Smith S J, Caudill S P, Steinberg K K, Thacker S B
Centers for Disease Control and Prevention, National Center for Environmental Health, Atlanta, GA 30333, USA.
Stat Med. 1995;14(5-7):531-44. doi: 10.1002/sim.4780140513.
Using data from a meta-analysis of the effects of oestrogen replacement therapy on the development of breast cancer, we compared alternative methods for combining dose-response slopes from epidemiological studies. We evaluated issues related both to summarizing data from single studies and to combining results from multiple studies. Findings related to the analysis of individual dose-response studies include: (1) a method of weighing studies that gives greater influence to dose-response slopes that conform to the linear relation of relative risk to duration can lead to large differences in calculated weights as a function of non-linearity; (2) a regression model using a variable-intercept resulted in a mean dose-response slope that increased as much as threefold when compared with the values obtained with a zero-intercept model. When combining results from multiple studies, we found: (1) calculating standard errors of mean dose-response slopes by methods that allow for both among-study and within-study variability (a random-effects type model) gave values different from a method that assumes homogeneity and equal within-study precision (a fixed-effects model); (2) the random-effects model gives mean and standard error results most similar to a bootstrap resampling method as increasing heterogeneity is observed (however, this model could give biased mean estimates compared with the bootstrap method); (3) a components-of-variance model compares favourably with the bootstrap and is easier to apply than the random-effects model. Based on these findings, we recommend the use of methods which incorporate heterogeneity to guard against underestimating the standard error. However, caution is urged because bias in point estimates can occur if extreme heterogeneity is present. Two other observations affect the interpretation of data combined from multiple studies. First, inclusion into a model of quality scores assigned by blinded reviewers had little effect on the mean dose-response slope and its standard error. Second, the number of studies required to achieve desired statistical power, varies with effect size.
利用一项关于雌激素替代疗法对乳腺癌发病影响的荟萃分析数据，我们比较了综合流行病学研究中剂量反应斜率的不同方法。我们评估了与单个研究数据汇总以及多个研究结果综合相关的问题。与个体剂量反应研究分析相关的发现包括：（1）一种对符合相对风险与持续时间线性关系的剂量反应斜率给予更大影响的研究加权方法，可能会导致计算权重因非线性而产生很大差异；（2）使用可变截距的回归模型得出的平均剂量反应斜率，与使用零截距模型得到的值相比，增加了多达三倍。在综合多个研究结果时，我们发现：（1）通过考虑研究间和研究内变异性的方法（随机效应类型模型）计算平均剂量反应斜率的标准误差，得出的值与假设同质性和研究内精度相等的方法（固定效应模型）不同；（2）随着观察到的异质性增加，随机效应模型给出的均值和标准误差结果与自助重采样方法最为相似（然而，与自助法相比，该模型可能给出有偏差的均值估计）；（3）方差成分模型与自助法相比具有优势，并且比随机效应模型更易于应用。基于这些发现，我们建议使用纳入异质性的方法，以防止低估标准误差。然而，由于如果存在极端异质性可能会出现点估计偏差，因此需谨慎。另外两个观察结果影响对多个研究综合数据的解释。首先，将由盲法评审员分配的质量评分纳入模型，对平均剂量反应斜率及其标准误差影响不大。其次，达到所需统计功效所需的研究数量随效应大小而变化。
