

BRIEF REPORT 

Year : 2014  Volume
: 5
 Issue : 3  Page : 115116 

Confidence interval how sure you are?
Areej Abdul Ghani Al Fattani
Department of Pediatrics, King Faisal Specialist Hospital and Research Center, Riyadh, Saudi Arabia
Date of Web Publication  30Sep2014 
Correspondence Address: Areej Abdul Ghani Al Fattani Department of Pediatrics, MBC58, King Faisal Specialist Hospital and Research Center, P.O. Box 3354, Riyadh 11211 Saudi Arabia
Source of Support: None, Conflict of Interest: None  Check 
DOI: 10.4103/16585127.142003
Previously, researchers were reported P value as a basis for conclusion, but in this era of evidencebased medicine we are interested now about the precision of the results obtained that allow us to make right decisions in health care practice. The confidence interval (CI) of a parameter goes beyond the P value by also reflecting the precision of the degree to which one can estimate the true population difference. For a particular size of the difference in the population, the larger sample size, the smaller the P value and the narrower will be the CI. Keywords: Confidence interval, P value, precision, significance
How to cite this article: Al Fattani AA. Confidence interval how sure you are?. J Appl Hematol 2014;5:1156 
Definition   
Confidence interval (CI) is an estimate to the range of values in which the true difference is likely lies. For a given mean of a sample, 95% CI from x to means that we are confident 95 out of 100 of the times that the unknown true mean of the population  which we have drown the sample from  to be lie between x and y values. ^{[1]} For example, an investigator studied the mean age of 1000 chronic myeloid leukemia patients, and it happens to be 55 years, we are still not sure if that mean represents the population or not. However if he provide the 95% CI , say (50  60) we would be more confident if we used the same sampling method to select different samples and computed an confidence interval for each sample, we would expect the true population mean to fall within 95 out of those 100 confidence intervals ^{[1],[2]} [Figure 1].  Figure 1: Relation of the confidence interval to the population mean (Brandon Foltz. June 2014, http://youtu.be/9GtaIHFuEZU)
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Relation Of Confidence Interval With P Value And Sample Size
Like P value CI is basically calculated using the estimated measure and standard error (s.e), and of course the both are closely related. The general formula for calculation CI based on normal distribution:
95% CI = estimate  (1.96 × s.e) to estimate + (1.96 × s.e)
If the 95% CI does not contain a null value (0 for mean and 1 for risk ratio and odds ratio), then we know the P value must be smaller than 0.05 and concluded as statistically significant. Vice versa; if the CI dose includes the null value, then we know the P value will be >0.05, so concluded as not statistically significant. For a particular size of difference in the population, the larger sample size the smaller the P value and the narrower will be the CI. Consequently, the narrower the CI the more precise the results. ^{[1],[2]}
Example
[Table 1] shows the results of five randomized controlled trial of three different drugs to lower blood pressure (BP) in middleaged hypertensive patients considered at high risk of heart attack. Patients were randomly assigned to receive either the drug or identical placebo. In each trial, BP were measured after 6 months. The effect of treatment was measured by the difference of systolic BP in the drug and control groups, which varied between trials. We will assume that a reduction of BP by 50 mmHg reflects substantial protection against heart attack while reduction by 30 mmHg reflects a moderate protection. ^{[3]}  Table 1: The results of five trials of three different drugs A, B and C to reduce BP
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What can we conclude from these five trials about the effect of the drugs in the population?
 Trial 1: Mean of systolic BP was reduced by 50 mmHg, but the sample size was only 40 in each group. The P value tells no evidence to reject the null hypothesis of no effect of drug A. Also, the CI is wide because the standard error is large, which reflects the sampling variations. So even though we got a big reduction in BP to the limit of 148 mmHg we couldn't recommend that drug for using. Notice that a large P value does not mean that the null hypothesis is true.
 Trial 2: Mean systolic BP was reduced by 50 mmHg, the sample size is large enough, and P value is significant. The CI CI shows clear reduction of BP at least by 40.2 to 59.1 mmHg. Giving this drug is cheap it is recommended for routine use.
 Trial 3: A reduction in mean was 30 mmHg but the trial was small, and CI ranged from reduction of 118.2 to increase of 58.2 mmHg. This drug might give important effect or important harm. The P value shows no significant effect of drug B in systolic BP.
 Trial 4: The reduction of mean was very small 3 mmHg, and P value is not significant. But because the trial is large we got a narrow CI. If we look at lower limit of CI, it corresponds to reduction of only 14.6 mmHg, so it excludes any substantial effect of drug B.
 Trial 5: the reduction of mean was 15 mmHg, and it is significant according to P value. The trial was large, and CI is totally in the reduction area. This drug is fairly proven to reduce systolic BP, but it's very unlikely to be recommended for use because its cost and the reduction is not the size required clinically. Notice that even with good statistical evidence the clinical importance should be considered. ^{[2],[3]}
References   
1.  Field Andy. Discovering Statistics Using SPSS. 3 ^{rd} ed. London: SAGE; 2013. 
2.  Hajeer AH, AlKnawy BA. Doctor′s Guide to Evidencebased Medicine. Riyadh: Alasr Printing Company; 2006. 
3.  Kirkwood BR, Sternc JA. Malden MA. Essential Medical Statistics. 2 ^{nd} ed. USA: Blackwell Publishing; 2003. 
[Figure 1]
[Table 1]
