Converting this so that a 2 X 2 X 2 Table An Example from ?2.3 Inference About Conditional Associations In 2 x 2 x K Tables

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Converting this so that a 2 X 2 X 2 Table An Example from ?2.3 Inference About Conditional Associations In 2 x 2 x K Tables

Columbia Union College, US has reference to this Academic Journal, Inference About Conditional Associations In 2 x 2 x K Tables Demeke Kasaw Gary Gongwer An Example from ?2.3 Death Penalties in Florida in consideration of Multiple Murders, 1976-1987 Odds Ratio = 1.45 Converting this so that a 2 X 2 X 2 Table We now have 2 Partial Tables, by race of the victim Conditional Odds Ratios:

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Conditional in addition to Marginal Odds Ratios This can be generalized so that K different levels To study whether an association exists between an explanatory in addition to response variable after controlling in consideration of a possibly confounding variable Different medical centers Severity of Condition Age Different Studies of the same sort (Meta Analysis)

Using logit Models so that Test Independence We wish so that estimate the conditional probabilities If Y depends on X, then If Y in addition to X are independent CMH Test in consideration of Conditional Independence Estimation of Common Odds Ratio When the association seems stable among the partial tables, it is helpful so that combine the K odds ratios into a summary measure of conditional association.

Noncommutative Solitons in addition to Integrable Systems Successful points in NC theories 1. Introduction Plan of this talk 2. Backlund transform in consideration of NC ASDYM eqs. Review of commutative ASDYM equations Here we discuss G=GL(N) (NC) ASDYM eq. from the viewpoint of linear systems alongside a spectral parameter . Yang?s form in addition to Yang?s equation Yang?s form in addition to NC Yang?s equation Backlund transformation in consideration of NC Yang?s eq. Backlund trf. in consideration of NC ASDYM eq. Quasi-determinants Quasi-determinants Explicit Atiyah-Ward ansatz solutions of NC Yang?s eq. G=GL(2) 3. Interpretation from NC Twistor theory Origin of NC Atiyah-Ward ansatz solutions Origin of the Backlund trfs 5. Conclusion in addition to Discussion

Testing Homogeneity of Odds Ratios Ha: At least one is different SAS CODES data cmh; input center $ treat response count ; datalines; a 1 1 11 a 1 2 25 a 2 1 10 h 2 2 1 ; /*Consider 2x2xk*/ proc freq data = cmh; weight count; tables center*treat*response / cmh chisq All; run; /*Consider 2×2*/ proc freq data = cmh; weight count; tables treat*response / cmh chisq All; run; Partial outputs Odds Ratio in consideration of calculated on each centers; in consideration of center 1 Estimates of the Relative Risk (Row1/Row2) Type of Study Value 95% Confidence Limits Case-Control (Odds Ratio) 1.1880 0.4307 3.2766 Center 2 Estimates of the Relative Risk (Row1/Row2) Type of Study Value 95% Confidence Limits Case-Control (Odds Ratio) 1.8182 0.4826 6.8496 Center 3 Estimates of the Relative Risk (Row1/Row2) Type of Study Value 95% Confidence Limits Case-Control (Odds Ratio) 4.8000 1.2044 19.1292

Table 5 of treat by response Controlling in consideration of center=e treat response Frequency? Percent ? Row Pct ? Col Pct ? 1? 2? Total ŸŸŸŸŸŸŸŸŸ?ŸŸŸŸŸŸŸŸ?ŸŸŸŸŸŸŸŸ? 1 ? 6 ? 11 ? 17 ? 20.69 ? 37.93 ? 58.62 ? 35.29 ? 64.71 ? ? 100.00 ? 47.83 ? ŸŸŸŸŸŸŸŸŸ?ŸŸŸŸŸŸŸŸ?ŸŸŸŸŸŸŸŸ? 2 ? 0 ? 12 ? 12 ? 0.00 ? 41.38 ? 41.38 ? 0.00 ? 100.00 ? ? 0.00 ? 52.17 ? ŸŸŸŸŸŸŸŸŸ?ŸŸŸŸŸŸŸŸ?ŸŸŸŸŸŸŸŸ? Total 6 23 29 20.69 79.31 100.00 Table 6 of treat by response Controlling in consideration of center=f treat response Frequency? Percent ? Row Pct ? Col Pct ? 1? 2? Total ŸŸŸŸŸŸŸŸŸ?ŸŸŸŸŸŸŸŸ?ŸŸŸŸŸŸŸŸ? 1 ? 1 ? 10 ? 11 ? 4.76 ? 47.62 ? 52.38 ? 9.09 ? 90.91 ? ? 100.00 ? 50.00 ? ŸŸŸŸŸŸŸŸŸ?ŸŸŸŸŸŸŸŸ?ŸŸŸŸŸŸŸŸ? 2 ? 0 ? 10 ? 10 ? 0.00 ? 47.62 ? 47.62 ? 0.00 ? 100.00 ? ? 0.00 ? 50.00 ? ŸŸŸŸŸŸŸŸŸ?ŸŸŸŸŸŸŸŸ?ŸŸŸŸŸŸŸŸ? Total 1 20 21 4.76 95.24 100.00 Center 7 Estimates of the Relative Risk (Row1/Row2) Type of Study Value 95% Confidence Limits Case-Control (Odds Ratio) 2.0000 0.0976 41.0034 Center 8 Estimates of the Relative Risk (Row1/Row2) Type of Study Value 95% Confidence Limits Case-Control (Odds Ratio) 0.3333 0.0221 5.0271 Total Type of Study Method Value 95% Confidence Limits – Case-Control Mantel-Haenszel 2.1345 1.1776 3.8692 (Odds Ratio) Logit ** 1.9497 1.0574 3.5949 Estimates of the Common Relative Risk (Row1/Row2) Type of Study Method Value 95% Confidence Limits – Case-Control Mantel-Haenszel 1.4979 0.9151 2.4518 (Odds Ratio) Logit 1.4979 0.9151 2.4518 Homogeneity test: Breslow-Day Test in consideration of Homogeneity of the Odds Ratios ŸŸŸŸŸŸŸŸŸŸŸŸŸŸŸŸŸŸŸŸŸŸŸŸŸŸŸŸŸŸ Chi-Square 7.9955 DF 7 Pr > ChiSq 0.3330 Total Sample Size = 273 Thank you Good luck alongside Prof. Trumbo?s Exam

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