N-of-1 Trial

N-of-1 Trial for Individual Treatment Decisions

An N-of-1 trial answers a prescribing question for one person, namely whether a particular medicine works better than placebo or an alternative for this patient, by giving the treatments in randomised, usually blinded, periods and comparing the patient's own outcomes. In health economics the design matters because targeting a long-term medicine to the patients who benefit from it can save drug spending and spare others side effects that bring them no gain. A single trial gives evidence about one patient, while a planned series of trials can be combined to estimate an average effect and to sharpen each person's estimate.

How a single-patient trial is built

The design applies the protections of a randomised controlled trial to one person. Guyatt and colleagues, in the New England Journal of Medicine, gave a single patient a series of pairs of treatments, one active and one placebo or alternative in each pair, in a double-blind order set by random allocation. The trial was continued until efficacy was established or disproved, and the authors set up a clinical service to make the method widely available in their community.

The CONSORT extension for N-of-1 trials, known as CENT 2015, restricts the term to a prospectively planned multiple crossover trial in a single individual, often written ABAB. It defines the building blocks of the design as follows.

Lillie and colleagues list randomisation of treatment order, carryover, washout and blinding as the main design choices, noting that a random order helps when a patient's disease or habits follow a cycle.

Conditions and treatments that suit the design

CENT 2015 calls the design ideal for chronic stable conditions and therapies whose effect starts and ends quickly. Scuffham and colleagues give five characteristics of a medicine suitable for an N-of-1 trial. The condition is chronic and relatively stable, the half-life of the medicine is short, its biological action starts and stops rapidly, its effect can be measured with a validated outcome measure, and it does not alter the underlying condition.

CENT 2015 adds that N-of-1 trials fit situations that large trials do not serve well, such as rare diseases, comorbid conditions and patients on concurrent therapies. Araujo, Julious and Senn explain why the design needs fewer patients. Each patient gives more observations, and differences between patients drop out of the comparison because each patient acts as their own control. A treatment that changes the disease course breaks the design, because later periods no longer measure the treatment currently given.

Estimating the effect for one patient

The simplest analysis of a single trial treats each pair of periods as one comparison. The mean of the within-pair differences estimates the treatment effect for that patient.

$$\bar{d} = \frac{1}{k}\sum_{j=1}^{k}\left(Y_{Aj} - Y_{Bj}\right), \qquad SE(\bar{d}) = \frac{s_d}{\sqrt{k}}$$

where $Y_{Aj}$ and $Y_{Bj}$ are the patient's mean outcomes during the treatment A and treatment B periods of pair $j$, $k$ is the number of pairs, $\bar{d}$ is the mean within-pair difference, $s_d$ is the standard deviation of the $k$ differences and $SE(\bar{d})$ is the standard error of the mean difference. A paired t statistic, $\bar{d}$ divided by its standard error on $k-1$ degrees of freedom, gives a confidence interval for the patient's effect.

Two features of single-patient data complicate this. Lillie and colleagues note that measurements taken close together in one person are serially correlated, so standard t-tests on the repeated measurements lead to erroneous inferences. Analysing one summary value per period, rather than every daily score, reduces the problem, and time-series methods address it directly. The second feature is carryover, the lingering influence of an earlier treatment on a later period, which washout periods and measuring outcomes only late in each period are meant to limit.

Worked example with three pairs of pain-score periods

All numbers in this example are illustrative. A patient with chronic neuropathic pain whose response to a medicine is uncertain takes part in a 12-week blinded trial of the medicine (A) against placebo (B), with three pairs of two-week periods in randomised order within each pair. The outcome is the mean daily pain score on a 0 to 10 scale in each period, and the clinician and patient agree beforehand that a mean reduction of at least 1 point would justify continuing.

1. Record the period means. The medicine periods average 4.2, 4.6 and 3.9, and the placebo periods average 5.6, 5.4 and 5.7.

2. Compute the within-pair differences. The differences are 4.2 minus 5.6 = minus 1.4, 4.6 minus 5.4 = minus 0.8 and 3.9 minus 5.7 = minus 1.8.

3. Estimate the effect. The mean difference is (minus 1.4 minus 0.8 minus 1.8) / 3 = minus 4.0 / 3 = minus 1.33 points. The squared deviations from the mean are 0.0044, 0.2844 and 0.2178, which sum to 0.5067, so the variance is 0.5067 / 2 = 0.2533 and $s_d$ = 0.503. The standard error is 0.503 / 1.732 = 0.291.

4. Build the interval. With 2 degrees of freedom the two-sided 95% t value is 4.303, so the margin is 4.303 × 0.291 = 1.25 and the 95% interval is minus 2.58 to minus 0.08. The t statistic is minus 1.33 / 0.291 = minus 4.59.

5. Interpret. All three pairs favour the medicine and the interval excludes zero. The interval runs from a reduction of 2.58 points to one of only 0.08, so it is compatible with a benefit well above the agreed 1-point threshold and with one far below it. The data support a real benefit for this patient, while its size remains uncertain after only three pairs. A further pair or two would narrow the interval, at the cost of more weeks on placebo.

Combining a series of trials and shrinking individual estimates

When many patients complete N-of-1 trials under a common protocol, the series resembles a repeated period crossover trial, and Senn shows why that matters. A parallel group trial cannot separate the extent to which treatment effects vary between patients from ordinary variation in each person, and a classical two-period crossover design cannot do so either. Repeated periods of each treatment in the same patient make the patient-by-treatment interaction identifiable, and Senn calls such trials the strongest form of evidence on it.

Zucker and colleagues proposed a hierarchical Bayesian random-effects model that combines N-of-1 trials to estimate the population effect and uses it to help interpret each patient's result. Araujo, Julious and Senn describe the same idea through mixed-effects models, which give shrinkage estimates that weight a patient's own data against the results from other patients. A standard normal-normal form of this weighting is shown below.

$$\tilde{\theta}_i = w_i\,\bar{d}_i + (1 - w_i)\,\hat{\mu}, \qquad w_i = \frac{\tau^2}{\tau^2 + s_i^2 / k_i}$$

where $\tilde{\theta}_i$ is the shrunken effect estimate for patient $i$, $\bar{d}_i$ is that patient's own mean difference, $\hat{\mu}$ is the estimated average effect across the series, $\tau^2$ is the variance of true effects between patients, $s_i^2$ is the variance of patient $i$'s within-pair differences, $k_i$ is that patient's number of pairs and $w_i$ is the weight given to the patient's own data.

Continuing the illustrative example, suppose earlier trials under the same protocol give $\hat{\mu}$ = minus 0.5 points and a between-patient standard deviation of 0.6, so $\tau^2$ = 0.36. The patient's sampling variance is 0.2533 / 3 = 0.0844, the weight is 0.36 / (0.36 + 0.0844) = 0.81, and the shrunken estimate is 0.81 × (minus 1.33) + 0.19 × (minus 0.5) = minus 1.08 minus 0.095 = minus 1.175 points. With longer trials the weight moves towards one and the patient's own data dominate. Araujo and colleagues liken this to fixed and random effects in meta-analysis, since a simple paired test can show whether a treatment has any effect but cannot deliver shrinkage estimates.

Costs, prescribing and economic evaluation

The economic case for N-of-1 trials rests on targeting medicines to the patients who benefit. Scuffham and colleagues followed three Australian trial series for 12 months, in osteoarthritis, chronic neuropathic pain and ADHD. In the neuropathic pain series gabapentin was more effective than placebo for 29% of participants, placebo was better for 2% and no difference was found for 69%. Annual health system costs were significantly lower after the osteoarthritis and neuropathic pain trials than before them, mostly through fewer medical consultations. The study had no control group, and the authors note that regression to the mean may have exaggerated the fall in costs. They estimated the marginal cost of a trial at about 600 Australian dollars per participant in the research setting and about 100 in routine practice, and proposed that a funder could make subsidised access to a high-cost medicine conditional on a positive N-of-1 result.

In an earlier two-year single-patient trial service at an academic medical centre, Larson and colleagues found that of 34 completed trials, 18 showed the active treatment to be ineffective, harmful or apparently equivalent, which led to it being stopped or not started, and direct costs were about USD 450 to USD 500 per trial. Karnon and Qizilbash argued that collecting economic data within N-of-1 trials could allow individualised estimates of cost-effectiveness, which their title frames as getting cost-effectiveness analysis closer to the margin.

As an illustrative calculation, consider 100 patients with uncertain response to a medicine costing GBP 1,200 per patient per year. If all continue it for a year, drug spending is 100 × 1,200 = GBP 120,000. If each first completes an N-of-1 trial costing GBP 250 and only the 30 responders continue, spending is 100 × 250 + 30 × 1,200 = GBP 25,000 + GBP 36,000 = GBP 61,000, a saving of GBP 59,000, or GBP 590 per patient. On cost alone, the trials pay for themselves within a year whenever the trial cost per patient is below the non-responder share multiplied by the annual drug cost, here 0.7 × 1,200 = GBP 840 against a trial cost of GBP 250. The calculation ignores drug use during the trial and patients who do not persist with the decision, and any responder misclassified as a non-responder loses benefit that counts against the saving. A full evaluation would compare the strategy with open trial and error and value the reduced uncertainty, as value of information analysis does.

How the design differs from neighbouring approaches

An N-of-1 trial is a crossover trial carried to its limit, with one participant and many periods. A group crossover trial uses the within-person comparison to estimate an average effect more efficiently, whereas an N-of-1 trial aims at the effect in the person studied.

CENT 2015 treats N-of-1 trials as a subset of the single case experimental designs used in the behavioural sciences. A series of N-of-1 trials also differs from an individual patient data meta-analysis of parallel trials, because only the repeated within-patient periods can reveal heterogeneous treatment effects at the level of the person. The design is one practical route to precision medicine for established treatments, testing response directly instead of predicting it from a biomarker.

Limitations and common misreadings

The design is narrow by construction. It cannot evaluate treatments for acute or progressive disease or medicines whose effect persists, and each trial takes weeks of the patient's time, including periods on placebo.

1. Calling a patient a responder after one comparison. Senn shows that one crossover cannot separate a personal response from ordinary variation, and argues that the common belief in a strong personal element in response is not based on sound statistical evidence.
2. Ignoring carryover. A lingering effect from the previous period biases the comparison, usually towards no difference when an active treatment carries into a placebo period.
3. Poor reporting. CENT 2015 cites a review of 100 trial reports in which 79% did not state the primary outcome and 64% did not comment on adverse events.

Sources

• Araujo A, Julious S, Senn S. Understanding variation in sets of N-of-1 trials. PLoS One. 2016;11(12):e0167167. https://doi.org/10.1371/journal.pone.0167167
• Guyatt G, Sackett D, Taylor DW, Chong J, Roberts R, Pugsley S. Determining optimal therapy: randomized trials in individual patients. New England Journal of Medicine. 1986;314(14):889-892. https://doi.org/10.1056/NEJM198604033141406
• Karnon J, Qizilbash N. Economic evaluation alongside n-of-1 trials: getting closer to the margin. Health Economics. 2001;10(1):79-82. https://pubmed.ncbi.nlm.nih.gov/11180571/
• Larson EB, Ellsworth AJ, Oas J. Randomized clinical trials in single patients during a 2-year period. JAMA. 1993;270(22):2708-2712. https://doi.org/10.1001/jama.1993.03510220064035
• Lillie EO, Patay B, Diamant J, Issell B, Topol EJ, Schork NJ. The n-of-1 clinical trial: the ultimate strategy for individualizing medicine? Personalized Medicine. 2011;8(2):161-173. https://pmc.ncbi.nlm.nih.gov/articles/PMC3118090/
• Scuffham PA, Nikles J, Mitchell GK, Yelland MJ, Vine N, Poulos CJ, et al. Using N-of-1 trials to improve patient management and save costs. Journal of General Internal Medicine. 2010;25(9):906-913. https://pmc.ncbi.nlm.nih.gov/articles/PMC2917656/
• Senn S. Mastering variation: variance components and personalised medicine. Statistics in Medicine. 2016;35(7):966-977. https://doi.org/10.1002/sim.6739
• Vohra S, Shamseer L, Sampson M, Bukutu C, Schmid CH, Tate R, et al. CONSORT extension for reporting N-of-1 trials (CENT) 2015 Statement. BMJ. 2015;350:h1738. https://doi.org/10.1136/bmj.h1738
• Zucker DR, Schmid CH, McIntosh MW, D'Agostino RB, Selker HP, Lau J. Combining single patient (N-of-1) trials to estimate population treatment effects and to evaluate individual patient responses to treatment. Journal of Clinical Epidemiology. 1997;50(4):401-410. https://doi.org/10.1016/S0895-4356(96)00429-5