As planned the telomere data should consist of 80 HANDLS participants with DNA collected at two occasions (waves 1 & 3).
Telomere length data were missing for one participant at both waves (ID = 818-22693-02). The analytic sample has 79 participants separated by an average of 4.8 years.
The design is race (African Americans v. whites) × poverty status (below v. above 125% household poverty level) × sex:
, , PovStat = Above
Race
Sex White AfrAm
Women 10 10
Men 9 10
, , PovStat = Below
Race
Sex White AfrAm
Women 10 10
Men 10 10
For preliminary analyses, we're interested in whether change in telomere length is associated with race, poverty status, sex, age, or their interactions.
One way to look at these data is to examine the follow-up time differences (difAge) and change in telomere length (difLen) for each group:
Follow-up duration by sex, race, and poverty status
Sex Race PovStat difAge.n difAge.mean difAge.sd difAge.min difAge.max
1 Women White Above 10 4.2 1.33 2.3 5.8
2 Women White Below 10 5.0 0.67 4.0 5.8
3 Women AfrAm Above 10 4.6 0.56 3.7 5.6
4 Women AfrAm Below 10 4.8 0.47 3.8 5.5
5 Men White Above 9 4.4 1.52 2.3 7.0
6 Men White Below 10 5.2 0.50 4.6 6.0
7 Men AfrAm Above 10 4.4 0.48 4.0 5.4
8 Men AfrAm Below 10 5.4 1.25 4.3 8.8
Change in telomere length by sex, race, and poverty status
Sex Race PovStat difLen.n difLen.mean difLen.sd difLen.min difLen.max
1 Women White Above 10 -0.260 0.64 -1.5 0.6
2 Women White Below 10 -0.410 0.65 -1.9 0.5
3 Women AfrAm Above 10 -0.250 0.64 -1.3 0.8
4 Women AfrAm Below 10 -0.750 0.72 -2.3 0.6
5 Men White Above 9 0.067 0.46 -0.8 0.8
6 Men White Below 10 -0.940 0.79 -2.0 0.3
7 Men AfrAm Above 10 -0.350 0.45 -1.1 0.4
8 Men AfrAm Below 10 -0.010 0.57 -1.0 0.7
There are no age differences in the sample associated with sex, race, or poverty status:
Association of age at wave 1 with sex, race, and poverty status
Estimate Std. Error t value Pr(>|t|)
(Intercept) 47.025 2.01 23.414 3.20e-36
SexMen 0.907 2.01 0.452 6.53e-01
RaceAfrAm -0.951 2.01 -0.474 6.37e-01
PovStatBelow 0.744 2.01 0.371 7.12e-01
Association of age at wave 3 with sex, race, and poverty status
Estimate Std. Error t value Pr(>|t|)
(Intercept) 51.260 2 25.628 7.68e-39
SexMen 1.131 2 0.565 5.74e-01
RaceAfrAm -0.867 2 -0.433 6.66e-01
PovStatBelow 1.471 2 0.736 4.64e-01
However, participants below the poverty level have a 0.7 year greater follow-up duration than participants above the poverty level:
Association of follow-up duration with sex, race, and poverty status
Estimate Std. Error t value Pr(>|t|)
(Intercept) 4.2347 0.207 20.49 1.84e-32
SexMen 0.2234 0.207 1.08 2.83e-01
RaceAfrAm 0.0846 0.207 0.41 6.83e-01
PovStatBelow 0.7274 0.207 3.52 7.37e-04
Another way to look at these data is to examine whether change in telomere length (difLen) is correlated with initial age (Age.1) or follow-up time (difAge). This assumes implicitly that time between assays is identical for all participants, which we know is false based on the preceding breakdowns in follow-up times by sex, race, and poverty status.
Age.1 difAge difLen
Age.1 1.00 -0.06 0.16
difAge -0.06 1.00 0.00
difLen 0.16 0.00 1.00
n = 79
None of these correlations are significant, but these results do not preclude differences in rates of change in telomere length and particularly interactions among sex, race, poverty status, and age. A longitudinal analysis by mixed-model regression is the appropriate technique for examining these effects. This method explicitly includes age differences among the effects.
We start with a fully articulated model (all the effects and all their interactions), after which we will selectively remove some nonsignificant interactions by backward elimination.
Simultaneous Tests for General Linear Hypotheses
Fit: lmer(formula = tLength ~ (Age + Sex + Race + PovStat)^4 + (1 |
HNDid), data = telo)
Linear Hypotheses:
Estimate Std. Error z value Pr(>|z|)
(Intercept) == 0 6.67619943 1.06188262 6.28714 3.2338e-10
Age == 0 -0.01739304 0.02159663 -0.80536 0.420612
SexMen == 0 -1.53027865 1.84018506 -0.83159 0.405641
RaceAfrAm == 0 1.46433319 1.46479836 0.99968 0.317464
PovStatBelow == 0 1.46673931 1.71432869 0.85558 0.392232
Age:SexMen == 0 0.03366020 0.03649757 0.92226 0.356394
Age:RaceAfrAm == 0 -0.05676770 0.02975566 -1.90780 0.056418
Age:PovStatBelow == 0 -0.03132318 0.03355455 -0.93350 0.350562
SexMen:RaceAfrAm == 0 1.16346020 2.35897457 0.49321 0.621867
SexMen:PovStatBelow == 0 3.75186830 2.61773028 1.43325 0.151786
RaceAfrAm:PovStatBelow == 0 -2.97058395 2.24559760 -1.32285 0.185886
Age:SexMen:RaceAfrAm == 0 0.01224493 0.04681569 0.26156 0.793664
Age:SexMen:PovStatBelow == 0 -0.07548214 0.05116318 -1.47532 0.140126
Age:RaceAfrAm:PovStatBelow == 0 0.06005666 0.04443246 1.35164 0.176491
SexMen:RaceAfrAm:PovStatBelow == 0 -4.51968933 3.33186139 -1.35651 0.174938
Age:SexMen:RaceAfrAm:PovStatBelow == 0 0.08591297 0.06545300 1.31259 0.189321
(Univariate p values reported)
The 4-way interaction is nonsignificant (age × sex × race × poverty status). After removing it, there's a significant interaction for age × race × poverty status. There are also significant effects for race × poverty status and age × race.
Simultaneous Tests for General Linear Hypotheses
Fit: lmer(formula = tLength ~ (Age + Sex + Race + PovStat)^3 + (1 |
HNDid), data = telo)
Linear Hypotheses:
Estimate Std. Error z value Pr(>|z|)
(Intercept) == 0 6.220760999 0.991658957 6.27309 3.5396e-10
Age == 0 -0.007919872 0.020123472 -0.39356 0.6939030
SexMen == 0 -0.248875875 1.524163516 -0.16329 0.8702926
RaceAfrAm == 0 2.311250428 1.295561124 1.78398 0.0744275
PovStatBelow == 0 2.507570293 1.467288238 1.70898 0.0874541
Age:SexMen == 0 0.007816443 0.030030575 0.26028 0.7946456
Age:RaceAfrAm == 0 -0.074383370 0.026175454 -2.84172 0.0044871
Age:PovStatBelow == 0 -0.052122333 0.028551421 -1.82556 0.0679166
SexMen:RaceAfrAm == 0 -0.957102956 1.663648380 -0.57530 0.5650860
SexMen:PovStatBelow == 0 1.139286476 1.652308246 0.68951 0.4905011
RaceAfrAm:PovStatBelow == 0 -4.899281632 1.660189160 -2.95104 0.0031671
Age:SexMen:RaceAfrAm == 0 0.055147370 0.032419363 1.70106 0.0889312
Age:SexMen:PovStatBelow == 0 -0.023584147 0.031575921 -0.74690 0.4551222
Age:RaceAfrAm:PovStatBelow == 0 0.099102569 0.032319658 3.06632 0.0021671
SexMen:RaceAfrAm:PovStatBelow == 0 -0.230517240 0.624667098 -0.36902 0.7121097
(Univariate p values reported)
It's notoriously difficult to interpret these results by just looking at the coefficients. It's far easier to visualize these assocations by plotting the effects.
These plots show the effects in the model expressed over age and are interpreted as an estimate of the age-associated effects on telemere length generated from a repeated measures analysis.
The relationships are difficult to discern with so many groups in the plot. It's a little easier to see after separating women and men.
The pattern of age-associated change in telomere length is quite different in women and men.
For women, the interaction between race and poverty status is apparent in the cross-overs by poverty status for both African Americans & whites. Below poverty status is associated with steep declines in African American and white women below poverty (amber lines). Above poverty African American women decline sharply at a rate similar to that of white women below poverty. White women above poverty show little change in telomere length.
For men, only whites below poverty show substantial decline, although African American men above poverty also decline. Neither white men above poverty nor African American men below poverty show much change in telomere length.