STATISTICS REVIEW

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STATISTICS REVIEW

• Robert V. Wetz, M.D.
• Associate Director of Medicine
• Department of Medicine
• Staten Island University Hospital

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DATA COLLECTION

• Accuracy- the ability of a measurement to be
  correct, on the average. It correctly measures
  what its supposed to measure.
• Precision- (reproducibility, reliability) the
  ability of the measurement to give the same
  results on repeated testing.

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DATA COLLECTION

• Validity-
• Internal results are applicable to the study
  population
• External results can be extrapolated to the
  general population.
• Responsiveness- can the instrument detect small
  but clinically significant changes.

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DATA COLLECTION

• Incidence- number of NEW cases in a population at
  risk.
• Prevalence- number of EXISTING cases in a defined
  population
• At point in time point prevalence
• Over a period of time period prevalence
• Prevalence incidence x duration
• Cumulative incidence number of new cases over a
  period of time.
• Prevalence Now Cumulative incidence
  cured/expired people.

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DATA COLLECTION

• Mean
• Median
• Range
• Standard Deviation (SD) the spread from the
  mean.
• 1 SD about the middle 68 of data
• 2 SD about the middle 95 of data

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DATA COLLECTION

• 95 Confidence Intervals (CI) 1.96 SE from the
  mean. SE SD/?n
• The larger the study population (n) the SMALLER
  the confidence intervals. The smaller the CI,
  the more likely the result is the true result.
• Null hypothesis results are by chance
• Alternate hypothesis results are real
• Reject the null hypothesis if the results are
  statistically significant.

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TYPES OF DATA

• Nominal- naming of categorical variables that
  have no measurement.
• Example- Skin Color
• Yellow 1
• Black 2
• White 3
• Red 4

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TYPES OF DATA

• Dichotomous- split into two.
• Examples-
• 1 living 2 dead
• 1 normal skin color 2 abnormal skin color
• 1 well 2 sick

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TYPES OF DATA

• Ordinal- variables that are able to be put in
  order but are NOT continuous.
• Example-
• Edema 1, 2, 3, 4
• Murmurs I/VI to VI/VI
• Resp. Distress absent, mild, mod., severe

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TYPES OF DATA

• Continuous- variables that a measured on a
  continuous scale.
• Example-
• Weight
• Height
• Blood Pressure
• Serum glucose level

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TYPES OF DATA

• Continuous Scales can be of two types
• Interval- distance between variables are equal
  but the zero point is arbitrary and not a true
  zero. Ex. Fahrenheit scale.
• Ratio- as above but zero is the true zero
  point.
• Example-
• Weight 0 is the absence of weight
• Kelvin 0 is the absence of heat
• Blood pressure 0 is no pressure

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TYPES OF STUDIES

• Case-control-
• Strengths- useful for rare conditions relatively
  inexpensive short duration yields odds ratio
• Weaknesses- potential sampling bias limited to
  one-outcome variable does NOT yield prevalence,
  incidence or relative risk

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TYPES OF STUDIES

• Cross-sectional-
• Strengths- short duration can study several
  outcomes controls subject selection controls
  measurements yields prevalence
• Weaknesses- does not establish cause unmeasured
  diff. between groups

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TYPES OF STUDIES

• Cohort-
• Strengths- establishes sequence of events avoids
  bias in measuring predictors yields incidence,
  relative risk, and excess risk
• Weaknesses- relatively expensive long duration
  requires large sample size not useful for rare
  outcomes

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TYPES OF STUDIES

• Prospective Cohort- take a group of people
  (cohort), identify risk factors (variables) and
  follow into the future for outcomes.
• Retrospective Cohort- take a group of people
  (cohort) from the past, identify risk factors
  (variables) and collect outcome data from the
  present time.

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TYPES OF STUDIES

• Meta-analysis- pooled data from different
  studies.
• Strengths- increases statistical power for
  outcomes helpful when studies disagree
• Weaknesses- quality of secondary data study
  differences

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TYPES OF STUDIES

• Experimental (Randomized Control)-
• Strengths- strongest evidence for cause and
  effect able to mask
• Weaknesses- expensive long duration not
  suitable for many questions not useful for rare
  outcomes limited generalizability (external
  validity)

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TYPES OF ERROR

• Types of Bias-
• Measurement bias-
• Examples- weighing people with clothes on or
  using lab data from different labs
• Selection bias- happens if patients are allowed
  to choose intervention or placebo group.
• Sickest patients will enter trials more often and
  potentially worsen the results.

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TYPES OF ERROR

• Types of Bias-
• Recall bias- people who had an adverse event are
  more likely to recall past info. because they
  think about it more.
• Example- A mother of a child born with an anomaly
  is more likely to remember different exposures or
  pregnancy problems than a mother of a normal
  child.

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TYPES OF ERROR

• Types of Bias (in cross-sectional study)-
• Late-look bias- fewer pts. with severe dz.
  because they died before detection.(Neyman)
• Length bias- people with less aggressive dz. are
  selected because they live longer.
• Lead-time bias- find dz. in earlier stage by
  screening asymptomatic pts., regardless of
  aggressiveness. Makes pts. seem like theyre
  living longer with their disease.

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TYPES OF ERROR

• Confounding- confusion of 2 supposedly causal
  variables, so that the part or all of the
  purported effect of one variable is actually due
  to the other variable.
• Example- initially it was found that the more
  pregnancies a woman had, the lower her rate of
  breast cancer. Later it was found that early age
  of pregnancy was protective and NOT the number of
  pregnancies.

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TYPES OF ERROR

• Type 1 report a significance and there is not
  one.
• Type 2 report no significance and there is one.
• To avoid Type 1 error decrease the p value,
  leaving less to chance.
• To avoid Type 2 error increase the population
  size. (see power)

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Powering a study

• To interpret a p value, one needs to look at the
  power of a study.
• Need to calculate the number of patients to
  enroll prior to starting the study.
• Usually power of 80 or better (80 chance to
  detect a significance).
• What can be said about a calculated p value when
  the n is very small or large?

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STATISTICS

• p value the chance that findings happened by
  chance. ? 0.05 (5) is considered significant.
• Let the statistician pick the correct test to
  find the p value.

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STATISTICS
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Assessing Risk
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Assessing Risk

• Relative Risk Ratio a/(ab) c/(cd)
• (cohort study, prospective)
• Odds Ratio a/b c/d
• (case-control)
• Odds ratio tends to overestimates the risk

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STATISTICS

• Relative Risk Graph- (or odds ratio)

1
lt 1
gt 1
x
x
x
x
x
x
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STATISTICS

• Lets say a study was done on HRT and the
  incidence of breast cancer. The study had three
  arms and the relative risk and confidence
  intervals were

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STATISTICS

• Lets say a study was done on HRT and the
  incidence of breast cancer. The study had three
  arms and the relative risk and confidence
  intervals were
• What if the p value for the difference between
  the estrogen alone and est. prog. groups was
  0.001 or 0.07 or 0.40?

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STATISTICS

• Likelihood Ratio sens./1-spec.
• It is the power of a test to rule in
• It is the likelihood of having the disease if the
  test is
• Likelihood Ratio - 1-sens./spec.
• It is the power of a test to rule out
• It is the likelihood of having the disease if the
  test is -

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About Likelihood Ratios
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About Likelihood Ratios

• LR of 2, 5, 10 increases probability by 15,
  30, 45 respectively
• LR of 0.5, 0.2, 0.1 decreases probablity by
  15, -30, -45 respectively

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Using LR to Affect Probability

• Convert prevalence or pretest prob to odds
• Pretest odds pretest prob/(1 - pretest prob)
• Posttest odds pretest odds x LR
• Posttest Prob posttest odds/(posttest odds 1)

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Using LR to Affect Probability

• Pretest prob 36 and LR 8
• Pre odds 0.36/(1-0.36) 0.56
• Post odds 0.56 x 8 4.5
• Post Prob 4.5/(14.5) 0.82 or 82

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STATISTICS

• Receiver Operating Curves (R.O.C.)-

Sensitivity
1 - Specificity
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STATISTICS

• Sensitivity Specificity-
• SpIn a Specific test rules a disease in.
• SnOut a Sensitive test rules a disease out.
• A screening test should be sensitive.
• A confirmatory test should be specific.

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STATISTICS

• Bayes Theorem is the impact on a test result by
  the patients PRE-test probability of having the
  disease. In basic form, it is merely the formula
  for positive predictive value.

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STATISTICS

• Sensitivity TP / (TP FN)
• Specificity TN / (TN FP)
• Pos. Pred. Value TP / (TP FP)
• Neg. Pred. Value TN / (TN FN)

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STATISTICS

• The 2x2 Table- (make it 3x3)

DISEASE
DISEASE -
TOTALS
TEST
TEST -
TOTALS
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STATISTICS

• A new rapid throat culture for strep has been
  developed. It has a sensitivity of 90 and a
  specificity of 80. The prevalence of strep
  pharyngitis in your population is 2. What is
  the likelihood that a positive test result means
  you have strep pharyngitis?
• Use 2x2 table, find Pos. Pred. Value

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STATISTICS

• A new rapid throat culture for strep has been
  developed. It has a sensitivity of 90 and a
  specificity of 80. The prevalence of strep
  pharyngitis in your population is 20. What is
  the likelihood that a positive test result means
  you have strep pharyngitis?
• Use 2x2 table, find Pos. Pred. Value

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STATISTICS

• In other words, for the boards
• Pos. Pred. Value Post-test Probability
• Prevalence Pre-test Probability
• Incidence Absolute Risk

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Analyzing a Diagnostic Test
100 Sensitivity Cut Point
100 Specificity Cut Point
Disease
No Disease
Sensitivity
Specificity
Negative
Positive
Treatment Decision
Typical Testing Cut Point
False -
False
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STATISTICS

• Relative Risk Reduction
• Placebo Treatment
• Placebo
• Absolute Risk Reduction Placebo Tx
• Number Needed to Treat 1/ARR

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STATISTICS

• A new study shows that pill z lowered the risk
  of stroke from 20 in the control (placebo) group
  to 10 in the treatment group. What are the RRR,
  ARR and NNT?
• RRR 20 10/20 50
• ARR 20 10 10
• NNT 1/.10 10

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STATISTICS

• A new study shows that pill z lowered the risk
  of stroke from 2 in the control (placebo) group
  to 1 in the treatment group. What are the RRR,
  ARR and NNT?
• RRR 2 1/2 50
• ARR 2 1 1
• NNT 1/.01 100