ANTC67 exam- stats n on.docx

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University of Toronto Scarborough
Larry Sawchuk

Assessing Etiology RISK FACTOR (present/absent) association DISEASE (yes /no) STATISTICAL EVALUATION Odds Ratio & Chi square Stratified Odds Ratio Hypothesis Testing Indicate whether the observed difference in the two groups can simply be attributed to chance. The significance test accept or reject? Common elements are presented in summary form before the actual tests of significance The expression of the Disease is independent (not associated) of the specified Risk Factor Compare computed chi square (observed) to expected chi square (critical value) If chi-square value exceeds the expected, reject the null hypothesis of no association there is an ASSOCIATION Critical Chi Square Value Allowing for 5% error in our decision OR 95% confident regarding the null hypothesis Step 1: State the Hypotheses Null Hypothesis (Ho): A probabilistic statement about population parameter that is being tested by sample. Ho always contains the equality statement A and B have no relationship Alternative hypothesis (H1): Determined by the question implicit in the statement of the problem. A and B have relationship Step 2: Select the Level of Statistical Significance Once the null hypothesis is stated, a decision be: 1. Reject Ho 2. Accept Ho 3. Reserve judgement concerning Ho (the decision is too close to call). Step 3: Select the Appropriate Test Statistic Decide which test to use. Depends on assuptions Chi-square (Pearson, 1900) A non-parametric test whose model does not specify conditions about the parameters from which the sample was drawn. However, non-parametric tests still contain some assumptions Step 4: Define the Region of Rejection In general, a significance level of .05 or .01 is used in hypothesis testing. a = 0.05, there are 5 chance in 100 that Ho will be rejected when it is actually true.. 95% confident that we have made the correct decision about Ho. Chi-square value vs. critical chi-square with 1 df Df of a test is defined by: the sample size -1 ( eg., Z test) Or the number of classes (r-1 * c -1) (Odds ratio test) Step 5: Compute the test statistic and assess Ho. If the computed chi square value exceeds that expected at 0.05 level, Observed relationship between the two factors is not likely to be due to chance factors alone. 95% confident that the association between the two factors is not due to chance. When one moves to the .01 level, the critical chi square value necessarily becomes larger. Step 6: Assess the meaning of your finding. Generate further hypotheses that follow from your assessment of initial Ho. Chi square Rules of thumb Whole numbers only No zero In a 2 by 2 if the total is less than 30, use fishers exact Less than 200 some suggest that you use continuity correction MH chi-square Chi square = {(|ad-bc|-N/2)^2 * N} / (C1*C2*R1*R2) Assumptions Random sample data A sufficiently large sample size Type I error: a true null hypothesis is incorrectly rejected Type II error: one fails to reject a false null hypothesis No accepted cutoff. Adequate cell sizes. All cells of a 2-by-2 table, and 5 or more in 80% of cells in larger tables, but no cells with zero. When this assumption is not met, Yates' correction is applied. Independent observations. Same observation can only appear in one cell. Chi-square cannot be used to test correlated data (ex., before-after, matched pairs, panel data). All observation has the same underlying distribution. Distribution is known in advance Non-directional hypotheses Chi-square tests the hypothesis that two variables are related only by chance. Finite values Normal distribution of deviations (observed minus expected values) Chi-square is a non-parametric test in the sense that is does not assume the parameter of normal distribution for the data - only for the deviations. Data level Odds Ratio = (a*d) / (b*c) Yes No Total Yes A B A+b No C D C+d Total A+c B+d A+B+C+D If OR is not equal to 1, there is an association. The further away OR is, the stronger the association. General Guidelines for Interpreting Values of OR Value Effect of Exposure 0-0.3 Strong negative 0.4-0.5 Moderate negative 0.6-0.8 Weak 0.9-1.1 No effect 1.2-1.6 Weak 1.7-2.5 Moderate positive = or >2.6 Strong positive One Risk Factor Step 1 Simple comparisons between the Disease and various Risk Variables Get ORs Get levels of significance Possible Risk Computed chi-squares Factors Judged to be A sex Not significant Disease B smoke Not significant C diet Significant D drug Not significant Step 2 Data are then stratified for heterogeneity Compute OR with disease and Risk Factor C and then stratified by other Risk Factor (A) Examine the two ORs (are they the same?) Evaluate interactive chi-square value is greater than critical value, assume interaction is present and there are differences in Disease and C depending on the level of strata STRATIFIED Level A sex Level B BASIC Level A Disease diet smoke Level B drug Level A Level B Step 3 If interaction is present, report the strata-specific measures of association If interaction is not present, report the crude (unadjusted for the strata) estimates of association Step 4 Report your Results Confounding the masking effect A situation in which a measure of association or effect and outcome is distorted by the presence of another variable An extraneous variable that wholly or partially accounts for the observed effect of a risk factor on disease status Positive the observed association is biased away from the null Negative when the observed association is biased toward the null To be a confounder: 3 conditions It is risk factor for the disease, no relationship with the putative risk factor - testable It is associated with putative risk factor - testable It is not in the causal pathway between exposure and disease - conceptual How to identify confounders? Your acquired knowledge Prior experience with data The three criteria for confounders cited earlier Example Diabetes No diabetes CHD 2249 91 2340 No CHD 190 26 216 2439 117 2556 OR = 3.38 The odds of having diabetes among those with coronary heart disease is 3.3 times as high as the odds of having diabetes among those who do not have coronary heart disease In this case, since OR = 3.38 is greater than 1, there is some kind of association. Would diabete mean elevated CHD? Potential confounder: Hypertension (elevated blood pressure/no elevated blood pressure) Diabetes & CHD among non- Hypertensives Diabetes No diabetes CHD 6 77 83 No CHD 51 1572 1623 57 1649 1706 OR = 2.40 Diabetes & CHD among hypertensives Diabetes No diabetes CHD 20 113 133 No CHD
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