Schedule of exams usually
  composed of (1) age to begin screening exams,
  (2) Intervals between exams and (3) possibly the
  age to end exams.
• Positive screening exam would motivate a more
  definitive exam (e.g. biopsy).
• Costs of a public health screening program may be
  very large.
• Statistical challenge How does one optimize
  public health screening programs? There are too
  many variables to carry out clinical trials to
  find optimal schedules.

11
Example Breast Cancer Screening Using
Mammography

• The American Cancer Society recommends that
  annual screening begin at age 40 for women at
  average risk. Costs of a screening mammogram
  range from 100-150. (70 M women over the age of
  40 in U.S.) Cost would be in billions of dollars
  if a significant number of women complied.
• United Kingdom The National Health Service
  offers screening beginning at age 50 with three
  year intervals for subsequent exams.
• Nordic countries The recommendation is that
  screening begin at age 50 with two year intervals
  for subsequent exams.
• Statistical challenge How to choose
  appropriate public health programs based on risk.

12
Over Diagnosis

• It is possible for some diseases to be diagnosed
  early which would never have clinical symptoms in
  a persons lifetime.
• Ordinarily the disease is treated when diagnosed
  it is not known whether the disease may exhibit
  clinical symptoms during a persons lifetime.
• Statistical challenge Estimate the probability
  of over diagnosis.

13
Need for Models

• Issues in the previous slide (optimal schedules,
  over diagnosis) cannot be addressed by RCTs.
• Too many variables, takes too long, too costly ,
  ethical concerns.
• Issues may be addressed by models
• The need for stochastic models is the principal
  statistical challenge in the theory and practice
  of early detection of disease.

14
Models

• S0 Disease free state Does not have disease or
  has disease which cannot be detected by exam.
• Sp Pre-clinical state Has disease but no signs
  or symptoms capable of being detected by exam.
  Individual is asymptomatic.
• Sc Clinical state diagnosis by usual care.
• S0 ? Sp? Sc Progressive disease model (Breast
  cancer)
• Sp
• S0 Sc Progressive disease model
  subgroup
• Sp never goes on to clinical disease (Prostate
  cancer)
• S0 ? Sp ? Sc Non-progressive disease model
  (HPV ,Cervical cancer)

15
Issues in the interpretation of data

• Suppose a group of patients undergo screening for
  a particular disease and a number of subjects are
  diagnosed and treated.
• The subjects in this screened group have longer
  survival than a control group (no screening). Is
  this scientific evidence of the benefit of
  screening?
• No ---- Length biased sampling and lead time bias
  may introduce significant biases

16
Natural History of Progressive Disease
Duration of Pre-clinical State

Lead Time (forward recurrence time)
Age
Age of Screening
Clinical Inception Point
Diagnosis Of disease (Early diagnosis)
S0 Sp
Sp Sc
17
Length biased sampling

• Consider a population of cases

Time
Screening point

• Horizontal line duration of time in
  pre-clinical state
• Diagnosis equivalent to placing a random
  vertical line. Intersection represents case
  diagnosed.
• Vertical line is more likely to intersect longer
  horizontal lines.

18
Lead Time Bias Usual care

• S0 ? Sp Sp ? Sc
  Death

Age
50 55
60
clinical diagnosis
Survival from Clinical Diagnosis 60 55 5
Years

• S0 disease free state, Sp pre-clinical state
• Sc clinical state

19
Early Detection But Survival Is Not Enhanced
S0?Sp
Death
Sp?Sc
53
55
Age
50
60
Screening Point and Diagnosis
Diagnosis usual care
Survival from Screening Diagnosis 60 53 7
Years
Survival (with usual care diagnosis) 60 - 55 5
years
20
Dynamics of the Natural History (1) Usual care

• Disease States
• S0 Disease free state disease free or
  disease state which cannot be detected
• Sp Pre-clinical state - asymptomatic with no
  signs/symptoms
• Sc Clinical state when diagnosed by routine
  methods
• Sd Death state (death due to disease)

Disease incidence
Death from disease

Age x not observed
Age
x
t
y
S0 Sp
Sc Sd
Sp Sc
Usual care disease is diagnosed and treated at
t.
.
21
Dynamics of the Natural History (1) Usual care

• Disease States
• S0 Disease free state disease free or
  disease state which cannot be detected
• Sp Pre-clinical state - asymptomatic with no
  signs/symptoms
• Sc Clinical state when diagnosed by routine
  methods
• Sd Death state (death due to disease)

Disease incidence
Death from disease

Age x not observed
Survival
(y t)
Age
x
t
y
S0 Sp
Sc Sd
Sp Sc
Usual care disease is diagnosed and treated at
t.
.
22
Dynamics with Screening (2) Exam detected case
at tS
S0 disease free Sp pre-clinical Sc clinical
Sd death from disease

Exam detected

y
t
x
Age

ts
Sd
S0 Sp
Sp Sc
Not observed Disease Interrupted at ts

• Ages t and x are not observed.
• Treatment begins at tS

23
Dynamics with Screening (2) Exam detected case
at tS
S0 disease free Sp pre-clinical Sc clinical
Sd death from disease

• (y ts)

Observed Survival
Exam detected

y
t
x
Age

ts
Sd
S0 Sp
Sp Sc

• Ages t and x are not observed.
• Treatment begins at tS
• Observed survival time (y ts)

24
Dynamics with Screening (2) Exam detected case
at tS
S0 disease free Sp pre-clinical Sc clinical
Sd death from disease

• (y ts)

Observed Survival
Exam detected

y
t
x
Age

ts
Sd
S0 Sp
Sp Sc
Lead Time
Lead Time

• Ages t and x are not observed.
• Treatment begins at tS
• Observed survival time (y ts)
• (t ts ) is lead time.

25
Dynamics with Screening (2) Exam detected case
at tS
S0 disease free Sp pre-clinical Sc clinical
Sd death from disease

• (y ts)

Observed Survival
Exam detected

y
t
x
Age

ts
Imputed Survival
Sd
S0 Sp
Sp Sc
Lead Time
Lead Time

• Ages and x are not observed.
• Treatment begins at tS
• Observed survival time (y ts)
• (t ts ) is lead time.
• Imputed survival Survival with origin ?
  (observed survival) ( lead time)

26
Dynamics with Screening (3) Exam detected case
at tS
S0 disease free Sp pre-clinical Sc clinical
Sd death from disease

• (y ts)

Observed Survival
Exam detected

y
t
x

t0 t1
tj-1 tj
Age

ts
Imputed Survival
Sd
Exam times
Sp Sc
Exam times
S0 Sp
Lead Time
Lead Time

• Ages and x are not observed.
• Treatment begins at tS
• Observed survival time (y ts)
• (? ts ) is lead time.
• Imputed survival Survival with origin ?
  (observed survival) ( lead time)
• There may be a number (unknown) of false
  negative exams

27
Dynamics with Screening (3)
Interval Case Case diagnosed between tr-1 and tr
Survival (y - )
t
y
t
x
Time

tj-1
tj tr-1
tr

t0
t1
S0 Sp
Sp Sc
Sd
Exams at t0 lt t1 lt lt tr-1
28
Notes on Modeling

• Survival begins at point of clinical diagnosis
  for usual care group (control).
• In order to make comparisons with control group,
  all cases in screened group (early diagnosis,
  interval) must have survival beginning at point
  of clinical diagnosis. This is true for
  interval cases, but not true for screened
  diagnosed cases.
• It is necessary for model to subtract lead time
  (random variable, not observed) from survival
  for screened cases so that survival is measured
  from point of imputed clinical diagnosis (not
  observed).
• Screened cases are subject to length biased
  sampling. This feature must be incorporated in
  the model.

29
Applications to Breast and Prostate Cancer

• Breast Cancer Screening (Mammography)
• Benefit for women in their 40s?
• Public Health Programs
• Choosing screening intervals
  according to risk.
• Comparison of U.S., U.K. and
  Nordic countries
• Prostate Cancer
• Over diagnosis

30
Data Inputs for Breast Cancer Applications (
From Clinical Trials)

• Mean sojourn time in pre-clinical state varies by
  age
• ? age 40 2 years
• ? age 50 and above 4 years
• Sensitivity varies by age
• ? age 40 sensitivity 0.7
• ? age 50 and above sensitivity 0.9

31
Screening Younger Women 40, 49 for Breast
Cancer Using Mammography

• Dispute whether women in their 40s benefit from
  screening. (clinical trials inadequate in this
  age group)
• Screening women in age group 40, 49
• Relatively low chance of developing breast cancer
• Mammogram sensitivity is lower for this age group
• Relatively high cost
• 1997 NIH Consensus Development Panel
• Review of data from 8 clinical trials
• The available data did not warrant a single
  recommendation for all women in their forties.
• Nevertheless ACS and NCI recommend screening
  women in their 40s.

32
Use of Model Evaluating Benefit for Women Aged
40-49

• STRATEGY. Compare the mortality of a screened
  group ( exams only for women in their 40s) with
  a control group.
• Note that these subjects may die of disease past
  the age of 49. The population who were in the
  pre-clinical state in their 40s is the target
  population who can benefit.
• Clinical trials and recent data indicate a
  stage shift ( relative to usual diagnosis) with
  early detection for this age group. Node
  negative (good prognosis) 77 (screening) vs.
  53 (usual care).

33
Mortality reduction Screening in 40s only
Counts all breast cancer deaths for ages 40-79.
Exam Schedules by Age

• 40, 41, 42, 43, 44, 45, 46, 47, 48, 49 (annual)
• 40, 42, 44, 46, 48, 49
• 40, 43, 46, 49
• 40, 45, 49
• 40, 49

Conclusion Women benefit from screening in
their 40s. However it would take an enormous
clinical trial to demonstrate this benefit
Conclusion Women benefit from screening in
their 40s. However it would take an enormous
clinical trial to demonstrate this benefit
34
Public Health Programs Choosing Exam Schedules

• Exam schedule consists of initial age to begin
  screening, the time between exams and the age to
  terminate exams.
• Schedule should be dependent on risk status .
  Risk status depends on
• Natural history of disease ( Most chronic
  diseases are age dependent)
• Model for disease
• Incidence, prevalence
• Special factors --- family history, co-morbid
  diseases,etc
• Characteristics of examinations
• Sensitivity
• Specificity
• Costs

35
Equal Intervals Between Exams

• When are equal intervals optimal?
• A necessary and sufficient condition that equal
  intervals between exams are optimal is when
  disease incidence is independent of time (age).
• Not true for many chronic diseases incidence
  may increase with age.
• Hence many recommendations are sub-optimal.

36
Choosing Intervals According Risk Threshold
Method

• Choose an age t0 to begin initial screening exam.
  This age corresponds to a probability P(t0 ) of
  being in the pre-clinical state (calculated from
  model).
• Have an exam whenever the the probability of an
  individual reaches this threshold probability.
• Alternatively, choose a threshold probability
  (P0) and have exams at ages ti whenever P(ti )
  P0.

37
Illustration of Threshold Method Breast cancer
Exam whenever risk is
the same as at age 50.
Intervals between exams
38
Threshold Method

• Women ages 50-79
• Threshold value P0(50)0.0062
• 11 exams at ages (rounded) 50, 54, 57, 61, 63,
  66, 69, 71, 74, 76, 78.
• Avg. interval between exams 2.5 years
• Proportion of cases diagnosed by screening exam
  for ages 50-79 73
• Proportion of cases diagnosed by screening exam
  for ages 0-79 61

39
Mammogram Exam Schedules for Ages 50, 79

• Annual U.S. ACS/NCI Recommendation
• Every 2 Years Scandinavian Recommendation
• Every 3 Years U.K. Recommendation
• Mortality Reduction
• Mortality (controls) Mortality
  (screened ) Mortality (controls)

40
Overdiagnosis Prostate Cancer

• Background Prostate Specific Antigen (PSA) test
  is widely used to diagnose prostate cancer. A
  positive result triggers a biopsy Nearly all
  diagnosed cases by PSA are asymptomatic.
• Question Would the prostate cancer exhibit
  clinical symptoms during a mans lifetime? If
  not --- PSA diagnosis is an overdiagnosis

Over diagnosis Lead Time gt Residual Survival
Residual Survival (Time from early diagnosis to
death from other causes)
Lead Time
Age
S0?Sp PSA Death Sp?Sc Diagnosis
41
Numerical Calculation Prostate Cancer

• Men ages, 50 to 80, have positive PSA test
  which leads to a positive biopsy. What is the
  probability of over diagnosis ?
• Prob no clinical cancer in mans lifetime
  PSA diagnosis at age A
• Probability of over diagnosis depends on age
  and mean sojourn time in pre-clinical state.

42
1.0
mean sojourn of 5 yr
0.8
mean sojourn of 7.5 yr
mean sojourn of 10 yr
mean sojourn of 12.5 yr
mean sojourn of 15 yr
0.6
Probability of Over Diagnosis
0.4
0.2
0.0
Age
50
60
70
80
Probability of over diagnosis conditional on age
of early detection Prostate cancer
Probability of over diagnosis conditional on age
of early detection Prostate cancer
43
Conclusions

• Early detection of chronic diseases has the
  potential of significant benefit (lower mortality
  , increased cure rates)
• Current recommendations for special exam
  programs not based on analytic considerations
  weighing costs vs. benefits.
• Clinical trials to evaluate benefit require long
  term follow-up. Statistical models may be able to
  predict outcome using early clinical trial data.
• The advances in genomics are likely to generate
  candidate markers which may be used for the early
  detection of disease. Require a way of carrying
  out clinical trials which do not take a long time
  to complete.
• Need to estimate probability of over diagnosis
  with the discovery of markers.

44
My Collaborators

• Sandra J. Lee , Dana_Farber Cancer Institute and
  Harvard School of Public Health
• Yu Shen, M.D Anderson Cancer Center
• Ping Hu , National Cancer Institute
• Ori Davidov, Haifa University

45
Thank you for coming
46
(No Transcript)
47
Why would screening result in benefit ?

• If screen diagnosed cases are found in an earlier
  disease stage compared to usual care then there
  is likely to be benefit. This is referred to as a
  stage shift.
• Stage shift can be due to a long lead time
  i.e.cases are diagnosed before they transit to a
  more advanced prognostic stage.
• Stage shift may also arise from the length biased
  sampling. The selection of cases by screening
  may also be associated with earlier prognostic
  stages.

48
Natural History of Disease

• S0 Disease Free State or Cannot Be Detected
• Sp Pre-clinical State
• Sc Clinical State

Time in stages I and II
Stage II Stage I
Time (age)
Sp? Sc
S0?Sp
49
Stage Shift and Earlier Diagnosis

• S0 Disease Free State or Cannot Be Detected
• Sp Pre-clinical State
• Sc Clinical State

Stage II Stage I
Time (age)
Sp? Sc
S0?Sp
Early Diagnosis
Note the longer the mean lead time the greater
the probability of diagnosing disease in an
earlier stage.
50

• Mean lead time is calculated from theoretical
  distribution
• Proportion of negative nodes is data from
  clinical trials.

51
Summary on Stage Shift Breast cancer

• Trial Stage Control Study Screen Interval
• Detected Detected
• HIP N 52 41 30 50
• 2-County II-IV 46 30 19 45
• Malmo I 59 39 23 56
• Edinburgh 87 64
  50 72
• --------------------------------------------------
  -------------------------
• II-IV Stages II - IV ( AJCC)

• The interval cancers tend to have the same stage
  as a control group.
• If stage shift was due to length biased sampling,
  the interval cancers would tend to have more
  advanced stage than a control group. This is not
  the case.

52
Summary on Stage Shift Breast cancer

• Trial Stage Control Study Screen Interval
• Detected Detected
• HIP N 52 41 30 50
• NBSS-I 42 42 35 49
• NBSS-2 (MP) 41 35 50
• (PO) 43 42
  41
• 2-County II-IV 46 30 19 45
• Malmo I 59 39 23 56
• Stockholm 63 42
• Edinburgh 87 64
  50 72
• --------------------------------------------------
  -------------------------
• MP mammogram physical exam
• PO physical exam
• 1981-5
• II-IV Stages II - IV ( AJCC)