Katrina A. B. Goddard,1 John S. Witte,1 Brian K. Suarez,2
William J. Catalona,3 and Jane M. Olson1
1Department of Epidemiology and Biostatistics, Rammelkamp Center for Research
and Education, MetroHealth Campus, Case Western Reserve University, Cleveland; and
2Departments of Psychiatry and Genetics and 3Division of Urologic
Surgery, Washington University School of Medicine, St. Louis
Received December 15, 2000; accepted for publication March 15 2001; electronically
published April 13, 2001.
Address for correspondence and reprints: Dr. Katrina A. B. Goddard Department of Epidemiology
and Biostatistics, Case Western Reserve University, 2500 MetroHealth Drive, Cleveland, OH
44109-1998. Email: katrina@darwin.cwru.edu
© 2001 by The American Society of Human Genetics. All rights reserved
0002-9297/2001/6805-0014$02.00
As with many complex genetic diseases, genome scans for prostate cancer have given
conflicting results, often failing to provide replication of previous findings. One factor
contributing to the lack of consistency across studies is locus heterogeneity, which can
weaken or even eliminate evidence for linkage that is present only in a subset of families.
Currently, most analyses either fail to account for locus heterogeneity or attempt to account
for it only by partitioning data sets into smaller and smaller portions. In the present study,
we model locus heterogeneity among affected sib pairs with prostate cancer by including
covariates in the linkage analysis that serve as surrogate measures of between-family linkage
differences. The model is a modification of the Olson conditional logistic model for affected
relative pairs. By including Gleason score, age at onset, male-to-male transmission, and/or
number of affected first-degree family members as covariates, we detected linkage near three
locations that were previously identified by linkage (1q24-25 [HPC1; LOD score 3.25,
p = .00012], 1q42.2-43 [PCAP; LOD score 2.84, p = .0030], and 4q [LOD score 2.80, p = .00038]),
near the androgen-receptor locus on Xq12-13 (AR; LOD score 3.06, p = .00053), and at five new
locations (LOD score > 2.5). Without covariates, only a few weak-to-moderate linkage signals
were found, none of which replicate findings of previous genome scans. We conclude that
covariate-based linkage analysis greatly improves the likelihood that linked regions will be
found by incorporation of information about heterogeneity within the sample.
Introduction
Prostate cancer {CaP [MIM 176807]) is one of the most common causes of cancer mortality
among men in the United States and accounts for ~31,900 deaths annually (Greenlee et al. 2000).
Substantial differences in the prevalence of CaP are observed among populations, with African
Americans having the highest prevalence of the disease and with Asian populations having the
lowes1 prevalence {Parkin et al. 1993; Whittemore 1994). Individuals either with several
affected first-degree relative or with an affected brother who had an early age at onset have
a higher risk of development of CaP {Keetch et al. 1995), suggesting that genetic factors
playa role in the development and progression of CaP. Studies of the familial clustering of
CaP also indicate a heritable component of the disease, although there have been conflicting
reports about the mode of inheritance. Some studies suggest an autosomal dominant mode of
inheritance for early-onset disease (Carter et al. 1992; Gröberg et al. 1997), whereas
others suggest a recessive or X-linked mode of inheritance (Monroe et al. 1995).
Numerous studies have indicated evidence for linkage to regions that may contain a
disease-susceptibility locus for CaP. The first region, reported by Smith et al. (1996), was
on chromosome 1q24-25 (HPC1 [MIM 601518]). Subsequent reports presented conflicting results
in this region. Some studies showed little or no support for a locus in this region (McIndoe
et al. 1997; Berthon et al. 1998; Eeles et al. 1998; Berry et al. 2000a; Goode et al.
2000), whereas others showed moderate support, usually in subsets of the data restricted to
families with early age at onset (Hsieh et al. 1997; Gröberg et al. 1999), families meeting
the criteria for hereditary CaP (Cooney et al. 1997), or families with male-to-male disease
transmission, early age at onset, and a large number of affected individuals (Xu and
International Consortium for Prostate Cancer Genetics 2000). A second locus on chromosome 1,
located at 1q42.2-43 (PCAP [MIM 602759]), was reported by Berthon et al. (1998). However,
additional studies have failed to support the evidence for linkage in this region (Gibbs et
al. 1999a; Whittemore et al. 1999; Berry et al. 2000a), although the genome
scan by Smith et al. (1996) had earlier reported a small-to-moderate signal in this region.
A third locus on chromosome 1, located at 1p36 (CAPB [MIM 603688]), was implicated in families
that also have a history of brain cancer (Gibbs et al. 1999b); however, one other study
showed negative LOD scores in this region in 13 families with prostate and brain cancer
(Berry et al. 2000a).
Additional loci, on chromosomes other than chromosome 1, also have been implicated in CaP
and recently were reviewed by Ostrander and Stanford (2000). In brief, Xu et al. (1998)
reported a locus, on the X chromosome (HPCX [MIM 300147]), that had supportive evidence of
linkage in another study (Lange et al. 1999). Berry et al. (2000b) identified evidence
for linkage to a locus on chromosome 20, among pedigrees with no male-to-male transmission, a
high average age at diagnosis (>66 years), and a relatively small number of
affected individuals (fewer than five affected). These families are the least likely to have
linkage to the regions that were identified previously. More recently, the HPC2/ELA C2 gene
on chromosome 17p was found to be associated with an increased risk of CaP (Rebbeck et al.
2000; Tavtigian et al. 2000). Finally, two recent genome scans have identified suggestive
evidence for linkage on chromosomes 2, 12, 15, and 16 (Suarez et al. 2000) and on
chromosomes 1,8,10,12,14, and 16 (Gibbs et al. 2000). The strongest evidence for linkage was
found on chromosome 16, in the affected-sib-pair (ASP) study by Suarez et al. (2000), and on
chromosomes 8 and 10, under a recessive model, in the Gibbs et al. (2000) study.
The mixed results observed both within and between studies is an indication of the complex
nature of CaP. CaP is likely to be a genetically heterogeneous disorder, with several genetic
and environmental factors contributing to the development of disease. Two additional factors
are likely to contribute to the lack of consistency across studies. First, there may be
population differences both within and between studies; for example, in the original report
for HPC1, two African American pedigrees contributed substantially to the total LOD score
suggesting linkage in the region, whereas many subsequent studies included a large proportion
of white families. Second, differences in the ascertainment criteria used to identify
pedigrees can lead to different genes segregating in the study population (McCarthy et al.
1998; Goddard 1999). Many of the studies listed above selected large pedigrees with a large
number of affected individuals, whereas others included only nuclear families with at least
two affected individuals.
Previous analyses have used several methods to deal with heterogeneity, including
alternative models in parametric linkage analysis; model-free methods, such as the
nonparametric linkage (NPL) score; and stratification of the sample on one or more
covariates. An alternative method that may provide additional power to detect linkage is the
model-free conditional logistic model for affected-relative-pair (ARP) linkage analysis
(Olson 1999), an extension and reparameterization, in terms of log risk ratio, of the
Greenwood and Bull (1999) multinomial covariate model for ASPs. Greenwood and Bull established,
using simulations, that inclusion of family-specific covariates increases the power to detect
linkage, provided that the covariate reflects underlying locus heterogeneity. They also found
that inclusion of covariates does not substantially impact the accuracy of asymptotic
approximations to the distribution of the appropriate likelihood-ratio statistic, regardless
of whether constraints on the mode of inheritance are applied that reduce the number of
parameters in the model.
These methods are model free in the sense that model parameters at the trait locus do not
need to be specified. Discrete or quantitative covariates included in the model increase
power to detect linkage when the covariate measures differences, between families, that are
important to locus heterogeneity. The method incorporates locus heterogeneity due to the
covariate, by allowing the genetic relative risk to depend on the covariate, so that, in
effect, the allele sharing at the marker locus differs for different values of the covariate.
The original model proposed by Olson (1999) requires two additional parameters for each
covariate and therefore may not provide optimal power. In the present study, we instead use a
modification that requires only one additional parameter per covariate.
We apply this modification of the Olson (1999) conditional logistic model to a genome scan
of sibships with CaP. We test four covariates: Gleason score, age at onset, male-to-male
transmission, and number of first-degree relatives with CaP. In contrast to the original
analysis of these data by Suarez et al. (2000), we find strong confirmatory evidence of
linkage in four genomic locations, as well as substantial evidence for linkage in several
new locations.
Subjects and Methods
Subjects
The recruitment of study subjects has been described elsewhere (Suarez et al. 2000; Witte
et al. 2000). For this analysis, a total of 564 men from 254 families with both CaP and
measured Gleason scores were available. This sample included 189 families with two affected
brothers, 41 families with three affected brothers, 2 families with four affected brothers,
and 1 family with two pairs of affected brothers who were cousins (for a total of 326 ASPs).
We considered four covariates: (1) the sum of the sib-pair Gleason scores, (2) age at onset
(measured as family mean age at diagnosis), (3) an indicator for male-to-male transmission in
the nuclear family, and (4) the number of affected first-degree relatives in the nuclear
family. Gleason score is a measure of tumor aggressiveness and has been analyzed previously,
as an outcome variable, by use of these data (Witte et al. 2000). Family mean age at diagnosis
was used in place of the sum of the sib-pair age at onset, because of the large number of
missing values for the latter. Overall, 4% of the ASPs had missing values for male-to-male
transmission, and 11% of ASPs had missing values for the family mean age at diagnosis.
Missing values for covariates other than Gleason score were given the mean value for that
covariate.
Genotyping
Genotyping was performed at the Center for Medical Genetics, Marshfield Medical Research
Foundation, with DNA from each subject's peripheral blood, extracted by standard methods. The
samples were typed through use of Marshfield Screening Set 9 (Yuan et al. 1997), which
includes 364 autosomal simple-tandem-repeat polymorphisms, with ~9-cM spacing between markers
across the genome and an average heterozygosity of 77% (Broman et al. 1998). We confirmed the
sib-pair relationship in all sibships, through use of all markers in the screening set, with
the program RELTEST from the Statistical Analysis for Genetic Epidemiology (S.A.G.E.) software
package, release 4.0 beta. Pairs that were not full siblings or that were MZ twins were
excluded from the analysis, as in previous analyses of these data (Suarez et al. 2000; Witte
et al. 2000).
Statistical Analysis
To detect linkage in our ASPs, we performed a model-free likelihood analysis that allowed
incorporation of co-variates. Olson (1999) showed that the original Risch (1990) ASP LOD
score can be reparameterized in terms of the natural logarithms of relationship relative
risks, by putting 
1 = exp (ß1) and
2 = exp (ß2), where
1 (2)
is the relative risk for a pair of relatives that shares exactly 1 (2) alleles identical by
descent (IBD) and where ß1 (ß2) is the natural logarithm of
1 (2).
In this analysis, multipoint IBD-sharing estimates for autosomal loci were obtained with the
GENIBD program from the S.A.G.E. package, release 4.0 beta, and those for the X chromosome
were obtained with MAPMAKER/SIBS (Kruglyak and Lander 1995). Addition of covariates to this
model requires two additional parameters for each covariate. Instead, we constrained the
relative risks so that 2
= 3.6341 - 2.634, reducing, from two to one, both
the number of parameters in the basic model and the number of additional parameters needed
for each added covariate. This particular constraint was chosen on the basis of work by
Whittemore and Tu (1998), who showed that a minmax one-parameter ASP LOD score preserved type
I error but had more power for most genetic models than did the usual two-parameter LOD score.
Our constraint is simply a reparameterization of the Whittemore-Tu minmax constraint and
assumes a genetic model approximately halfway between a recessive and a dominant mode of
inheritance. We then incorporated covariates into our analysis by putting
1 = exp (ß1 +
Kyii,) where xi,
i = 1, ...,K, are the covariates included in the model and where yi are the
corresponding parameters. The same model may be used on X-linked markers after the correct
prior and conditional allele-sharing probabilities for X- linked loci and brother-brother
pairs are obtained, where the interpretation of 
1
is specific to that pair type.
In this analysis, inclusion of a covariate allows for linkage heterogeneity due to the
covariate; for example, a binary covariate indicating population membership allows for
population heterogeneity in linkage to a particular location, and including such a covariate
is equivalent to analyzing each subpopulation separately and summing the LOD scores.
Continuous covariates have a similar interpretation in that they allow for linkage
heterogeneity due to the covariate. Using the parameter estimates, one can then calculate
sibling relative risks at particular values of the covariate:
s(x) = ¼ +
½1(x) +
¼2(x), subject to the minmax constraint
described above.
In our analyses, we assumed that genetic constraints {Holmans 1993) hold at the sample
mean covariate value, but not necessarily at other covariate values {see Greenwood and Bull
1999); each covariate was standardized to have mean 0 and variance 1. By centering the
covariate around 0, we avoid the need to further constrain y to be consistent with a genetic
model at the mean covariate value {Olson 1999). In addition, the sign of y indicates the
direction of covariate effect on linkage evidence; for example, if linkage is present in
families with early age at onset but absent in families with late age at onset, inclusion of
x {as mean age at onset [centered]) as a covariate will substantially increase the LOD score,
and the estimate of y will be negative, generating the highest values of
s(x) for the lowest values of x. In addition to
centering each covariate, we also standardized by dividing by the estimated SD. The sole
purpose was to reduce the number of possible computational problems encountered by the
maximization algorithm MAXFUN from the S.A.G.E. package, release 2.2; >15,000 separate
maximizations were performed in this analysis.
Critical values for the corresponding likelihood-ratio statistics {LRS; i.e., 4.605 x LOD
score) can be obtained easily, by use of the methods of Self and Liang {1987). The
distribution of the LRS for the basic one-parameter model is a 50:50 mixture of a point mass
at 0 and a x2 distribution with 1 df. Addition of K covariates gives an LRS with a
distribution that is a 50:50 mixture of a x2 with K df and a x2 with K
+ 1 df. The difference in LRS between nested models that differ by J covariates has a x2
distribution with J df. One can therefore test both the significance of the contribution of a
covariate and the overall evidence for linkage.
Clearly, addition of covariates increases the LOD cut-point needed in order to allow us to
declare that there is significant linkage. As a result, we encourage both a priori selection
of candidate covariates to be included in routine linkage analysis and careful differentiation
between planned and exploratory analyses. We chose co-variates that we believed had a high
probability of measuring some aspect of locus heterogeneity and analyzed each covariate
individually. In regions where more than one covariate contributed significantly to linkage
evidence (P <.05), we obtained parsimonious final models, using multiple-regression
methods.
Results
Plots of LOD score versus map distance (in cM) are shown in
figure 1, for five models:
the one-parameter model, without covariates, and four models, each with one covariate
(Gleason score, mean age at onset, male- to-male transmission indicator, or number of affected
relatives). The one-parameter model, represented by the black line, is always the smallest of
the five LOD scores and can be viewed as a "baseline" in the context of the
analysis of covariate effects on linkage. Five regions have baseline LOD scores >1; these
regions are summarized in table 1,
along with the corresponding two-parameter LOD score and the NPL score reported, by Suarez et
al. (2000), for the same data set. The largest one-parameter LOD score is on chromosome 2q
(LOD score 2.48). We detected the same regions reported by Suarez et al. (2000), with some
differences in relative magnitude of the signal, which, presumably, reflect differences in
method power and the fact that Suarez et al. included more markers in these regions and used
a larger sample size by including ASPs with no reported Gleason score. Comparison of the
one- and two-parameter LOD scores shows the dependence of the results on the constraints that
were chosen for the one-parameter model. These results indicate that, at the cost of an
additional parameter, the two-parameter model adds little additional evidence for linkage, a
finding that is consistent with the results of Whittemore and Tu (1998) that also suggest
that the one-parameter model is usually more powerful. Similar increases in the LOD score
were found by maximizing over the mode-of-inheritance parameter (two-parameter model) for
models that included the covariates (data not shown).
Covariate effects significant at the .01 level are detailed in
table 2, as are regions
for which the total LOD score (including the covariate) is >2.0. We included considerable
detail in this table so that various features of the new models can be observed more easily.
Because all covariates were standardized prior to inclusion, Covariate-parameter estimates
(y) are interpreted as unit changes in loge offspring relative risk
l of the standardized
covariate. The means and SDs of the original covariates are given in footnote "b"
of table 2.
Some of the most interesting results were on chromosome 1. In the region that purports to
contain HPC1, a large peak (LOD score 3.25) was found only when Gleason score was included as
a covariate. The highest point of our peak was located -30 cM centromeric to the most
significant marker described by Smith et al. (1996). The LOD score without covariates is only
0.03, and the effect of Gleason score on linkage at this location is highly significant
(P = .00012). This signal is the largest Gleason-score effect in our genome scan. The sign of
the covariate parameter is positive, indicating that ASPs with high Gleason scores show the
strongest evidence for linkage. Sibling relative risks for various Gleason scores are given
in table 3, to
illustrate the dependence of relative risk on Gleason score; ASPs with total Gleason scores
in the upper 2.5% of the sample distribution have sibling relative risks >2.52.
A second peak on chromosome 1 is in the region of the PCAP signal reported by Berthon et al.
(1998). Again, the model without covariates shows little evi- dence for linkage (LOD score
0.32), whereas the model that includes male-to-male transmission gives a LOD score of 1.90 (P
= .007 for the covariate effect). Families that have male-to-male transmission show the most
evidence in favor of linkage. In addition, Gleason score and number of affected relatives both
are significant at the .05 level. As a result, we fit multiple conditional logistic-regression
models (table 4). The
best-fitting, most-parsimonious model includes both Gleason score and male-to-male
transmission (total LOD score 2.84, p = .003). The interaction term has a negligible effect,
indicating an excellent fit to a model in which these covariates affect offspring relative
risk Al multiplicatively. The signs of the covariate parameters in the final model indicate
that ASPs with male-to-male transmission and low Gleason scores contain the most evidence for
linkage to the PCAP region on chromosome 1. The number of affected relatives does not add
linkage information once Gleason score and male-to-male transmission are taken into account.
A second large signal due primarily to Gleason score was found on chromosome X (P = .0003
for covariate effect), ~10 cM telomeric from the androgen-receptor locus (AR [MIM 313700]),
an important candidate locus for CaP. CAG- and GGN-repeat polymorphisms in the AR locus have
been related to CaP in association studies (e.g., see Giovannucci et al. 1997; Ingles et al.
1997; Stanford et al. 1997; Hsing et al. 2000) but not in linkage studies (Lange et al. 2000).
For this signal, the LOD score without the covariate was only 0.26, compared with the LOD
score including the covariate, which was 3.06, a strongly significant value (P = .00058). In
contrast to what has been observed in the HPCX region (Xu et al. 1998; Lange et al. 1999), we
did not observe an increase in the evidence for linkage among families with transmission that
was consistent with an X-linked mode of inheritance (i.e., families that did not have
male-to-male transmission). We could not examine the chromosome X region previously reported
by Xu et al. (1998) because we did not have markers in this region near Xqter.
A third large signal, due entirely to Gleason score, was found on chromosome 5 (P = .00058
for covariate effect), in a location different from the location identified by Witte et al.
(2000) when they used Gleason score as a dependent variable in a Haseman-Elston regression.
Gleason score also increases the signal on chromosomes 2 (two regions), 8, and 16. The
largest effect of age at onset was on chromosome 14, where the linkage signal increased from
0.18 to 2.74. chromosomes 4, 6, 7, and 20 showed smaller age-at-onset effects, which were
significant at the .01 level. The largest effect of male-to-male transmission was found on
chromosome 21, where the LOD score increased from 0.32 to 3.12. Chromosomes 1-5 also showed
effects from this covariate, which were significant at the .01 level.
The largest effects of the number of affected relatives were on chromosomes 3 (increase in
LOD score from 0.00 to 4.66), 4 (from .03 to 2.76), and 8 (from 0.00 to 2.56), with another
smaller but significant effect on chromosome 8. The signal on chromosome 4 is in the region
of the second-largest signal reported by Smith et al. (1996). In this region, male-to-male
transmission also shows an individual effect, which is significant at the .05 level, but it
does not add linkage evidence to the model that includes the number of affected relatives.
None of the other large covariate effects corresponds to a region for which previous strong
linkage evidence has been reported.
The signal on chromosome 3 appears unusually narrow and may be overestimated or improperly
maximized. However, we were unable to discover any difficulties with the maximization
procedures at this location. An additional indication of possible overestimation is revealed
by the fact that the linkage-parameter estimate (ß) is 0 but the covariate-parameter estimate
(y) is large in absolute value; in other words, the offspring relative risk for much of the
covariate distribution is considerably less than 1. In our analyses, we constrained only the
mean covariate value to be consistent with genetic-triangle constraints, because it remains
unclear what, if any, genetic constraints should be imposed when a covariate cannot be
considered to differentiate subpopulations in which the genetic constraints should separately
conform (e.g., different mating populations).
Nonetheless, one generally expects true relative risk values to be >1;
on the other hand, if linked and unlinked subsets are indeed present, estimated relative
risks in the unlinked subset will be <1, with probability 1/2, by chance alone; in fact,
we believe that chance evidence against linkage in unlinked (and unidentified) subsets is one
of the primary reasons that linkage is often not detected in the first place. Therefore, we
hesitate to discount signals that yield some implausible relative-risk values, while
recognizing that, in some regions, the size of the detected covariate effect may be distorted
and that the LOD score may be inflated.
Discussion
A reanalysis of the genome-scan data first reported by Suarez et al. (2000) provides
confirmatory evidence of linkage in two regions, first reported by Smith et al. (1996), on
chromosome 1 (i.e., HPCl) and on chromosome 4, and in one region, highlighted by Berthon et
al. (1998), on chromosome 1 (i.e., PCAP), which also had a moderate-sized signal reported by
Smith et al. (1996). Our peaks on chromosome 4 and lq42.2-43 appear to be within 10-20 cM of
their previously reported locations. We estimate that our HPCl peak may be 30 cM centromeric
to its previously reported location. In addition, we observed a strong new signal, on
chromosome Xq12-13, that appears to be within 10-15 cM of the AR locus, a major candidate
locus for CaP. We were able to detect these signals by including in the link- age analysis
those covariates that account for some of the genetic heterogeneity presumed to exist in this
complex disease. Linkage analysis without covariates failed to detect the signals in these
regions. We believe that analyses that include additional phenotypic information will greatly
improve the ability of genome scans to detect genetic loci for complex diseases.
Other covariate-based linkage methods have been proposed in addition to those of Olson
(1999) and Greenwood and Bull (1999). Schaid et al. (2001 [in this issue]), in the context of
model-based linkage analysis, specify the heterogeneity parameter as a function of covariates
and apply the method to CaP. Gauderman and Siegmund (2000) have proposed a method in which
gene-by-environment interaction is included in ASP linkage analysis. Although linkage
analysis with covariates is not yet commonplace, it is similar in spirit to the common
practice of subgroup analysis, in that subgroup analysis also aims to account for locus
heterogeneity. One advantage of the conditional logistic model is that it provides a more
general way in which covariate information can be easily included in the linkage analysis.
The form of the model allows for multiple covariates-including quadratic terms and
interactions-to be modeled, without the need to subdivide a sample into smaller and smaller
portions. For continuous covariates, it is not necessary to choose a cutpoint on the basis of
which the data are to be subgrouped. One possible disadvantage is that the model assumes
multiplicativity in offspring relative risk; however, this restriction can be partly overcome,
if necessary, to provide a better fit, by the inclusion of higher-order terms or by the
transformation of covariates.
Addition of covariates increases the LOD-score cutpoint needed in order to allow us to
declare significant linkage. In addition, indiscriminate use of covariate analyses can result
in greatly increased experiment-wise type I error, because of multiple testing. As a result,
we encourage both a priori selection of candidate covariates to be included in routine
linkage analysis and careful distinction between pre specified and exploratory analyses.
More-rigorous rules for multiple testing await further research.
The influence of missing data on the results of an analysis is always a concern. Here,
missing data for covariates were replaced with the mean covariate value. The age-at-onset
covariate had the largest proportion of missing data, with 11% of the ASPs having missing
values. Removing from the analysis the ASPs having missing values for this covariate slightly
reduced the LOD score; however, it is unclear whether this is an indication of a biased
result due to use of the mean covariate value or of additional information that is gained by
inclusion of the ASPs having missing values.
Witte et al. (2000) analyzed these data by using Gleason score as a dependent variable in
a (new) Haseman-Elston regression (Elston et al2000); there was little, if any, overlap
between the signals reported in the present article and the signals reported by Witte et al.
We believe that the two analyses detect different types of information relevant to linkage.
Using Gleason score as a dependent variable in a sample of ASPs is likely to provide the most
power to detect genes that modify tumor aggressiveness in patients with CaP but that do not
confer susceptibility to CaP itself-that is, genes that contribute to within-family
variability in Gleason score; on the other hand, inclusion of Gleason score as a covariate in
an ASP linkage analysis is likely to have the most power to detect genes that confer
susceptibility solely to subtypes of CaP that are characterized by aggressive tumors-that is,
genes that contribute to between-family variability in Gleason score.
However, we note that, for individual-specific covariates, covariate information relevant
to locus hetero-geneity may be present in the sib-pair covariate sum, the sib-pair covariate
difference, or both. One can include the sib-pair difference as an additional covariate if
one believes that between-family differences in within- family variability contribute to
locus heterogeneity. For the five largest Gleason-score signals, we added the sib- pair
difference to the model but found no significant increase in LOD score. We are currently
using simulations to explore these and other models of covariate action, and we plan to
report the findings in a future publication. The one-parameter conditional logistic model
for ARPs is expected to be available in the next release of S.A.G.E.; a beta version of the
program is currently available from the Human Genetic Analysis Resource Web site.
Acknowledgments
This work was supported, in part, by U.S. Public Health Service grants HGOl577 from the
National Center for Human Genome Research, RRO3655 from the National Center for Research
Resources, CA88l64 from the National Cancer Institute, and MHl4677; by U.S. Army Medical
Research and Material Command grants DAMDl7-00-l0l08 and DAMDl7-98-l- 8589; and by grants
from the Urologic Research Foundation. Some of the results in this article were obtained by
S.A.G.E. software, which is supported by National Center for Research Resources grant
RR03655.
Electronic-Database Information
Accession numbers and URLs for data in this article are as follows:
Human Genetic Analysis Resource, http://darwin.cwru.edu/
(for S.A.G.E. software)
Online Mendelian Inheritance in Man (OMIM), http://www .ncbi.n1m.nih.gov/Omim/ (for CaP [MIM
176807], AR [MIM 313700], HPC1 [MIM601518], PCAP [MIM 602759], HPCX [MIM 300147], and CAPB
[MIM 603688])
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