洛德的‘悖论’解释：关于在观察性数据中使用‘变化分数’的50年警示
Lord's 'paradox' explained: the 50-year warning on the use of 'change scores' in observational data
AI总结：
洛德悖论揭示了在观察性数据中使用变化分数的局限性，强调了明确研究问题和正确处理外生变化的重要性。
摘要：
1967年，弗雷德里克·洛德提出了一个困扰科学家超过半个世纪的难题。随后被称为洛德的‘悖论’，这个谜题的核心在于两种不同的方法估算暴露对‘结果变化’的效应时会产生截然不同的结果。方法1涉及比较暴露组之间的平均‘变化分数’，方法2则涉及在基线结果条件下比较随访结果。解决这个谜题始于认识到变量可能改变值的三个原因：（A）‘内生变化’，代表基线的自相关性，（B）‘随机变化’，代表来自瞬时随机过程的变化，（C）‘外生变化’，代表所有非内生、非随机的变化，并包含所有可能由其他基线变量修改的变化。在观察性数据中，方法1和方法2都不能可靠地估计暴露对‘外生变化’的因果效应。方法1在暴露导致或由基线结果引起时，容易产生稀释或相反符号的估计值。方法2则由于基线结果的测量误差和时间变化的混杂偏倚，容易产生高估。测量误差可以通过对基线结果进行多次测量来减少，而时间变化的混杂可以通过g方法来减少。洛德的‘悖论’为观察性数据科学提供了几个持久的教训，包括研究问题定义的重要性以及分析变化分数在观察性数据中的问题。
英文摘要：
In 1967, Frederick Lord posed a conundrum that has confused scientists for over half a century. Subsequently named Lord's 'paradox', the puzzle centres on the observation that two different approaches to estimating the effect of an exposure on the 'change' in an outcome can produce radically different results. Approach 1 involves comparing the mean 'change score' between exposure groups and Approach 2 involves comparing the follow-up outcome between exposure groups conditional on the baseline outcome. Resolving this puzzle starts with recognising the three reasons that a variable may change value: (A) 'endogenous change', which represents autocorrelation from baseline, (B) 'random change', which represents change from transient random processes, and (C) 'exogenous change', which represents all non-endogenous, non-random change and contains all change that is potentially modifiable by other baseline variables. In observational data, neither Approach 1 nor Approach 2 can reliably estimate the causal effect of an exposure on 'exogenous change' in an outcome. Approach 1 is susceptible to diluted or opposite-sign estimates whenever the exposure causes, or is caused by, the baseline outcome. Approach 2 is susceptible to inflated estimates due to measurement error in the baseline outcome and time-varying confounding bias when the baseline outcome is a mediator. The measurement error can be reduced with multiple measures of the baseline outcome, and the time-varying confounding can be reduced using g- methods. Lord's 'paradox' offers several enduring lessons for observational data science including the importance of a well-defined research question and the problems with analysing change scores in observational data.
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