Mastering variation: variance components and personalised medicine

Abstract

Various sources of variation in observed response in clinical trials and clinical practice are considered, and ways in which the corresponding components of variation might be estimated are discussed. Although the issues have been generally well-covered in the statistical literature, they seem to be poorly understood in the medical literature and even the statistical literature occasionally shows some confusion. To increase understanding and communication, some simple graphical approaches to illustrating issues are proposed. It is also suggested that reducing variation in medical practice might make as big a contribution to improving health outcome as personalising its delivery according to the patient. It is concluded that the common belief that there is a strong personal element in response to treatment is not based on sound statistical evidence.

Keywords: components of variation; cross-over trials; n-of-1 trials; personalised medicine; random effects.

Figure 1

A parallel group trial in asthma with outcome measured in litres of FEV₁. The left‐hand panel shows a theoretical situation that could never be observed, whereby each patient provides an outcome for each treatment. The right‐hand panel shows what would be observed in practice. FEV₁, forced expiratory volume in 1 s.

Figure 2

A double cross‐over trial in asthma with difference treatment – placebo calculated for each of two pairs of periods. The difference for the second pair is plotted against that for the first. The solid lines show the mean difference of 0.5 L; the dashed lines represent an arbitrary threshold for ‘response’ at 0.3 L. Black plus signs: responded on both occasions. Open circles: responded on neither occasion. A patient who responded on one occasion only is plotted as an x. The correlation between differences is 0.9. Marginal distributions are also shown as histograms and a smoothed density. FEV₁, forced expiratory volume in 1 s.

Figure 3

A double cross‐over trial in asthma with difference treatment – placebo calculated for each of two pairs of periods. The difference for the second pair is plotted against that for the first. The solid lines show the mean difference of 0.5 L; the dashed lines represent an arbitrary threshold for ‘response’ at 0.3 L. Black plus signs: responded on both occasions. Open circles: responded on neither occasion. A patient who responded on one occasion only is plotted as an x. The correlation between differences is 0.02. Marginal distributions are also shown as histograms and a smoothed density. FEV₁, forced expiratory volume in 1 s.

Figure 4

Tonsillectomy rates for persons under 15 years of age for 3 years (2009–2011) by local authority, together with 95% confidence limits.

Figure 5

Shrunk tonsillectomy rates for persons under 15 years of age for 3 years (2009–2011) by local authority plotted against raw rate by local authority given in Figure 4. The diagonal solid line is a line of equality of shrunk and original effects. Dashed horizontal lines indicate minimum, mean and maximum shrunk values. A dashed vertical line gives the mean original value.