Answer to a Reader’s Question About Sample Size Calculation

Last week, a reader emailed me with questions about sample size calculation mentioned in one of my videos. To be honest, ever since that video went live, people have been sending private messages asking about it — and after I’d answer, they’d simply vanish without a word. That’s rather impolite. Free-riding isn’t really free; knowledge deserves respect.

This reader raised two questions: first, how to identify the outcome measure for sample size calculation, and second, how to determine the allowable error (δ). Both are fairly common questions, so they’re worth addressing in a dedicated post.

Asking the first question suggests a lack of understanding of why we calculate sample size in the first place. Simply put, sample size calculation ensures that your results have statistical power — that your findings are valid within a defined scope (say, for 90% of a similar population). So what drives the calculation? Primarily your research design, and most importantly, which data you plan to report in the final paper.

In your research protocol, you must clearly define the primary outcome measure. In principle, there should be only one. Traditional Chinese Medicine (TCM) research is somewhat special — you may have both a TCM and a Western medicine primary outcome, but one must take precedence. When choosing, pick the indicator that is most critical, most important, most representative, and most closely aligned with your paper’s theme.

This reader’s confusion was that the paper they found reported three outcome measures — JOA, SF-36, and VAS — and they didn’t know which one to use for sample size calculation. The answer is straightforward: whichever is your primary outcome measure in your own study, use that one. If you’re unsure which qualifies as primary, calculate the required sample size for all of them and go with the largest number. That will always be the safest bet. In short, the calculated sample size represents the minimum needed to achieve statistical power; within budget, bigger is always better.

The second question concerns allowable error (δ), which involves complex statistical principles. Generally, you should use the overall between-group difference from a pilot study as the allowable error value. If no pilot study exists, you can estimate it at roughly 0.3 times (range: 0.25–0.5) the standard deviation. The smaller the allowable error, the larger the sample size required. This is a highly variable range, and the error typically doesn’t need to be especially small. For a detailed discussion, see: Ni Yanyan, Zhang Jinxin. Rational Selection of Allowable Error δ in Sample Size Estimation for Hypothesis Testing. Journal of Evidence-Based Medicine, 2011, 11(6): 370–372.

For example, if the JOA low back pain score is the primary outcome measure for two groups, the allowable error δ = 20.56 − 19.45 = 1.11

That covers both questions. If you’d like to discuss further, feel free to leave a comment below.

上周有同学发邮件询问视频里样本量计算的相关问题，其实视频发布之后一直有人私信在问，我给回答完之后就了无音讯，非常没有礼貌，白嫖是不能白嫖的，要尊重知识。

这位同学问了两个问题，一是如何寻找结局指标计算样本量，二是如何寻找允许误差。

这都是比较典型的问题，有必要专门回答一下。

能问出第一个问题是由于不明白为什么要计算样本量。简单点说，计算样本量就是为了让数据结果具备统计效力，让你的数据能够在有限的范围（比如90%的类似人群）内有效。那么，计算样本量的依据是什么呢？主要是你的研究设计，其中最重要的是你的研究最后要报告哪些数据。

在研究设计方案中，必须明确主要观察指标，这个指标原则上只应该有一个，中医研究特殊一些，可以有中医和西医两个主要观察指标，但必须以一个为主，我们在选择的时候往往选择最关键、最重要、最有代表性、与论文主题最贴切的那个指标。

这位同学的困惑在于，他找的这篇论文里报告了JOA、SF-36、VAS三个指标，不知道选择哪一个用来计算样本量。所以这个回答很简单，在你的研究里，主要观察指标是哪一个就选用哪一个来计算样本量。如果你不知道哪个可以作为主要观察指标，那就把这几个指标数据都算一遍，选用样本量最多的那个，这一定是最靠谱的。总之，算出来的样本量是能够达到统计效力最小值，在成本可控的前提下，样本量多多益善。

第二个问题是允许误差的计算，这里面牵扯到复杂的统计学原理，一般要用预实验的总体组间差距作为容许误差值，如果没有预实验则可以大约估计使用0.3倍左右（0.25-0.5）的标准差来计算允许误差。允许误差越小，样本量越大，这是一个浮动非常大的空间，一般不需要特别小，具体讨论可参考（倪延延, 张晋昕. 假设检验时样本含量估计中容许误差 δ 的合理选取.循证医学, 2011,11(6): 370-372）。

例如，如果以两组JOA下腰痛评分为主要观察指标，容许误差δ=20.56-19.45=1.11

回答完毕，如需商榷请直接在文后回复。