Screening & Conditional probability

Dr. Unaib Rabbani

Session Objectives:

• Describe the concept of screening and its importance• Know different types of screening and the criteria for a

good screening test• Appreciate the concept of lead time and lag time bias in

screening test• Understand the important Epidemiological terms related

to screening test, including • Validity (sensitivity& specificity), Reliability, and Yield

(positive/negative predictive values)• Apply Bayes’ theorem and conditional probability in

computing sensitivity, specificity and predictive values for screening test

What is Screening?Basic Public Health Concepts

• Screening is a strategy used in a population to detect a disease in individuals prior to the occurrence of signs/symptoms of that disease

• Screening tests are performed on persons without any clinical sign or symptoms of disease

• The purpose of screening is to identify disease in a community early, thus enabling earlier intervention and management to reduce disease mortality and morbidity

Screening Test are Concerned with a Functional Definition of Normality versus Abnormality

Difference b/w screening and diagnostic test

Screening Diagnostic testDone on apparently healthy people Done on sick people with S/S

Applied to groups Applied to individual patients

Usu. one disease considered Diff. diagnosis is ruled out

Based on one criteria Based on evaluation of various S/S

Less accurate More accurate

Less expensive More expensive

Not a basis of treatment Used as a basis of treatment

Initiative comes from investigator Initiative comes from pt. with S/S

Types of screening

Several types of screening exist: • Mass screening: involves screening of all individuals in a certain

category (for example, all children of a certain age)

• Case finding/High risk or selective screening involves screening a smaller group of people based on the presence of risk factors (for example, because a family member has been diagnosed with a hereditary disease)

• Multi-phasic screening involves application of two or more screening tests in combination, to a large number of people at one time than to carry out separate screening tests for single diseases i.e questionnaire, blood tests, urine D/R

Key Elements of screening

• Disease/disorder/defect

• Screening test

• Population

When a disease should be screened?

• Disease/disorder should be an important public health problem • High prevalence• Serious outcome

• Early detection in asymptomatic (pre-clinical) individuals is possible• Early detection and treatment can affect the course of

disease (or affect the public health problem)• Effective treatment is available

Criteria for Evaluating a Screening Test

• Validity: provide indication of who does and does not have disease• Sensitivity of the test• Specificity of the test

• Reliability: (precision): gives consistent results when given to same person under the same conditions

• Yield: Amount of disease detected in the population, relative to the effort• Prevalence of disease/predictive value

Validity of Screening Test (Accuracy)

Sensitivity: Is the test detecting true cases of disease.(Ideal is

100%: 100% of cases are detected)

Sensitivity=True positives/Total diseased

=a/a + c

Specificity: Is the test excluding those without disease? (Ideal

is 100%: 100% of non-cases are negative)

Specificity=True negatives/Total non diseased

=d/b+ d

Screening for Glaucoma using IOP

True Cases of Glaucoma Yes No

IOP > 22: Yes 50 100

No 50 1900 (Total) 100 2000

• Sensitivity = 50% (50/100) False Negative=50%• Specificity = 95% (1900/2000) False Positive=5%

• Screening for categorical variables • Screening for continuous variables

Example

• 520 women were positive for Breast cancer when fine needle aspiration cytology(FNAC) was used on 5,000 women, whom 500 were positive. Out of 520 positive by (FNAC) and 420 were found positive on excision biopsy. What is validity and of (FNAC) for diagnosing the Breast Cancer?

Receiver operator Characteristic ROC Curve• A plot of the true positive rate against the false positive

rate for the different possible cut-points of a diagnostic test is called a ROC curve• It shows the tradeoff between sensitivity and specificity

(any increase in sensitivity will be accompanied by a decrease in specificity)• The closer the curve follows the left-hand border and

then the top border of the ROC space, the more accurate the test

Example

Cut-point True Positives

False Positives

5 0.56 0.017 0.78 0.199 0.91 0.58

Where do we set the cut-off for a screening test?

Consider:

• The impact of high number of false positives: • anxiety of patient• cost of further • testing cause burden on health

system

• Importance of not missing a case:seriousness of disease

Reliability (reproducibility)

• Intra-subject variation• Intra-observer variation• Inter-observer variation• Overall % agreement for inter-observer variation=a/a+b+c• Kappa statistic = % agreement observed-% agreement expected by chance alone 100%- % agreement expected by chance aloneOR

Yield from the Screening Test: Predictive Value

• Predictive Value of a Positive Test (PPV): • Likelihood that a person with a positive test has the disease• PPV= true positive /test positive= a/a + b

• Predictive Value of a Negative Test (NPV): • Likelihood that a person with a negative test does not have the

disease• NPV=true negative/test negative =d/c + d

• Relationship with Sensitivity, Specificity, and Prevalence of Disease• High Prevalence ------ High PPV• High specificity & sensitivity--------High Predictive Values

Example

• Prevalence of a disease in a community was 15%. A screening test with 85% sensitivity and 50% specificity was applied on 1000 individuals.• Calculate predictive values• What if prevalence changes to 20%?

Yield from a Screening Test for Disease XPredictive Value

Principles for Screening Programs(Wilson’s Criteria)

1. The condition sought should be an important health problem.2. There should be an accepted treatment for patients with recognized disease.3. Facilities for diagnosis and treatment should be available.4. There should be a recognizable latent or early symptomatic stage.5. There should be a suitable test or examination.6. The test should be acceptable to the population.7. The natural history of the condition, including development from latent to

declared disease, should be adequately understood.8. There should be an agreed policy on whom to treat as patients.9. The cost of case-finding (including diagnosis and treatment of patients diagnosed)

should be economically balanced in relation to possible expenditure on medical care as a whole.

10. Case-finding should be a continuing process and not a “once and for all” project.

Advantages and disadvantages of screening

Advantages• Screening can detect medical conditions at early stage before

symptoms when treatment is more effective than for later detection• In the best of cases lives are savedDisadvantages• Tests used in screening are not perfect• The test result may show false positive, or false negative• Screening for low probability condition---absolute number of

false +ves high though the % of true +ves is low

Disadvantages of screening……cont

• Adverse effects of screening procedure (e.g. stress and anxiety, discomfort, radiation exposure, chemical exposure)

Disadvantages of screening……cont

Lead time bias• The intention of screening is to diagnose a disease earlier

than it would be without screening• Without screening disease discovered when symptoms

appear• Even if in both cases a person will die at the same time,

because we diagnosed the disease earlier with screening the survival time since diagnosis is longer with screening; but life span has not been prolonged, and there will be added anxiety as the patient must live with knowledge of the disease for longer• Looking at statistics of survival time since diagnosis, screening

will show an increase (this gain is called lead time)

Disadvantages of screening……cont

Lag time bias• Many screening tests involve the detection of cancers• It is often hypothesized that slower-growing tumors have

better prognoses than tumors with high growth rates• Screening is more likely to detect slower-growing tumors

(due to longer pre-clinical time), which may be less deadly• Thus screening may tend to detect cancers that would

not have killed the patient or even been detected prior to death from other causes

Conditional probability and its application of in

computing sensitivity, specificity and predictive values for screening test

Conditional Probability

• Probability of occurrence of an event given that another event B has already occurred• Notation: = P(A and B) P(B) • provided P(B) is not eq. to zero• Applications:• Diagnosis of medical conditions (Sensitivity/Specificity)• Data Analysis and model comparison

BAP

Conditional Probability Example

• Diagnosis using a clinical test • Sample Space = all patients tested• Event A: Subject has disease• Event B: Test is positive

Interpret: Probability patient has disease and positive test (correct!)

Probability patient has disease BUT negative test (false negative) Probability patient has no disease BUT positive test (false positive)

Probability patient has disease given a positive test

Probability patient has disease given anegative test

'

'

'

BAp

BAp

BAp

BAp

BAp

Conditional probability for test validity

• Sensitivity=a/a+c

• P(T/D)=P(T∩D)/P(D)

'

'

'

BAp

BAp

BAp

BAp

BAp

Conditional probability for test validity

• Specificity=d/b+d

• P(T-/D-)=P(T-∩D-)/P(D-)

Bayes theorem

• A theorem describing how the conditional probability of each of a set of possible causes for a given observed outcome can be computed from knowledge of the probability of each cause and the conditional probability of the outcome of each cause

• Bayes' theorem shows how to determine inverse probabilities: knowing the conditional probability of B given A, what is the conditional probability of A given B?

Bayes theorem…cont

• We can use Bayes Rule to find the predictive values if we know the sensitivity and the specificity of the screening instruments

• Let D and D- denote the events that the disease is actually present and absent respectively T+ is the event that the screening test gives a positive result and T- is the event that the screening test gives a negative result

• Let P(D)=The probability of disease in the general population

• Using Bayes Rule we get

Bayes theorem…cont

• P(D T+)=P(T+ D)P(D) P(T+ D)P(D)+P(T+ D-)P(D-)

Calculating predictive values using Bayes rule

• PPV=P(D T)=P(T D)P(D) P(T D)P(D)+P(T D-)P(D-) = sensitivity*prevalence e (sensitivity*prevalence)+(1-specificity)*(1-prevalence)

Calculating predictive values using Bayes rule

• NPV=P(D- T-)=P(T- D-).P(D-) P(T- D-)P(D-)+P(T- D)P(D) = specificity*(1-prevalence) specificity*(1-prevalence)+ (sensitivity)* prevalence

Statistics vs. ProbabilityIn statistics, you put your hand into a black box of marbles of diff color, examine your handful, and try to ans the question ``What is in the box?'' In probability, you look into a transparent box, count the different colored marbles in it, mix them up well, and then blindly take out one handful; without opening your eyes, you predict how many marbles of each kind are in your hand