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Statistical methods for assessing agreement between two methods of clinical measurement  

2012-10-30 06:34:21|  分类: 医学进展新干线 |  标签: |举报 |字号 订阅

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STATISTICAL METHODS FOR ASSESSING AGREEMENT BETWEEN TWO METHODS OF CLINICAL MEASUREMENT

J. Martin Bland, Douglas G. Altman

Department of Clinical Epidemiology and Social Medicine, St. George's Hospital Medical School, London SW17 ORE; and Division of Medical Statistics, MRC Clinical Research Centre, Northwick Park Hospital, Harrow, Middlesex

SUMMARY

In clinical measurement comparison of a new measurement technique with an established one is often needed to see whether they agree sufficiently for the new to replace the old. Such investigations are often analysed inappropriately, notably by using correlation coefficients. The use of correlation is misleading. An alternative approach, based on graphical techniques and simple calculations, is described, together with the relation between this analysis and the assessment of repeatability.

INTRODUCTION

Clinicians often wish to have data on, for example, cardiac stroke volume or blood pressure where direct measurement without adverse effects is difficult or impossible. The true values remain unknown. Instead indirect methods are used, and a new method has to be evaluated by comparison with an established technique rather than with the true quantity. If the new method agrees sufficiently well with the old, the old may be replaced. This is very different from calibration, where known quantities are measured by a new method and the result compared with the true value or with measurements made by a highly accurate method. When two methods are compared neither provides an unequivocally correct measurement, so we try to assess the degree of agreement. But how?

The correct statistical approach is not obvious. Many studies give the product-moment correlation coefficient (r) between the results of the two measurement methods as an indicator of agreement. It is no such thing. In a statistical journal we have proposed an alternative analysis, [1] and clinical colleagues have suggested that we describe it for a medical readership.

Most of the analysis will be illustrated by a set of data (Table 1) collected to compare two methods of measuring peak expiratory flow rate (PEFR).

SAMPLE DATA

The sample comprised colleagues and family of J.M.B. chosen to give a wide range of PEFR but in no way representative of any defined population. Two measurements were made with a Wright peak flow meter and two with a mini Wright meter, in random order. All measurements were taken by J.M.B., using the same two instruments. (These data were collected to demonstrate the statistical method and provide no evidence on the comparability of these two instruments.) We did not repeat suspect readings and took a single reading as our measurement of PEFR. Only the first measurement by each method is used to illustrate the comparison of methods, the second measurement being used in the study of repeatability.

PEFR MEASURED WITH WRIGHT PEAK FLOW AND MINI WRIGHT PEAK FLOW METER
Wright peak flow meter Mini Wright peak flow meter
First PEFR Second PEFR First PEFR Second PEFR
Subject (l/min) (l/mi) (l/min) (l/min)
1 494 490 512 525
2 395 397 430 415
3 516 512 520 508
4 434 401 428 444
5 476 470 500 500
6 557 611 600 625
7 413 415 364 460
8 442 431 380 390
9 650 638 658 642
10 433 429 445 432
11 417 420 432 420
12 656 633 626 605
13 267 275 260 227
14 478 492 477 467
15 178 165 259 268
16 423 372 350 370
17 427 421 451 443

PLOTTING DATA

The first step is to plot the data and draw the line of equality on which all points would lie if the two meters gave exactly the same reading every time (fig 1). This helps the eye in gauging the degree of agreement between measurements, though, as we shall show, another type of plot is more informative.

Scatter diagram showing PEFR (mini meter) on vertical axis and PEFR (large meter) on horizontal axis, with line of equality.  Points are all fairly close to this line. D

Fig 1. PEFR measured with large Wright peak flow meter and mini Wright peak flow meter, with line of equality.

INAPPROPRIATE USE OF CORRELATION COEFFICIENT

The second step is usually to calculate the correlation coefficient (r) between the two methods. For the data in fig 1, r = 0.94 (p < 0.001). The null hypothesis here is that the measurements by the two methods are not linearly related. The probability is very small and we can safely conclude that PEFR measurements by the mini and large meters are related. However, this high correlation does not mean that the two methods agree:

(1) r measures the strength of a relation between two variables, not the agreement between them. We have perfect agreement only if the points in fig 1 lie along the line of equality, but we will have perfect correlation if the points lie along any straight line.

(2) A change in scale of measurement does not affect the correlation, but it certainly affects the agreement. For example, we can measure subcutaneous fat by skinfold calipers. The calipers will measure two thicknesses of fat. If we were to plot calipers measurement against half-calipers measurement, in the style of fig 1, we should get a perfect straight line with slope 2.0. The correlation would be 1.0, but the two measurements would not agree --- we could not mix fat thicknesses obtained by the two methods, since one is twice the other.

(3) Correlation depends on the range of the true quantity in the sample. If this is wide, the correlation will be greater than if it is narrow. For those subjects whose PEFR (by peak flow meter) is less than 500 l/min, r is 0.88 while for those with greater PEFRs r is 0.90. Both are less than the overall correlation of 0.94, but it would be absurd to argue that agreement is worse below 500 l/min and worse above 500 l/min than it is for everybody. Since investigators usually try to compare two methods over the whole range of values typically encountered, a high correlation is almost guaranteed.

(4) The test of significance may show that the two methods are related, but it would be amazing if two methods designed to measure the same quantity were not related. The test of significance is irrelevant to the question of agreement.

(5) Data which seem to be in poor agreement can produce quite high correlations. For example, Serfontein and Jaroszewicz [2] compared two methods of measuring gestational age. Babies with a gestational age of 35 weeks by one method had gestations between 34 and 39.5 weeks by the other, but r was high (0.85). On the other hand, Oldham et al. [3] compared the mini and large Wright peak flow meters and found a correlation of 0.992. They then connected the meters in series, so that both measured the same flow, and obtained a "material improvement" (0.996). If a correlation coefficient of 0.99 can be materially improved upon, we need to rethink our ideas of what a high correlation is in this context. As we show below, the high correlation of 0.94 for our own data conceals considerable lack of agreement between the two instruments.

MEASURING AGREEMENT

It is most unlikely that different methods will agree exactly, by giving the identical result for all individuals. We want to know by how much the new method is likely to differ from the old: if this is not enough to cause problems in clinical interpretation we can replace the old method by the new or use the two interchangeably. If the two PEFR meters were unlikely to give readings which differed by more than, say, 10 l/min, we could replace the large meter by the mini meter because so small a difference would not affect decisions on patient management. On the other hand, if the meters could differ by 100 l/min, the mini meter would be unlikely to be satisfactory. How far apart measurements can be without causing difficulties will be a question of judgment. Ideally, it should be defined in advance to help in the interpretation of the method comparison and to choose the sample size.

The first step is to examine the data. A simple plot of the results of one method against those of the other (fig 1) though without a regression line is a useful start but usually the data points will be clustered near the line and it will be difficult to assess between-method differences. A plot of the difference between the methods against their mean may be more informative. Fig 2 displays considerable lack of agreement between the large and mini meters, with discrepancies of up to 80 l/min, these differences are not obvious from fig 1. The plot of difference against mean also allows us to investigate any possible relationship between the measurement error and the true value. We do not know the true value, and the mean of the two measurements is the best estimate we have. It would be a mistake to plot the difference against either value separately because the difference will be related to each, a well-known statistical artefact. [4]

Plot of difference, large minus mini, against average of the two meters, no obvious relationship between variables. Horizontal straight lines, mean+2SD, mean, and mean-2SD, enclose points. D

Fig 2. Difference against mean for PEFR data.

For the PEFR data, there is no obvious relation between the difference and the mean. Under these circumstances we can summarise the lack of agreement by calculating the bias, estimated by the mean difference d, and the standard deviation of the differences (s). If there is a consistent bias we can adjust for it by subtracting d from the new method. For the PEFR data the mean difference (large meter minus small meter) is -2.1 l/min and s is 38.8 l/min. We would expect most of the differences to lie between d - 2s and d + 2s (fig 2). If the differences are Normally distributed (Gaussian), 95% of differences will lie between these limits (or, more precisely, between d - 1.96s and d + 1.96s ). Such differences are likely to follow a Normal distribution because we have removed a lot of the variation between subjects and are left with the measurement error. The measurements themselves do not have to follow a Normal distribution, and often they will not. We can check the distribution of the differences by drawing a histogram. If this is skewed or has very long tails the assumption of Normality may not be valid (see below).

Provided differences within d +/- 2s would not be clinically important, we could use the two measurement methods interchangeably. We shall refer to these as the "limits of agreement". For the PEFR data we get:
d - 2s = -2.1 - (2x38.8) = -79.7 l/min
d + 2s = -2.1 + (2x38.8) = 75.5 l/min
Thus, the mini meter may be 80 l/min below or 76 l/min above the large meter, which would be unacceptable for clinical purposes. This lack of agreement is by no means obvious in fig 1.

PRECISION OF ESTIMATED LIMITS OF AGREEMENT

The limits of agreement are only estimates of the values which apply to the whole population. A second sample would give different limits. We might sometimes wish to use standard errors and confidence intervals to see how precise our estimates are, provided the differences follow a distribution which is approximately Normal. The standard error of d is root(s2/n), where n is the sample size, and the standard error of d - 2s and d + 2s is about root(3s2/n). 95% confidence intervals can be calculated by finding the appropriate point of the t distribution with n - 1 degrees of freedom, on most tables the columns marked 5% or 0.05, and then the confidence interval will be from the observed value minus t standard errors to the observed value plus t standard errors.

For the PEFR data s = 38.8. The standard error of d is thus 9.4, For the 95% confidence interval we have 16 degrees of freedom and t = 2.12. Hence the 95% confidence interval for the bias is -2.1 - (2.12x9.4) to -2.1 + (2.12x9.4), giving -22.0 to 17.8 l/min. The standard error of the limit d - 2s is 16.3 l/min. The 95% confidence interval for the lower limit of agreement is -79.7 - (2.12x16.3) to -79.7 + (2.12x16.3), giving -114.3 to -45.1 l/min. For the upper limit of agreement the 95% confidence interval is 40.9 to 110.1 l/min. These intervals are wide, reflecting the small sample size and the great variation of the differences. They show, however, that even on the most optimistic interpretation there can be considerable discrepancies between the two meters and that the degree of agreement is not acceptable.

EXAMPLE SHOWING GOOD AGREEMENT

Fig 3 shows a comparison of oxygen saturation measured by an oxygen saturation monitor and pulsed oximeter saturation, a new non-invasive technique. [5] Here the mean difference is 0.42 percentage points with 95% confidence interval 0.13 to 0.70. Thus pulsed oximeter saturation tends to give a lower reading, by between 0.13 and 0.70. Despite this, the limits of agreement (-2.0 and 2.8) are small enough for us to be confident that the new method can be used in place of the old for clinical purposes.

Difference against average of the two monitors, no obvious relationship. Horizontal straight lines, mean+2SD, mean, and mean-2SD, enclose all but one point. D

Fig 3. Oxygen saturation monitor and pulsed saturation oximeter

RELATION BETWEEN DIFFERENCE AND MEAN

In the preceding analysis it was assumed that the differences did not vary in any systematic way over the range of measurement. This may not be so. Fig 4 compares the measurement of mean velocity of circumferential fibre shortening (VCF) by the long axis and short axis in M-mode echocardiography. [6] The scatter of the differences increases as the VCF increases. We could ignore this, but the limits of agreement would be wider apart than necessary for small VCF and narrower than they should be for large VCF. If the differences are proportional to the mean, a logarithmic transformation should yield a picture more like that of figs 2 and 4, and we can then apply the analysis described above to the transformed data.

Difference, long minus short, against average VCF. Obvious relationship: variability of the differences increases dramatically as VCF increases. D

Fig 4. Mean VCF by long and short axis measurements.

Fig 5 shows the log-transformed data of fig 4. This still shows a relation between the difference and the mean VCF, but there is some improvement. The mean difference is 0.003 * on the log scale and the limits of agreement are -0.098 * and 0.106. * However, although there is only negligible bias, the limits of agreement have somehow to be related to the original scale of measurement. If we take the antilogs of these limits, we get 0.80 and 1.27. However, the antilog of the difference between two values on a log scale is a dimensionless ratio. The limits tell us that for about 95% of cases the short axis measurement of VCF will be between 0.80 and 1.27 times the long axis VCF. Thus the short axis measurement may differ from the long axis measurement by 20% below to 27% above. (The log transformation is the only transformation giving back-transformed differences which are easy to interpret, and we do not recommend the use of any other in this context.)

Difference, log transformed long minus short, against average log VCF. Possible relationship: variability of the differences increases slightly as VCF increases. D

Fig 5. Data of fig 4 after logarithmic transformation.

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,ndard l mo eom agaiAus relaocto es wainement betweethese that thmin<rrt1, D WITH WRIGHTaatAK FLOWION BEWRI WRIGHTaatAK FLOWIngTERt1, horgn="midn/I" 1gt;S wholeata. 1, horgn="midn/I" 1gt;F% wteata. 1, horgn="midn/I" 1gt;S wholeata. 1, horgn="to ht" 1gt;S horgn="midn/I" 1gt;( 80 loe 1, horgn="to ht" 1gt;horgn="midn/I" 1gt;4n fD 1, horgn="midn/I" 1gt;4nhorgn="midn/I" 1gt;51horgn="midn/I" 1gt;52horgn="to ht" 1gt;horgn="midn/I" 1gt;39horgn="midn/I" 1gt;39 horgn="midn/I" 1gt;43horgn="midn/I" 1gt;41horgn="to ht" 1gt;horgn="midn/I" 1gt;5encD 1, horgn="midn/I" 1gt;5ehorgn="midn/I" 1gt;52horgn="midn/I" 1gt;D>horgn="to ht" 1gt; fD 1, horgn="midn/I" 1gt;4ad D 1, horgn="midn/I" 1gt;4c1vD 1, horgn="midn/I" 1gt;42horgn="midn/I" 1gt;44d D 1, horgn="to ht" 1gt;horgn="midn/I" 1gt;4 beD 1, horgn="midn/I" 1gt;47horgn="midn/I" 1gt;D>horgn="midn/I" 1gt;D>horgn="to ht" 1gt;beD 1, horgn="midn/I" 1gt;55 horgn="midn/I" 1gt;611vD 1, horgn="midn/I" 1gt;6terD 1, horgn="midn/I" 1gt;62horgn="to ht" 1gt; horgn="midn/I" 1gt;4conD 1, horgn="midn/I" 1gt;41horgn="midn/I" 1gt;36d D 1, horgn="midn/I" 1gt;46erD 1, horgn="to ht" 1gt;horgn="midn/I" 1gt;44horgn="midn/I" 1gt;431vD 1, horgn="midn/I" 1gt;3hesD 1, horgn="midn/I" 1gt;39esD 1, horgn="to ht" 1gt;9sD 1, horgn="midn/I" 1gt;65esD 1, horgn="midn/I" 1gt;63horgn="midn/I" 1gt;65horgn="midn/I" 1gt;6 meD 1, horgn="to ht" 1gt;ed D 1, horgn="midn/I" 1gt;43onD 1, horgn="midn/I" 1gt;429sD 1, horgn="midn/I" 1gt;D>< D 1, horgn="midn/I" 1gt;43meD 1, horgn="to ht" 1gt;e1vD 1, horgn="midn/I" 1gt;4>horgn="midn/I" 1gt;42horgn="midn/I" 1gt;43meD 1, horgn="midn/I" 1gt;42horgn="to ht" 1gt;emeD 1, horgn="midn/I" 1gt;65beD 1, horgn="midn/I" 1gt;63onD 1, horgn="midn/I" 1gt;62beD 1, horgn="midn/I" 1gt;60< D 1, horgn="to ht" 1gt;eonD 1, horgn="midn/I" 1gt;26horgn="midn/I" 1gt;27< D 1, horgn="midn/I" 1gt;26erD 1, horgn="midn/I" 1gt;22horgn="to ht" 1gt;ed D 1, horgn="midn/I" 1gt;47horgn="midn/I" 1gt;49meD 1, horgn="midn/I" 1gt;47horgn="midn/I" 1gt;46horgn="to ht" 1gt;e< D 1, horgn="midn/I" 1gt;17horgn="midn/I" 1gt;16< D 1, horgn="midn/I" 1gt;259sD 1, horgn="midn/I" 1gt;26horgn="to ht" 1gt;ebeD 1, horgn="midn/I" 1gt;42onD 1, horgn="midn/I" 1gt;37meD 1, horgn="midn/I" 1gt;35esD 1, horgn="midn/I" 1gt;37horgn="to ht" 1gt;ehorgn="midn/I" 1gt;42horgn="midn/I" 1gt;421vD 1, horgn="midn/I" 1gt;451vD 1, horgn="midn/I" 1gt;443 1, St will beroese as thfisg of twainst he tfnfaHbe menes/nd are lefstalinical mstaequala goe so on !!" >hon="Sardiogrime !!" sof beroata. ( e mes er annhht en e a 1.2a. tata. (ic0us s er annhofni (lne d 1.tilds src="http://ofo- dofatyrc="ac.uk/~mb55//nd /ba1k.ac" >t maDele="dba1kk.a" >1gt; 1, are noeonngbAus relae het ncrt thaa. t of figsaft ei of and w Thata. /nd are therolonw eo e mea. tic0us s erieire1

are Htm#logere e hAs wovement" (0.9raph2" rU/ndmmo Thw eowainst he teit to:bD 1, ul misg of thain relatio.titionw eoese as thfisg of twor.nd ofequalnetip8 lese as thftransicts. ce is 0it boe 1 % ofioloroo eobe ccnfa anhor a> We c ofis meequalnetip8 lvement" (0.9icts. ce is 0% ofioloroences rao htnbe c bD 1, We credct e pl eitdiffe hs eoese as thmeF liigh corre of fig/nd aref/ bcuowaeo thf Thbceskine n wency45.e forof fcy45.efis me/nd arefwaine eckn mnpronfaf Thoump of ore1ouomeion fcy45.ef/nd are the ue plot inf- fcy45.ef/nd are thed emmw eo/eythonfafoe 1, ofsofnarrr oformetip8 l foro htnbe cilds We cw eowainstd are lefec rnarrtionese a ment of rnarrtionmixhf The eckn mnprond the salonw eowainstthe tiriit is(lo e hsethods,hcnw eg >D 1, is/ bjtertran> isata. (bce tsspet ces ereter /I> is 0.95ter 80 l, 1, islds is 0.9w eoin aand vement" (0.hnfanfi4> We credwrnarroweabFig ttuoc0uemeo These as thde hwrcs owt ce5ter 80 l2a. twrcs he ana5ter 80 l2o . Pede hi liiet nbodM-mSit isean also arcsh dnho eit ncsuom agaitowainst he tein any syes whistematic ifferena sn e eiJncf vaore s iffe wovement" (0.9e ha high g tnnd ly >D 1,

(4) rd hortsof eo Thw eowains he twire1

ar> We credwrnarroweamazberoictsains he twvelrgni ttuo/nd arefw eo remed to meif ore1tion

are T eowere nfa/P>

(4) rd e hiothl significancequo sul moctese as th >D 1, Dansfornfimstuooweit a whiese as thf fignngy smed en 0fe wovement" (0.e fFxygigh correSetions. Foa. tample, Serfo[2] veand J ttains he twnfa/nd arberoal age. Babies ihBAusprosubjeatal age. Babies onfa35t oekrolon(lo s he aeqrrr veJlion nisg of tad a. t39= - oekrolonw eoiw er> We c1, rO mw eoommend . s O. On t ofol-mo3] veand J tt eo e mea. tic0us ed the mini and large .2a. tfndox rumpC Wyor sberot eo,ndaen e A simoi liand Poem>,nnhoe fWislnd stuolate Wyoof em want eobe confidene h Such doom ing bmeasuremen n :ficts.e hi htion.0 and tuoca do cinot enoughHbe meneseatt mosrdlone of . minethant eoon wh he Wyot eobe c li do t eotainemlagsuremeaterhoumpe eotainata. /n erno ore1un Such douor satmiad lrecansforring bagen stm"ifashoiriaon ed 80 l, of rnarrminethant eoic0us s er Wyot eo e mes er owca do he mhe dsring back-hwrnarrtionediffendh8ndon ecrt ardlthe hoe al the>rO mw eoommend . s icts eo e erno rnarr ing bmWyoete 80 l, s eo e mes ertwrnarroweun Such douooweuld be unlikelHtmhf liagai a/nd arl thend . owesubjnd rI ar ed e ltofnarroweIdeally,it shJard tordefinit e weit er mosrdlonermps eo e he sveand illure ntuocod do t eo reflec to >D 1, hor nrndowsh dntuoean also aweancecnst aven

lon CF. owg of th. s d are lefh

rmps eotains d are lef hi hs eoo meao sua laosofequahouThwrnarroweat eveJielduomeions eoring baf ehae plot he diffiffera agtnnessrtowca do s eoring baf ehis measu

arlduo firs ifd ag-latedsveJ

D 1, St will beroese as thfisg of twainst he tfnfaHbe menes/nd are lefstalinical mstaequala goe so on !!" >hon="Peionrmpring baf ee !c0us sieren e ms ie, long minus srmps eotains ernge of the two monitors, n owg of t relatio.o obvious relationship. Horizontal straight lines, mean+2SD, mean, ce is ." >src="http://ofo- dofatyrc="ac.uk/~mb55//nd /ba2k.ac" >t maDele="dba2kk.a" >1gt; 1, rS wanring baf ednare1 Such doome nt cea hiche t foiWe ul misca do sofequan rD 1, eaamopwicsul hoAh/ wholedpopeaawrnarrr satring baftnbetrfe fWismo htnits limits. We mi do veJfd<

< hie nH2ff,ndard it eriffdntuonfidof e mo8ndainrely sua laecaren tinethodot eoring baf eeoe nt cea t foiWe ul m nsfori haare ibution whiche ihT. veJfd<

l ele 1, d<

d + 1, cilo tmd eoateh ht eovelumnsshorkpoi5%ixygnf05 are ns e mw eoH2ff,ndard it erifflis measueis it eorval widoiffern e th1, d<

d<

rD 1, d<

Fxygs eoell H2ff,ndard it eriffliofequalencIdt toecrmpf toI> are n1, d<

rD 1, ring baf e1i h0. me4agcehe al ce is 0.Fw eell H2ff,ndard it eriffl0.13esoh0.7mihT. thpwido nlibu eriuldmparul s,nddntuor saturt cagnmiad lr> Wyoowg of t0.13ere n0.7mihDeleene1t 1.tit eo70. Despite this, tn(-2.ese li2.8) are1mhe .0 and i li thsohoweH2ff,ndaonw Thw eobe confide1 . owe dodmcaameard rmpt eoon wi liHbe menecceptable fD 1, St will beroese as thfisg of twainst he tfnfaHbe menes/nd are lefstalinical mstaequala goe so on !!" >hon="Ding back- ie, longe minus mini, againsosrc="http://ofo- dofatyrc="ac.uk/~mb55//nd /ba3k.ac" >t maDele="dba3kk.a" >1gt; 1,
re nsof . t eA>har eit eoi

In tvele cal wobin soht eourdAei laodmve thoD 1, St will beroese as thfisg of twainst he tfnfaHbe menes/nd are lefstalinical mstaequala goe so on !!" >hon="Ding back-e !loro e renmofn > re, long minus sVCFhoObvio th

ul CF.:n relaus relarmpt eoring baf emmit mianproof a loce ncIf VCFmca mianpr " clos"http://ofo- dofatyrc="ac.uk/~mb55//nd /ba4k.ac" >t maDele="dba4kk.a" >1gt; 1,
rls f thet ere1i htransnegorgbsceothertit eo70. Despite this, tnequalits of esohowe

odmwoht eofni bee lated to the originahoumpsofeJield eoi e( oe t eond ( oeIrmpt eoring baf e owg of ttainifferenlo ronmg lated i hdsri thntrt/I> iparulihT. 70. Desessd dnt h i lihe e cell rmpcanprot eomofn ld 1.2/ndFig 4 co rmpVCFmis measuowg of tf Vese li1.2.so onsht eo7oeroi 1.2VCFihT. dnt eomofn ld 1.2/ndFig 4 co hortring bmeasuremenolorod 1.2/ndFig 4 co iyo20%dowt ciwoh27%wobin 20%T eo oeIurdAei la lol m1.2t eotransurdAei la lol mr sberob re nsof totionmo8 a th nt eo do lctenceommendcaat 1.eH2fwexl.othe1, St will beroese as thfisg of twainst he tfnfaHbe menes/nd are lefstalinical mstaequala goe so on !!" >hon="Ding back-e !leIurdAei laodm!loro e renmofn > re, long minus s!leIVCFihPnst aven

lon CF.:n relaus relarmpt eoring baf emmit mianprosorghcencIf VCFmca mianpr " clos"http://ofo- dofatyrc="ac.uk/~mb55//nd /ba5k.ac" >t maDele="dba5kk.a" >1gt; 1,
odmwoht eo/ndA f of . har eironmg urdAei la lol fWist eaa lack ofpht eotndA re n eJfd, and the standard deviatiIf beporahoT eo/ndA ring baf e mofnarr ere1owezere mit ist eo reeo e he liIf dod20%umpt eo/ndA ring baf e i h/P>

(4) cencring bafh iis ezere f of ( tionoweatehewoh do t eove thwoh will pmin e tus rey1owca do he difflateledal lctt eole siz/ndFig 4 co i htdiffeberot eom whole lit eocin8nss lct/ndFig 4 co i hton iberot eod to mea.these 38.8 lell rmpring baf eeowohowe/I> is 0.9wain eJfd, and e fori hi hw eove caisul moctec ds. Id dtu lon-m[7]oump of . hwiumo t eom plcring baf eowohowezere t 1.eH2odie ffec i het nc/Pimeaawohy sua la:nsofsd tre1o s eoving back-.tiad nt empup,ovi>,ndmiyo1, re neJield eosd tre1I>d titohr ofs eo eJfd, and lctt eoving back-. fD 1, ul oowg of ts eoving back- re ns eo to lctt eoata. fT ere1i differencesrsv oflinrt% or fWisequalmosre c nt i h/ndFig 4 co i lis eoi

In > rls f thesofs e8.8 tt h e liIf s, a n e eiunuld be unlikel(Iaamor8 coir(lo rnarrotrfnt i h/ bjterhasT eoium lctt eoving back-.fsd tredmc h13479ritcs eo eJfd, and the ving back-.fowg of ts eo>St will beroese as thfisg of twainst he tfnfaHbe menes/nd are lefstalinical mstaequala goe so on !!" >hon="Ding back-oowg of tt eotains dFig 4 cos lctata. dbero e mes erhde, longe minus mini, againsndFig 4 coe fNocrbvio th

ul t for A ving back-.foflinlo % of differe-4esre n+honf" clos"http://ofo- dofatyrc="ac.uk/~mb55//nd /ba6k.ac" >t maDele="dba6kk.a" >1gt; 1,
d
, and the s eo get e /ndFig 4 cont">Stt h m In lct relaardn a8]osnsforc hbeyoe ns e la shclctt c hJi iv o fD 1, C DS FS1, In i li will meroit to theovele cal wobin hoT eoy sua laclctthere Fnd owemetdiffee s We ct eoy sua laclcts eo eJfd, and the s eoving back-.fis measutuuhmhe s Wwca do hemo lctt eoodiffe lctmin e odm/ndFig 4 coh

islofequaltains dFig 4 cos ld the saiyo firs e he > r hcaat eooateh fWis cancs eo eJfd, and the ving back-.fowg of tmin e odm/ndFig 4 cont">St firs e he a agtnnessr, 1, re ne eo eJfd, and lctt eoving back-.oowg of tt eo/ndt hi li firs e he , 1, d
, and lctving back-., 1, rT.i hc hJpcinibution wI>d +21, We cicts ere1ore1ring back-.oowg of tt eotains he twtion 38licasceotrtmin e tus reyo rror hJ!lon mi.ahoit err8 l mowg of tm In tlcts wanIhmeiotitor oht msubjethwy s lctt eo4 (p < 0.001)lctdtc

ul t for Sts hwyxeroy sho do 92% s lct/ndFig 4 co fiyotainring bac a/n he twsohFndnd nnes s eo lack of l mlct1, rO rd t eoH2othlrdloneopcinfirooIf beelcputechniqti oht f sFnd miadmlctecteJ

nIfko"whyo th you do t i hteJ

In tpa4ageosnsfor do it 2oth8 lteJ

,nd s y showhly a. mianrt hi litiondh lgritcare1r sa hoD 1, Stt the ean iy s re n wieve ardtiem and lgrDr>De>,n Rrval man>nle sizbrf thofs eocinot eesoh ts Dr>P >D'Arowta re nDr>H fSeStt snerot eo a tcripo fD 1, RELATS1, Althoe DG, B a taM20%1983I>rMndFig 4 coiemt/nemee c:pohtte

In tlct he veand illus ctero1, D 1, rO. On tHG, B sig MM, McDermott M20Ceagai illunmpohttbe coe mldmpeer and trcaspit e/n t msubjeohttve ad,mntP >Rhlrdlon CF. owg of tcaisue bloe s mowiure1oe neerofo subjetmiat the>r1, Tytlt mJA,fSeD 1, <-9ihD 1, dsouI sutu l ro1, drD 1, 1, rD rD rD rD rD rD > rD sv wi="gi htni ht shnnesbcr i ht shnnesbcr-be "> rD 喜欢 推荐 0人  |  rD 转载 rD > rD > rD > rD > rD sv wi="snl"> rD smeyth="dt mety:tere"nv wi="ghidc bdwb bds2 bdc0hrd8va"n,n="$_vi>R> rD s,n="yodaoad"sv wi="bdwb bds2 bdc0"tveyth="dt mety:tere;_zoom:1;"> > rD s,n="$_be O. BlogLenpBottomDiv"sv wi='topsfc03sv oflfix'> > sv wi="

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    • ${fn1(x.t tth,60)|elea4a}${fn2(x.putechnT on,'yyyy-MM-d nHH:mm:ss')} {/if} {/leve}
    <#--被推荐日志--> i{levetec w x} {ict!!x}
  • ${fn(x.sutth,26)|elea4a} {/if} {/leve} <#--上一篇,下一篇--> {ict!!(blogDosrel. moBlogPt fftnk)}   sv wi="nla hohidc">${blogDosrel. moBlogT tth|elea4a}> {/if} {ict!!(blogDosrel.nyxeBlogPt fftnk)}   sv wi="ni htnohidc">${blogDosrel.nyxeBlogT tth|elea4a}> {/if} <#-- 热度 me> {levetec w x} {ict!!x} sv wi="honI eahbscockcnbw-frd nbw-f40"> {ictx.putechnerUtagnree==>,ntj l. dorNree} rD rD {e se} rD {/if} sv wi="cwgevnreeiohidc"> ${fn(x.putechnirNecknree,8)|elea4a} >   > {/if} {/leve} <#-- 网易新闻广告 me> sv wi="ttlbcr fc06endwb bdc0hbds0">网易新闻> sv wi="be s8va"> ${hof tn mrt tth|elea4a}
      {ictve caed('be sleve')&&be sleve.length>0} {levetbe sleven w x} {ictx_canex>7}{ oeak}{/if}
    • ·${x.o tth|elea4a} {/leve} {/if}
    sv wi="dfw.t ad163be s"> 下载网易新闻客户端 1gt; >
    > <#--右边模块结构me> sv wi="uine 1ze a">> 被推荐日志 最新日志 该作者的其他文章 博主推荐 随机阅读 首页推荐 sv wi="tm"i">更多1gt;1gt;>

    s,n="yodaoad_r"nieyth="dt mety:tere;_zoom:1;">> s,n="lmal r_dberlt">> s,n="blogPutecaAccf va">> <#--评论模块结构me> isv wi="putechn1ze a">> sv wi="ndwh bds2 bdc0hphidc"s,n="yodaoad_2" ieyth="_zoom:1;">> sv wi="ze asbdwh bds2 bdc0"> sv wi="canp">> sv wi="v oflfix">> > <#--引用模块结构me> sv wi="cl> i">   > sv wi="ze asphidc">> <#--博主发起的投票me> {levetec w x} {ict!!x} ${x.nn kNree|elea4a}  投票给 { renle si_ops l m=Iurue;} {levetx.>oteDosrelLevete heoteToOps l } {icteoteToOps l ==1} {ictle si_ops l ==fo se},{/if}  “${b[eoteToOps l _canex]}”   {/if} {/leve} {ict(x.r ne!="-1") },“我是${c[x.r ne]}”  {/if}         ${fn1(x.>oteT on)} {ictx.utagNree==''}{/if} {/if} {/leve} > renwumiiPt fLtnkm=I"http://blog.163.vea/linical m/blog/ve iv/16ete32201293063421852/"; //文章的永久链接,作为文章的唯一标识 renwumiiTagsm=I""; //文章标签,以英文逗号分隔,如:"标签1,标签2" renwumiiSenePthfixm=I"http://blog.163.vea/linical m/"; //博客的主页地址,作为博客的唯一标识 renwumiiPflamsm=I"&num=5&more=3&pf=blog163"; //num为默认显示的相关文章数目,more为默认的显示模式(1为文字,2为图片,3为自动) > sv wi="lav hete"> > sv wi="elvr hete"> > > sv wi="nb-mb lvr bh snJce"> sv wi=" bl bh"> > sv wi="elbr bh"> > sv wi="c bc bh lvr"> > > > > sv wi=" sl g lg hete"> > sv wi=" sl on e"> > sv wi=" sl b lb"> > sv wi="enwr g rg hete"> > sv wi="enwr hre"> > sv wi="enwr b rb"> > > > sv wi="nb-qmovnb-smb">sv wi="wkg h snJce">sv wi=" h"> >sv wi="r h"> >sv wi="c h"> >>> sv wi="nb-qmovnb-foa"> sv wi="wkg h">

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