Association between the Risk of Heart Disease and Smoking - Essay Example

Question a. The odd’s ratio for association between the risk of heart disease and smoking is calculated as follows: Interpretation: The odd’s ratio for the relationship between the risk of heart disease and smoking is 1.55 which is slightly over the 1.0 value. Since the odd ratio measures the relationship between the risk of heart disease and exposure to smoking, we can assume that the study generating these results is not biased and hence infer that the risk of a heart disease is 1.55 times for cigarette smokers than for non smokers. Therefore we can conclude that there is significant association between the two attributes and that there is 1.55 fold increase in odd’s associated with smokers. b. s.e. (OR) = Hence the standard error of log odds ratio is 0.1286 95% C.I for OR:- Lower limit = OR- (1.96 xs.e.(OR)) = 0.4383 – (1.96 x 0.1286)= 0.1862 Upper limit = OR+ (1.96 xs.e.(OR)) = 0.4383 + (1.96 x 0.1286)= 0.6904 95% C.I for population OR:- Lower limit = exp (0.1862) = 1.21 Upper limit = exp(0.6904) = 1.99 Interpretation: From our calculation, our odds ratio is skewed in nature and therefore it is not possible to make a direct calculation of the standard error. We have a 95% confidence level and the population odds ratio for heart disease associated with smokers lies within 1.21 (an increased odd of 1.21 fold) and 1.99 (an increased odd of 1.99) fold. When a confidence interval does not include the value of 1, we know that the odds of the measured outcome are different for both attributes even without a significance test. In this case, the confidence interval does not contain value 1.0, hence there is significant association between smoking and heart disease. c. Proportion in Smoking group: Proportion in non-smoking group: The risk ratio is given as: The SE of LN(RR) is given as: 2 Hence the standard error of log risk ratio is 0.0762 95% C.I for RR:- Lower limit = RR- (1.96 x s.e.(RR)) = 0.2575– (1.96 x 0.0762)= 0.1081 Upper limit = RR+ (1.96 x s.e.(RR)) = 0.2575 + (1.96 x 0.0762)= 0.4069 95% C.I for population RR:- Lower limit = exp (0.1081) = 1.11 Upper limit = exp(0.4069) = 1.50 d. The Odd’s ratio is 1.55, the smokers are having 1.55 times more risk of having heart disease on the other hand, the risk ratio is 1.2939, means for smokers there is 29.39% more chance to having risk of heart disease. Both the confidence intervals do not contain the value 1, hence the results of both Odd’s ratio and risk ratio are significant. The z value for Odd’s ratio is: Hence the associated p value is 0. On the other hand, the z value for Risk ratio is: Hence the associated p value is 0. Observe that for both Odd’s ratio and Risk ratio, the p value is 0, hence both the measures are equally significant. The odds ratio value is skewed and therefore it is not possible to directly calculate the standard error of the statistics. The no difference value for this statistics is 1 and therefore when a confidence interval includes the value of 1, we know that the odds of the measured outcome are the same even without a significance test. To evaluate the p value, we can use the chi-square approach but in this case, it is not appropriate therefore it would be proper to use Fisher’s exact solution. Odd’s ratio is preferred in case of a nested control study because it is an efficient method of analysis in terms of both time and cost. It also makes it possible to investigate a wide range of possible risk factors. Odd’s ratio is also particularly suitable to investigate rare diseases with a long induction period. Odd ratio is also preferred because it a good method of studying populations that are dynamic and where follow up proves to be difficult. Question 2 a. For Obese: The odd’s ratio hence becomes: Hence the odd’s ratio is 1.101 For non-obese The odd’s ratio hence becomes: Hence the odd’s ratio is 1.228 b Here we are given the weights of obese and non obese stratum. The following table is used for calculation of Mantel- Haenszel estimate of the pooled odds ratio (ORMH).   OR Wi OR*wi Obese 1.1012 21.13779 23.27693 Non obese 1.2279 27.57974 33.86516   Sum 48.71752 57.14209 Hence Mantel-Haenszel estimate of the pooled odds ratio (ORMH) is 1.1729 c. In first question, we have calculated the odd’s ratio for the association between smoking and the risk of heart disease for women as 1.55. In last part, we have calculated the pooled odd’s ratio adjusted for obesity as 1.17. Observe that after considering obesity, the odd’s ratio is decreased. The pooled odd’s ratio is much lesser than the unadjusted odd’s ratio. Hence we conclude that after considering the obesity, the risk of having heart disease for smokers is 1.17. Hence obesity can be considered a confounder seen as an intermediate in the causal pathway. In this case, it is possible for the most serious type of overmatching to occur when one matches on a factor that is both affected by exposure and a cause of disease. Ignoring the matching in the analysis would only compound the error by driving the odds ratio even closer to unity. d. We have, the Mantel-Haenszel estimate of the pooled odds ratio (ORMH) is 1.1729 and the standard error of the natural logarithm of the Mantel-Haenszel estimate of the pooled odds ratio ((ORMH)) is 0.14. The adjusted OR is 1.15 which translates to approximately 15% increased factor. This proves that there is evidence of association between the smokers and the heart disease. Consider, 95% C.I for ORMH):- Lower limit = (ORMH)- (1.96 x s.e.((ORMH)) = 0.14– (1.96 x 0.14)= -0.1344 Upper limit = (ORMH)+ (1.96 x s.e.((ORMH))= 0.14 + (1.96 x 0.14)= 0.4144 95% C.I for population ORMH:- Lower limit = exp (-0.1344) = 0.87 Upper limit = exp(0.4144) = 1.51 The confidence interval contains the value 1. Therefore when a confidence interval includes the value 1, can therefore observe that the odds of the measured outcome are the same for both even without a significance test. Therefore odds ratio is not significant while adjusted for obesity. Question 3 This study is conducted to see whether there is impact of Smoking on heart disease. Here the study has been conducted with 1012 patients consisting of 419 cases and 593 controls. The odd’s ratio for association between the risk of heart disease and smoking is 1.15, which is greater than 1, hence we can therefore make a conclusion that there is significant association between two attributes. It is more likely to have Heart disease for smokers than non-smokers. The 95% confidence interval for this odd’s ratio is 1.205 to 1.9948, which does not contain 1, hence a proof that the odd’s ratio is significant. The risk ratio of smoking and heart disease is 1.2939 (with 95% confidence interval 1.1145 to 1.5022), from this risk ratio, we conclude that 15% of smokers have risk of having heart disease. Also, this confidence interval does not contain the value 1, hence the risk ratio is significant. In the second part of this study, we have tested whether the obesity can be considered as a confounder. The Mantel- Haenszel estimate of the pooled odds ratio (ORMH) is calculated in order to test whether obesity can be a confounder. Observe that the Mantel- Haenszel estimate of the pooled odds ratio is 1.1729. There is much difference between the odd’s ratio as calculated in the first case and the adjusted odd’s ratio. Hence we conclude that obesity can be seen as a confounder. In this way we have made use of odd’s ratio and risk ratio in order to test whether there is significant association between two attributes. Question 4: a. The difference between two proportions and its standard error is calculated as follows: The proportion for Oral ibuprofen group p1=99/180=0.55 The proportion for placebo group p2=54/180=0.3 The 95% confidence interval for difference between proportions is given as: Hence the confidence interval becomes (0.199, 0.3) The z statistic is given as: The p value for this z value is 0. Hence table 4.1 is completed as follows: Trial n per group Difference in sample proportions (oral ibuprofen-placebo) 95% confidence interval p value 1 55 0.15 -0.03 to 0.33 0.074 2 180 0.25 0.20 to 0.3 0.0001 b. For trial 1, the p value is 0.074, also the confidence interval contains the value 0, and hence we conclude that there is no significant difference between two proportions in this case. On the other side, the p value for trial 2 is 0.0001 which implies that there is significant difference between two population proportions. The confidence interval does not contain the value zero, this fact also supports our claim. c. It can be observed that the first test resulted in the conclusion that the difference between treatment and placebo may not be significant. But the second test has proven that the difference between treatment and placebo is significant. Hence we can recommend oral ibuprofen for treating migraines of children. Read More