Shrier Ian, Steele Russell
Centre for Clinical Epidemiology and Community Studies, Lady Davis Institute for Medical Research, SMBD-Jewish General Hospital, McGill University, Canada.
Clin J Sport Med. 2006 Mar;16(2):107-10. doi: 10.1097/00042752-200603000-00004.
Many articles provide only odds ratios (OR) and non relative risks (RR) as the effect estimate. For a variety of important reasons, multiple logistic regression used to adjust for confounders routinely provides only the adjusted OR (ORadj). However, from the clinician's perspective, the ORadj is only easily interpretable when it approximates the adjusted RR (RRadj). In general, the relationship between the OR and RR (adjusted or nonadjusted) is dependent on prevalence of disease in the control group (Po) and has always been presented as nonlinear. Therefore, it is difficult for the clinician to convert the OR to RR when reading the published data. A formula was proposed by Zhang and Yu, but the relationship remains nonlinear.
To develop a simple method to convert OR to RR without the use of computer.
Algebraic manipulation.
Through algebraic manipulation, we show that although the OR and RR relationship is nonlinear over the range Po, the ratio OR/RR has a linear relationship with Po with a slope of "OR-1": OR/RR=(OR-1)xPo+1. This makes the prediction of RR on the basis of OR more transparent. It is clear that if Po is small, the RR approximates the OR, but only if the OR is also small. Previous problems with confidence intervals noted with the Zhang and Yu formula remain (ie, they are too narrow under some conditions) and the result should be interpreted with this limitation. Relationships between ORadj and risk difference or number needed to treat remain curvilinear, but some overall approximations can be made.
A simple relationship exists that allows readers to easily convert ORadj to RRadj. Limitations of the approach remain but seem to be less restrictive than the limitations of not converting ORadj to RRadj.
许多文章仅提供比值比（OR）而非相对风险（RR）作为效应估计值。由于多种重要原因，用于调整混杂因素的多重逻辑回归通常仅提供调整后的比值比（ORadj）。然而，从临床医生的角度来看，只有当ORadj接近调整后的相对风险（RRadj）时，它才易于解释。一般来说，OR与RR（调整后或未调整）之间的关系取决于对照组中疾病的患病率（Po），并且一直呈现为非线性关系。因此，临床医生在阅读已发表的数据时很难将OR转换为RR。Zhang和Yu提出了一个公式，但这种关系仍然是非线性的。
开发一种无需使用计算机即可将OR转换为RR的简单方法。
代数运算。
通过代数运算，我们表明，尽管在Po范围内OR与RR的关系是非线性的，但OR/RR与Po具有线性关系，斜率为“OR - 1”：OR/RR = (OR - 1)×Po + 1。这使得基于OR预测RR更加直观。显然，如果Po较小，RR接近OR，但前提是OR也较小。Zhang和Yu公式中提到的置信区间的先前问题仍然存在（即，在某些情况下它们太窄），结果应在考虑此限制的情况下进行解释。ORadj与风险差或需治疗人数之间的关系仍然是曲线关系，但可以进行一些总体近似。
存在一种简单的关系，使读者能够轻松地将ORadj转换为RRadj。该方法仍然存在局限性，但似乎比不将ORadj转换为RRadj的局限性限制更少。
