Statistics notes - Analysing controlled trials with baseline and follow up measurements
Statistics notes - Analysing controlled trials with baseline and follow up measurements
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DOI：
10.1136/bmj.323.7321.1123
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发表时间：
2001-11-10
影响因子：
105.7
通讯作者：
Altman, DG
中科院分区：
文献类型：
--
作者：
Vickers, AJ;Altman, DG
在许多随机试验中，研究人员在基线时测量连续变量，并再次作为随访时评估的结果。基线测量在慢性病试验中很常见，研究人员想要了解一种治疗是否可以降低先前存在的疼痛、焦虑、高血压等水平。在这类试验中，可以通过几种方式进行统计比较。对随访(治疗后)评分的比较将得出这样的结果：“在试验结束时，治疗组的平均疼痛评分降低了15 mm(95%可信区间为10到20 mm)。”或者，也可以通过从基线分数中减去随访分数来计算变化分数，从而得出这样的声明：“治疗组的疼痛减轻比对照组多20毫米(16到24毫米)。”如果每组的平均基线分数相同，使用这两种简单方法估计的治疗效果将是相同的。如果治疗有效，两种方法治疗效果的统计学意义将取决于基线和随访评分之间的相关性。如果相关性较低，使用更改分数将增加变化，并且后续分数更有可能显示显着结果。相反，如果相关性很高，仅使用跟踪分数将丢失信息，并且更改分数更有可能是显著的。然而，选择哪个分析得出更有意义的发现是不正确的。分析方法应在试验方案中具体说明。一些人使用改变分数来考虑治疗组之间基线的机会不平衡。然而，分析变化不能控制基线失衡，因为回归到平均值1 2：基线值与变化负相关，因为基线得分低的患者通常比得分高的患者改善得更多。一个更好的方法是使用协方差分析(ANCOVA)，尽管它的名字是，但它是一种回归方法。3有效地获得两条平行直线(线性回归)，将每组的结果评分与基线评分联系起来。它们可以归结为一个回归方程：随访得分=常量+a×基线得分+b×分组
In many randomised trials researchers measure a continuous variable at baseline and again as an outcome assessed at follow up. Baseline measurements are common in trials of chronic conditions where researchers want to see whether a treatment can reduce pre-existing levels of pain, anxiety, hypertension, and the like.Statistical comparisons in such trials can be made in several ways. Comparison of follow up (posttreatment) scores will give a result such as “at the end of the trial, mean pain scores were 15 mm (95% confidence interval 10 to 20 mm) lower in the treatment group.” Alternatively a change score can be calculated by subtracting the follow up score from the baseline score, leading to a statement such as “pain reductions were 20 mm (16 to 24 mm) greater on treatment than control.” If the average baseline scores are the same in each group the estimated treatment effect will be the same using these two simple approaches. If the treatment is effective the statistical significance of the treatment effect by the two methods will depend on the correlation between baseline and follow up scores. If the correlation is low using the change score will add variation and the follow up score is more likely to show a significant result. Conversely, if the correlation is high using only the follow up score will lose information and the change score is more likely to be significant. It is incorrect, however, to choose whichever analysis gives a more significant finding. The method of analysis should be specified in the trial protocol. Some use change scores to take account of chance imbalances at baseline between the treatment groups. However, analysing change does not control for baseline imbalance because of regression to the mean1 2: baseline values are negatively correlated with change because patients with low scores at baseline generally improve more than those with high scores. A better approach is to use analysis of covariance (ANCOVA), which, despite its name, is a regression method. 3 In effect two parallel straight lines (linear regression) are obtained relating outcome score to baseline score in each group. They can be summarised as a single regression equation: follow up score= constant+ a× baseline score+ b× group