Cross-over Trials in Clinical Research / Edition 2 available in Hardcover
Cross-over Trials in Clinical Research / Edition 2
- ISBN-10:
- 0471496537
- ISBN-13:
- 9780471496533
- Pub. Date:
- 08/30/2002
- Publisher:
- Wiley
Cross-over Trials in Clinical Research / Edition 2
Hardcover
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$169.95Overview
* Comprehensive coverage of the design and analysis of cross-over trials.
* Each technique is carefully explained and the mathematics is kept to a minimum.
* Features many real and original examples, taken from the author's vast experience.
* Includes discussion of analysis using SAS, S-Plus and, GenStat, StatXact and Excel.
* Written in a style suitable for statisticians and physicians alike.
Primarily aimed at statisticians and researchers working in the pharmaceutical industry, the book will also appeal to physicians involved in clinical research and students of medical statistics.
Product Details
| ISBN-13: | 9780471496533 |
|---|---|
| Publisher: | Wiley |
| Publication date: | 08/30/2002 |
| Series: | Statistics in Practice , #5 |
| Edition description: | Subsequent |
| Pages: | 340 |
| Product dimensions: | 6.26(w) x 9.19(h) x 1.19(d) |
About the Author
Read an Excerpt
Cross-over Trials in Clinical Research
By Stephen Senn
John Wiley & Sons
ISBN: 0-471-49653-7Chapter One
Introduction1.1 THE PURPOSE OF THIS CHAPTER
In clinical medicine, cross-over trials are experiments in which subjects, whether patients or healthy volunteers, are each given a number of treatments with the object of studying differences between these treatments. The commonest of all such designs is one in which approximately half of the patients are first given an active treatment or verum and on a subsequent occasion a dummy treatment or placebo whereas the rest of the patients are first given placebo and then on a subsequent occasion verum. This is a simple example of a type of design which we shall consider in detail in Chapter 3.
The purpose of this chapter, however, is simply to provide some gentle exposition, in very general terms, of some features of cross-over trials. In particular we shall:
define cross-over trials;
explain why they are performed;
mention clinical specialties for which they are useful;
point to some dangers and difficulties in performing them;
as well as explain some general attitudes which will be adopted throughout the book.
Methods for analysing cross-over trials will not be dealt with in this chapter but form the subject matter of Chapters 3 to 7 inclusive. The fact that we defer the issue of analysis until later enables us to begin the discussion of cross-over trials with the help of a very famous (but relatively complex) example, of considerable historical interest, which we now consider below.
1.2 AN EXAMPLE
Example 1.1 Cushny and Peebles (1905) reported the results of a clinical trial conducted on their behalf by Richards and Light of the effect of various optical isomers on duration of sleep for a number of inmates of the Michigan Asylum for Insane at Kalamazoo. Three treatments in tablet form were examined:
laevorotatory hyoscine hydrobromate, 0.6 mg (which we shall refer to either as L-hyoscine HBr or laevo-hyoscine);
racemic hyoscine hydrobromate, 0.6 mg (R-hyoscine HBr or racemic hyoscine);
laevorotatory hyoscyamine hydrobromate, 0.6 mg (L-hyoscyamine HBr or simply hyoscyamine).
Patients were given each of these treatments on a number of evenings and also studied on a number of control nights for which no treatment had been administered. According to the authors,
As a general rule a tablet was given on each alternate evening... (on) the intervening control night... no hypnotic was given. Hyoscyamine was thus used on three occasions and then racemic hyoscine, and then laevo-hyoscine. Then a tablet was given each evening for a week or more, the different alkaloids following each other in succession (Cushny and Peebles, 1905, p. 509.)
Table 1.1 summarizes the results in terms of hours of sleep for the patients studied.
Remark These data are of particular historical interest not only because Cushny was a pioneer of modern pharmacology and did important work on optical isomers (Parascondola, 1975) but because they were quoted (incorrectly) by Student (1908) in his famous paper, 'The probable error of a mean'. The data were in turn copied from Student by Fisher (1990a), writing in 1925, and used as illustrative material in Statistical Methods for Research Workers. These data thus have the distinction of having been used in the paper which inaugurated the modern statistical era (since it was the first to deal explicitly with small sample problems) and also in what is arguably the single most influential textbook written on the subject. (See Plackett and Barnard, 1990, and Senn and Richardson, 1994, for historical accounts.)
The particular feature of these data which is of interest here, however, is that they were obtained by giving each of a number of subjects a number of treatments to discover something about the effects of individual treatments. They thus come from what we would now call a cross-over trial (sometimes also called a change-over trial) which we may now define as follows.
Definition A cross-over trial is one in which subjects are given sequences of treatments with the object of studying differences between individual treatments (or sub-sequences of treatments).
Remark It is probable that the word cross-over has come to be used for trials in which patients are given a number of treatments, because in the commonest type of trial of this sort (see Section 1.1 above) two treatments A and B (say) are compared. Patients are given either A or B in the first period and then 'crossed over' to the other treatment. In more complicated designs, however, such simple exchanges do not occur but the word cross-over is nevertheless employed. The essential feature of the cross-over is not crossing over per se but is as captured in our definition above.
Further remark Note that the fact that patients in a given clinical trial are assigned to sequences of treatment does not alone cause the trial to be a cross-over. For example in clinical trials in cancer it is usual for patients to be given many treatments: some simultaneously, and some sequentially. In a trial investigating a new therapy, patients might well be assigned in the first instance either to a standard first-line treatment or to the new therapy with the purpose of studying the difference of the effects of treatment on remission. Patients who failed to respond or suffered a relapse would then be given alternative therapies and so on. At the end of the trial the difference between the effects of the new and alternative therapy on time to remission (or relapse) might form the object of an analysis. We could then regard the patients as having been allocated different treatments with the purpose of studying differences between them. Alternatively, we might study the effect on survival as a whole of allocating the patients to the different sequences (starting with new or alternative therapy). We would then be examining the difference between sequences. For neither of these two ends could we regard ourselves as having conducted a cross-over trial.
Before going on to consider cross-over trials in more detail some general points may usefully be made using the Cushny and Peebles data quoted in Example 1.1.
The first point to note is the ethical one. It may reasonably be questioned as to whether the initial investigation of substances of this sort ought to be carried out in the mentally ill who may be not in a position to give their free consent on the basis of an understanding of the potential risks and benefits of the trial. Such agreement on the part of the patient is referred to as informed consent in the literature on clinical trials. (It should be noted, however, that Cushny and Peebles tried the drugs out on themselves first. A similar step is undertaken in modern pharmaceutical development where so-called Phase I trials are undertaken with healthy volunteers in order to establish tolerability of substances.) Ethical considerations provide an important constraint on the design of all clinical trials and cross-over trials are no exception. This is a point which should constantly be borne in mind when designing them. In particular the fundamental right, which should not only be granted to all patients but also made clear to them, to be free to withdraw from a trial at any time, is one which can, if exercised, cause more problems of interpretation for cross-over trials than for alternative designs.
The second point to note concerns purpose. The trial had a specific scientific purpose. Cushny and Peebles wished to discover if there were any differences between two optical isomers: laevorotatory (L) and dextrorotatory (D) hyoscine HBr. For practical reasons the differences had to be inferred by comparing the effect of L-hyoscine HBr to the racemic form (the mixture of L and D), R-hyoscine HBr. This pharmacological purpose of the trial was of more interest to Cushny and Peebles than any details of treatment sequences, patient allocation or analysis. I mention this point because in my opinion some of the methodological research in cross-over trials over the past few decades can be justified more easily in terms of mathematical interest per se rather than in terms of its utility to the practising scientist.
Nevertheless, the third point to note concerns sequences of treatments. These were not necessarily wisely chosen and in any case are not clearly described. If we label a control night, C, L-hyoscyamine HBr, X, R-hyoscine HBr, Y, and L-hyoscine HBr, Z, it seems that the general rule was to use a sequence:
X C X C X C Y C Y C Z C Z C Z C X Y Z X Y Z X Y Z
(Preece, 1982). This would certainly produce the number of observations recorded for patients 1 and 2, although not for any other. If there were any general tendency for patients to improve or deteriorate such a scheme would bias comparisons of treatments since, for example, Z is on average given later than X.
Despite this criticism, the fourth point, which relates to the proper interpretation of this trial, is to note that the conclusions of Cushny and Peebles (1905), which are that 'hyoscyamine is of no value in the dose given as a hypnotic, while the laevorotatory and racemic forms of hyoscine have about the same influence in inducing sleep' (p. 509), being based on the right data, are probably not unreasonable. This may be seen by studying Figure 1.1. The figure gives the mean hours of sleep for the three treatments as well as the controls for patients number 1 to 10. If we compare the four results for each patient with each other, we shall see that the on the whole the values for the two forms of hyoscine are the highest of the four obtained but similar to each other. On the other hand, Student and Fisher, using incorrectly labelled data, concluded that there was a difference between optical isomers of hyoscine HBr. The moral is that the contribution to correct conclusions made by good data is greater than that made by sophisticated analysis. (In making this point I mean no disrespect to either Student or Fisher.)
The final point concerns conduct of the experiment. It may be noted that the patients did not each receive an equal number of treatments. Whether this was through careless planning or accident in execution one cannot say but the result is that the data bear the hallmarks of a real experiment: the data are imperfect. Missing observations continue to be one of the major problems in interpreting clinical trials, and cross-overs are no exception.
1.3 WHY ARE CROSS-OVER TRIALS PERFORMED?
We mentioned in Section 1.2 that not all trials in which patients are assigned to sequences of treatments are cross-over trials. For the trial to be a cross-over the sequences have to be of incidental interest and the object of the trial must be to study differences between the individual treatments which make up the sequences.
This was, in fact, the purpose of the trial in hyoscines reported as Example 1.1 above. Here the sequence in which the patients were given the drugs was not of interest. In fact, as we may deduce from their conduct and reporting of the trial, Cushny and Peebles (1905) probably considered the sequence in which the individual treatments were allocated as being of no consequence whatsoever. (As we pointed out above this is not always a wise point of view to take but, on the other hand, not always as disastrous as some modern commentators imply.) The purpose of the trial was to investigate the difference between the individual treatments. It is this which makes it a cross-over trial.
It is instructive to consider an alternative procedure that might have been used above. Each patient could have been assigned one treatment only. We should then have a parallel group trial. If we ignore the observations for patient 11 above it would thus have been necessary to study 40 (i.e., 4 x 10) patients to have obtained as many mean results per treatment as were obtained above. Even so the information would not have been as useful. In looking at Figure 1.1 it is noticeable that on the whole (there were some exceptions) patients who had high control values had high values for the three treatments. This point can be brought out by recasting the data (as Peebles and Cushny did, in fact, themselves) in the form of differences to control as has been done in Table 1.2 below. The data are also shown in this form in Figure 1.2. (No control values for patient 11 having been recorded, he is omitted from this table and figure.)
Just presenting the data in this form is revealing. Immediately it highlights the relatively poor performance of L-hyoscyamine HBr compared to the two forms of hyoscine HBr. (Even more revealing for this purpose, of course, would be calculating the difference between these treatments for each patient.) This feature of the data has been brought out by using every patient as his own control, a device which permits a particular source of variation, between-patient variation, to be eliminated. Thus, we can see that, although when the L-hyoscine HBr values and the control values from Table 1.1 are mixed together there is considerable overlap, seven of the values under treatment being lower than the highest control value, yet only one of the differences, that for patient 5, is negative.
These then are the main reasons why a cross-over trial may be preferred to a parallel group trial. First, to obtain the same number of observations fewer patients have to be recruited. Second, to obtain the same precision in estimation fewer observations have to be obtained. A cross-over trial can thus lead to a considerable saving in resources.
1.4 WHAT ARE THE DISADVANTAGES OF CROSS-OVER TRIALS?
There are disadvantages as well as advantages to the cross-over trial when compared to the parallel group trial. It is worth considering what these are.
First, there is the problem of drop-outs. These are patients who discontinue their programme of treatment before the trial is complete. Drop-outs cause difficulties for analysis and interpretation in parallel group trials as well but here at least the time until discontinuation for a patient may yield information which can be recovered. In cross-over trials this is extremely difficult to do and of course the patient can provide no direct information on the treatments he did not even start if, for example, he drops out during the first treatment period.
Continues...
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Table of Contents
Preface to the Second Edition.Preface to the First Edition.
1. Introduction.
2. Some Basic Considerations Concerning Estimation in Clinical Trials.
3. The AB/BA Design with Normal Data.
4. Other Outcomes and the AB/BA Design.
5. Normal Data from Designs with Three or More Treatments.
6. Other Outcomes from Designs with Three or More Treatments.
7. Some Special Designs.
8. Graphical and Tabular Presentation of Cross-over Trials.
9. Various Design Issues.
10. Mathematical Approaches to Carry-over.
References.
Author Index.
Subject Index.