Underestimation of Risk Associations Due to Regression Dilution in Longterm Follow-up of Prospective Studies

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1 American Jurnal f Epidemilgy Cpyright O 999 by The Jhns HpWns University Schl f Hygiene and Public Health ADrightsreserved V). 50, N. 4 Printed hi U.S.A Underestimatin f Risk Assciatins Due t Regressin Dilutin in Lngterm Fllw-up f Prspective Studies Rbert Clarke, Martin Shipley, 2 Sarah Lewingtn, Linda Yungman, Rry Cllins, Michael Marmt, 2 and Richard Pet n prspective studies, disease rates during fllw-up are typically analyzed with respect t the values f factrs measured during an initial baseline survey. Hwever, because f "regressin dilutin," this generally tends t underestimate the real assciatins f disease rates with the "usual" levels f such risk factrs during sme particular expsure perid. The "regressin dilutin rati" describes the rati f the steepness f the uncnnected assciatin t that f the real assciatin. T assess the relevance f the usual value f a risk factr during particular expsure perids (e.g., first, secnd, and third decades) t disease risks, regressin dilutin ratis can be derived by relating baseline measurements f the risk factr t replicate measurements frm a reasnably representative sample f study participants after an interval equivalent t abut the midpint f each expsure perid (e.g., at 5, 5, and 25 years, respectively). This reprt illustrates the impact f this time interval n the magnitude f the regressin dilutin ratis fr bld pressure and bld chlesterl. The analyses were based n biennial remeasurements ver 30 years fr participants in the Framingham Study (Framingham, Massachusetts) and a 26-year resurvey fr a sample f men in the Whitehall Study (Lndn, England). They shw that uncrrected assciatins f disease risk with baseline measurements underestimate the strength f the real assciatins with usual levels f these risk factrs during the first decade f expsure by abut ne-third, the secnd decade by abut ne-half, and the third decade by abut tw-thirds. Hence, t crrect apprpriately fr regressin dilutin, replicate measurements f such risk factrs may be required at varying intervals after baseline fr at least a sample f participants. Am J Epidemil 999; 50: prspective studies; risk analysis; risk assessment Much f ur knwledge abut the imprtance f risk factrs such as bld pressure and bld chlesterl cmes frm prspective studies, in which varius characteristics f a chrt are recrded at a "baseline" survey and the baseline characteristics f persns wh subsequently develp a particular disease are then cmpared with thse wh d nt (, 2). Hwever, because f the cmbined effects f measurement errrs and lnger-term fluctuatins r changes within persns, this prcedure des nt reliably indicate the real assciatin between the "usual" level f sme risk factr during a particular perid and the disease rate during that same (r sme later) perid (3-7). The uncrrected assciatin between the baseline measurement Received fr publicatin July 2, 997, and accepted fr publicatin December 6, 998. Clinical Trial Service Unit and Epidemilgical Studies Unit (CTSU), Nuffield Department f Clinical Medicine, Radcliffe nfirmary, Oxfrd, England. 2 Department f Epidemilgy and Public Hearth, University Cllege Lndn Medical Schl, Lndn, England. Reprint requests t Dr. Rbert Clarke, Clinical Trial Service Unit and Epidemilgical Studies Unit, Nuffield Department f Clinical Medicine, Radcliffe nfirmary, Oxfrd, OX2 6HE, England. f a risk factr and subsequent disease rates is generally shallwer than the crrected assciatin between the usual value f that risk factr during a particular perid and disease (althugh exceptins are pssible). Replicate measurements f the risk factr in a reasnably representative sample f persns in a prspective study can be used t estimate the imprtance f, and crrect fr, this "regressin dilutin" effect (6). Hwever, if the aim is t relate the disease rates t the usual risk factr levels during sme much later expsure perid, then crrectins based n remeasurements made within just a few years f baseline may nt take apprpriate accunt f the effects f within-persn variability ver mre prlnged perids. T assess the relevance f the usual levels f a risk factr during sme particular expsure perid (e.g., the secnd decade f fllw-up) t disease risk, crrectin factrs may need t be based n remeasurements made after an interval apprximately equivalent t the midpint f the relevant perid (e.g., after abut 5 years f fllw-up). This reprt describes apprpriate ways f crrecting prspective study results fr regressin dilutin. Other aims were t ) assess quantitatively the effects f regressin dilutin n bld pressure and chlesterl, 34

2 342 Clarke et al. accrding t interval f fllw-up, by using repeated measurements f these factrs during 30 years in the Framingham Study (, 8); 2) determine, fr these particular factrs, whether regressin dilutin is imprtantly different fr men and wmen r fr peple f different ages; 3) cmpare the findings frm the Framingham Study after an interval f 26 years (i.e., the apprximate midpint f the third decade f fllw-up) with thse frm the Whitehall Study f Lndn civil servants after a similar interval (9-); and 4) assess the extent t which, fr these factrs, the prgressive increase in the imprtance f regressin dilutin with increasing duratin f fllw-up may be explained by the early deaths f thse at highest risk. MATERALS AND METHODS Study ppulatins The prspective Framingham Study initially included 5,209 men and wmen frm Framingham, Massachusetts, wh were aged years when first examined between 948 and 952 (, 8). Every 2 years during 6 cnsecutive surveys, the remaining participants were invited t have their bld pressure measured and a bld sample cllected frm a frearm vein. During each visit, a physician used a standard mercury sphygmmanmeter t make tw cnsecutive recrdings f systlic and diastlic bld pressure, but nly the first f the tw measurements was used in ur analyses. (Using the average f these tw bld pressure measurements rather than just the first wuld have increased the crrelatins between measurements at different times by nly abut 0.03.) Ttal chlesterl was measured by using the clrimetric methd f Sperry (2) during the first examinatin, but the Abell- Kendall methd was used fr all subsequent measurements (3). The prspective Whitehall Study initially included 9,09 male civil servants frm Lndn, England, wh were aged years when first examined between 967 and 970 (9-). During that baseline visit, a specially trained nurse made a single bld pressure measurement n the left arm by using the Lndn Schl f Hygiene sphygmmanmeter. Systlic bld pressure was recrded at the first appearance f the arterial flw sunds and diastlic bld pressure was recrded at bth the muffling (phase V) and the disappearance (phase V) f the sunds, but nly the phase V values were used in ur analyses. During this first examinatin, bld samples were cllected frm earlbes int 2 mm glass tubing, and ttal chlesterl was measured by using a Technicn methd (4); thse values are thught t have been abut 0 percent t lw because the cllectin methd used caused dilutin f samples (0,). n 995, after an average interval f 26 years, a randm sample f 40 participants in the Whitehall Study nt knwn by the Office f Natinal Statistics (Lndn, England) t have died was selected fr resurvey (5). Seventy-three percent cmpleted a pstal questinnaire; 6 percent had their bld pressure recrded twice after 5 minutes in the seated psitin, with a 2-minute interval between readings, and bld taken frm a frearm vein at the ffice f the family physician. Whle-bld samples were mailed t the study labratry (77 percent arrived within 24 hurs and 92 percent within 48 hurs), where ttal chlesterl was measured with a Beckmann aut-analyzer (Beckman nc., Fullertn, Califrnia) by using an enzymatic methd. Transprt studies have shwn that bld chlesterl levels can be measured reliably frm samples cllected in this way (6). Statistical methds Cnsider sme adverse utcme, such as mrtality frm a certain disease during a particular time perid (the "risk perid"), whse rate f ccurrence is t be related t the "usual" level f a certain risk factr during sme particular time perid (the "expsure perid"). The risk perid may well be the same as the expsure perid, but it des nt have t be: fr example, mrtality rates during the secnd decade f fllwup culd be related t usual levels f the risk factr during the first decade. The magnitude f the regressin dilutin assciated with a particular expsure perid can be estimated either nnparametrically r parametrically frm pairs f measurements made in the same persns n different ccasins separated by an apprpriate time interval. Fr example, t infer the real assciatins between the usual level f sme particular expsure during the first decade f fllw-up and disease rates (during the first decade r sme later perid), crrectin factrs culd be based n pairs f measurements separated by abut 5 years (i.e., the length f time frm baseline t the midpint f the expsure perid). With the nnparametric methd f estimating and crrecting fr the regressin dilutin assciated with a particular expsure perid, pairs f measurements f the relevant risk factr that are separated by an apprpriate interval (e.g., abut 5 years if the expsure perid is the first decade) are subdivided int a few grups accrding t the value f just the first measurement in each pair. The range f the initial values (r) is defined as the difference between the means f these first measurements in the grups with the lwest and highest values. Even thugh the value f the secnd measurement in each pair did nt determine in which grup that pair belnged, the means f the secnd Am J Epidemil Vl. 50, N. 4, 999

3 Regressin Dilutin in Prspective Studies 343 measurements prvide unbiased estimates f the "usual" levels f the risk factr in each grup during the particular expsure perid, against which the disease rates can be cmpared. Generally, the range f these mean usual values (rj will be substantially narrwer than the range f the initial values (r^), s the rati f these tw ranges (R = rjr) will be substantially less than. This "regressin dilutin rati" prvides an assumptin-free estimate f the imprtance f regressin dilutin during the expsure perid that is valid n matter what the surces f variatin might have been ver the particular time perid (e.g., randm errr, measurement errr, selective survival, r the "hrse-racing" effect (7)) and is apprximately independent f the number f grups chsen and f the bundaries used t define these grups. Mrever, the regressin cefficient relating disease risk t the usual levels f the factr during the expsure perid can be estimated as \R times the "uncrrected" regressin cefficient relating risk t the baseline levels f the risk factr (6). Under special circumstances, "parametric" statistical methds can als be used t estimate the regressin dilutin rati. Fr example, when the variances f the recrded values at baseline and at remeasurement are similar (as fr bld pressure and chlesterl in ur study; refer t Results), the crrelatin cefficient between pairs f measurements separated by a particular interval (i.e., the "self-crrelatin") is abut the same as the rati f the ranges fr that interval (6). Estimates f the imprtance f regressin dilutin that are based n self-crrelatins tend t have slightly less randm variatin than thse based n the ratis f ranges and s may be preferred when nly a limited amunt f data is available (as in varius subgrups by gender, age, and year f first measurement in ur analyses). Hwever, since the nnparametric methd requires n assumptins abut cnstant variances, the rati f the ranges may generally be mre apprpriate than self-crrelatin cefficients fr estimating the magnitude f regressin dilutin during lnger-term fllw-up. Because measurements were made every 2 years in the Framingham Study, it was pssible t classify measurements fr each participant int multiple pairs separated by the same time interval. Fr example, t calculate the regressin dilutin rati frm measurements separated by a 6-year interval (i.e., the apprximate midpint f the first decade), up t 3 pairs f measurements per persn were cnstructed by using data frm the first (i.e., baseline) and furth (i.e., year 6) examinatins, the secnd and fifth, the third and sixth, and s n, up t the 3th and 6th examinatins. Thus, the 5,209 persns initially in the Framingham Study cntributed 44,000 pairs f measurements with a 6- Am J Epidemil Vl. 50, N. 4, 999 year interval between them fr assessment f regressin dilutin during the first decade f expsure. Pairs separated by 6- and 26-year intervals (i.e., the apprximate midpints f the secnd and third decades f expsure) were cnstructed in a similar way. (A missing value in either ne f a pair f measurements resulted in a missing value fr that pair.) T explre the influence f gender, age, and secular trends n the regressin dilutin rati, the selfcrrelatin cefficients fr bld pressure and bld chlesterl in the Framingham Study were calculated separately fr men and wmen, fr different age grups at the time f first measurement (ages 30-39, 40-49, 50-59, 60-69, and years), and fr pairs in which the first measurement was made in the first, secnd, and third decade f fllw-up (i.e., at examinatins -5, 6-0, and -5). The impact f early death and f antihypertensive medicatin use n the regressin dilutin ratis fr bld pressure and bld chlesterl was investigated by cnsidering separately thse wh survived t at least year 26 and thse wh did nt receive such treatment. Estimates f the regressin dilutin rati assciated with the third decade f fllw-up were als calculated frm the Whitehall Study by cmparing the baseline measurements made in with the repeat measurements made abut 26 years later, in 995, n the same persns. RESULTS Characteristics f the study ppulatins Table prvides the mean values f selected characteristics f 2,336 men and 2,873 wmen at baseline (year 0) and after 6,6, and 26 years f fllw-up in the Framingham Study and f 9,09 men at baseline and 243 men after 26 years f fllw-up in the Whitehall Study. The increase in mean age with fllw-up was slightly smaller than the increased duratin f fllwup because f higher mrtality amng lder persns. There was little change in mean chlesterl, height, and weight, but a mdest decline ccurred in mean diastlic bld pressure and, in the Whitehall Study, in mean systlic bld pressure. (Hwever, the abslute values f the initial chlesterl measurements in the Whitehall Study might well have been smewhat t lw; refer t Materials and Methds.) Differences n bld pressure and chlesterl ver time Table 2 shws the mean values f bld pressure and chlesterl at baseline and after 6, 6, and 26 years f fllw-up amng men in Framingham wh were aged 30-39, 40-49, and years at the baseline survey

4 344 Clarke et al. TABLE. Selected characteristics* f the study ppulatins at baseline (year 0) and at later remeasurements n the Framlngham and Whitehall studies N. f persns^ Age (years) Systlic bld pressure (mmhg) Diastlic bld pressure (mmhg) Ttal chlesterl (mml/liter) Height (m) Weight (kg) N. f paired cmparisns^ 0 2,336 2,873 44(9) 44(9) 36(20) 35(24) 86(2) 84(3) (.) (.2).72 (0.07).59(0.06) 76() 64(2) Framingham Study: year f measurement 6 2,240 2,88 50(9) 50(9) 32 (20) 34(25) 84(2) (2) 6. (.) 6.2(.2) 77() 65() 8, 25,20 6,929 2,592 59(8) 59(8) 38(2) 40 (24) 82() 82() 6.0(.) 6.5(.2) 77(2) 65(2) 9,874 3,75 26,458 2,82 67(8) 68(8) 35(9) 37(2) 78 (0) 76 (0) 5.6(.0) 6.2(.).70(0.07).57 (0.06) 77(2) 64(2) 3,030 4,492 Whitehall Study: year f measurement 0 9,09 52(7) 36(2) 85(4) 5. (.2).76(0.07) 76() 26t (7) 3 (7) 8 (2) 5. (.3).73(0.07) * Values expressed as ttal number r as mean (standard deviatin). t Mean values after 26 years in the Whitehall Study are based n respnses by 243 persns t a pilt resurvey. X Each persn in the Framingham Study was t be seen biennially fr 30 years and s culd cntribute up t 3 paired cmparisns with a 6-year interval between measurements and up t 8 and 3 paired cmparisns with intervals f 6 and 26 years, respectively. (left side f table 2, all men; right side, all men with these measurements frm all f these resurveys). Either fr all men initially screened at baseline r fr just thse with measurements at all surveys, cmparisns can be made between peple f different ages at the same survey r between peple in the same birth chrt at different surveys. Hwever, nne f these cmparisns prvides a simple descriptin f the ways in which a persn's bld pressure r chlesterl typically changes with age. Fr example, crss-sectinal cmparisns f all men wh attended a particular survey (i.e., within clumns in table 2) shwed sme differences between thse in different age grups, but such cmparisns were between different generatins with different life experiences rather than between the same persns. Als, the prir effect f selective mrtality amng thse with high bld pressure r chlesterl wuld have been greater fr thse aged years at the time f the survey than fr thse aged years (particularly if, as in the right half f table 2, attentin was restricted t men still alive at year 26 f fllw-up). 76() 243 Cmparisns within birth chrts f all wh attended the baseline survey with thse wh attended later surveys (i.e., within rws in the left half f table 2) might likewise have been biased by selective remval f thse with high bld pressure r chlesterl. This bias can be avided by restricting such cmparisns t thse persns wh survived t attend all fur surveys (i.e., within rws in the right side f table 2). Hwever, even these lngitudinal cmparisns amng the same persns might be biased by changes in measurement techniques (including subject habituatin) and by differences ver time in risk factr management. Thus, in terms f the natural histry f bld pressure, it was difficult t interpret the bservatin that amng the,09 persns wh attended all surveys, systlic bld pressure decreased slightly between years 0 and 6, increased by an average f 8 mmhg between years 6 and 6, and then remained cnstant between years 6 and 26, whereas diastlic bld pressure hardly changed between baseline and 6 years and had then decreased by an average f 5 mmhg at Am J Epidemil Vl. 50, N. 4, 999

5 Regressin Dilutin in Prspective Studies 345 TABLE 2. Effect f age n bld pressure and chlesterl at baseline (year 0) and at 6,6, and 26 years f fllw-up* amng all men n the Framlngham Study and amng thse men with these measurements frm all fur f the resurvey visits N. f men Age at baseline (years) O N. f men Age at baseline (years) N. f men Age at baseline (years) All men n the Framlngham Study: year f measurement 0 2, , , Systlic bld pressure (mmhg), , , Diastllc bld pressure (mmhg), ,69 8, Ttal chlesterl (mml/liter), , ' Mean values at each fllw-up visit are shwn fr each age grup. year 26. Likewise, amng thse with measurements frm all surveys, it was difficult t interpret either the average increase f 0.5 mml/liter in bld ttal chlesterl by year 6 r the later 0.6 mml/liter decrease. These uncertainties abut abslute values and trends d nt, hwever, affect the epidemilgic cmparisns f risk between persns f the same age at the same survey, which were the chief cncern f this reprt. Shrinkage f ranges with ncreasing intervals between measurements n cntrast t the relatively mdest changes in the verall mean values f bld pressure and chlesterl measurements that ccurred ver time in the Framingham Study (table 2), large artifactual differences were bserved in the mean values at subsequent fllw-up f persns subdivided int five similar-sized grups accrding t the value f just the first f each pair f measurements (figure ). n general, there was a sharp cnvergence by year 2 due t the cmbined effects f measurement errr and f shrt-term fluctuatins in the baseline measurements, which was fllwed by a mre mdest cnvergence ver the next few decades. Fr example, the mean systlic bld pressure f persns wh were in the tp fifth initially (i.e., thse with a systlic bld pressure value f 46 mmhg r mre at the first measurement) declined frm 62 Subset with all (ur measurements: year f measurement 0, , , , , , , , mmhg at year 0 t 56 mmhg after 2 years, 55 mmhg after 6 years, 53 mmhg after 6 years, and 47 mmhg after 26 years (figure and left side f table 3). Similarly, the mean systlic bld pressure f persns in the bttm fifth initially (i.e., thse with a value f less than 8 mmhg at the first measurement) increased frm mmhg at year 0 t 7 mmhg after 2 years, 20 mmhg after 6 years, 26 mmhg after 6 years, and 30 mmhg after 26 years. The abslute difference, r range, between the mean values in the tp and bttm grups declined thrughut the three successive decades f fllw-up frm 5 mmhg at year 0 t 35 mmhg after 6 years, 27 mmhg after 6 years, and nly 8 mmhg after 26 years. Similarly, fr diastlic bld pressure and ttal chlesterl, there was a sharp change after 2 years, fllwed by mre mdest shrinkage in the abslute differences between the mean values in the tp and bttm baseline-defined grups. After an interval f 26 years, the changes in these ranges were similar in the Framingham and Whitehall studies (table 3). Changes in regressin dilutin ratis with increasing intervals between measurements The cnvergent patterns in figure (and table 3) illustrate the prgressive increase ver time in the imprtance f regressin dilutin fr certain measurements. Table 4 prvides nnparametric estimates f the Am J Epidemil Vl. 50, N. 4, 999

6 O 0) Systlic Bld Pressure nitial VtllKS (mmhg) 46+ S-4S Dlastllc Bld Pressure tntfld Viliwi (mmhg) O Bld Chlesterl (D 0J S 70- < ' Ring*: (mmhg) 60- Rang*: 3a 8 2 h (mmhg) nterval between paired measurements (years) nterval between paired measurements (years) nterval between paired measurements (years) 8 RGURE. Serial shrinkage f the ranges fr bld pressure and chlesterl values in grups defined by the first f a pair f measurements in the Framingham Study. Mean values ini- ^ daily and at subsequent fllw-up are pltted fr persns subdivided int five similar-sized grups accrding t the value f just the first f each pair f measurements. The size f each "_! square is prprtinal t the quantity f statistical infrmatin available, and the 95% cnfidence intervals fr the tp and bttm grups are represented by the vertical bars. Mean val- < ues in the tp and bttm grups, and the abslute differences (ranges) between them, are given at year 0 (i.e., the initial measurement f the pairs) and at years 6,6, and 26 (i.e., the t apprximate midpints f the first, secnd, and third decades, respectively, after the initial measurement).

7 Regressin Dilutin in Prspective Studies 347 TABLE 3. Mean values f Md pressure and chlesterl after different ntervals between pairs f measurements amng men n the Framlngham and Whitehall studies Framlngham Study: years between measurements Systlic bld pressure (mmhg) 26 Whitehall Study: years between measurements 0 26 N. f measurements 8,* 8, 9,874 3, Baseline fifths V V Difference (V-l) N. f measurements Baseline fifths V V Difference (V-l) N. f measurements Baseline fifths V V Difference (V-l) 8,* ,03* Diastllc bld pressure (mmhg) 8, , Ttal chlesterl (mml/llter) 2, * Values fr the Framingham Study are based n the means f multiple pairs f measurements with the same nterval between measurements, gruped accrding t the value f the first measurement in each pair (refer t Materials and Methds). The values at year 0 are the means f the first measurements fr thse pairs with secnd measurements als available after a 6-year interval (and wuld differ slightly if based nly n pairs with a 6- r 26-year interval). 5, , , regressin dilutin rati derived frm the rati f the range f values in the baseline-defined grups after a particular interval t the range at baseline (refer t Materials and Methds). Fr bld pressure and chlesterl, the regressin dilutin ratis became substantially mre extreme with increasing duratin f fllwup, whereas the ratis fr height and weight remained clse t (as might be expected, since these latter measures invlve substantially less within-persn variability). Table 4 als shws parametric estimates f the regressin dilutin ratis derived frm crrelatin cefficients between pairs f measurements separated by a particular interval ("self-crrelatins"; refer t Materials and Methds). n general, the nnparametric and parametric methds yielded fairly similar results. Fr example, fr systlic bld pressure in the Framingham Study, the regressin dilutin rati assciated with measurements made 6 years apart (i.e., the apprximate midpint f the secnd decade f expsure) was estimated t be 0.52 by using the rati f the ranges and 0.45 by using the self-crrelatin. With either methd, this value f abut 0.5 implies that the regressin cefficient relating risk in the secnd decade r later t a baseline measurement f systlic bld pressure is nly abut half as steep as the crrected regressin cefficient relating this risk t the usual systlic bld pressure during the secnd decade. Gender, age, and the regressin dilutin rati Fr systlic bld pressure, diastlic bld pressure (nt shwn), and bld chlesterl, the decrease in the Am J Epidemil Vl. 50, N. 4, 999

8 348 Clarke et al. TABLE 4. Nnparametric and parametric estimates f regressin dilutin fr bld pressure, chlesterl, height, and weight amng men n the Framlngham and Whitehall studies Framlngham Study years between measurements 6 6 Systlic bld pressure 26 Whitehall Study: years between measurements 26 Rati f fllw-up t baseline ranges Crrelatin with initial measurement Rati f fllw-up t baseline ranges Crrelatin with initial measurement Rati f fllw-up t baseline ranges Crrelatin with initial measurement Rati f fllw-up t baseline ranges Crrelatin with initial measurement Rati f fllw-up t baseline ranges Crrelatin with initial measurement regressin dilutin rati with increasing duratin f fllw-up was similar fr men and wmen in the Framingham Study (figure 2). Fr example, the regressin dilutin ratis derived frm the self-crrelatin cefficients fr men decreased frm 0.68 after 6 years t 0.53 after 6 years t 0.46 after 26 years; in wmen, they decreased frm 0.68 t 0.52 t 0.42, respectively. A similar decrease in the regressin dilutin ratis with increasing duratin f fllw-up was als bserved in the five 0-year age grups at baseline (figure 3). Fr example, the regressin dilutin rati estimates fr chlesterl after an interval f 6 years were 0.7 fr thse aged years, 0.65 fr thse aged years, 0.69 fr thse aged years, 0.70 fr thse aged years, and 0.7 fr thse aged years. Similar patterns, but with slightly mre randm variatin, were btained by using regressin dilutin ratis derived frm the ratis f ranges (data nt shwn). Secular trends and the regressin dilutin rati Diastlic bld pressure Chlesterl Height Weight Fr systlic bld pressure, the regressin dilutin rati derived frm the crrelatin cefficient between measurements made at 6-year intervals was 0.72 if the first f the tw measurements was made in the 950s (visits -5), 0.65 if made in the 960s (visits 6-0), and 0.5 if made in the 970s (visits -5). This finding suggests that there may have been a smewhat lwer signal-t-nise rati during the 970s than during the 950s (with, in this cntext, the signal being the extent t which peple's usual bld pressures really differ frm each ther, and the nise being the extent t which particular measurements f bld pressure are liable t differ frm that persn's usual bld pressure). By cntrast, there was n such trend in the regressin dilutin ratis fr bld chlesterl: self-crrelatin cefficients between measurements made at 4-year intervals were 0.74 if the first f the tw measurements was made in the 950s, 0.72 if made in the 960s, and 0.7 if made in the 970s. (Chlesterl was nt measured at visits, 2, r 6, s estimates f the regressin dilutin ratis fr 6-year intervals culd nt be derived fr the 970s, but they were 0.72 fr the 950s and 0.68 fr the 960s.) Early deaths, treatment, and the regressin dilutin rati Table 5 shws the extent t which estimates f the regressin dilutin rati during the third decade f fllw-up in the Framingham and Whitehall studies may have been influenced by differential mrtality acrss the baseline-defined grups. The mean values at baseline fr the ttal study ppulatin were cmpared with the mean values at baseline fr thse persns wh were still alive after 26 years. Fr bld chlesterl, these mean values were similar in the tp grup and in the bttm grup, whereas fr systlic bld pressure the range was smewhat narrwer amng the survivrs. Am J Epidemil Vl. 50, N. 4, 999

9 S! 8 t CO c j0- Systlic Bld Pressure X Bld Chlesterl O S T CD CO 3 g ' " nterval between paired measurements (years) nterval between paired measurements (years) T3 CO FGURE 2. Serial changes in the regressin dilutin ratis fr systlic bld pressure and Wd chlesterl with ncreasing duratin f fllw-up amng men and wmen in the Framingham Study. Parametric estimates f regressin dilutin ratis, derived frm the crrelatin cefficients between pairs f measurements in persns (self-crrelatins), are pltted against the intervals between measurements. Symbls and cnventins as shwn in figure. a. a> en 2

10 Q.00-i sa- Systlic Bld Pressure Sc JO c M! (Ml Bld Chlesterl u 0 3- CD a Midpint f age at subsequent measurements (years) Midpint f age at subsequent measurements (years) <O FGURE 3. Serial changes in the regressin dilutin ratis fr systlic bld pressure and bld chlesterl fr participants at different ages in the Framingham Study. Parametric estimates f the regressin dilutin ratis, derived frm the crrelatin cefficients between pairs f measurements in persns (self-crrelatins), are pltted against the estimated ages at the times f remeasurement. Symbls and cnventins as shwn in figure.

11 Regressin Dilutin in Prspective Studies 35 TABLE 5. Mean values f baseline measurements: nfluence f selective lss due t earty deaths n systlic bld pressure and chlesterl amng men n the Framingham and Whrtehal studies Framingham Study Whitehall Study Ttal ppulatin Survivrs at year 26 Ttal ppulatin Survivrs at year 26 Bld pressure (mmhg) N. f men 2,336,458 9,03 9,9 Baseline fifths V V Difference (V-l) Ttal chlesterl (mml/ltter) N. f men Baseline fifths V V Difference (V-l), Hwever, these differences between the ttal ppulatin and the survivrs were much less extreme than the cnvergence in the ranges shwn in table 3, which suggests that selective mrtality f persns with high bld pressure r chlesterl des nt accunt fr much f the shrinkage ver 26 years. n the Framingham Study, any treatment with a diuretic r ther antihypertensive medicatin was recrded frm year 6 nward. The prprtin f survivrs wh received such treatment increased thrughut the fllw-up perid, but treatment did nt materially affect the prgressive decrease in the regressin dilutin rati fr bld pressure with increasing duratin f fllw-up. Fr example, the estimates fr systlic bld pressure, derived frm self-crrelatins, f 0.64,0.50, and 0.37 fr all survivrs after 6, 6, and 26 years, respectively, were similar t the crrespnding values f 0.6, 0.47, and 0.33 fr thse survivrs wh did nt receive any antihypertensive therapy. Other factrs and the regressin dilutin rati Althugh the multiple pairs f measurements frm the Framingham Study are nt independent, estimates f the regressin dilutin rati derived frm these multiple pairs were similar t thse btained when the baseline measurement was always the first f a relevant pair (i.e., when the data frm any ne visit were Am J Epidemil Vl. 50, N. 4, , , used nly nce). Fr example, fr systlic bld pressure, the regressin dilutin rati derived frm the self-crrelatin at 6 years was 0.7 when year 6 was cmpared with baseline fr 2,009 men, whereas the rati was 0.63 when btained frm the 8, pairs with a 6-year interval between measurements (table 4). Estimates f the regressin dilutin rati were als largely unaffected by the change in the methd used t measure chlesterl after baseline in the Framingham Study. Fr example, amng men, the crrelatin between pairs f measurements with a 6-year interval between them was 0.69 fr year 6 cmpared with baseline (the nly examinatin fr which the Sperry methd (2) was used; refer t Materials and Methds) and 0.7 fr year 8 cmpared with year 2. Similarly, the estimates f the regressin dilutin rati were unaffected by the initial decrease in mean systlic bld pressure in the Framingham Study (table 2). Fr example, amng men, the crrelatin between pairs f measurements with a 6-year interval between them was 0.7 fr year 6 cmpared with baseline and 0.68 fr year 8 cmpared with year 2. DSCUSSON The present analyses addressed the extent t which within-persn variability in risk factr measurements distrts assessment f the strength f the assciatin 3.4

12 352 Clarke et al. between the usual level f a risk factr during sme particular expsure perid and the incidence f disease during the same r a later perid. Fluctuatins in the values f risk factrs may be due t measurement errr and t shrt-term bilgic variability (such as diurnal r seasnal variatin), r they may be due t lngerterm systematic changes. The effects f the frmer can be limited by repeating baseline measurements several times and by cntrlling the cnditins under which measurements are taken. Hwever, underestimatin f the strength f the assciatin f the usual level f a risk factr during sme later expsure perid with disease will still ccur unless replicate measurements made sme years later are used t crrect directly fr regressin dilutin. The effects f shifts in mean bld pressure r chlesterl due t lng-term physilgic changes (such as the prgressive increase in systlic bld pressure with age r the decrease due t the nset f disease r t the effects f treatment) are included in what is referred t as "regressin dilutin," as are the effects f selective mrtality. n ur analyses f the Framingham and Whitehall studies, the prgressively smaller ranges f mean values in the baseline-defined grups fr bld pressure and chlesterl with lnger intervals f fllw-up (table 3) indicate that the effects f within-persn variability becme prgressively mre imprtant with lnger fllw-up. t has been suggested that this finding might be due largely t selective death f thse at highest risk (8), but analyses restricted t survivrs in these studies indicated that nly a small fractin f the shrinkage f these ranges culd have been due t selective mrtality (and, in any case, this wuld still need t be allwed fr in the way demnstrated abve). Mrever, we fund that unless apprpriate crrectins are made fr the regressin dilutin assciated with particular expsure perids, the strength f assciatins f disease with usual bld pressure r chlesterl levels might be underestimated by abut ne-third during the first decade, ne-half during the secnd decade, and tw-thirds during the third decade f expsure. The crrectins that are needed are independent f any assumptins abut the cnstancy f relative risks ver time r abut the bilgic mechanisms by which expsures affect disease (and are nt much affected by age r gender). Bth the nnparametric and parametric statistical methds that have been used t estimate the magnitude f the regressin dilutin rati shuld prvide similar results when the variances f the values recrded at baseline and at remeasurement are similar. Hwever, since the nnparametric methd based n the rati f ranges requires n such assumptins, it may be mre suitable fr lnger intervals f fllw-up. Apprpriate adjustment fr regressin dilutin in prspective studies requires remeasurements t be available at intervals during fllw-up frm at least a subsample f the survivrs. f particular studies lack such data, then applying the present results frm the Framingham and Whitehall studies fr bld pressure and chlesterl may prvide reasnable apprximatins fr the crrectins needed fr each f the first three decades f expsure. ACKNOWLEDGMENTS This study was supprted by grants frm the British Heart Fundatin and Medical Research Cuncil, Lndn, England. Dr. Paul Srlie frm the Natinal Heart, Lung, and Bld nstitute f the Natinal nstitutes f Health, Bethesda, Maryland, facilitated use f data frm the Framingham Study. Drs. David Len and Astrid Fletcher facilitated use f data frm the Whitehall Study and prvided helpful cmments, as did Drs. Richard Dll and Cathie Sudlw. Paul Sherliker and Paul Appleby prduced the figures. REFERENCES. Grdn T, Srlie P, Kannel WB. 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