Hypothesis Test Null and Alternative Hypotheses H There is no association

# Hypothesis test null and alternative hypotheses h

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Hypothesis Test: Null and Alternative Hypotheses H 0 : There is no association between CAT level and 7- year cumulative incidence of CHD C 1 = C 0 C 1 - C 0 = 0 C 1 /C 0 = 1 ln (C 1 /C 0 )= 0 H a : There is an association between CAT level and 7- year cumulative incidence of CHD C 1 ≠ C 0 C 1 - C 0 ≠ 0 C 1 /C 0 ≠ 1 ↔ ln (C 1 /C 0 ) ≠ 0 Methods for Count Data Hypothesis Test: Choice of X 2 1 0 2 0 2 ~ | | H X Var H X E X Z Note: The “Roadmap” shows the formulas for this statistical test based on setting X = a, the number of exposed cases. As an exercise, compute the test-statistic based on the formulas from the “Roadmap”.
Harvard TH Chan School of Public Health EPI202 – Epidemiologic Methods II Fall 2016 20 Methods for Count Data Hypothesis Test: Variance of X 00106 0 487 1 122 1 609 71 1 609 71 N 1 N 1 C 1 C T M C where N C 1 C N C 1 C H CID Var H X Var 0 1 1 0 1 0 0 . ) ( , ) ( ) ( ) | ( ) | ( Methods for Count Data Construct and Interpret the Hypothesis Test These data are not very compatible with the state of nature described by the null. If the null were true, we would expect to observe results as extreme or more extreme 6 times per 100,000 iterations of this study. If we were interested in a testing framework, with a pre- specified 2-sided alpha of 0.05, we would reject the null hypothesis and conclude that there is a statistically significant association between catecholamine level at baseline and the 7-year cumulative incidence of CHD (assuming no confounding, no selection bias, no information bias).
Harvard TH Chan School of Public Health EPI202 – Epidemiologic Methods II Fall 2016 21
Harvard TH Chan School of Public Health EPI202 – Epidemiologic Methods II Fall 2016 22 95% Confidence interval for CID: These data are consistent with 7-year cumulative incidence differences ranging from 5 to 21% with 95% confidence (assuming no confounding, no selection bias, no information bias) ) 0.209 0.053, ( = 0.001582 1.96 0.131 Methods for Count Data Point estimate for the Cumulative Incidence Ratio There is a 2.5-fold higher 7-year cumulative incidence of CHD among those with high CAT levels compared to those with low levels (assuming no confounding, no selection bias, no information bias). 45 . 2 09 . 0 22 . 0 487 44 122 27 ˆ 0 1 N b N a R I C
Harvard TH Chan School of Public Health EPI202 – Epidemiologic Methods II Fall 2016 23 Methods for Count Data Variance for ln ( Cumulative Incidence Ratio) ( ln (CIR)) 95% Confidence interval: Let X = ln (CÎR) = ln (2.45) = 0.8959 ar(X) V ˆ 1.96 X 0.0495 = 487 * 44 443 + 122 * 27 95 = N b b - N + N a a - N = C N C - 1 + C N C - 1 = R) I C ( ar V = (X) ar V 0 0 1 1 0 0 0 1 1 1 ˆ ˆ ˆ ˆ ˆ ln ˆ ˆ Methods for Count Data Confidence Interval for Cumulative Incidence Ratio (CIR) 95% Confidence interval for ln (CIR): 95% Confidence interval for (CIR): These data are consistent with cumulative incidence ratios ranging from 1.6 to 3.8 with 95% confidence (assuming no confounding, no selection bias, no information bias) 1.332) (0.4598, = 0.0495 1.96 0.8959 3.79) (1.58, = e =

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• Fall '16
• MURRAY
• Epidemiology, Statistical hypothesis testing, TH Chan School of Public Health, Harvard TH Chan, TH Chan School

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