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Statistical estimation is the process of conducting a clinical trial on a part of the population (sample) to investigate the entire population and estimate its average value, using the basic statistics of the observed data. The sample may have had a smaller or larger mean than the whole (population). It is dangerous to conclude that the mean of a sample randomly selected in this manner is the mean of the whole (population). Therefore, the average value obtained is assigned a certain range.
In other words, the mean of the sample is said to be, “between ○○○ and ○○○,” and the mean value of the population is estimated.
The method of estimating the statistics of the population by assigning a range to the sample mean in this way is called the “interval estimation method.” However, by increasing the sample size (n), the width of this interval can be reduced. We explain how to avoid the pitfalls of such estimations.
Confidence Interval (CI)
When we state, “between ○○○ and ○○○,” that is, “M1 to M2,” we consider M1 as the “lower limit,” and M2 as the “upper limit.” The interval between the two is called the confidence interval(CI). (vol. 2)
The width of the confidence interval is determined by the coefficient of the confidence interval and standard error (SE).
The coefficient of the confidence interval is the value determined by the 5% significance level in hypothesis testing. The coefficient is 1.96 if the population follows a normal distribution, and a value derived from the t-distribution, otherwise. A 99% CI may be applied separately from a 95% CI.
How to find the 95% confidence interval
The formula for calculating the 95% confidence interval is:
Lower limit = mean – 1.96×standard error (SE)
Upper limit = mean + 1.96×standard error (SE)
As the sample size (n) increases, the standard error (SE) decreases, and the width of the 95% confidence interval becomes narrower. It is then increasingly likely that a confidence interval for a difference will “not cross 0” and a confidence interval for a ratio will “not cross 1.”
We explained that, when testing, “whether there is a meaningful difference” should be thoroughly evaluated from the results of clinical trials, but what about estimation?
In estimation, what corresponds to the “clinical trial result” in the test is the unbounded value, in other words, the point estimate of the mean or ratio.
For example, with a confidence interval for the risk ratio, if you have data with a point estimate of 0.80 and a 95% confidence interval of 0.55 to 1.05, you can narrow the 95% confidence interval as much as you want by increasing the sample size (n number). For example, if it goes from 0.63 to 0.97, it can be said to be statistically significant because it does not cross 1. However, the point estimate of 0.80 does not change significantly with increasing sample size (n).
It follows that we should assess not only whether the confidence interval crosses one, but also whether the point estimate of the risk ratio of 0.80 is meaningful. It is also important to properly evaluate the number of point estimates before providing the range, which is the result of the statistical analysis.
[Figure 1]
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