DESVENTAJAS DE LA LEY MINERA

line was recorded electronically and the raw data stored. The use of the guide lines was not essential but imposes the discipline of recording air spaces * in series * along a

given line, although the lines themselves are parallel; (this removes any temptation to record the largest or most prominent airspaces). The transect lengths are not selected in any other way, the pen being moved to measure the next airspace in sequence.( Although occasionally a very large airspace might have two parallel lines crossing it, at the magnification used (x 180) this was a relatively rare occur­ rence. )

The airspace was defined from epithelium to epithelium and no measurement of the thickness of the alveolar wall or blood vessels was made. No selection of the area to be measured was made by the observer before measurement and the measurements were made on slides which were not identifiable as belonging to a particular animal [or genotype in the case of the m i c e ] .

The lungs were not mounted in any particular orientation and a full range of cuts was made before deciding that a sagittal slice through the whole inflated lung was the most useful. Measurements were also made in two different planes by moving the acetate onlay through 90° in order that com­ pression bias should be minimised, although the same air­ spaces were not measured more than once except to assess intraobserver consistency. The selection of the areas of lung to be measured were made as randomly as possible by unsighted manipulation of the stage movers and measurement of whatever part of the lung was displayed at low power. Two hundred consecutive measurements of airspaces were made and the correction factor for magnification inserted into

the computer. One advantage of the method is that no subjec­ tive assessment is made of any of the measurements and no overall judgment of the severity or extent of any possible lesion.

At least five randomly selected but nonrepetitive or over­ lapping fields were examined so that measurements from 200 airspaces could be taken.

After my move to the Institute of Ophthalmology I ac­ quired, through a generous donation from Allied Dunbar's Sackville Street Charity Fund in 1989, an image analysis system using an Archimedes computer linked to a digitising tablet and a television linked Sony camera (rather than a mirrored projection system) which meant that 'real-time' images could be generated and stored as digitised (x 1368) images or screens from a light microscope. This system was accessed through Digit software developed within the Insti­ tute . An example of the figures produced by this system is to be found in appendix 5.

2.3d

Statistics and choice of method

The raw data results of the transect lengths corrected for the magnification were stored in a computer and lengths were printed out as histograms of lO^m binsize . The data were collected and calculated on an individual basis and then examined by pooled analysis of groups defined by differing treatment in the case of the rat lung (appendix 2.1) [or by genotype and age in the mice (appendix 3a.2)]

parametric analysis of cumulative data was undertaken using Mackintosh software and manual manipulations.

(After the analysis using Digit software more extensive IBM packages were used; some data analyses were specifically designed for this project B. Shine: PR McCartney; unpub­ lished programs).

Although the means and standard deviation results yielded some information [see figure 3a.12], much more interesting results were obtained using nonparametric results and analy­ sis of cumulative plots.

In a disease such as emphysema where it is expected that there is to be an increase in larger airspaces, this may not necessarily be at the expense of the smallest airspaces, so that a simple analysis of mean and standard deviation may not be an adequate representation as to how that figure is achieved. By recording the distribution and examining the data at several centiles a more accurate representation of the data can be achieved. [The cumulative frequency plots were made using a Harvard graphics package].

[ Non parametric statistics have been referred to as *quick and dirty methods' (J.W. Tukey quoted by Armitage 1971) presumably because there are often fewer calculations in­ volved in these distribution-free methods with little empha­ sis on parameters thus avoiding functional forms for a population distribution.]

Groups were compared using the Kolmogorov-Smirnov two sample test and the results expressed graphically by ogive plotting. The selection of a non -parametric test was essen­ tial given the distribution of the initial data and this

test (Kolmogorov 1933 and Smirnov 1939) uses as its test statistic the largest absolute difference between the cumu­ lative proportions in two groups at any of the 10/xm inter­ vals. This cumulative data is expressed as a graph using an ogive [S.O.E.D. 'the diagonal groin or rib of a vault, two of which cross at the centre, or a pointed 'Gothic' arch] plot where the transect length in lO/xm intervals is plotted on the horizontal axis and the frequency scale (0-1) on the vertical. The median transect length therefore lies on the ogive corresponding to 50%, 0.5, and the 95th centile is that corresponding to a cumulative proportion of 0.95. The median value corresponds to the concept of an average in such skewed distributions rather than the mean which may either be misleadingly high (Snedecor and Cochrane 1967 ) or alternatively obfuscate important changes at one end of the distribution or the other.

The Kolmogorov- Smirnov test has both one and two sample testing value. The one sample test is concerned with the agreement between the distribution of a set of sample values and a specified theoretical distribution whereas the two sample test compares the cumulative distributions of two sets of sample values. If they have been drawn from the same or similar populations then there should be only random deviations from the population distribution in both samples;

if however they are from differing populations the sample populations should become 'too far apart' and a large enough deviation between the distributions is evidence for reject­

ing the null hypothesis (Siegel 1956). The test focuses on the largest of these deviations [D] . The level of signif­

2.2 It is interesting that the Kolmogorov-Smirnov (K-S) test has a high power efficiency when compared to the Student's t test at a level of 96% for small samples but that this efficiency falls slightly as the sample size increases: Siegel 1956 indicates that the Mann-Whitney Ü can be more powerful with these larger numbers but regards the K-S as more powerful than either the chi-squared or median tests. The significance values for chi squared were taken from the critical values Table C from Siegel and Castellan (1988) from the two degrees of freedom range.

[That there is still some relevance in simpler tests is shown in the display of the mean values for the mouse lungs obtained after more extensive testing than was available at the time of preparation of our McCartney et al 1988 paper.

[This data shown in Figure 3a.12 of transect length mean values for mice of all phenotypes when plotted shows a clear separation of control from affected animals even though the data is very skewed].

2. 4a

Results of the effects of instillation of PPE and saline on transect length in rat lungs

2.4al Effects of single bolus administration of elastase The effects of instilling a single bolus of 18 units of purified porcine pancreatic elastase (PPE) are seen in Figure 2.3. The ogive plot shows that in the six animals (Group l.a) who received this dose and were killed on the fourth day of the experiment, after exposure to the effects of the enzyme for 72 hours, their airspaces were larger (transect length longer) both at the mean (fiftieth centile

Figure 2.3. Ogive plot of the effects of instillation of a single dose of 18 units of purified porcine elastase (PPE) into rat lungs.

The plot of the cumulative frequency of pooled transect lengths across airspaces of 6 rats killed at 72 hours (4 days) compared to the distribution in 6 rats killed at 12 0 hours (6 days ) after the intracheal instillation, shows that both differ significantly from the curve for the 3 normal (non instilled animals) and that the effects of the elastase are significantly greater when measured at 4 days rather than 6 (p< 0.05)