The LD50 test: Some considerations of precision

7’oxicology

Letters,

Elsevier Biomedical

303

10 (1982) 303-307 Press

THE LDso TEST: SOME CONSIDERATIONS

D.O. CHANTER

OF PRECISION

and R. HEYWOOD

Huntingdon Research Centre, Huntingdon, Cambs, PE18 6ES (U.K.) (Received

July Sth, 1981)

(Revision

received August

(Accepted

August

25th,

5th, 1981) 1981)

SUMMARY Substantial modifications

improvements

ment of outdated

techniques

With such improvements, about

in the statistical

to the design of the experiments of statistical

aspects (including

analysis

it would be possible

10 or 12) while still achieving

precision

of the LD 50 test are possible. the use of sequential

with more appropriate

methods)

These

include

and the replace-

methods.

to reduce appreciably

the number

similar to that obtained

with present

of animals

used (to

methods.

1NTRODUCTlON

The use of the procedure known as the LDso test as an indicator of the acute toxicity of a compound has for some time been the subject of mounting criticism. This criticism is mainly of two kinds. First, the LDso is not a biological constant and the outcome of any particular experiment is dependent on a host of environmental and experimental conditions. Morrison et al. [ 141 list ten factors which are known to affect the results. Second, precise knowledge of LDso values is of little practical use. A rough idea of magnitude of toxicity is all that is required, and only rarely are precise estimates needed. Zbinden and Flury-Roversi [19] have called for substantial modifications of standard acute toxicity protocols, with the classical LDso test replaced by more comprehensive short-term tests with smaller numbers of animals. Although we can see no valid arguments to support the current use of LDso estimates, these proposals are likely to meet with resistance from some quarters because the LD~o estimates obtained will be less precise. It is our contention that this need not be the case: the present methods of design and analysis of LDXI studies are so poor and inefficient that, by improving these factors, significant reductions in the numbers of animals used could be achieved without sacrificing any precision of LDso estimates. 0378-4274/82/0000-0000/$02.75

0 Elsevier

Biomedical

Press

304

THE

PRECISION

OF LDso VALUES

The precision with which an LDYJ value is estimated can be indicated by means of a confidence interval. A confidence interval is a numerical interval which has a known probability of including the true value. In toxicology (as in many other areas) it is traditional to use a 95% confidence interval; thus if an LD5o experiment were repeated ad infinitum, 95% of the confidence intervals produced would enclose the true LD5o. The narrower the confidence interval, the more precisely the LD5o has been estimated. The precision actually achieved in a given experiment depends on a number of factors, including the number of dose levels used and their numerical values, the number of animals used at each dose, and the method of statistical analysis used. While it is generally accepted that, for humane reasons, the total number of animals used to estimate an LD5o value should be kept as low as possible, it is not generally appreciated that much of the precision which is lost by using small numbers of animals can be regained by a more efficient choice of dose levels (i.e. the design of the experiment) and by using modern methods of statistical analysis. EXPERIMENTAL

DESIGN

A typical LDx) test might involve four dose levels with animals (5 CY + 5 0) at each dose. The dose levels are often chosen after a small pilot experiment. It is traditional to use equally spaced dose levels (on a log scale), with equal numbers of animals per dose level, but in fact the precision of the LD50 estimate can be increased if more animals are given the doses near to the LD50 and fewer given those doses further away from it. Unfortunately there is no simple relation between the way dose levels are chosen and the precision obtained for the estimated LD50. For a further discussion of this problem, see Finney [8, 91. One way of automatically ensuring that a sensible allocation of animals to dose levels is achieved, is to carry out the experiment sequentially: that is, animals are treated in sequence and the dose level used for each animal depends upon the response observed with the previous one. One such method is the ‘up-and-down’ method [7], which has been estimated to need no more than two-thirds (often far fewer) of the animals needed for a conventional study to yield the same degree of precision [5]. Sufficient precision can usually be obtained with about 10 animals, although the actllal number needed depends on the accuracy of the guessed LD5o at the start of the experiment. Although this method clearly introduces logistic problems which are not present in a conventional study, these are not nearly as great as they might at first seem, and there is an added advantage that no pilot trial is necessary. Hsi [lo] and Wetherill [ 181 give further discussion of sequential methods in this field.

305

STATISTICAL

ANALYSIS

Considerable

improvement

on present

standards

is possible

at this stage.

The

most commonly [13], Litchfield

used methods and Wilcoxon

listed by Loomis [ 121 are those of Miller and Tainter [l l] and Weil [17]. All three of these methods were

introduced before computers became generally available, and the main reason for their development was to provide a ‘quick and easy’ method which avoided the arithmetically complex calculations involved in the superior method of probit analysis introduced by Bliss [3, 41. With computing facilities now readily available there is no longer any need to use these alternative methods if they are not as reliable as probit analysis. The methods of Miller and Tainter [13] and of Litchfield and Wilcoxon [l l] are graphical, involving the fitting of a line by eye. They are reasonably efficient (compared with probit analysis) when there are extensive data, but with sparse data they become extremely unreliable, especially when used by people with little or no training in statistical methods. Also, as pointed out by Cornfield and Mantel [6], the confidence limits obtained do not take into account all the relevant sources of error. Such methods are therefore unsuitable for routine use in toxicological work. The method of Weil [ 171 uses a moving-average technique developed by Thompson [16]. Although this method is more reliable than the graphical methods mentioned earlier, it also has disadvantages when small numbers of animals are used. Because of the way in which the confidence limits are calculated, these limits tend to be too narrow whenever there are doses which have given a 0% or 100% response. This method is also unsuitable for modification to cope with improved designs which have different numbers of animals at different doses. One reason why the method of probit analysis is not more widely used today is that it usually requires at least two doses which give a response intermediate between 0% and 100% before an LDso can be estimated. Because this requirement is not always met, the method is thought to be unreliable. This difficulty, however, can easily be overcome. One way of doing this is to use a large number of doses, but fewer animals at each dose. In fact, there is no theoretical reason why the number of animals at each dose should not be reduced to one, provided that the doses are closely enough spaced to ensure that most animals are tested for doses between the LDlo and LD90. This approach invokes no scientific penalties and, although it is not permitted by some regulatory authorities, there are no scientifically valid objections to it. Another method of increasing the usefulness of probit analysis is to take advantage of the modern developments in generalised linear models [ 151. These enable probit lines to be fitted simultaneously to several groups of data which might reasonably be expected to share a common slope (e.g. different sexes, or groups of similar compounds). By pooling information about slope in this way, estimates of the various LDsos can be obtained with better precision than is possible when each

306

one is estimated separately. A check can be incorporated that the data do not provide evidence that the slopes are in fact different. Computer packages are available for using these methods, e.g. GLIM [2] and GENSTAT [I]. CONCLUSIONS

The design and analysis of LDso studies in toxicology at present leave much to be desired. With improved methods, which are already available but not widely used, the LDso estimates could be obtained with the same precision that is currently achieved, but using substantially fewer animals. We join Zbinden and FluryRoversi 1191 in calling for changes in the regulatory requirements pertaining to LDso estimation, to encourage an appropriate revision of the standard protocols in this field.

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