CDA1 - Categorical Data Analysis Independent(Explanatory Variable is Categorical(Nominal or Ordinal Dependent(Response Variable is Categorical(Nominal

CDA1 - Categorical Data Analysis Independent(Explanatory...

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Categorical Data Analysis Independent (Explanatory) Variable is Categorical (Nominal or Ordinal) Dependent (Response) Variable is Categorical (Nominal or Ordinal) Special Cases: 2x2 (Each variable has 2 levels) Nominal/Nominal Nominal/Ordinal Ordinal/Ordinal
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Contingency Tables Tables representing all combinations of levels of explanatory and response variables Numbers in table represent Counts of the number of cases in each cell Row and column totals are called Marginal counts
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Example – EMT Assessment of Kids Explanatory Variable – Child Age (Infant, Toddler, Pre-school, School-age, Adolescent) Response Variable – EMT Assessment (Accurate, Inaccurate) Assessment Age Acc Inac Tot Inf 168 73 241 Tod 230 73 303 Pre 254 53 307 Sch 379 58 437 Ado 652 124 776 Tot 1683 381 2064 Source: Foltin, et al (2002)
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2x2 Tables Each variable has 2 levels Explanatory Variable – Groups (Typically based on demographics, exposure, or Trt) Response Variable – Outcome (Typically presence or absence of a characteristic) Measures of association Relative Risk (Prospective Studies) Odds Ratio (Prospective or Retrospective) Absolute Risk (Prospective Studies)
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2x2 Tables - Notation Outcome Present Outcome Absent Group Total Group 1 n 11 n 12 n 1. Group 2 n 21 n 22 n 2. Outcome Total n .1 n .2 n ..
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Relative Risk Ratio of the probability that the outcome characteristic is present for one group, relative to the other Sample proportions with characteristic from groups 1 and 2: . 2 21 2 ^ . 1 11 1 ^ n n n n = = π π
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Relative Risk Estimated Relative Risk: 2 ^ 1 ^ π π = RR 95% Confidence Interval for Population Relative Risk: 21 2 ^ 11 1 ^ 96 . 1 96 . 1 ) 1 ( ) 1 ( 71828 . 2 ) ) ( , ) ( ( n n v e e RR e RR v v π π - + - = = -
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Relative Risk Interpretation Conclude that the probability that the outcome is present is higher (in the population) for group 1 if the entire interval is above 1 Conclude that the probability that the outcome is present is lower (in the population) for group 1 if the entire interval is below 1 Do not conclude that the probability of the outcome differs for the two groups if the interval contains 1
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Example - Coccidioidomycosis and TNF α -antagonists Research Question: Risk of developing Coccidioidmycosis associated with arthritis therapy? Groups: Patients receiving tumor necrosis factor α (TNF α ) versus Patients not receiving TNF α (all patients arthritic) COC No COC Total TNF α 7 240 247 Other 4 734 738 Total 11 974 985 Source: Bergstrom, et al (2004)
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Example - Coccidioidomycosis and TNF α -antagonists Group 1: Patients on TNF α Group 2: Patients not on TNF α ) 76 . 17 , 55 . 1 ( ) 24 . 5 , 24 . 5 ( : % 95 3874 . 4 0054 . 1 7 0283 . 1 24 . 5 0054 . 0283 . 0054 . 738 4 0283 . 247 7 3874 . 96 . 1 3874 . 96 . 1 2 ^ 1 ^ 2 ^ 1 ^ = - + - = = = = = = = = - e e CI v RR π π π π Entire CI above 1 Conclude higher risk if on TNF α
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Odds Ratio Odds of an event is the probability it occurs divided by the probability it does not occur Odds ratio is the odds of the event for group 1 divided by the odds of the event for group 2 Sample odds of the outcome for each group: 22 21 2 12 11 . 1 12 . 1 11 1 / / n n odds n n n n n n odds = = =
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Odds Ratio
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