How Many Glomerular Profiles Must Be Measured to Obtain Reliable Estimates of Mean Glomerular Areas in Human Renal Biopsies?
Wendy E. Hoy*,
Terence Samuel,
Michael D. Hughson,
Jennifer L. Nicol* and
John F. Bertram
* Centre for Chronic Disease, Discipline of Medicine, University of Queensland, Royal Brisbane & Women’s Hospital, Herston, Queensland, Australia; Department of Anatomy and Cell Biology, Monash University, Clayton, Victoria, Australia; and Department of Pathology, University of Mississippi Medical Center, Jackson, Mississippi
Address correspondence to: Dr. Wendy Hoy, Centre for Chronic Disease, Discipline of Medicine, University of Queensland, Royal Brisbane & Women’s Hospital, Herston, Queensland, Australia 4029. Phone: +617-3346-4809; Fax: +617-3346-4812; w.hoy{at}uq.edu.au
Received for publication July 26, 2005.
Accepted for publication November 23, 2005.
The objective of this study was to investigate the number ofglomerular profiles that are required for accurate estimatesof mean profile area in a renal biopsy series. Slides from 384renal biopsies from one center were reviewed. They containeda median of seven glomerular profiles or of four profiles withoutsclerosis. Profile areas were measured using stereologic pointcounting. The "true individual mean" for each biopsy was calculatedand the "true population mean" for groups of biopsies derived.Individual and population "random sample means" then were calculatedfrom a random sampling of profiles in each biopsy and were comparedwith true means for the same biopsies. The effect on the truepopulation means of the entire group of biopsies was also assessed,as the minimum number of glomerular profiles that were requiredfor inclusion was changed. In a single biopsy, random samplingof 10 profiles without exclusions and of eight profiles or morewithout sclerosis reliably estimated the true mean areas. Ina group of 30 biopsies, random sampling of five or more glomeruliper biopsy reliably estimated the true population mean. In theaggregate series, inclusion of all 384 biopsies produced themost robust true population mean; the reliability of the estimatesdecreased as the numbers of eligible biopsies diminished withincreasing requisite minimum numbers of profiles per biopsy.We conclude that, while 10 profiles might be needed for reliablearea estimates in a single biopsy, far fewer profiles per biopsycan suffice when groups of biopsies are studied. In analysesof groups of biopsies, all available biopsies should be usedwithout consideration of the number of glomerular profiles ineach. Stipulation of a specific minimum number of glomeruliin each biopsy for inclusion reduces the power of analyses becausefewer biopsies are available for evaluation.
It is increasingly recognized that the size of glomeruli inthe kidney has important clinical and prognostic implications(1–4). Variations are described by body surface area,by birth weight and nephron number, by degree of sclerosis,and by category and stage of renal disease (5–8). It hasbeen proposed that the susceptibility of some high-risk populationsto renal disease is marked by glomerulomegaly, which, in turn,might mark nephron underdosing. Enlarged glomeruli seem to beat risk for premature sclerosis, whether by hyperperfusion mechanismsor other processes (9–12).
The gold standard method of assessment of glomerular size isthrough volume estimates by the Cavalieri method, which involvessectioning at standard intervals through whole glomeruli. Thisis more readily done on blocks of kidney tissue, such as wedgebiopsies or at autopsy (13,14), although it can be applied tocore kidney biopsies if adequate numbers of intact glomeruliare present. However, this is a time-intensive and laboriousprocedure that is unlikely to be incorporated in routine preparationof tissue for diagnostic examination.
Assessment of the areas of glomerular profiles on routinelysectioned and prepared biopsy material is the most feasibleapproach to estimates of size in disease processes. Much morecould be learned from study of glomerular size from the manybiopsies that already are archived in most major centers. Areaestimates can be translated into volume estimates by use offormulas such as that of Weibel and Gomez. This method usesthe formula glomerular volume = profile area1.5x /, where is1.01, a size distribution coefficient that assumes a coefficientof variation for glomerular size within a single specimen ofapproximately 10%, and is the shape coefficient of 1.38, thevalue of a sphere (15). However, such assumptions introducebias, and it is not clear that they offer any advantage overarea estimates in studies of groups of biopsies.
Several factors contribute to variations in glomerular profilesize observed in histologic sections. One is the level of theglomerulus sampled by the section: sections that go throughor close to the equator of a glomerulus yield large profiles,whereas those at the poles yield small profiles. Another concernis the variability of glomerular size in an individual, eventhose without renal disease, which, as we recently defined,can vary between two- and eight-fold (16). There is likely tobe even more variation in diseased kidneys. In theory, sizeestimates should be biased in favor of larger glomeruli, whosecross-sectional profiles are more likely to be represented inany random section. The issue of including glomeruli with andwithout sclerosis should also be considered, given the variationsin glomerular size with sclerosis, both by degree and by typeof sclerosis (segmental, ischemic) (8,17). From these perspectives,the variability of mean glomerular profile area should be lessenedprogressively as more profiles are included in the sample.
When the objective is to estimate glomerular size in an individualkidney biopsy, the more glomeruli that are sampled, the morereliable that estimate should be. McLeod et al. (18) suggestthat at least eight profiles need to be studied in this setting,even with rigorous study of "true" individual glomerular volumeby the Cavalieri method. However, when groups of biopsies arebeing studied to evaluate associations of glomerular size withdemographic, morphologic, or diagnostic variables, the minimumnumber of glomerular profiles that define eligibility of a biopsyfor its inclusion is debated. Different reports of glomerularsize differences by disease entity or sclerosis have includedbiopsies with at least four, at least five, and at least sevenprofiles (2,8,17,19–21), and a recent critique (unpublished)recommended a minimum number of eight glomerular profiles perbiopsy.
Such stipulations can influence the ability to conduct a studyon a given series of biopsies. In view of the variable and restrictednumber of glomeruli in needle kidney biopsies, the number ofbiopsies that are available for inclusion in any analytic serieswill decrease as the minimum number of glomerular profiles thatare stipulated for eligibility increases. This can precludethe ability to conduct a study if too few biopsies are eligiblefor inclusion, especially when subcategory analyses (e.g., byindividual disease entity) are proposed. Conversely, the lowerthe minimum number of necessary profiles stipulated, the morebiopsies will be eligible for inclusion in any series, withthe potential for the power of increased numbers to offset thepotentially less accurate individual means in the participatingbiopsies.
We investigated the number of glomerular profiles that are requiredfor reasonably accurate estimates of mean glomerular area ina series of renal biopsies that were performed and processedat a single center.
Renal Biopsies
Slides from renal biopsies from 384 patients with nondiabeticrenal disease, performed from January 1, 1994, to December 31,2001, and archived in the Department of Pathology at the Universityof Mississippi (Jackson, MS), were reviewed. The mean age ofpatients was 36.7 ± 17.5 yr. The biopsy tissue had beenfixed in 10% buffered formaldehyde, embedded in paraffin, cutin series of 25 sections at 3 µm, and stained with hematoxylinand eosin, periodic acid-Schiff (PAS; the 12th and 24th sectionsin every block), Masson’s trichome, and periodic acid-methenaminesilver stains. The PAS-stained section with the most corticaltissue from each biopsy was projected onto a white surface usingan Olympus BH-2 microscope at a final magnification of approximatelyx600 for estimates of glomerular profile areas.
Measurement of Glomerular Profile Area
The tuft area of each individual glomerular profile was measuredusing a traditional stereologic point-counting method and anorthogonal grid system (each grid square measured 2.5 x 2.5cm). Glomerular profiles that were closer than one glomerulardiameter to the edge of the sections were excluded from thestudy. All glomerular profiles within the more central partsof the biopsies were measured. A semiquantitative assessmentof the extent of sclerosis in every tuft profile was made, rangingfrom 0 (no sclerosis) to 4 (75 to 100% sclerosis). Only grade0 profiles were considered to be "nonsclerosed." The averagearea estimates of all profiles in each biopsy were calculated—the"true individual mean" for that biopsy. The means of these individualbiopsy means were then calculated for groups of biopsies toderive "true population means." The distribution of these meanswas always skewed but was normalized by log transformation,and the average was expressed as the geometric mean (gmean)(confidence interval [CI]). All area measurements were expressedas µm2 x 103.
The means of specified numbers of randomly sampled glomeruliin each biopsy were then calculated, the "random sample individualmeans." Their average was derived as the "random sample populationmeans," which were similarly expressed as the gmean (CI). Theindividual random sample means were compared with the true individualmean within a single biopsy, and the population random samplemeans were compared with the true population means when groupsof biopsies were compared. All analyses were conducted in twostages, first with all glomerular profiles considered withoutregard to presence and degree of sclerosis, and second, withonly profiles without perceptible sclerosis considered.
Statistical Analyses
All analyses were performed using STATA statistical software,version 8.2, (Stata Corp., College Station, TX). The randomselection of a specified number of glomerular profiles withinindividual biopsies was performed by a specific STATA program(22,23), and the geometric mean of their areas was calculated.This process was repeated as the number of randomly chosen profilesincreased from one through 12.
Lin’s concordance correlation coefficient (Rc) was calculatedto determine the level of agreement between the individual randomlysampled means and the true individual mean for each biopsy inthe stable series of 30 biopsies using a downloadable STATAprogram (24). This technique combines measures of both precisionand accuracy to determine whether the observed data deviatesignificantly from the 45-degree line of perfect concordance(i.e., line of identity). Agreement is generally consideredunsatisfactory when Rc < 0.6, satisfactory when Rc 0.6 to0.9 and excellent when Rc > 0.90.
Ethics Approvals
This study was approved by the Ethics Committees of the Universityof Mississippi Medical Center and Monash University School ofMedicine.
Biopsies contained from one to 23 glomerular profiles with amedian of seven profiles, when all glomerular profiles wereconsidered, and contained zero to 17 profiles, with a medianof four, when only profiles without visible sclerosis on thatsection were considered. Figure 1 illustrates the distributionsof the numbers of glomerular profiles in the biopsies and thesubstantial reductions in numbers when profiles with sclerosisare excluded. Figure 2 shows groupings of the biopsies accordingto the minimum number of glomerular profiles that each contained.Without exclusions as a result of sclerosis, 96.1% of the biopsieshad four or more glomerular profiles, 49.7% had eight or moreglomerular profiles, and only 21.3% had 12 profiles. When onlyprofiles without sclerosis were included, the proportions ofbiopsies with four or more, eight or more, and 12 profiles fellto 55.7, 26.2, and 9.3%, respectively. These findings are importantin relation to population data, when the issue of sample sizeor the number of biopsies that contribute to the group datais of great significance.
Table 1. Comparison of the individual glomerular profile mean area (µm2 x 103) calculated from sampling increasing numbers of random profiles with the true individual glomerular profile mean in one biopsy with 23 glomerular profiles
Table 2. Comparison of the population glomerular profile geometric mean area (µm2 x 103) calculated from sampling increasing numbers of random glomerular profiles with the true population glomerular profile geometric mean in 30 biopsies with 12 nonsclerosed glomeruli (range 12 to 23).
Table 3. Comparison of the population glomerular profile geometric mean area (µm2 x 103) calculated from sampling increasing numbers of random glomerular profiles with the true population glomerular profile geometric mean using all of the eligible biopsies in the series
Estimating Individual Mean Areas: Sampling Increasing Numbers of Randomly Chosen Glomeruli in a Single Biopsy
This effect was analyzed in a biopsy with 23 glomerular profiles,14 of which were without discernible sclerosis on that section.Estimates from increasing numbers of randomly sampled glomeruliwere compared with the true individual mean for that biopsy,based on assessment of all eligible glomeruli. As shown in Table 1and Figure 3, the more glomeruli that were included in therandom sample, the better the estimates were. The estimateswere particularly stable when 10 or more profiles were sampled,without regard to sclerosis, and when eight or more profileswithout sclerosis were sampled.
Figure 3. Mean (confidence interval [CI]) of individual glomerular area estimates (µm2x 103) with sampling of increasing numbers of randomly chosen glomerular profiles in a single biopsy, with a total of 23 profiles. The true individual biopsy mean (CI) is shown for comparison. *Unable to estimate CI due to small numbers.
Estimating Populations Mean Areas: Sampling Increasing Numbers of Glomerular Profiles When the Number of Participating Biopsies Remains Constant Table 2 and Figure 4 show the effect of sampling a progressivelylarger number of randomly chosen glomerular profiles in biopsieswith abundant glomeruli, for which the number of participatingbiopsies did not change. This was ascertained on a group of30 biopsies that each had 12 nonsclerosed glomeruli (range 12to 23). Mean estimates from three or more randomly sampled nonsclerosedglomerular profiles all reliably reflected the "true populationmean." Their stability was particularly good when five or moreglomeruli were sampled, and the CI of the estimate were notsubstantially reduced by sampling greater numbers. Lin’sconcordance coefficient was >0.9 when four or more glomeruliwithout exclusions and three or more nonsclerosed glomeruliwere sampled, indicating excellent agreement between the truebiopsy means and the random sampled means. There was littleextra benefit from sampling eight or 12 glomeruli compared withthe sampling of five or more at both the population and theindividual biopsy levels.
Figure 4. Population random sample means (CI) of glomerular profile area (µm2x 103) as increasing numbers of glomerular profiles are randomly sampled, versus the population mean (CI), in 30 biopsies with 12 nonsclerosed glomerular profiles.
Estimating Population Mean Areas: Sampling Increasing Numbers of Glomerular Profiles with Progressively Lower Numbers of Eligible Biopsies
In practice, many biopsies do not have plentiful glomerularprofiles. The challenge is to understand whether there needsto be a minimum number of glomerular profiles specified forinclusion of a biopsy in an analyzed series and what this numbermight be. We used the entire biopsy series to inform this question.
The first approach was to evaluate the true population meanvalues as the minimum requisite number of glomerular profilesfor inclusion of any biopsy was changed (Table 3). The numbersof biopsies that were included in every estimate can be cross-referencedin Figure 2. Figure 5 shows that none of the population meanvalues differed significantly from one another (the CI alwaysoverlapped). However, inclusion of biopsies with minimum numbersof glomerular profiles from one or more to four or more gavethe most robust estimates with the least variance (reflectedby the narrowest CI). The variance increased as the minimumnumber of glomeruli profiles for inclusion increased, as a resultof lower numbers of participating biopsies, and was especiallyconspicuous when a minimum of more than seven or eight profilesin each participating biopsy was stipulated.
Figure 5. True population mean (CI) of mean glomerular area (µm2x 103) according to the minimum number of profiles specified for biopsy eligibility.
Figure 5 also shows that population means of glomerular profileareas without sclerosis tended to be higher than the populationmean areas of profile areas without exclusions and that theformer remained stable as more glomerular profiles were included,whereas the latter tended to fall. These differences presumablyreflect inclusion of profiles of small scarred glomeruli inthe latter and their greater chance of being sampled as moreprofiles were evaluated.
Figure 6 shows, in these same groupings of biopsies, that therandom sample mean reliably estimated the true population meanwhen biopsies with five or more glomerular profiles were included,without regard to sclerosis, and when those with four or moreglomeruli without sclerosis were included. As increasing minimumnumbers of glomerular profiles per biopsy were stipulated, themean values remained similar to the true populations mean, butthere was increasing variation about the mean. This was especiallyapparent with requirements of sampling of more than eight profileswithout exclusion and for biopsies with more than six or sevennonsclerosed glomerular profiles.
Figure 6. True population mean (CI) of glomerular profile area (µm2x 103) according to the minimum number of profiles specified for biopsy eligibility.
Analysis of Subgroups of Biopsies
The limiting effect of specifying larger minimum numbers ofglomeruli for eligibility of biopsies for inclusion is exacerbatedwhen biopsies are divided into groups, for example by diagnosticcategory or race. Table 4 shows the major diagnostic categoriesin the biopsy series already cited. Requirement for robust numbersof glomeruli more likely would jeopardize the feasibility ofa study on glomerular size in hypertension or membranoproliferativeglomerulonephritis than a study on the first three categoriesof disease. If the outcome of interest is mean area of glomeruliwithout sclerosis, then the number of qualifying biopsies islimited further, especially in disease states with extensiveglomerulosclerosis.
Table 4. Major diagnostic categories in the biopsy series citeda
Figure 7 shows the average area of nonsclerosed glomeruli bydisease categories, as the minimum required number of nonsclerosedglomeruli was increased from two to eight. They are arrangedin order of glomerular size, and membranoproliferative glomerulonephritisis excluded. The destabilizing effects on the mean estimatesimposed by smaller numbers of participating biopsies is especiallyevident with mesangial proliferative glomerulonephritis andwith lupus nephritis class V (SLE V).
Figure 7. Population mean glomerular profile area (µm2x 103) by disease categories, with increasing number of nonsclerosed glomerular profiles per biopsy required for inclusion. MCD, minimal-change disease; HT, hypertension; SLE O, lupus nephritis other than class V; Mes GN, mesangioproliferative glomerulonephritis; FSGS, focal segmental glomerulosclerosis; Memb GN, membranous glomerulonephritis; SLE V, lupus nephritis class V.
Table 5 shows how the ability to detect a difference of significancebetween two categories of disease can be lost as the minimumglomeruli required for inclusion of a biopsy in a series isincreased. The size difference in nonsclerosed glomeruli betweenlupus nephritis other than class V (SLE O) and SLE V, suggestedin Figure 6, is clearly significant when biopsies with one ormore, two or more, or four or more nonsclerosed glomerular profilesare included but becomes marginal when six or more glomeruliare required, and the significance is lost among biopsies witheight or more nonsclerosed glomeruli.
Table 5. Testing the null hypothesis for differences in mean area (µm2 x 103) of nonsclerosed glomeruli in biopsies of people with SLE O and SLE V, according to the minimum number of nonsclerosed glomeruli required for inclusion of each biopsy
In an individual biopsy, good estimates of mean glomerular profilearea were obtained by measuring as few as eight nonsclerosedglomerular profiles. In an analysis in which the number of biopsieswas held constant, sampling of as few as five glomerular profilesin each biopsy gave a good representation of the populationmean profile area. Inclusion of glomeruli with sclerosis introducedmore variation and increased the requisite number of profiles.In a series in which the numbers of participating biopsies decreasedas the minimum number of glomerular profiles required for inclusionrose, the best estimates of the population mean profile areaswere supplied by including as many biopsies as possible; therewere no grounds for exclusion of any biopsy on the basis ofminimum numbers of profiles.
One of the arguments for recommending evaluation of a generousminimum number of glomerular profiles in every biopsy in anyparticular series is based on the purported potential for thebiopsy mean profile area to fall as increasing numbers of profilesare sampled, as a result of minimization of the effect of preferentialsampling of larger glomeruli. It could be argued, however, thatlarger glomeruli will always be overrepresented in systematicallysampled series of sections. In any case, the phenomenon wasnot apparent in our analyses when glomeruli with sclerosis wereexcluded from consideration.
In a single biopsy, the more glomeruli that are available formeasurement, the more valid the final estimate of glomerularprofile area should be. In a group of biopsies with plentifulglomeruli, the same should apply, although our data showed minimalbenefit in sampling more than six or seven profiles. However,the situation is different with grouped data, for which a compromiseis needed between the desired stability of the glomerular sizeestimates and the diminishing number of eligible biopsies, asthe minimum number of glomerular profiles required for inclusionis increased. The potentially weakened accuracy of the profilearea estimates if biopsies with relatively few glomeruli areincluded in any series is more than balanced by the increasein power contributed by inclusion of the larger numbers of "eligible"biopsies. In this analysis, inclusion of biopsies with fouror more nonsclerosed glomeruli permitted inspection of 2.5 timesas many biopsies than did inclusion of biopsies with a minimumof eight nonsclerosed glomeruli, but gave a similar mean andnarrower CI. When no biopsies were excluded, four times as manybiopsies could be evaluated, and the mean area estimates wereequally or even more robust.
In practice, biopsies contain variable and limited numbers ofglomeruli, and all qualifying glomerular profiles of biopsieswith "sufficient" profiles are measured to achieve an individualbiopsy mean. If the minimum specified number of profiles istoo high, then the sample size to analyze any phenomenon ordifferences by groupings might well be too small. This studyshows that it is not reasonable to limit ability to discriminatea difference by restricting, in advance, the number of biopsiesthat are available for inclusion by specifying a larger requisiteminimal number of glomerular profiles. Rather, the associationsof glomerular tuft volume with features of interest can be exploredwithin any biopsy series. If variation operates randomly, thenthe inclusion of data from biopsies with lower numbers of glomerulishould not bias the findings in any particular direction, andenrichment of numbers of contributing biopsies adds power. Ifthe conclusions and associations are statistically significantand biologically plausible, then they are likely to be correct.This approach is no less valid than exploring a body of epidemiologicdata for associations of interest, even when those data werenot originally collected for that specific purpose. In thisinstance, it allows large bodies of archived material to beput to great use in exploring matters of great interest.
The concepts outlined here should be generalizable across biopsyseries, although the specific quantitative findings are likelyto vary somewhat, according to the number of available biopsies,biopsy practices (numbers of glomeruli included in biopsies),subgroupings of interest, the degrees of glomerulosclerosis,and other factors.
Footnotes
Published online ahead of print. Publication date availableat www.jasn.org.
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Abstract
Introduction
10 profiles without exclusions and of eight profiles or more without sclerosis reliably estimated the true mean areas. In a group of 30 biopsies, random sampling of five or more glomeruli per biopsy reliably estimated the true population mean. In the aggregate series, inclusion of all 384 biopsies produced the most robust true population mean; the reliability of the estimates decreased as the numbers of eligible biopsies diminished with increasing requisite minimum numbers of profiles per biopsy. We conclude that, while 
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