Ophthalmic Statistics Note 4: analysing data from randomised controlled trials with baseline and follow-up measurements.
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PubMed Central - PubMed
Affiliation: Clinical Trials and Evaluation Unit, School of Clinical Sciences, University of Bristol, Bristol Royal Infirmary, Bristol, UK.
In clinical trials, continuous outcomes, such as intraocular pressure and visual acuity, are often measured both before treatment (ie, at baseline) and after treatment... Analysing change scores (ie, the difference between the post-treatment measurement and baseline measurement for each participant)... Using a statistical package, we can obtain estimates of a, b1, b2 and e... The estimate a is a constant, and b1 quantifies the size of the treatment effect (ie, the mean difference between treatments A and B)... The post-treatment measurements or change scores (methods (2) and (3)) would typically be compared using a two-sample t test... However, by chance, this was accompanied by a slightly higher mean baseline BCVA... The results from each analysis are shown in table 2 and discussed below... The 95% CI tells us that we are 95% confident that the difference in mean BCVA is somewhere between 4.8 letters in favour of ranibizumab and 1.4 letters in favour of bevacizumab... While in this example all three methods led to the same conclusion, it is possible for different models to yield estimates that might lead to different conclusions... If, for example, the more precise estimate had had a CI which excluded zero, while the less precise estimates did not, we might infer evidence of a treatment effect from one model only... This would test the hypothesis that the change from baseline is zero separately for each treatment group... The estimates obtained would give the mean change from baseline in each group, with a corresponding 95% CI, but we would not be able to draw a conclusion about, or quantify the difference between, the two drugs... If we were to perform two paired t tests on our data, we would conclude that there was a significant improvement in BCVA with both ranibizumab and bevacizumab, with a mean improvement of 4.9 letters (95% CI 3.1 to 6.7) and 4.1 letters (95% CI 2.4 to 5.8), respectively... Approaches include omitting the cases with missing data, which is an inefficient use of the data, reducing precision and power; imputing the missing values, which must be done with care; and fitting a more sophisticated model where the baseline and post-treatment measurements are modelled ‘jointly’, which allows participants with partial missing data to be included. Related in: MedlinePlus |
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Mentions: This is the preferred method of analysis. Here, we are estimating the difference in the mean BCVA between the two groups, again taking account of how good the participant's vision was at the start of the trial, but relaxing the restriction on the relationship between baseline and post-treatment measurements. From the results, we would conclude that BCVA improved by an estimated 1.1 letters more, on average, in the ranibizumab group than in the bevacizumab group, with a 95% CI from 3.4 letters in favour of ranibizumab to 1.3 letters in favour of bevacizumab. As with the other two models, there is no suggestion of a difference between the groups because the CI includes zero. The estimated relationship between the baseline and post-treatment measurements for each drug is illustrated in figure 1. The mean difference between the two drugs (1.1 letters) is the vertical distance between the two parallel lines. |
View Article: PubMed Central - PubMed
Affiliation: Clinical Trials and Evaluation Unit, School of Clinical Sciences, University of Bristol, Bristol Royal Infirmary, Bristol, UK.
In clinical trials, continuous outcomes, such as intraocular pressure and visual acuity, are often measured both before treatment (ie, at baseline) and after treatment... Analysing change scores (ie, the difference between the post-treatment measurement and baseline measurement for each participant)... Using a statistical package, we can obtain estimates of a, b1, b2 and e... The estimate a is a constant, and b1 quantifies the size of the treatment effect (ie, the mean difference between treatments A and B)... The post-treatment measurements or change scores (methods (2) and (3)) would typically be compared using a two-sample t test... However, by chance, this was accompanied by a slightly higher mean baseline BCVA... The results from each analysis are shown in table 2 and discussed below... The 95% CI tells us that we are 95% confident that the difference in mean BCVA is somewhere between 4.8 letters in favour of ranibizumab and 1.4 letters in favour of bevacizumab... While in this example all three methods led to the same conclusion, it is possible for different models to yield estimates that might lead to different conclusions... If, for example, the more precise estimate had had a CI which excluded zero, while the less precise estimates did not, we might infer evidence of a treatment effect from one model only... This would test the hypothesis that the change from baseline is zero separately for each treatment group... The estimates obtained would give the mean change from baseline in each group, with a corresponding 95% CI, but we would not be able to draw a conclusion about, or quantify the difference between, the two drugs... If we were to perform two paired t tests on our data, we would conclude that there was a significant improvement in BCVA with both ranibizumab and bevacizumab, with a mean improvement of 4.9 letters (95% CI 3.1 to 6.7) and 4.1 letters (95% CI 2.4 to 5.8), respectively... Approaches include omitting the cases with missing data, which is an inefficient use of the data, reducing precision and power; imputing the missing values, which must be done with care; and fitting a more sophisticated model where the baseline and post-treatment measurements are modelled ‘jointly’, which allows participants with partial missing data to be included.