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6.

Pericak-Vance
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25.

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W A statistical distribution of wide applicability. *J Appl Mech.* 1951;18293- 297

Original Article

May 2004

Ara S. Khachaturian, PhD^{}; Christopher D. Corcoran, PhD^{}; Lawrence S. Mayer, MD^{}; et al
Peter P. Zandi, PhD^{}; John C. S. Breitner, MD^{}; Cache County Study Investigators^{}

Author Affiliations
Article Information

From Khachaturian and Associates Inc, Potomac, Md (Dr Khachaturian);Center for Epidemiologic Studies and Department of Mathematics, Utah StateUniversity, Logan (Dr Corcoran); Alzheimer's Research Center, Banner GoodSamaritan Medical Center, Phoenix, Ariz (Dr Mayer); Department of Mental Health,Bloomberg School of Public Health, The Johns Hopkins University, Baltimore,Md (Drs Mayer, Zandi, and Breitner); Geriatric Research Education and ClinicalCenter, Veterans Affairs Puget Sound Healthcare System, Seattle, Wash (DrBreitner); and Department of Psychiatry and Behavioral Sciences, Universityof Washington, Seattle (Dr Breitner).

Arch Gen Psychiatry. 2004;61(5):518-524. doi:10.1001/archpsyc.61.5.518

Abstract

**Background**
The incidence of Alzheimer disease (AD) increases strongly with age,
but little is known about the cumulative incidence of AD over a lifetime of
100 years, or its relationship to the polymorphic *APOE* locus
that encodes apolipoprotein E. *APOE* is a strong genetic
risk factor for AD

**Objectives**
To estimate the occurrence of AD as a function of age and number of *APOE* ϵ4 alleles; and to explore evidence for heterogeneity
of AD risk related to*APOE* genotype and to other sources.

**Design**
Nonparametric and parametric survival analyses of AD incidence in prospective
longitudinal study.

**Setting and Participants**
A total of 3308 elderly residents of Cache County, Utah.

**Main Outcome Measures**
Cumulative incidence of AD; in mixture models assuming susceptible and
nonsusceptible individuals, the proportion of individuals not susceptible
to AD at any age.

**Results**
Models that assumed a proportion of invulnerable individuals provided
strongly improved fit to the data. These models estimated the 100-year lifetime
incidence of AD at 72%, implying that 28% of individuals would not develop
AD over any reasonable life expectancy. We confirmed the acceleration of AD
onset in individuals with 1 or, especially, 2 *APOE*, *ϵ4 alleles*but observed no meaningful difference in
100-year lifetime incidence related to number of ϵ4 alleles.

**Conclusions**
The *APOE* ϵ4 allele acts as a potent risk
factor for AD by accelerating onset. However, the risk of AD appears heterogeneous
in ways independent of APOE.Some individuals seem destined to escape AD, even
over an extended lifespan. Their relative invulnerability may reflect other
genes or environmental factors that can be investigated.

The incidence of Alzheimer disease (AD) doubles with each 5 years ofage through 90 years,^{1}^{,2} so thatthe prevalence of AD may reach 45% or higher after age 85 years.^{3} Lessis known about the proportion who will develop AD over a theoretical lifeexpectancy of 100 years or more. The Framingham study estimated the unadjustedcumulative incidence of AD at 43.0% (men) and 48.3% (women) by age 99 years,^{4} while similar analyses from East Boston, Mass, suggested49.6% by age 90 years.^{5} Neither of these studiesincluded many observations after age 90 years, however, nor were they ableto examine the lifetime incidence of AD in relation to genotype at *APOE*, the polymorphic genetic locus for apolipoprotein E.^{6}^{,7}

The Cache County, Utah, population affords an unusual opportunity toexamine these questions. With 5092 initial respondents, the Cache County Studyis among the largest single-population investigations of the occurrence ofAD. The population is one of the longest lived in the United States^{8} and includes some 719 individuals older than 85 yearsand 249 individuals 90 years and older. Low rates of chronic diseases associatedwith tobacco and alcohol use facilitate the detection and differential diagnosisof dementia among its oldest members.^{9} Responserates are high,^{10} and 97% of the populationhas donated buccal DNA for analysis of *APOE* genotype.These attributes enabled us to analyze the lifetime incidence of AD and otherdementias in relation to *APOE* genotype by fittingboth nonparametric and parametric survival models to the onset of AD.

METHODS

STUDY POPULATION AND DATA GATHERING METHODS

Between 1995 and 1997, the Cache County Study invited participationof all elderly county residents 65 years and older, enrolling 5092 individuals(90%). *APOE* genotype was determined by restrictionisotyping of buccal DNA.^{10} A multistage screeningand assessment protocol for dementia ("wave I")^{10}^{,11} beganwith the modified Mini-Mental State Examination^{12} or,for those unable to participate, a brief informant questionnaire to identifythose with apparent cognitive difficulty.^{13} Wethen administered the informant-based Dementia Questionnaire^{14} tocollateral informants for these impaired participants, and for all membersof a stratified subsample of 960 individuals (19% of all participants) weightedto include the oldest elements of the population and those with 1 or 2 copiesof the *APOE* ϵ4 allele. Clinical assessment (CA)of this 19% subsample (regardless of their results on the modified Mini-MentalState Examination and the Dementia Questionnaire) and of screen-positive individualsincluded the following: (1) a brief medical history and examination; (2) achronologic history of cognitive symptoms; (3) a structured neurologic examination(all administered by trained nurses); and (4) a 1-hour battery of neuropsychologicaltests. After review of these data, 86% of living individuals who receivedworking diagnoses of dementia were examined by a geriatric psychiatrist orneurologist and referred for laboratory studies including neuroimaging. Eighteenmonths later, we reexamined surviving participants whose initial evaluationhad suggested dementia or any substantial cognitive impairment. A consensusconference of experts in neurology, neuropsychology, and geriatric psychiatrythen assigned final diagnoses. These experts also reevaluated previous estimatesfor age at onset, defined as the year when participants unambiguously met *DSM-III-R* criteria for dementia.^{15} Thesemethods identified 340 individuals with dementia prevalent at their initialinterview.

Between 1998 and 2000 we applied similar screening procedures and anidentical CA protocol among 3396 (83%) of the 4104 living Cache County Studyparticipants who had not received wave I diagnoses of dementia ("wave II").These procedures identified 152 instances of incident dementia, and another15 individuals with dementia prevalent at wave I who had escaped detectionby our earlier screening procedures. Adding 33 individuals with incident dementiadiscovered in the later stages of wave I yielded a total of 185 individualswith incident dementia. Of these, 123 (122 with known genotype at *APOE*) received diagnoses of definite, probable or possible AD.^{16} A remaining 3123 participants completed the waveII study procedures per protocol and were judged to be free of dementia. Asin wave I, we administered all screening and assessment procedures as wellas a CA to the 441 surviving members of the 19% subsample (excluding thosewith dementia at wave I). Comparing these screening results with CA findings,we estimated the sensitivity of the wave II dementia screening proceduresat 86%.^{17}

ANALYTIC APPROACH

Nonparametric Models of Disease-Free Survival

We used the Kaplan-Meier product-limit method^{18} toestimate the probability of disease-free survival by age in the 3-year intervalbetween waves I and II. This method considers each participant's person-yearcontribution during the follow-up interval, and then combines these contributionsto yield estimates of cumulative disease-free survival through any specifiedyear of age. Because the outcome of interest was onset of AD, we censoredobservations on individuals who developed other types of dementia from theiryear of onset onward. The crude cumulative survival *S(t)* from age 65 years to age *t* (conditioned ondisease-free survival to the beginning of the observation period) may be estimatedas

where *y _{j}* is the number of person-yearsof observation at age

We adjusted the foregoing formula to account for the refusal of 10%of wave II subjects to participate in a requested CA, and also to accountfor the estimated sensitivity of our screening procedures (86%) in identifyingindividuals appropriate for referral to CA. This adjustment considered separatelyonsets that occurred within subsample (*e′ _{j}*)and others (

We considered the problem of response bias (disproportionate occurrenceof dementia among nonrespondents) by recalculating survival estimates fromequation 1 modified to reflect an extreme assumption of doubled occurrenceof dementia among nonresponders as compared with responders. An extensionof the adjusted Kaplan-Meier approach was then used to calculate empiricalsurvival curves for strata of the population bearing 0, 1, or 2 ϵ4 allelesat *APOE.*

Parametric Models of Disease-Free Survival

The foregoing, nonparametric approach does not consider whether thepopulation may be heterogeneous with regard to susceptibility of developingAD, ie, whether there are definable subpopulations with substantially differentrisk profiles. Standard parametric survival analyses also assume homogeneityof risk, allowing only for random differences in age-specific risk of AD.Thus, they model the onset of AD under the assumption that its probabilityis represented by a single distribution so that the hazard of AD onset increaseswithout bound as age increases. Equivalently, the entire population must developAD if its members live long enough, and the probability of disease-free survivalapproaches zero by some (perhaps very) late age.

An extension of this approach permits testing of the assumption of homogeneityby embedding the above single-distribution model in a more complex frameworkthat posits heterogeneity in susceptibility. In its simplest form, such arevised framework postulates the existence of 2 subpopulations, one with aproportion ρ of individuals susceptible to AD and the other with a complementaryproportion 1 − ρ of people who will never fall ill no matter howlong they live. The probability distribution for disease onset by age in thecorresponding mixtures distribution is the sum of the distributions for the2 subpopulations, the standard onset distribution applying only to the susceptiblesubpopulation. Conventional modeling techniques are then used to estimate ρas well the parameters that characterize the age distribution of onsets inthe susceptible subpopulation (if ρ = 1, then the mixture distributionreduces to the more familiar single-distribution model). One may also defineadditional subpopulations by their number of *APOE* ϵ4alleles, estimating the distribution of onsets for the mixture distributionthat combines these subpopulations. Still more complex formulations are alsopossible, but their drawbacks are substantial (see the "Comment" section).

Following this approach, we used the Weibull distribution to model theprobability of AD onset as a function of time *t,* hereas years of participant age. This distribution is used widely in epidemiologicand other types of time-to-event analyses, to model the onset of disease.^{19} Its probability density function *f(t)* is written as *f(t)* = λ*t ^{(λ−1)}exp*[(

Being more flexible than the exponential distribution (a special caseof the Weibull where λ = 1), the Weibull model allows for hazards thatmonotonically increase with age when λ>1 or decrease when λ<1.As with other standard distributions, when λ>1 the Weibull hazard increasesceaselessly with increasing *t*, implying that thehazard (incidence) of AD increases without bound. In other words, if an individuallives long enough, he or she will inevitably develop AD.

A useful generalization of the Weibull function adds a second parameter *a* that introduces scale but does not otherwise alter theshape of the onset probability density. Our analyses used this form, whichmay be written as follows:

(2) *f*(*t*) = (λ/α)(*t*/α)^{(λ−1)}*exp*[(−*t*/α)^{λ}].

Our first analyses compared the fit to the Cache County incidence dataof the above 2-parameter Weibull model vs a 3-parameter model that consideredthe population as comprising a proportion ρ susceptible to AD and a complementaryproportion of nonsusceptible individuals. We fitted these parametric modelsby means of maximum likelihood estimation, which is fully efficient (it achievesmaximum inference theoretically available from the data) and generates asymptoticallyunbiased minimum variance estimators of the distribution's underlying parameters.Maximum likelihood estimation requires a "likelihood equation," which yieldsthe likelihood (probability after the fact) of each observation under thespecified set of parameters. Because there are many such independent observations,the likelihood over the entire data set with a given set of parameters isthe product of the individual likelihoods. Varying the likelihood equation'sparameters iteratively yields a unique set of parameters with the highest(maximum) likelihood value for the data set. This operation is typically simplifiedby calculating the natural logarithm of the individual likelihoods and summingthe individual log-likelihoods to search for the unique set of parametersthat yields the maximum log-likelihood. Using log-likelihoods affords thefurther advantage of allowing the use of a likelihood ratio χ^{2} testfor nonchance improvement in the fit of more complex models with larger numbersof parameters (this derives from the fact that −2 times the differencein the log likelihoods under the less complex vs the more complex model isasymptotically distributed as a χ^{2} distribution with degreesof freedom equal to the difference in the number of parameters in the 2 models).

We used PROC NLIN in SAS (version 8; SAS Institute Inc, Cary, NC) tocalculate maximum likelihood estimation parameters in models of increasingcomplexity, using a number of assumptions and procedures that we note here:(1) Although the likelihood equations were written as if they were continuous,we did not have continuous data. Instead, we had onsets dated to the nearestyear of chronologic age. Therefore, we calculated likelihoods as if they werestep functions with integer intervals, ie, we dealt with annualized discrete-timeprobabilities. (2) For each individual year of observation, the likelihoodfunction was conditioned on the participant having survived free of diseaseuntil the specified age. This conditioning is needed to account for the existenceof other individuals born in the same year who might have experienced earlierdisease onsets. We would have no knowledge of such events, so the availabledata are "left-truncated." (3) Each person-year of observation up to and includinga year containing an onset was regarded as independent of each other yearof observation. Therefore, the likelihood calculations considered each suchyear individually. Specifically, individuals who entered the 3-year observationwindow and remained free of disease for the entire time contributed 3 independentannual observations; other individuals with disease onset in the third yearof the window also contributed 3 observations (2 disease free and 1 with anonset), but those who developed AD in the second year contributed only 2 yearsof observation, etc. In this sense, the available data were also "right-censored."(4) The likelihood expressions differed for observation years that includedan onset vs those that did not. For years with an onset, the likelihoods werewritten as the (annualized) probability density of onset within the participant'syear of age, conditioned on disease-free survival up to the age of observation.This is equivalent to the discrete annualized hazard of onset in the statedyear, and may be written as follows:

(3) *H*(*t*) = *f*(*t*)/[1−*F*(*t*−1)],

where *f*(*t*) is theprobability density function at age *t* as describedby equation 2, and *F*(*t*−1)is the cumulative probability of onset (using the same distribution) throughall ages before *t.* For those who survived an observationyear free of disease, the likelihood was written as the complement of theprior expression. (5) In mixture models that included a parameter ρ describingthe proportion of susceptible individuals, we assumed that all individualswith an AD onset were susceptible. By contrast, those with no onset mighthave been members of the nonsusceptible subpopulation, or they might havebeen susceptible but have escaped disease onset in the year of observation(ie, they were "destined" to develop AD at a later age). Therefore, the likelihoodexpression for affected individuals was written as ρ · *H*(*t*) and the likelihood for nonsusceptibleindividuals was (1 − ρ) + {ρ · [1 − *H*(*t*)]}, which reduces to 1 − ρ · *H*(*t*), the complement of the priorexpression. (6) As is exemplified in the last point, the value of the likelihoodexpressions for disease onset or escape at age *t* mustsum to 1; this satisfies the logical requirement that a specified individualeither did or did not experience an onset in his or her *t*th year.

Following a similar approach, we also constructed and evaluated morecomplex formulations that estimated different Weibull parameters λand scale parameters α for individuals with 0, 1, or 2 ϵ4 allelesat *APOE*, and still more elaborate models that estimatedseparate Weibull parameters along with separate estimates of ρ in thosewith different numbers of ϵ4 alleles.

RESULTS

Table 1 presents *APOE* genotypes and demographic characteristics of the analysis poolof 3308 individuals who contributed 10 541 person-years of risk. Figure 1A displays the product-limit estimateswith and without adjustment for incomplete ascertainment. Figure 1B displays the (unadjusted) product-limit graphs for participantswith 0, 1, and 2 ϵ4 alleles at *APOE*, showingthe familiar acceleration of AD onsets in those with 1 or, particularly, 2ϵ4 alleles. The pooled plots of Figure1A corroborate our prior analysis^{1} suggestinga decline in AD risk as measured by the hazard after the mid-90s; they suggesta relaxation in the rate of new disease in 122 person-years of observationafter age 93 years and an absence of incident AD cases in 16 person-yearsafter age 97 years. Figure 1A alsoshows that adjustment for incomplete ascertainment produced a relatively modestchange in the estimate of 100-year disease-free survival: 0.19, with 95% confidenceinterval of 0.05 to 0.33 vs 0.25 (95% confidence interval, 0.06-0.44). Althoughnot shown, the assumption of double rates of dementia among nonrespondersyielded a cumulative survival of 0.10 (95% confidence interval, 0.03-0.18).

Table 2 shows the maximumlikelihood estimation parameter estimates (with standard errors) for the 4different parametric models as suggested in the "Analytic Approach" subsectionof the "Methods" section. Model 1 assumes homogeneity, ie, the entire populationis susceptible or, equivalently, ρ = 1, with onset age distributed accordingto a 2-parameter Weibull formulation. Model 2 assumes that the populationincludes 2 subpopulations, one of susceptible persons in proportion *ρ*, and the balance of nonsusceptible individuals. Forthe former subpopulation, onset age has a Weibull distribution with scaleand location parameters as indicated. The table shows that this 3-parametermodel with a mixture parameter ρ yields a considerably improved log likelihood(*P*<.001). Figure2 depicts models 1 and 2, along with the empirical Kaplan-Meiersurvival estimates. Model 2 estimates ρ at 0.74; ie, about three fourthsof the population appear to be susceptible.

Model 3 (Table 2) includesa mixture parameter ρ but also estimates separate shape parameters λand scale parameters α for each *APOE* stratum.The log likelihood of this 7-parameter model is thereby improved substantiallyover the previous 3-parameter formulation (χ^{2}_{4} =124.2, *P*<.001). Figure 3 shows this expanded model, along with empirical Kaplan-Meiersurvival graphs for the 3 *APOE* strata. The 3 shapeparameter estimates are similar, but the scale parameters vary distinctly,reflecting acceleration in rate of onset for the groups with 1 or, especially,2 *APOE* ϵ4 alleles. This model estimates themixture parameter ρ at 0.72, essentially unchanged from model 2's valueof 0.74.

Finally, model 4 estimates separate mixture parameters for each of the3 *APOE* groups. This model therefore estimates 9 uniqueparameters, including not only distinct Weibull parameters λ and αfor the 3 groups but also 3 corresponding mixture parameters ρ. Predictably,the added parameters in the model improve the likelihood value (ie, the fitto the data), but the improvement is modest, and the likelihood ratio χ^{2} test suggests that this improvement is well within the range expectedby chance (χ^{2}_{2} = 2.4, *P* =.32). Under the principle of parsimony, model 3 thus appears to provide thebest description of disease onsets in the data. Even the large Cache Countysample is therefore unable to provide evidence that *APOE* affects the proportions of susceptible and nonsusceptible individualsin the population. Instead, its influence appears to reside primarily in itsinfluence on timing of AD onset.

COMMENT

These analyses support our previous observation^{1}^{,20} that *APOE* genotype primarily influences *when,* and not *whether,* individuals will developAD. They also provide evidence that the Cache County population is heterogeneousin its vulnerability to AD, and that the onset of dementia is not an inevitableconsequence of aging. Instead, the population appears heterogeneous in itssusceptibility to AD, and some of this heterogeneity is unrelated to the countof *APOE* ϵ4 alleles. A sizable proportion ofthe population appears relatively nonsusceptible to AD regardless of *APOE* genotype.

Our findings do *not* dispute the importanceof *APOE* as a risk factor for AD. They do, however,suggest a different role for *APOE* than is sometimesdiscussed. Through its effects on the timing of disease expression, the geneappears to influence the age-specific risk of AD onset. In typical (age-adjusted)epidemiologic analyses, the acceleration of onset with 1 or, especially, 2ϵ4 alleles translates to a strongly increased age-specific risk of AD,especially in early old age. We note, however, that the inclusion in the populationof relatively nonsusceptible individuals predicts a complementary findingin late old age, when most susceptible individuals with 1 or, especially,2 ϵ4 alleles will have developed dementia. Then the relative risks withthese genotypes is predicted to decline below 1 because individuals in thereference group with no ϵ4 alleles will continue to accumulate new ADonsets,^{21} while the portion with ϵ4 willbe largely depleted of susceptible persons. Indeed, our group previously observedsuch an inversion of the prevalence odds ratios among Cache County's elderlypopulation^{10} and also reported^{1} thatthe incidence of AD in Cache County declines after age 97 years. The presentanalyses suggest that this decline reflects a depletion of susceptible individualsat extreme old ages, while substantial numbers of relatively nonsusceptibleindividuals remain in the person-year denominators of the incidence calculations.

The present analyses yield conclusions similar to those previously obtainedusing prevalence data.^{20} Our parametric modelsassigned equal weights to all person-year observations and are therefore unlikely(as product-limit estimates might be) to have been influenced unduly by arelatively small number of observations at late ages. The study was aidedin this respect by the relatively good physical health and the longevity ofthe Cache County population, which surpasses US norms by nearly 10 years^{22} and afforded 230 person-years of observations afterage 90 years.

We note several limitations of our analyses, however. First, survivalestimates can easily be distorted in analyses that preferentially excludesome categories of individuals. For example, residents with incident dementiamay have disproportionately refused the study's wave II procedures (responsebias), or they may have suffered excess mortality in the wave I–waveII interval (informative censoring). Both possibilities could yield an underestimateof true incidence (ie, an overestimate of cumulative survival). The threatof response bias is diminished somewhat in Cache County by the population'sunusually high response rates. Beyond this, a hypothetical analysis that assumeddouble enrichment for dementia among nonresponders did not alter our findingthat a proportion of individuals will not develop AD within their lifespan.The threat of informative censoring was also somewhat attenuated by a relativelybrief follow-up interval of 3 years. Participants who developed incident ADin this interval would have been ill only about an average of 1.5 years or(probably) less—a duration not likely to incur a many-fold excess inmortality. Further assurance on this point came from analyses of postmortemDementia Questionnaire interviews administered to collateral informants of433 participants who had died in the wave I–wave II interval. Comparisonof these interview results with those among the fully examined subsample suggestedthat 42 cases of incident dementia (9.7%) went undetected among the decedents,as contrasted with an age-adjusted figure of 11.7% in the responding sample.

Another potential problem is sensitivity bias, or underascertainmentof cases by screening measures with imperfect sensitivity. With its subsamplestrategy, the Cache County Study design afforded estimates of screening sensitivityfor all-cause dementia,^{17} and we applied theseestimates when calculating adjusted product-limit estimates (equation 1).Unfortunately, we know of no convenient method to adjust for sensitivity biasin parametric models. However, the adjusted empirical analyses and the study'soverall screening sensitivity of 89% suggest that this bias alone is unlikelyto explain the appreciable numbers who survived disease free into late oldage.

A different source of error relates to the diagnostic process itself.Especially when dealing with very old people, one might easily "explain away"dementia as a simple consequence of age or physical illness. We specificallytried to avoid this error. In other analyses, we compared conventional clinicaldementia diagnoses with algorithmic diagnoses based purely on objective psychometricmethods.^{23} Reanalyzing these comparisons byage group, we found no age-related differences in agreement between the 2diagnostic approaches.

Similarly, our diagnoses of AD among those with dementia might havebeen either excessively stringent or overly inclusive. Comparison of our differentialdiagnoses with neuropathological findings showed sensitivity of AD diagnoses(85%) comparable to findings from university clinics. Even so, we evaluatedthe potential consequences of errors in AD diagnosis first by consideringas cases only individuals with a diagnosis of AD and no other dementing disorder.At the opposite extreme, we reran the analyses including as an AD "case" anyindividual with dementia. In both instances our major conclusions were unchanged.We emphasize that all of these diagnoses required the initial finding of *clinical dementia*; we do not have sufficient autopsiesfrom elderly participants without dementia to know whether they have substantialAD pathologic changes, or whether their measure of such pathologic changesvaries with *APOE* genotype.

Another question is the aptness of our analytical assumptions^{24} and, in particular, our choice of the Weibull distribution.^{25} Not surprisingly, the 2-parameter Weibull distributionfit the Cache County data much better than a single-parameter exponentialmodel. However, there are other distributions with variable hazards. Thus,we also attempted to fit a survival model with a gamma distribution to thesedata^{26} but, probably owing to the mathematicalcomplexity of the gamma function, we were unable to obtain convergence withinour algorithms to produce maximum likelihood estimates for the 2 gamma parameters.

We know of no previous empirical investigation of the heterogeneityof susceptibility in a population survey of AD. Our method of dichotomizingthe population into a proportion ρ of susceptible individuals and a complementaryproportion who are nonsusceptible is therefore of interest. This method isalmost certainly an oversimplification, however, and a more realistic modelmight postulate degrees of *relative* instead of absolutesusceptibility or nonsusceptibility. Unfortunately, estimation of such a modelwould require the specification not only of one or more parameters analogousto ρ but also of other parameters describing the relative susceptibilityof the various corresponding population subsets. Without prior knowledge ofits structure, such a model would seem too complex to estimate from the availabledata. One can readily speculate, nonetheless, on several sources of relativesusceptibility, including genes other than *APOE* (severalsuch are under investigation), and a variety of environmental risk factors(eg, head injury or homocysteinemia) or postulated protective factors (eg,exposure to nonsteroidal anti-inflammatory drugs or antioxidant vitamins).

Finally, although the unusual sociocultural attributes of the CacheCounty sample facilitate the study of AD, these same attributes may suggestlack of generalizability of our results. In particular, we caution that thepresent estimates ρ of the proportion susceptible could differ substantiallyfrom estimates in other populations.

As noted elsewhere,^{1} heterogeneity insusceptibility to AD predicts an eventual decline in the incidence of dementiain late old age.^{2} In keeping with the knowninfluence of *APOE* on AD onset, this decline becomesapparent at different ages for individuals with 0, 1, or 2 ϵ4 alleles.Independent of *APOE*, however, there is heterogeneityin the risk of AD. This heterogeneity suggests other genetic or environmentalfactors that can influence AD pathogenesis. To the extent that one could identifynonsusceptible individuals, as suggested by the present work, analyses thatcontrasted these with other individuals should provide important new opportunitiesfor research into the causes and prevention of AD.

Cache County Study Investigators

Cache County Study Investigators involved in the project in additionto the authors are as follows: James Burke, MD; Michelle Carlson, PhD; MarionDavid, PhD; Robert Green, MD; Andrea Hart, MS; Kathleen M. Hayden, PhD; MichaelHelms, MS; Carole Leslie, MS; Constantine Lyketsos, MD; Maria Norton, PhD;Brenda Plassman, PhD; Russell Ray; Christine Reagan; Ingmar Skoog, MD; DavidC. Steffens, MD; Martin Steinberg, MD; Jeannette J. Townsend, MD; JoAnn T.Tschanz, PhD; Kathleen A. Welsh-Bohmer, PhD; Nancy West, MS; Michael Williams,MD; and Bonita W. Wyse, PhD.

Neuropsychological testing procedures were developed by Drs Tschanzand Welsh-Bohmer. Dr Tschanz reviewed all individual test results. The board-certifiedor board-eligible geriatric psychiatrists or neurologists who examined thestudy members included Drs Steinberg, Breitner, Steffens, Lyketsos, and Green.Dr Williams also examined several subjects and provided expert neurologicconsultation. Autopsy examinations were conducted by Dr Townsend. Ms Lesliecoordinated the autopsy enrollment program. Diagnosticians at the expert consensusconferences included Drs Breitner, Burke, Lyketsos, Plassman, Steffens, Steinberg,Tschanz, Welsh-Bohmer, and Williams.

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Article Information

Corresponding author and reprints: John C. S. Breitner, MD, GRECC(S-182), Veterans Affairs Puget Sound Healthcare System, 1660 S ColumbianWay, Seattle, WA 98108 (e-mail: jcsb@u.washington.edu).

Accepted for publication January 20, 2004.

This study was supported by grant AG-11380 from the National Institutesof Health, Bethesda, Md (Dr Beitner), and grant MH-14592 from the NationalInstitute of Mental Health (Dr Zandi).

We thank the neurogenetics laboratory of the Bryan Alzheimer's DiseaseResearch Center at Duke University, Durham, NC, for the APOE genotyping, andTony Calvert, RN, Barb Gau, MSN, Tiffany Newman, Cara Brewer, and Joslin Werstakfor expert technical assistance. Marshal Folstein, MD, suggested the 7-minutevideotape procedure used at clinical assessments.

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Screening for Depression in Adults
WMA Declaration of Helsinki, 7th Revision

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