In our most recent meeting on May 10, we wanted to examine (1) the curvilinear relationships of age with BMD; (2) separate associations of age with BMD for younger (≤50 yo) and older (>50 yo) participants; and, (3) the effects of diabetic control or insulin resistance (HbA1c or HOMA-IR) and vitamin D and calcium intake.

Based on data assembled on 2013-05-13 for participants who have no osteophytes, we have two BMD assays for 1617 participants with mean age of 48.3 years at initial examination.

For simplicity, I'll present the first two analyses. Depending on the outcomes, we can decide to which analysis we want to add measures of diabetic control and intake. We haven't discussed whether we want to analyze women and men separately. Thus far, we've found significant differences between women and men but we haven't examined them separately. We may want separate-sex analyses so we can compare our data to published data, which is mostly for older women.

Table 1. Sample characteristics at initial assessment separately by poverty status and race.

omitted for now

Curvilinear age associations

In these analyses, we explore whether there is a curvilinear relationship between age and BMD. Evidence for such a relationship is expressed by significant terms for age2 (called ageDecad2 in these analyses). We examine whether there is a significant overall curvilinear relationship (ageDecad2) and signficant differences in curvilinearity by sex and race (interactions with ageDecad2). The curvilinear term is what provides estimates for the "curvi-ness" in Figures 1 and 2.

There are significant differences in hip BMD associated with age, sex, race, BMI, cigarette smoking, and curvilinear age by sex (Table 2).

There are significant differences in lumbar BMD associated with age, race, poverty status, BMI, age by race, and curvilinear age by race (Table 3).

A significant age by race interaction means that the rates of change in lumbar BMD are difference in African Americans and whites. A significant curvilinear age by race interaction means that shapes of the curvilinear association of age with race are different in African Americans and whites. These differences should be apparent in Figure 2.

I'm researching whether we can estimate percent change from analyses with curvilinear terms.

Table 2. Association of log transformed hip and lumbar bone mineral density with age, sex, race, poverty status, body mass index, current alcohol use, and current cigarette smoking.

Hip


     Simultaneous Tests for General Linear Hypotheses

Fit: lmer(formula = logHip ~ ageDecade * (Sex + Race) + ageDecad2 * 
    (Sex + Race) + PovStat + PhysBMI + MedHxAlcCurr + MedHxCigaretteCurr + 
    (ageDecade | HNDid), data = dxa[dxa$ageGroup == "<50", ], 
    na.action = na.omit)

Linear Hypotheses:
                            Estimate Std. Error z value      Pr(>|z|)
(Intercept) == 0           -0.239255   0.021069  -11.36       < 2e-16
ageDecade == 0             -0.031199   0.012279   -2.54        0.0111
SexMen == 0                 0.024672   0.008862    2.78        0.0054
RaceAfrAm == 0              0.056312   0.008924    6.31 0.00000000028
ageDecad2 == 0             -0.015854   0.008129   -1.95        0.0511
PovStatBelow == 0           0.003985   0.008386    0.48        0.6346
PhysBMI == 0                0.009890   0.000600   16.49       < 2e-16
MedHxAlcCurrYes == 0       -0.018261   0.009704   -1.88        0.0599
MedHxCigaretteCurrYes == 0 -0.022431   0.008356   -2.68        0.0073
ageDecade:SexMen == 0       0.000318   0.013095    0.02        0.9806
ageDecade:RaceAfrAm == 0    0.004927   0.013576    0.36        0.7167
SexMen:ageDecad2 == 0       0.023694   0.008800    2.69        0.0071
RaceAfrAm:ageDecad2 == 0   -0.012239   0.009048   -1.35        0.1761
(Univariate p values reported)

Lumbar spine


     Simultaneous Tests for General Linear Hypotheses

Fit: lmer(formula = logLum ~ ageDecade * (Sex + Race) + ageDecad2 * 
    (Sex + Race) + PovStat + PhysBMI + MedHxAlcCurr + MedHxCigaretteCurr + 
    (ageDecade | HNDid), data = dxa[dxa$ageGroup == "<50", ], 
    na.action = na.omit)

Linear Hypotheses:
                            Estimate Std. Error z value Pr(>|z|)
(Intercept) == 0           -0.202162   0.026408   -7.66  1.9e-14
ageDecade == 0             -0.091249   0.019055   -4.79  1.7e-06
SexMen == 0                 0.016998   0.012840    1.32   0.1856
RaceAfrAm == 0              0.054156   0.012977    4.17  3.0e-05
ageDecad2 == 0              0.002886   0.011982    0.24   0.8096
PovStatBelow == 0           0.030601   0.010295    2.97   0.0030
PhysBMI == 0                0.007120   0.000731    9.74  < 2e-16
MedHxAlcCurrYes == 0        0.003915   0.012045    0.33   0.7452
MedHxCigaretteCurrYes == 0 -0.000724   0.010188   -0.07   0.9433
ageDecade:SexMen == 0       0.036139   0.020273    1.78   0.0747
ageDecade:RaceAfrAm == 0   -0.062114   0.021045   -2.95   0.0032
SexMen:ageDecad2 == 0       0.023069   0.012945    1.78   0.0747
RaceAfrAm:ageDecad2 == 0   -0.054588   0.013329   -4.10  4.2e-05
(Univariate p values reported)

Figure 1. Rate of change in log transformed hip bone mineral density for African Americans and whites above and below 125% of the poverty level.
Rate of change in log transformed hip bone mineral density for African Americans and whites above and below 125% of the poverty level.

Figure 2. Rate of change in log transformed lumbar bone mineral density for African Americans and whites above and below 125% of the poverty level.
Rate of change in log transformed lumbar bone mineral density for African Americans and whites above and below 125% of the poverty level.

Separate analyses for participants initially aged <50 and ≥50

We need separate analyses by age to compare our data to other published studies many of which include only older women. Consequently I divided the sample into two segments at age 50, which is roughly the median age ( 48.6 years). Note that dividing the sample reduces our power to find significant effects.

The results are displayed below without any commentary.

<50

Table 2. Association of log transformed hip and lumbar bone mineral density with age, sex, race, poverty status, body mass index, current alcohol use, and current cigarette smoking for participants initially <50 years old.

Hip


     Simultaneous Tests for General Linear Hypotheses

Fit: lmer(formula = logHip ~ ageDecade * (Sex + Race) + PovStat + 
    PhysBMI + MedHxAlcCurr + MedHxCigaretteCurr + (ageDecade | 
    HNDid), data = dxa[dxa$ageGroup == "<50", ], na.action = na.omit)

Linear Hypotheses:
                            Estimate Std. Error z value   Pr(>|z|)
(Intercept) == 0           -0.226980   0.021059  -10.78    < 2e-16
ageDecade == 0             -0.014740   0.008027   -1.84     0.0663
SexMen == 0                 0.048668   0.009934    4.90 0.00000096
RaceAfrAm == 0              0.038802   0.009916    3.91 0.00009112
PovStatBelow == 0           0.004594   0.008383    0.55     0.5837
PhysBMI == 0                0.009976   0.000599   16.66    < 2e-16
MedHxAlcCurrYes == 0       -0.018325   0.009707   -1.89     0.0591
MedHxCigaretteCurrYes == 0 -0.021429   0.008347   -2.57     0.0102
ageDecade:SexMen == 0      -0.025305   0.008934   -2.83     0.0046
ageDecade:RaceAfrAm == 0    0.017786   0.009075    1.96     0.0500
(Univariate p values reported)

Lumbar spine


     Simultaneous Tests for General Linear Hypotheses

Fit: lmer(formula = logLum ~ ageDecade * (Sex + Race) + PovStat + 
    PhysBMI + MedHxAlcCurr + MedHxCigaretteCurr + (ageDecade | 
    HNDid), data = dxa[dxa$ageGroup == "<50", ], na.action = na.omit)

Linear Hypotheses:
                            Estimate Std. Error z value  Pr(>|z|)
(Intercept) == 0           -0.109925   0.025408   -4.33 0.0000152
ageDecade == 0             -0.095152   0.011060   -8.60   < 2e-16
SexMen == 0                 0.007365   0.011276    0.65     0.514
RaceAfrAm == 0              0.054170   0.011233    4.82 0.0000014
PovStatBelow == 0           0.029047   0.010348    2.81     0.005
PhysBMI == 0                0.007205   0.000735    9.80   < 2e-16
MedHxAlcCurrYes == 0        0.004876   0.012079    0.40     0.686
MedHxCigaretteCurrYes == 0  0.000403   0.010250    0.04     0.969
ageDecade:SexMen == 0       0.007658   0.012323    0.62     0.534
ageDecade:RaceAfrAm == 0    0.004818   0.012508    0.39     0.700
(Univariate p values reported)

Figure 3. Rate of change in log transformed hip bone mineral density for African Americans and whites above and below 125% of the poverty level who were initially <50 years old.
Rate of change in log transformed hip bone mineral density for African Americans and whites above and below 125% of the poverty level who were initially <50 years old.

Figure 4. Rate of change in log transformed lumbar bone mineral density for African Americans and whites above and below 125% of the poverty level who were initially <50 years old.
Rate of change in log transformed lumbar bone mineral density for African Americans and whites above and below 125% of the poverty level who were initially <50 years old.

≥50

Table 3. Association of log transformed hip and lumbar bone mineral density with age, sex, race, poverty status, body mass index, current alcohol use, and current cigarette smoking for participants initially ≥50 years old.

Hip


     Simultaneous Tests for General Linear Hypotheses

Fit: lmer(formula = logHip ~ ageDecade * (Sex + Race) + PovStat + 
    PhysBMI + MedHxAlcCurr + MedHxCigaretteCurr + (ageDecade | 
    HNDid), data = dxa[dxa$ageGroup == "≥50", ], na.action = na.omit)

Linear Hypotheses:
                            Estimate Std. Error z value Pr(>|z|)
(Intercept) == 0           -0.321306   0.026198  -12.26  < 2e-16
ageDecade == 0             -0.047164   0.011743   -4.02  5.9e-05
SexMen == 0                 0.100720   0.010120    9.95  < 2e-16
RaceAfrAm == 0              0.075103   0.009852    7.62  2.5e-14
PovStatBelow == 0          -0.015555   0.010353   -1.50     0.13
PhysBMI == 0                0.009621   0.000752   12.80  < 2e-16
MedHxAlcCurrYes == 0       -0.012543   0.010540   -1.19     0.23
MedHxCigaretteCurrYes == 0 -0.010213   0.010510   -0.97     0.33
ageDecade:SexMen == 0       0.015148   0.013481    1.12     0.26
ageDecade:RaceAfrAm == 0    0.015490   0.013496    1.15     0.25
(Univariate p values reported)

Lumbar spine


     Simultaneous Tests for General Linear Hypotheses

Fit: lmer(formula = logLum ~ ageDecade * (Sex + Race) + PovStat + 
    PhysBMI + MedHxAlcCurr + MedHxCigaretteCurr + (ageDecade | 
    HNDid), data = dxa[dxa$ageGroup == "≥50", ], na.action = na.omit)

Linear Hypotheses:
                            Estimate Std. Error z value Pr(>|z|)
(Intercept) == 0           -0.216767   0.033685   -6.44  1.2e-10
ageDecade == 0             -0.093873   0.014088   -6.66  2.7e-11
SexMen == 0                 0.081833   0.013265    6.17  6.9e-10
RaceAfrAm == 0              0.069027   0.012941    5.33  9.6e-08
PovStatBelow == 0           0.006257   0.013289    0.47     0.64
PhysBMI == 0                0.006985   0.000965    7.24  4.4e-13
MedHxAlcCurrYes == 0        0.004502   0.013590    0.33     0.74
MedHxCigaretteCurrYes == 0 -0.011605   0.013423   -0.86     0.39
ageDecade:SexMen == 0       0.015207   0.016082    0.95     0.34
ageDecade:RaceAfrAm == 0    0.006711   0.016145    0.42     0.68
(Univariate p values reported)

Figure 5. Rate of change in log transformed hip bone mineral density for African Americans and whites above and below 125% of the poverty level who were initially ≥50 years old.
Rate of change in log transformed hip bone mineral density for African Americans and whites above and below 125% of the poverty level who were initially ≥50 years old.

Figure 6. Rate of change in log transformed lumbar bone mineral density for African Americans and whites above and below 125% of the poverty level who were initially ≥50 years old.
Rate of change in log transformed lumbar bone mineral density for African Americans and whites above and below 125% of the poverty level who were initially ≥50 years old.