mathematics

Minimal important difference

Minimal important difference is a mathematics topic covered in the lgStudy science library. This page brings together a partial reference excerpt, illustrations, worked examples, real-world applications and a short study plan, so you can understand Minimal important difference rather than just read about it. In short: The minimal important difference (MID) or minimal clinically important difference (MCID) is the smallest change in a treatment outcome that an individual patient would identify as important and which would indicate a change in the patient's management. Purpose Over the years great steps have been taken in reporting what really matters in clinical research.

Key takeaways

Minimal important difference belongs to mathematics; place it in that map before memorising details.
Learn the definition first, then one example that makes the definition concrete.
Connect Minimal important difference to a quantity you can measure, compute or draw — that is where exam questions come from.
Reproduce the core statement of Minimal important difference from memory before moving on to harder problems.

Reference excerpt

The minimal important difference (MID) or minimal clinically important difference (MCID) is the smallest change in a treatment outcome that an individual patient would identify as important and which would indicate a change in the patient's management.

Purpose Over the years great steps have been taken in reporting what really matters in clinical research. A clinical researcher might report: "in my own experience treatment X does not do well for condition Y". The use of a P value cut-off point of 0.05 was introduced by R.A. Fisher; this led to study results being described as either statistically significant or non-significant. Although this p-value objectified research outcome, using it as a rigid cut off point can have potentially serious consequences: (i) clinically important differences observed in studies might be statistically non-significant (a type II error, or false negative result) and therefore be unfairly ignored; this often is a result of having a small number of subjects studied; (ii) even the smallest difference in measurements can be proved statistically significant by increasing the number of subjects in a study. Such a small difference could be irrelevant (i.e., of no clinical importance) to patients or clinicians. Thus, statistical significance does not necessarily imply clinical importance. Over the years clinicians and researchers have moved away from physical and radiological endpoints towards patient-reported outcomes. However, using patient-reported outcomes does not solve the problem of small differences being statistically significant but possibly clinically irrelevant. In order to study clinical importance, the concept of minimal clinically important difference (MCID) was proposed by Jaeschke et al. in 1989. MCID is the smallest change in an outcome that a patient would identify as important. MCID therefore offers a threshold above which outcome is experienced as relevant by the patient; this avoids the problem of mere statistical significance. Schunemann and Guyatt recommended minimally important difference (MID) to remove the "focus on 'clinical' interpretations" (2005, p. 594).

Methods of determining the MID There are several techniques to calculate the MID. They fall into three categories: distribution-based methods, anchor-based methods and the Delphi method.

Distribution-based methods These techniques are derived from statistical measures of spread of data: the standard deviation, the standard error of measurement and the effect size, usually expressed as a standardized mean difference (SMD; also known as Cohen's d in psychology).

Using the one-half standard deviation benchmark of an outcome measure entails that patient improving more than one-half of the outcome score's standard deviation have achieved a minimal clinically important difference. The standard error of measurement is the variation in scores due to unreliability of the scale or measure used. Thus a change smaller than the standard error of measurement is likely to be the result of measurement error rather than a true observed change. Patients achieving a difference in outcome score of at least one standard error of measurement would have achieved a minimal clinically important difference. The effect size is a measure obtained by dividing the difference between the means of the baseline and posttreatment scores by the SD of the baseline scores. An effect size cut off point can be used to define MID in the same way as the one half standard deviation and the standard error of measurement. Item response theory (IRT) also can create an estimate of MID using judges who respond to clinical vignettes illustrating different scenarios.

Anchor based The anchor based method compares changes in scores with an "anchor" as a reference. An anchor establishes if the patient is better after treatment compared to baseline according to the patient's own experience. A popular anchoring method is to ask the patient at a specific point during treatment: ‘‘Do you feel that the treatment improved things for you?’’. Answers to anchor questions could vary from a simple "yes" or "no", to ranked options, e.g., "much better", "slightly better", "about the same", "somewhat worse" and "much worse". Differences between those average scale score for who answered "better" and those who answered "about the same" create the benchmark for the anchor method. An interesting approach to the anchor based method is establishment of an anchor before treatment. The patient is asked what minimal outcome would be necessary to undergo the proposed treatment. This method allows for more personal variation, as one patient might require more pain relief, where another strives towards more functional improvement. Different anchor questions and a different number of possible answers have been proposed. Currently there is no consensus on the one right question nor on the best answers.

Delphi method The Delphi method relies on a panel of experts who reach consensus regarding the MID. The expert panel gets information about the results of a trial. They review it separately and provide their best estimate of the MID. Their responses are averaged, and this summary is sent back with an invitation to revise their estimates. This process is continued until consensus is achieved.

… excerpt ends here. Continue reading the full article.

Worked examples

Example 1 — a first encounter with Minimal important difference

Start with the simplest possible case. Write down what Minimal important difference claims or describes in one sentence, then invent the smallest concrete situation in which that sentence is true. In mathematics, the smallest case is usually a single object, a single equation or a single measurement. Check that every symbol or term in your sentence has a meaning in that case.

Example 2 — changing one variable

Take the situation from Example 1 and change exactly one quantity: double it, halve it, or set it to zero. Predict what should happen to Minimal important difference before you calculate. Comparing your prediction with the result is the fastest way to find out whether you understand the idea or only the words.

Example 3 — an exam-style question

Typical questions about Minimal important difference ask you to (a) state it precisely, (b) apply it to given data, and (c) explain a limitation. Practise writing all three answers in under five minutes; the third part is what separates a full-mark answer from an average one.

Applications of Minimal important difference

In research: Minimal important difference appears in mathematics research whenever the underlying quantities have to be modelled precisely. Papers usually cite it as a starting assumption and then explore where it breaks down.
In technology and industry: Engineering practice reuses Minimal important difference in design rules, simulations and safety margins. Knowing the idea lets you read a specification sheet and understand why the numbers look the way they do.
In the classroom: Minimal important difference is common in secondary-school and first-year university syllabi. It links to neighbouring topics Medical statistics, Patient reported outcome measures, so understanding it makes those chapters shorter.
In everyday life: Look for Minimal important difference outside the textbook — in sport, cooking, traffic, electronics or the sky above you. An example you found yourself is remembered far longer than one you were given.

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How to study Minimal important difference in 20 minutes

Read the reference excerpt below once, without taking notes.
Close the page and write down what Minimal important difference means in your own words.
Compare your version with the excerpt and mark what you missed.
Work through the three examples above with pen and paper.
Explain Minimal important difference out loud to somebody else — or to Teacher Smith in the lgStudy chat.

Frequently asked questions

What is Minimal important difference in simple terms?

Why does Minimal important difference matter?

Because it connects several mathematics ideas at once: it gives you a definition you can apply, a quantity you can calculate, and a way to check whether a result is plausible.

How should I study Minimal important difference?

Read the excerpt, restate it from memory, then work through the examples and applications listed on this page. The five-step study plan above takes about twenty minutes.

What does this page cover?

It gives you a compact reference excerpt plus original lgStudy explanations, examples, applications and study material on Minimal important difference.