Über die Autorin bzw. den Autor

Brian Everitt, Head of Biostatistics and Computing Department and Professor of Behavioural Statistics, Kings College London. He? has authored/co-authored over 50 books on statistics and approximately 100 papers and other articles, and is also joint editor of Statistical Methods in Medical Research.

Christopher R. Palmer, Director of the Centre for Applied Medical Statistics, University of Cambridge.

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Statistical methodology is of great importance to medical research and clinical practice. The Encyclopaedic Companion to Medical Statistics contains readable accounts of the key topics central to current research and practice. Each entry has been written by an individual chosen for both their expertise in the field and their ability to communicate statistical concepts successfully to medical researchers. Real examples from the biomedical literature and relevant illustrations feature in many entries and extensive cross–referencing signposts the reader to related entries.

Key Features:

• Contains accounts of over 400 statistical topics central to current medical research.
• 80% of first edition entries updated and revised.
• Presents the latest techniques used at the cutting edge of medical research.
• Covers common errors in statistical analyses in medicine.
• Real examples from the biomedical literature and relevant illustrations feature throughout.
• Contains contributions from over 70 experts in the field.

Medical researchers, researchers and practitioners in medical research and statistics will benefit greatly from this book.

Aus dem Klappentext

Statistical methodology is of great importance to medical research and clinical practice. The Encyclopaedic Companion to Medical Statistics contains readable accounts of the key topics central to current research and practice. Each entry has been written by an individual chosen for both their expertise in the field and their ability to communicate statistical concepts successfully to medical researchers. Real examples from the biomedical literature and relevant illustrations feature in many entries and extensive cross–referencing signposts the reader to related entries.

Key Features:

• Contains accounts of over 400 statistical topics central to current medical research.
• 80% of first edition entries updated and revised.
• Presents the latest techniques used at the cutting edge of medical research.
• Covers common errors in statistical analyses in medicine.
• Real examples from the biomedical literature and relevant illustrations feature throughout.
• Contains contributions from over 70 experts in the field.

Medical researchers, researchers and practitioners in medical research and statistics will benefit greatly from this book.

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Encyclopaedic Companion to Medical Statistics

John Wiley & Sons

Chapter One

accelerated factor See SURVIVAL ANALYSIS

accelerated failure time models See SURVIVAL ANALYSIS, TRANSFORMATION

active control equivalence studies The classic randomised CLINICAL TRIAL seeks to prove superiority of a new treatment to an existing one and a successful conclusion is one in which such proof is demonstrated. The famous MRC trial of streptomycin is a case in point (Medical Research Council Streptomycin in Tuberculosis Trials Committee, 1948). The trial concluded with a significant difference in outcome in favour of the group given streptomycin compared to the group that was not. In recent years, however, there has been an increasing interest in trials whose objective is to show that some new therapy is no worse as regards some outcome than an existing treatment. Such trials have particular features and difficulties that were described in an important paper by Makuch and Johnson (1989) in which they used the term 'active control equivalence studies' (ACES).

Actually, the term is not ideally chosen since, unlike bioequivalence studies, where the object is to show that the bioavailability of a new formulation is not only at least 20% less than that of an existing formulation, but also at most 25% more, and hence where equivalence to some degree is genuinely the aim, in ACES it is almost always the case that only noninferiority is the goal. It may be questioned as towhy the rather modest goal of noninferiority should be of any interest in drug regulation. There are several reasons. The first is that the new drug may have advantages in terms of tolerability. Second, the new drug, while showing no net advantage to the existing one, may increase patient choice and this can be useful. For example, many people have an aspirin allergy. Hence, it is desirable to have alternative analgesics, even if no better on average than aspirin. Third, it may become necessary to withdraw treatments from the market and one can never predict when this may happen. There are now several statins on the market. The fact that this is so means that withdrawal of cerivastatin does not make it impossible for physicians to continue to treat their patients with this class of drug. Fourth, introduction of further equivalent therapies before patent expiry of an innovator in the class may permit price competition to the advantage of reimbursors (although such competition is probably not particularly effective; Senn and Rosati, 2003). However, the fifth reason is probably the most important. Drug regulation is designed to satisfy some minimum requirements for pharmaceuticals: that they are of sufficient quality, are safe and efficacious. Efficacy is demonstrated if the treatment is better than placebo, even if it is not as good as some other treatments. The comparison of a new drug to an active treatment may be dictated by ethics but the object of the trial may simply be an indirect proof that the treatment is better than placebo through comparison to an agent whose efficacy is accepted.

Recently the issue of the indirect comparison to placebo has been taken more seriously. Consider the case where we have a single effective treatment on the market, say A, whose efficacy has been demonstrated in a series of trials comparing it to placebo. We now run some new trials comparing a further treatment, B, to A. Taking all these trials together, they then have the structure of an incomplete blocks design. The effect of B compared to placebo can then be estimated using the double contrast of B compared to A and A compared to placebo. This approach has been examined in detail by Hasselblad and Kong (2001). A consequence of taking this particular view of matters is that the precision with which the effect of A was established compared to placebo cannot be exceeded by the indirect comparison of B to placebo, since the variance of this indirect contrast is the sum of the variances of the two direct contrasts.

This is, however, not the only difficulty with such studies. The following are some of those that apply.

Establishing a clinically irrelevant difference. If the route of a formal analysis compared to placebo via an indirect contrast is taken, this particular difficulty may be finessed. The new treatment is shown to be 'significantly' better than placebo, albeit using an indirect argument, and the extent of its inferiority to the comparator is only of relevance to the extent that it impinges on the proof of efficacy compared to placebo. If this proof is provided, then the comparison to the active comparator is 'water under the bridge'. If this particular approach is not taken, however, then any proof of efficacy of the new treatment rests on a demonstration that it is not 'substantially inferior' to the comparator, which comparator is accepted as being efficacious. This raises the issue as to what it means for a drug to be not substantially inferior to another one. This appears to require that some margin Δ, Δ > 0, be adopted such that if t is the extent by which the new treatment is inferior to the standard (where τ < 0 indicates inferiority) then it is judged substantially inferior if &tau ≤ -Δ and not substantially inferior or 'equivalent' if τ > Δ.

Technical statistical aspects. In a Neyman–Pearson framework (see Salsbury, 1998) the test of noninferiority requires one to use a shifted NULL HYPOTHESIS. One might, therefore, adopt H₀:&tau ≤ -Δ. The situation is not as controversial as that for true bioequivalence, where the fact that two hypotheses have to be rejected, that of inferiority and that of superiority, means that an intuitive approach of seeing that the confidence limits for the difference lie within the limits of equivalence is not 'optimal' (Berger and Hsu, 1996), although the 'optimal' test may in practice be worse (Perlman and Wu, 1999; Senn, 2001). In practice, in the case of ACES if the lower conventional 1 -α two-sided CONFIDENCE INTERVAL for τ exceeds -Δ, the hypothesis of substantial inferiority may be rejected at the level a and noninferiority asserted. It might be thought that a one-sided confidence interval would be sufficient for this purpose. However, the general regulatory convention is that all tests designed to show superiority are two-sided (despite apparent purpose) and, since such tests are a special case of a noninferiority test with Δ = 0, use of one-sided tests for noninferiority would lead to inconsistencies (Senn, 1997; Committee for Proprietary Medicinal Products, 2000). In a Bayesian framework (see BAYESIAN METHODS) one might require that the posterior probability of noninferiority were less than some specified amount. Alternatively, use of a loss function would permit a decision analytic method, such as has been proposed for bioequivalence (Lindley, 1998), to be used.

Power of trials. Note that the reason one does not employ a value of Δ = 0 in practice is that unless it is expected that the new treatment really is better than the standard, the power of the resulting test could never exceed 50 %. However, the clinically irrelevant difference is likely to be less than the clinically relevant difference used in conventional trials. Hence, if the new treatment is actually no better than the standard treatment, then, for a given sample size, the noncentrality parameter, δ = Δ=SE(Δ) is...