优势比

优势比

int0030

2022 年 10 月 02 日

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学习名词解释

# 基本内容

优势比，odd ratio，又称比值比，OR值，对于发病率很低的疾病来说，是相对危险度的精确估计值[^1]。

([Odds ratio - Wikipedia](https://en.wikipedia.org/wiki/Odds_ratio)):

The odds ratio is the ratio of the [odds](https://en.wikipedia.org/wiki/Odds) of an event occurring in one group to the odds of it occurring in another group. The term is also used to refer to sample-based estimates of this ratio. These groups might be men and women, an experimental group and a [control group](https://en.wikipedia.org/wiki/Control_group), or any other [dichotomous](https://en.wikipedia.org/wiki/Dichotomy) classification. If the probabilities of the event in each of the groups are $p_1$ (first group) and $p_2$ (second group), then the odds ratio is:

$$
{p_{1}/(1-p_{1}) \over p_{2}/(1-p_{2})}={p_{1}/q_{1} \over p_{2}/q_{2}}={\frac  {\;p_{1}q_{2}\;}{\;p_{2}q_{1}\;}}

where $q_x = 1 − p_x$. An odds ratio of 1 indicates that the condition or event under study is equally likely to occur in both groups. An odds ratio greater than 1 indicates that the condition or event is more likely to occur in the first group. And an odds ratio less than 1 indicates that the condition or event is less likely to occur in the first group. The odds ratio must be nonnegative if it is defined. It is undefined if $p_2q_1$ equals zero, i.e., if $p_2$ equals zero or $q_1$ equals zero.

# 特点

1. logistic回归中，OR值=1，表示该因素对疾病的发生不起作用
   - OR值大于1，表示该因素是一个危险因素
   - OR值小于1，表示该因素是一个保护因素
   - 同时最好要算出它的95%CI
2. 当我们已知疾病的发生状况，比较疾病组与非疾病组危险因素暴露的情况差异时（即回顾性研究时），用OR进行定量描述。
3. OR是否有意义还要看其P值，一般95%CI 上限小于1时说明可能是保护因素，相反如果下限大于1则说明可能是危险因素
4. ln(OR)近似服从正态分布，因此在计算OR值置信区间的时候都是先计算ln(OR)置信区间，再计算OR置信区间[^2][^3][^4]

# 举例

1. 假定我们要鉴别一个基因（或者标记位点SNP）有两个等位基因（等位），记为Allele 1和Allele 2

-  |      | Allele 1 | Allele 2 |
     | ------ | ---------- | ---------- |
     | 病例 | A        | B        |
     | 对照 | C        | D        |
   - odds 值在病例和对照可以计算如下：

- 病例Allele 1 Odds = $\dfrac{A(A+B)}{B(A+B)} = \dfrac{A}{B}$
     - 对照Allele 1 Odds = $\dfrac{C(C+D)}{D(C+D)} = \dfrac{C}{D}$
     - 则Allele 1的OR值为$\dfrac{A/B}{C/D}=\dfrac{AD}{BC}$
   - 同样的，可以计算95% Confidence Intervals (CIs) 值：

- 95% CI of ln(OR) =$ ln(OR)±1.96(\frac{1}{A} + \frac{1}{B} + \frac{1}{C} + \frac{1}{D})^{0.5}$
     - 95% CI of OR = $e^{\mbox{95\% CI of }ln(OR)}$

[^1]: [OR值的意义和计算公式，和95% CI](https://blog.sina.com.cn/s/blog_4af3f0d20100b9dh.html)
    
[^2]: http://www.ncbi.nlm.nih.gov/pmc/articles/PMC1127651/
    
[^3]: http://bioterrorism.slu.edu/bt/products/bio_epi/scripts/mod12.pdf
    
[^4]: http://www.sjsu.edu/faculty/gerstman/StatPrimer/case-control.pdf

最后修改：2022 年 10 月 02 日