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[Example]
“Analysis using the Cox proportional hazards model showed a hazard ratio of 0.8 (95% CI: 0.68 to 0.92, p < 0.05) for product A to a placebo.”
In this case, the p-value is less than 5% and is considered statistically significant.
However, recent clinical trials papers have argued that merely declaring a p-value of less than 5% is not sufficient; more precise p-values (for example, p=0.018) are required. In addition, since the 1980s, it has been mandatory to also show a 95% confidence interval (CI) to observe the effect size.
Confidence interval for hazard ratio
The CI of the hazard ratio with a confidence level of 95% is called “95% CI.” This is to see if it holds true for 95% of the population.
For example, interpreting the result “with a hazard ratio of 0.8 and a 95% CI of 0.7 to 0.9 (100 clinical trials)” means that, 95 times out 100, the value falls within 0.7 to 0.9, while for the remaining five times, it does not.
We explained earlier (Vol. 15), that if the hazard ratio is less than “1,” it can be interpreted that product A reduces the mortality rate as compared to a placebo. However, if the 95% CI of the hazard ratio is across “1,” it is less than “1,” it is effective, and if it is more than “1,” it is not effective.
[Table] Hazard ratio and 95% CI (example of Vol. 15)
The 95% CI for the prescription drug is between 0.071 and 2.116, with “1” in between, therefore, it follows that product A did not prolong life, as compared to a placebo. Similarly, the 95% CI for smoking status is also across “1,” so it cannot be concluded that non-smoking, as compared to smoking, reduced mortality.
In this scenario, the number of cases was small, so it is better to say that the significant difference between the two groups could not be determined.
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