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harmful trivial beneficial probability value of effect statistic Clinical, Practical or Mechanistic Significance vs Statistical Significance for POPULATION Effects Will G Hopkins Auckland University of Technology Auckland, NZ
Overview Background: Making Inferences Hypothesis Testing, P Values, Statistical significance Clinical Significance via Confidence Limits Clinical Significance via Clinical Chances Precision of estimation Smallest worthwhile effect Interpreting Probabilities How to Publish Clinical Chances Probabilities of benefit and harm How to use possible, likely, very likely, almost certain Examples
Background: Making Inferences The main aim of research is to make an inference about an effect in a population based on study of a sample. Alan will deal with inferences about the effect on an individual. Hypothesis testing via the P value and statistical significance is the traditional but flawed approach to making an inference. Precision of estimation via confidence limits is an improvement. But what's missing is some way to make inferences about the clinical, practical or mechanistic significance of an effect. I will explain how to do it via confidence limits using values for the smallest beneficial and harmful effect. I will also explain how to do it by calculating and interpreting chances that an effect is beneficial, trivial, and harmful.
Hypothesis Testing, P Values and Statistical Significance Based on the notion that we can disprove, but not prove, things. Therefore, we need a thing to disprove. Let's try the null hypothesis: the population or true effect is zero. If the value of the observed effect is unlikely under this assumption, we reject (disprove) the null hypothesis. Unlikely is related to (but not equal to) the P value. P < 0.05 is regarded as unlikely enough to reject the null hypothesis (that is, to conclude the effect is not zero or null). We say the effect is statistically significant at the 0.05 or 5% level. Some folks also say there is a real effect. P > 0.05 means there is not enough evidence to reject the null. We say the effect is statistically non-significant. Some folks also accept the null and say there is no effect.
Problems with this philosophy… We can disprove things only in pure mathematics, not in real life. Failure to reject the null doesn't mean we have to accept the null. In any case, true effects are always "real", never zero. So… THE NULL HYPOTHESIS IS ALWAYS FALSE ! Therefore, to assume that effects are zero until disproved is illogical and sometimes impractical or unethical. 0.05 is arbitrary. The P value is not a probability of anything in reality. Some useful effects aren't statistically significant. Some statistically significant effects aren't useful. Non-significant is usually misinterpreted as unpublishable. So good data are lost to meta-analysis and publication bias is rife. Two solutions: clinical significance via confidence limits or via clinical chances.
Confidence limits define a range within which we infer the true or population value is likely to fall. Likely is usually a probability of 0.95 (for 95% limits). Clinical Significance via Confidence Limits Representation of the limits as a confidence interval : Area = 0.95 upper likely limitlower likely limit observed value probability value of effect statistic 0 positivenegative probability distribution of true value, given the observed value value of effect statistic 0 positivenegative likely range of true value
Problem: 95% is arbitrary. And we need something other than 95% to stop folks seeing if the effect is significant at the 5% level. The effect is significant if the 95% confidence interval does not overlap the null. 99% would give an impression of too much imprecision. although even higher confidence could be justified sometimes. 90% is a good default, because… Chances that true value is < lower limit are very unlikely (5%), and… Chances that true value is > upper limit are very unlikely (5%).
Now, for clinical significance, we need to interpret confidence limits in relation to the smallest clinically beneficial and harmful effects. These are usually equal and opposite in sign. They define regions of beneficial, trivial, and harmful values. trivial harmful beneficial smallest clinically harmful effect smallest clinically beneficial effect value of effect statistic 0 positivenegative
Putting the confidence interval and these regions together, we can make a decision about clinical significance. Clinically decisive or clear is preferable to clinically significant. 0 value of effect statistic positivenegative trivial harmful beneficial Yes: use it.Yes Yes: use it.Yes Yes: use it.No Yes: don't use it.Yes Yes: don't use it.No Yes: don't use it.No Yes: don't use it.Yes Yes: don't use it.Yes No: need more research. No Clinically decisive? Statistically significant? Why statistical significance is impractical or unethical! Bars are 95% confidence intervals.
Problem: what's the smallest clinically important effect? If you can't answer this question, quit the field. Example: in many solo sports, ~0.5% change in power output changes substantially a top athlete's chances of winning. The default for most other populations and effects is Cohen's set of smallest values. These values apply to clinical, practical and/or mechanistic importance… Correlations: 0.10. Relative frequencies, relative risks, or odds ratios: 1.1, depending on prevalence of the disease or other condition. Standardized changes or differences in the mean: 0.20 between-subject standard deviations. In a controlled trial, it's the SD of all subjects in the pre-test, not the SD of the change scores.
We calculate probabilities that the true effect could be clinically beneficial, trivial, or harmful (P beneficial, P trivial, P harmful ). These Ps are NOT the proportions of positive, non- and negative responders in the population. Alan will deal with these. Calculating the Ps is easy. Put the observed value, smallest beneficial/harmful value, and P value into a spreadsheet at newstats.org. More challenging: interpreting the probabilities, and publishing the work. Clinical Significance via Clinical Chances smallest harmful value P harmful = 0.05 P trivial = 0.15 probability distribution of true value smallest beneficial value P beneficial = 0.80 0 probability value of effect statistic positivenegative observed value
You should describe outcomes in plain language in your paper. Therefore you need to describe the probabilities that the effect is beneficial, trivial, and/or harmful. Suggested scheme: Interpreting the Probabilities The effect… beneficial/trivial/harmful is almost certainly not… Probability <0.01 Chances <1% Odds <1:99 is very unlikely to be…0.01–0.051–5%1:99–1:19is unlikely to be…, is probably not…0.05–0.255–25%1:19–1:3is possibly (not)…, may (not) be…0.25–0.7525–75%1:3–3:1is likely to be…, is probably… is very likely to be… is almost certainly… 0.75–0.95 0.95–0.99 >0.99 75–95% 95–99% >99% 3:1–19:1 19:1–99:1 >99:1
How to Publish Clinical Chances Example of a table from a randomized controlled trial: Mean improvement (%) and 90% confidence limits 3.1; ±1.6 2.0; ±1.298; very likely 1.1; ±1.474; possible Compared groups Slow - control Explosive - control Slow - explosive Chances (% and qualitative) of substantial improvement a 99.6; almost certain a Increase in speed of >0.5%. TABLE 1–Differences in improvements in kayaking sprint speed between slow, explosive and control training groups. Chances of a substantial impairment were all <5% (very unlikely).
Example in body of the text: Chances (%) that the true effect was beneficial / trivial / harmful were 74 / 23 / 3 (possible / unlikely / very unlikely). In discussing an effect, use clear-cut or clinically significant or decisive when… Chances of benefit or harm are either at least very likely (>95%) or at most very unlikely (<5%), because… The true value of some effects is near the smallest clinically beneficial value, so for these effects… You would need a huge sample size to distinguish confidently between trivial and beneficial. And anyway… What matters clinically is that the effect is very unlikely to be harmful, for which you need only a modest sample size. And vice versa for effects near the threshold for harm. Otherwise, state more research is needed to clarify the effect.
P value 0.03 value of statistic 1.5 Conf. level (%) 90 deg. of freedom 18 positivenegative 1 threshold values for clinical chances Confidence limits lowerupper 0.42.6 2.40.20 -0.75.519018 prob (%)odds 783:1 likely, probable clinically positive Chances (% or odds) that the true value of the statistic is783:1 likely, probable 191:4 unlikely, probably not 31:30 very unlikely Two examples of use of the spreadsheet for clinical chances: prob (%)odds 221:3 unlikely, probably not clinically trivial prob (%)odds 01:2071 almost certainly not clinically negative Both these effects are clinically decisive, clear, or significant.
Limitations of this approach to clinical decisions It deals with uncertainty about the magnitude of an effect in a population. Which is OK for effects like correlations or simple mean differences between groups, which don't apply to individuals. But effects like risk of injury or changes in physiology or performance can apply to individuals. Alas, this approach does NOT provide the uncertainty of the effect or chances of benefit and harm for an individual. Neither does statistical significance. More information and analyses are needed to make clinical decisions for individuals.
Summary Show the observed magnitude of the effect. Attend to precision of estimation by showing 90% confidence limits of the true value. Do NOT show p values, do NOT test a hypothesis and do NOT mention statistical significance. Attend to clinical, practical or mechanistic significance by… stating, with justification, the smallest worthwhile effect, then… interpreting the confidence limits in relation to this effect, or… estimating probabilities that the true effect is beneficial, trivial, and/or harmful (or substantially positive, trivial, and/or negative). Make a qualitative statement about the clinical or practical significance of the effect, using unlikely, very likely, and so on. Remember, it applies to populations, not individuals.
For related articles and resources: A New View of Statistics SUMMARIZING DATA GENERALIZING TO A POPULATION Simple & Effect Statistics Precision of Measurement Precision of Measurement Confidence Limits Statistical Models Statistical Models Dimension Reduction Dimension Reduction Sample-Size Estimation Sample-Size Estimation newstats.org