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Bias and Confounding

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					Bias and Confounding
STAR-course, Steno Diabetes Center, Nov-Dec 2004
Thursday 11 November




Bendix Carstensen
Steno Diabetes Center, Gentofte
& Department of Biostatistics, University of Copenhagen
bxc@steno.dk          www.biostat.ku.dk/~bxc
Epidemiology and natural history
• Birth — Genetically determined (often unknown) variability
  of susceptibility

• Exposure — Environment (family, social environment,
  macro environment occupation etc.) (rarely objective)

• Disease — Diagnostic threshold (not objective)

• Death — Heterogeneity with respect to lethality (unknown)

• Cause of death — Heterogeneity.

• Autopsy — Heterogeneity.

Thursday 11 November:   Bias and Confounding               1
Where do we get evidence from?
• Unstructured experiments

• Structured

• Epidemiology/observational studies

• Intervention studies




Thursday 11 November:   Bias and Confounding   2
Intervention studies and clinical trials
• Randomized double-blind clinical trial

• Randomized single-blind clinical trial

• Open trial

Aim: Compare the effect of different treatment regimens.




Thursday 11 November:   Bias and Confounding             3
Randomised Clinical Trial
• Blinding with respect to exposure

• Allocation by chance (randomization)

• Control for unknown prognostic factors (versus
  stratification)

• ”Simple” interpretation of results:
  differences betwee groups only from:
  1. Pure Chance
  2. Treatment effect.


Thursday 11 November:   Bias and Confounding       4
RCTs vs. Epidemiological studies
                                               RCT                Epidemiology

Exposure Controlled                            Yes                No
Objective exposure                             Yes                ?
Comparable groups                              Yes (randomized)   ?
Controlled behaviour                           Randomized         No
Case Ascertainment                             Complete           (In-)Complete
Conclusions                                    Strong —           Weak —
                                               but restricted     but general
Possibility                                    Planned            Analytical
                                               interventions

Thursday 11 November:   Bias and Confounding                                      5
Key problems in epidemiologal studies
• Study population

• Methods

• Measurements

• Multifactorial diseases

• Can all risk factors be measured ?

• Can all risk factors be imagined ?


Thursday 11 November:   Bias and Confounding   6
Validity of epidemiological association
• Chance finding

• Bias

• Confounding

Also relevant for negative (no-effect) studies.




Thursday 11 November:   Bias and Confounding     7
Chance finding?
• Statistical evaluation:
  – p-value:
    The probability of a result at least as extreme as the
    observed.
  – Confidence interval:
    The range of values compatible with the observed data.

• Retinopathy in a sample: 60% in males 40% in females

• What do you need to evaluate if there is gender difference?

                                               2 min. break
Thursday 11 November:   Bias and Confounding                  8
Types of problems
Bias: Any systematic error in data collection an
 epidemiological study that results in an incorrect estimate
 of the association between exposure and risk of disease.

Confounding: Confusion of the exposure effect under study
 with that of a third factor associated with the exposure and
 independent of that exposure be a risk factor for the disease




Thursday 11 November:   Bias and Confounding                   9
Bias
Any systematic error in en epidemiological study that results
in an incorrect estimate of the association between exposure
and risk of disease

Selection bias: Selection of the study population producing
 artifactual effects.

Observation or information bias: Recording of information
 from the population is wrong or inhomogeneous.




Thursday 11 November:   Bias and Confounding                  10
Avoiding selection bias
 Descriptive studies:
  Sample must be representative for the population.

 Analytical studies:
  Study population should be homogeneous.




Thursday 11 November:   Bias and Confounding          11
Descriptive studies

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                       qq q            q
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                                               Sampling strategy?
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Thursday 11 November:   Bias and Confounding                        12
Descriptive studies

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      qq              q q
    q                      q
      q                    q      q
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            q q q         q     q      q
                       qq q            q
          q
         q q                                   How is the sample
                                        q
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       q       q q qq          qq    qq        representative?
     q      q q     qq q             qq
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                                               Representative of
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                                q     q        what?
                  q   q q          q
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Thursday 11 November:   Bias and Confounding                       13
Descriptive studies
• Prevalence of complications among patients with type 2
  diabetes

• Screened population

• Population based sample.

• Patient sample from:
     Primary care
     Secondary care



Thursday 11 November:   Bias and Confounding               14
Descriptive studies — points to consider:
• Representativeness of sample

• Population based sampling — how is it done in practice?

• Responders

• Non-responders — differs with respect to:
  –   Socioeconomic status
  –   Morbidity
  –   Mortality
  –   Life style

Thursday 11 November:   Bias and Confounding                15
Selection bias and sampling probability
Will all with the disease have the same probability of being
diagnosed/sampled?

• Women and gallstones

• Men and gastric/duodenal ulcers

• Asbestos exposure and COLD/Cancer

What are possible pitfalls in these studies?

                                               2 min. break
Thursday 11 November:   Bias and Confounding                   16
Selection bias and sampling probability
Will all with the disease have the same probability of being
diagnosed/sampled?

• Women and gallstones

• Men and gastric/duodenal ulcers
  Different diagnostic thresholds.

• Asbestos exposure and COLD/Cancer:
  Economic incentive for diagnosis
  Organic solvents and dementia
  Asbestos and COLD/Cancer

Thursday 11 November:   Bias and Confounding                   17
Selection bias in case-control studies
Oral contraceptives and thromboembolism:
Possible sources of selection bias:

• Hospital based C-C studies

• Doctors’ awareness of the possible link

• Women with symptoms and using OC more likely to be
  hospitalised




Thursday 11 November:   Bias and Confounding           18
Observation / information bias
Consequence of systematic differences in the way data on
exposure or outcome are obtained from the various study
groups:

• Interviewer bias.

• Recall bias.




Thursday 11 November:   Bias and Confounding              19
Interviewer bias - solutions
• Blinding of interviewer

• Structured interviews

• Interview guides

• “Dummy questions” (exposures known to be unrelated to
  condition under study)




Thursday 11 November:   Bias and Confounding              20
Recall bias
Diseased individuals remember and report their previous
exposure experience differently from non-diseased.
Or:
Exposed individuals report events differently from unexposed.




Thursday 11 November:   Bias and Confounding               21
Recall bias — example
Birth defects among laboratory technicians working with
organic solvents (OS)

• Case-control study:
  Case = birth defect                            Control = normal child

• Exposure: self reported exposure to OS

• CC-study OR > 1.5                            (p < 0.01)

• Cohort study RR = 1.02                           (n.s.)

Why?                                                              2 min. break
Thursday 11 November:   Bias and Confounding                                     22
Confounding
Exposure effect estimated wrongly because a factor is
associated both with exposure and disease.
Age and sex are the most common confounders.
Confounder characteristics:

• Associated to exposure

• Risk factor in it self (associated to disease).

Associated to exposure only: Irrelevant
Associated to disease only: Independent Risk Factor
Thursday 11 November:   Bias and Confounding           23
Confounding and causal chain:
                                               Confounding:
     E                                    D
                                               Ignoring C gives biased
                                               estimate of the effect of E.

                                               Control of the confounding
                                               effect of C is necessary.
                        C

BMI — Age — DM



Thursday 11 November:   Bias and Confounding                            24
Confounding and causal chain:
                                               Intermediate variable:
     E                                    D
                                               Control of the effect of C
                                               is not wanted:

                                               C is a stage in the
                                               development of D.
                        C



Genotype — BMI — Insulin resistance
Thursday 11 November:   Bias and Confounding                               25
Confounding and causal chain:
                                               Intermediate variable and
     E                                    D
                                               and direct effect of E:

                                               Control of the effect of C
                                               is not wanted:

                                               C is a stage in the
                        C                      development of D.
                                               Cannot be destinguished
                                               from confounding.

Genotype — BMI — Insulin resistance
Thursday 11 November:   Bias and Confounding                               26
Confounding and causal chain:
                                               Preceeding exposure:
     E                                    D
                                               Control of the effect of C
                                               is not necessary.

                                               It will just decrease the
                                               precision of the effect
                        C                      estimate.

BMI effect on occurrence of DM.
Should risk factors for BMI be controlled?

Thursday 11 November:   Bias and Confounding                               27
Confounding and causal chain:
                                               Separate risk factor
     E                                    D
                                               (independent of E):

                                               Control of the effect of C
                                               is not necessary.

                                               But it will probably be
                        C                      useful to estimate the
                                               effect of both E and C.




Thursday 11 November:   Bias and Confounding                               28
Macrovascular disease risk
• Hypertension

• Dyslipidaemia

• Smoking

• Low physical activity

• Diabetes

Which variables go where in causal chain?
                                               2 min. break
Thursday 11 November:   Bias and Confounding                  29
Quantitative example: confounding by age
                                 Age         0.1 ¨¨
                                               ¨
                                               ¨
                                                        F                 Age        0.1 ¨¨
                                                                                       ¨
                                                                                       ¨
                                                                                                F
                                             ¨                                       ¨

                                 < 55   ¨
                                        rr
                                          ¨¨
                                                                          < 55   ¨
                                                                                 rr
                                                                                   ¨¨


                       0.8                                      0.4   
                                           rr                                       rr
                                               r                                       r
                                                rr                                       rr
                         
                          
                                             0.9   r
                                                        S             
                                                                       
                                                                                     0.9    r
                                                                                                S
                                                                 
                                                                
                                                               
                                                             
                d                                           d
                  d                                           d
                   d                                            d

                                                        F                                       F
                    d                                            d
                        d
                         d                   0.3 ¨¨               d
                                                                     d               0.3 ¨¨
                       0.2                                      0.6
                             d                ¨¨                      d               ¨¨
                                             ¨                                       ¨

                                 55+                                      55+
                              d           ¨¨                              d        ¨¨
                                        ¨
                                        rr                                       ¨
                                                                                 rr
                                           r                                        r
                                             rr                                      rr
                                               r                                        r
                                             0.7                                     0.7
                                                   rr                                    rr

                                 S                                                              S
               Unexposed subjects                           Exposed subjects



Thursday 11 November:      Bias and Confounding                                                     30
• Probability of failure for unexposed:

                             (0.8 × 0.1) + (0.2 × 0.3) = 0.14

• Probability of failure for exposed:

                             (0.4 × 0.1) + (0.6 × 0.3) = 0.22

• Difference entirely due to difference in age structure.

• When there is a true effect, its magnitude can be distorted
  by such influences.


Thursday 11 November:   Bias and Confounding                    31
Confounding when RR = 2
                                 Age         0.1 ¨¨
                                               ¨
                                               ¨
                                                        F                 Age        0.2 ¨¨
                                                                                       ¨
                                                                                       ¨
                                                                                                F
                                             ¨                                       ¨

                                 < 55   ¨
                                        rr
                                          ¨¨
                                                                          < 55   ¨
                                                                                 rr
                                                                                   ¨¨


                       0.8                                      0.4   
                                           rr                                       rr
                                               r                                       r
                                                rr                                       rr
                         
                          
                                             0.9   r
                                                        S             
                                                                       
                                                                                     0.8    r
                                                                                                S
                                                                 
                                                                
                                                               
                                                             
                d                                           d
                  d                                           d
                   d                                            d

                                                        F                                       F
                    d                                            d
                        d
                         d                   0.2 ¨¨               d
                                                                     d               0.4 ¨¨
                       0.2                                      0.6
                             d                ¨¨                      d               ¨¨
                                             ¨                                       ¨

                                 55+                                      55+
                              d           ¨¨                              d        ¨¨
                                        ¨
                                        rr                                       ¨
                                                                                 rr
                                           r                                        r
                                             rr                                      rr
                                               r                                        r
                                             0.8                                     0.6
                                                   rr                                    rr

                                 S                                                              S
               Unexposed subjects                           Exposed subjects



Thursday 11 November:      Bias and Confounding                                                     32
   2 min. break Fill out from previous tree:

• Probability of failure for unexposed:

                         (         ×           )+(   ×   )=

• Probability of failure for exposed:

                         (         ×           )+(   ×   )=

• The apparent relative risk:

                                                RRO =

Thursday 11 November:   Bias and Confounding                  33
• The true relative risk, RRT = 0.2/0.1 = 0.4/0.2 = 2

• Probability of failure for unexposed:

                             (0.8 × 0.1) + (0.2 × 0.2) = 0.12

• Probability of failure for exposed:

                             (0.4 × 0.2) + (0.6 × 0.4) = 0.32

• The apparent relative risk:

                                    RRO = 0.32/0.12 = 2.67

Thursday 11 November:   Bias and Confounding                    34
Controlling confounding
In controlled experiments there are two ways of controlling
confounding:

1. Randomization of subjects to experimental groups so that
   the distributions of the confounder are the same.

2. Hold the confounder constant.




Thursday 11 November:   Bias and Confounding              35
Standardization
In observational studies there are two ways of controlling
confounding:

1. Direct standardization simulates randomization by
   equalising the distribution of extraneous variables.

2. Indirect standardization simulates the second method:
   holding extraneous variables constant. This is a technique
   that is now replaced by proper statistical modelling.
   [Outside the scope of this course.]



Thursday 11 November:   Bias and Confounding                    36
Direct standardization
1. Estimate age-specific risks (or rates) in each group,

2. Calculate marginal risks (rates) if the age distribution were
   fixed to that of some agreed standard population.
   A standard population is another term for a common
   age-distribution.




Thursday 11 November:   Bias and Confounding                   37
                               Age           0.1 ¨¨
                                              ¨
                                               ¨
                                                       F                 Age          0.1 ¨¨
                                                                                        ¨
                                                                                        ¨
                                                                                                F
                                           ¨¨                                        ¨¨
                               < 55     ¨¨
                                        r
                                          rr                             < 55   ¨¨
                                                                                r
                                                                                  rr
                       0.5                   r
                                               rr              0.5                  r
                                                                                       rr

                                             0.9                                      0.9
                                                  r                                      r

                                                       S                                        S
                                                   r                                        r
                                                                     
                                                                
                                                               
                                                              
                                                            
                d                                          d
                  d                                          d
                   d                                           d

                                                       F                                        F
                    d                                           d
                        d
                         d                   0.3 ¨¨              d
                                                                    d                 0.3 ¨¨
                       0.5 dd                                  0.5
                                               ¨                                        ¨
                                             ¨                       d                ¨
                                          ¨¨                                       ¨¨
                               55+                                       55+
                                                                         d
                                        ¨¨
                                                                                 ¨
                                        rr                                      ¨
                                                                                rr
                                          rr                                      rr
                                             r                                       r
                                              rr                                        rr

                                 S           0.7   r
                                                                                      0.7  r
                                                                                                S
               Unexposed subjects                          Exposed subjects

Failure probability is: (0.5 × 0.1) + (0.5 × 0.3) = 0.2


Thursday 11 November:      Bias and Confounding                                                     38
Bias and confounding — what to do ?
Bias: Error in data leading to incorrect estimation of
 association between exposure and outcome.
   Solution: Improve data collection

Confounding: Incorrect estimation of association between
 exposure and outcome due to a third factor associated to
 exposure and disease.
   Solution: restriction; matching; stratification;
   regression analysis

Be clear about the hypotheses that we want to investigate!
Thursday 11 November:   Bias and Confounding                 39
Misclassification
Random (nondifferential misclassification): underestimates
the effect.
Systematic misclassification: Any result possible, depending
on the character of misclassification:

• By exposure: Certain exposures are more likely to be
  remembered than others.

• By event: Recall bias: Exposure more likely to be
  remembered by cases.


Thursday 11 November:   Bias and Confounding                  40
Measurement error
Continuous counterpart of misclassification.
Bias will occur if the measurement error is systematic.
Regression dilution bias:
The larger the measurement error on the predictor the larger
the underestimate of the “true” relationship.
But: The relationship will still be valid for prediction,
provided that samples come from the same population.




Thursday 11 November:   Bias and Confounding                41

				
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