Confidence intervals

confidence intervals

Reporting confidence intervals.

Confidence intervals are often used in biomedical research as a tool for describing the statistical significance of findings in a research study. An example of  such a study is “Examining the association between childhood asthma and parent and grandparent asthma status: Implications for Practice“. This study investigated the association between a family history of asthma and the incidence of asthma in a population of children. Specifically, the study tested for a statistically significant association between childhood asthma incidence and having a parent or grandparent who had asthma.

As shown in the figure (above, right), many research reports describe their findings by making use of odds ratios (OR), confidence intervals (CI) and p-values. In this study, children who had a parent with asthma were almost twice as likely (OR = 1.96) to have asthma compared to those children who did not have a parent with asthma. Children who had both a parent and a grandparent with asthma were over four times more likely to have asthma compared to those without a parent or grandparent with asthma (OR = 4.27).

These odds ratios were calculated by first measuring the incidence of asthma in several subgroups of the study population. To calculate an odds ratio, a reference group was defined such as children who did not have either a parent or a grand parent with asthma. The values for OR are calculated as the probability of childhood asthma in a specified subgroup divided by the probability of childhood asthma in a reference group.

How can we know if the odds ratios reported in this study (such as 1.96) are statistically significant? The authors of the study provided both calculated p-values and 95 % confidence intervals for each odds ratio. The greater observed incidence of asthma in children who had a parent with asthma was reported as an odds ratio of 1.96 and a 95 % confidence interval of 1.26-3.06 and a p-value of 0.0027. The 95 % confidence interval indicates a range of odds ratio values that might occur by chance. If the 95 % confidence interval includes 1.0 then there is a greater than 1 in 20 chance that random variation in outcome incidence among the two compared study subgroups can account for the observed difference in incidence between the test group and the reference group.

For p-values, a value less than 0.05 indicates that there is less than an estimated 1 in 20 chance that random variation in outcome incidence among the study subgroups can account for the observed difference in incidence between a test group and the reference group. For the “had a parent with asthma” test group, a p-value of 0.0027 was reported, so there was a greater than 95 % calculated probability that the 1.96 odds ratio indicates a significant difference in asthma incidence between the “had a parent with asthma” test group and the reference group of children who did not have a parent with asthma.

In this study, an example of an odds ratio that was not found to be statistically significant was 1.12 for children who had a parent (mother or father) who smoked (see the  table, above). The reported p-values were greater than 0.05 and the 95 % confidence intervals included 1.0.

The larger an odds ratio and the further the bottom of the 95 % confidence interval is from 1.0 the more likely that an observer odds ratio indicates a statistically significant difference in asthma incidence in the test group. For the test group of children with both a parent and a grandparent with asthma the odds ratio was 4.27, the 95 % confidence interval was 2.39-7.65. The calculated p-value was less than 0.0001. The smaller the p-value the more likely that a study finding is not due to random variations and actually indicated a real difference between two subgroups in the study.

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About johnwschmidt

Exploring medical physiology.
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