Using ADNI data for Cusp model fitting
Simple way
Auditory Verbal Learning Test fitted with Whole gray matter and covariables.
# Estevez-Gonzalez, A., Kulisevsky, J., Boltes, A., Otermin, P., & Garcia-Sanchez, C. (2003).
# Rey verbal learning test is a useful tool for differential diagnosis in the preclinical phase
# of Alzheimer's disease: comparison with mild cognitive impairment and normal aging.
# International Journal of Geriatric Psychiatry. 18 (11), 1021.
library("ADNIMERGE")
library(cusp)
library(psych) #for composite scores
# Let's get the data
tmp_np <- merge(adas, neurobat, by=c("RID", "VISCODE") )
mt2fa <- merge(tmp_np, adnimerge, by=c("RID", "VISCODE") )
rm(tmp_np)
# Calculate the subject age at every point
mt2fa$vAGE = mt2fa$AGE + mt2fa$Years
data <- data.frame(mt2fa$WholeBrain, mt2fa$ICV, mt2fa$vAGE, mt2fa$PTGENDER, mt2fa$PTEDUCAT, mt2fa$AVDEL30MIN, mt2fa$AVDELTOT)
datac <- data[complete.cases(data),]
datac$WB = datac$mt2fa.WholeBrain/datac$mt2fa.ICV
fit_avd <- cusp(y ~ mt2fa.AVDEL30MIN, alpha ~ WB +mt2fa.vAGE + mt2fa.PTGENDER +mt2fa.PTEDUCAT, beta ~ WB +mt2fa.vAGE + mt2fa.PTGENDER +mt2fa.PTEDUCAT, datac)
summary(fit_avd)
Amazing results
Call:
cusp(formula = y ~ mt2fa.AVDEL30MIN, alpha = alpha ~ WB + mt2fa.vAGE +
mt2fa.PTGENDER + mt2fa.PTEDUCAT, beta = beta ~ WB + mt2fa.vAGE +
mt2fa.PTGENDER + mt2fa.PTEDUCAT, data = datac)
Deviance Residuals:
Min 1Q Median 3Q Max
-2.06955 -0.26210 -0.03226 0.63723 3.40775
Coefficients:
Estimate Std. Error z value Pr(>|z|)
a[(Intercept)] -5.842305 0.325414 -17.953 < 2e-16 ***
a[WB] 5.365145 0.296437 18.099 < 2e-16 ***
a[mt2fa.vAGE] 0.004777 0.002000 2.388 0.0169 *
a[mt2fa.PTGENDERFemale] 0.364218 0.026875 13.552 < 2e-16 ***
a[mt2fa.PTEDUCAT] 0.078235 0.005217 14.995 < 2e-16 ***
b[(Intercept)] 7.001814 0.509934 13.731 < 2e-16 ***
b[WB] -5.970685 0.470236 -12.697 < 2e-16 ***
b[mt2fa.vAGE] -0.026695 0.003309 -8.069 7.11e-16 ***
b[mt2fa.PTGENDERFemale] 0.395185 0.044766 8.828 < 2e-16 ***
b[mt2fa.PTEDUCAT] 0.033672 0.008002 4.208 2.58e-05 ***
w[(Intercept)] -1.763659 0.012301 -143.381 < 2e-16 ***
w[mt2fa.AVDEL30MIN] 0.257004 0.001838 139.800 < 2e-16 ***
---
Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
Null deviance: 8677.7 on 6754 degrees of freedom
Linear deviance: 110910.4 on 6749 degrees of freedom
Logist deviance: NA on NA degrees of freedom
Delay deviance: 3610.5 on 6743 degrees of freedom
R.Squared logLik npar AIC AICc BIC
Linear model 0.1557933 -19036.661 6 38085.32 38085.33 38126.23
Cusp model 0.6142339 -7321.477 12 14666.95 14667.00 14748.77
---
Note: R.Squared for cusp model is Cobb's pseudo-R^2. This value
can become negative.
Chi-square test of linear vs. cusp model
X-squared = 2.343e+04, df = 6, p-value = 0
Number of optimization iterations: 40
Z-scores
Now let's compare the weights of each variable on the model. We need to translate everything to z-scores (or just do another linear transformation that carry every thing to comparable values)
datac$zWB = (datac$WB - mean(datac$WB))/sd(datac$WB)
datac$zAge = (datac$mt2fa.vAGE - mean(datac$mt2fa.vAGE))/sd(datac$mt2fa.vAGE)
datac$zEduc = (datac$mt2fa.PTEDUCAT - mean(datac$mt2fa.PTEDUCAT))/sd(datac$mt2fa.PTEDUCAT)
datac$zAVD = (datac$mt2fa.AVDEL30MIN - mean(datac$mt2fa.AVDEL30MIN))/sd(datac$mt2fa.AVDEL30MIN)
fit_avd_z <- cusp(y ~ zAVD, alpha ~ zWB + zAge + mt2fa.PTGENDER + zEduc, beta ~ zWB +zAge + mt2fa.PTGENDER + zEduc, datac)
summary(fit_avd_z)
The results are of course the same but the coefficients must be meaningful now,
Coefficients:
Estimate Std. Error z value Pr(>|z|)
a[(Intercept)] -0.708321 0.023240 -30.478 < 2e-16 ***
a[zWB] 0.290456 0.016048 18.099 < 2e-16 ***
a[zAge] 0.034254 0.014342 2.388 0.0169 *
a[mt2fa.PTGENDERFemale] 0.364218 0.026875 13.552 < 2e-16 ***
a[zEduc] 0.223024 0.014873 14.995 < 2e-16 ***
b[(Intercept)] 1.603759 0.046739 34.313 < 2e-16 ***
b[zWB] -0.323238 0.025457 -12.697 < 2e-16 ***
b[zAge] -0.191434 0.023726 -8.069 7.11e-16 ***
b[mt2fa.PTGENDERFemale] 0.395185 0.044766 8.828 < 2e-16 ***
b[zEduc] 0.095988 0.022812 4.208 2.58e-05 ***
w[(Intercept)] -0.688350 0.009603 -71.682 < 2e-16 ***
w[zAVD] 1.133500 0.008108 139.800 < 2e-16 ***
---
Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
Composite scores
First I'm going to try another NP test (Recognition)
fit_avr <- cusp(y ~ zAVR, alpha ~ zWB + zAge + mt2fa.PTGENDER + zEduc, beta ~ zWB +zAge + mt2fa.PTGENDER + zEduc, datac)
and this is not so good but still an improvement is done
> summary(fit_avr)
Call:
cusp(formula = y ~ zAVR, alpha = alpha ~ zWB + zAge + mt2fa.PTGENDER +
zEduc, beta = beta ~ zWB + zAge + mt2fa.PTGENDER + zEduc,
data = datac)
Deviance Residuals:
Min 1Q Median 3Q Max
-3.3337 -0.8146 -0.1929 0.2446 2.5763
Coefficients:
Estimate Std. Error z value Pr(>|z|)
a[(Intercept)] 0.74119 0.02784 26.625 < 2e-16 ***
a[zWB] 0.40520 0.01943 20.854 < 2e-16 ***
a[zAge] 0.08352 0.01681 4.967 6.79e-07 ***
a[mt2fa.PTGENDERFemale] -0.09332 0.03128 -2.983 0.00285 **
a[zEduc] 0.10035 0.01495 6.713 1.91e-11 ***
b[(Intercept)] 1.09138 0.05476 19.932 < 2e-16 ***
b[zWB] 0.02940 0.02921 1.007 0.31416
b[zAge] 0.11858 0.02729 4.345 1.39e-05 ***
b[mt2fa.PTGENDERFemale] 0.53540 0.04991 10.726 < 2e-16 ***
b[zEduc] 0.11832 0.02474 4.782 1.74e-06 ***
w[(Intercept)] 0.71871 0.01153 62.322 < 2e-16 ***
w[zAVR] 0.99105 0.00889 111.482 < 2e-16 ***
---
Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
Null deviance: 6633.7 on 6754 degrees of freedom
Linear deviance: 5952.1 on 6749 degrees of freedom
Logist deviance: NA on NA degrees of freedom
Delay deviance: 5049.6 on 6743 degrees of freedom
R.Squared logLik npar AIC AICc BIC
Linear model 0.1187225 -9157.572 6 18327.14 18327.16 18368.05
Cusp model 0.3758839 -7966.518 12 15957.04 15957.08 16038.85
---
Note: R.Squared for cusp model is Cobb's pseudo-R^2. This value
can become negative.
Chi-square test of linear vs. cusp model
X-squared = 2382, df = 6, p-value = 0
Number of optimization iterations: 38
Now, let's try a composite score
gfam <- data.frame(datac$zAVD, datac$zAVR)
famod <- fa(gfam, scores="regression")
datac$cs <- famod$scores
fit_cs <- cusp(y ~ cs, alpha ~ zWB + zAge + mt2fa.PTGENDER + zEduc, beta ~ zWB +zAge + mt2fa.PTGENDER + zEduc, datac)
And we get a very bad fit result
> summary(fit_cs)
Call:
cusp(formula = y ~ cs, alpha = alpha ~ zWB + zAge + mt2fa.PTGENDER +
zEduc, beta = beta ~ zWB + zAge + mt2fa.PTGENDER + zEduc,
data = datac)
Deviance Residuals:
Min 1Q Median 3Q Max
-2.9864 -0.5145 0.0386 0.5796 2.8034
Coefficients:
Estimate Std. Error z value Pr(>|z|)
a[(Intercept)] -0.166529 0.015351 -10.848 < 2e-16 ***
a[zWB] 0.508523 0.009612 52.905 < 2e-16 ***
a[zAge] 0.124850 0.017119 7.293 3.03e-13 ***
a[mt2fa.PTGENDERFemale] 0.251292 0.020108 12.497 < 2e-16 ***
a[zEduc] 0.230918 NA NA NA
b[(Intercept)] -0.224522 0.022933 -9.791 < 2e-16 ***
b[zWB] -0.231656 0.010449 -22.171 < 2e-16 ***
b[zAge] -0.128716 0.012640 -10.183 < 2e-16 ***
b[mt2fa.PTGENDERFemale] 0.845789 0.017774 47.587 < 2e-16 ***
b[zEduc] 0.204127 0.007479 27.293 < 2e-16 ***
w[(Intercept)] -0.035730 0.011210 -3.187 0.00144 **
w[cs] 1.012113 0.006090 166.187 < 2e-16 ***
---
Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
Null deviance: 5487.3 on 6754 degrees of freedom
Linear deviance: 4490.5 on 6749 degrees of freedom
Logist deviance: NA on NA degrees of freedom
Delay deviance: 5324.3 on 6743 degrees of freedom
R.Squared logLik npar AIC AICc BIC
Linear model 0.16171127 -8205.808 6 16423.62 16423.63 16464.52
Cusp model 0.03112304 -8567.331 12 17158.66 17158.71 17240.48
---
Note: R.Squared for cusp model is Cobb's pseudo-R^2. This value
can become negative.
Chi-square test of linear vs. cusp model
X-squared = 723, df = 6, p-value = 0
Number of optimization iterations: 106
That is, the composite score is not related through a cusp model to the independent variable analyzed here
A try for ADAS-Cog
data <- data.frame(mt2fa$WholeBrain, mt2fa$ICV, mt2fa$vAGE, mt2fa$PTGENDER, mt2fa$PTEDUCAT, mt2fa$Q4SCORE, mt2fa$Q8SCORE)
datac <- data[complete.cases(data),]
datac$WB = datac$mt2fa.WholeBrain/datac$mt2fa.ICV
datac$zWB = (datac$WB - mean(datac$WB))/sd(datac$WB)
datac$zAge = (datac$mt2fa.vAGE - mean(datac$mt2fa.vAGE))/sd(datac$mt2fa.vAGE)
datac$zEduc = (datac$mt2fa.PTEDUCAT - mean(datac$mt2fa.PTEDUCAT))/sd(datac$mt2fa.PTEDUCAT)
datac$dr = (mean(datac$mt2fa.Q4SCORE) - datac$mt2fa.Q4SCORE)/sd(datac$mt2fa.Q4SCORE)
datac$r = (mean(datac$mt2fa.Q8SCORE) - datac$mt2fa.Q8SCORE)/sd(datac$mt2fa.Q8SCORE)
fit_dr <- cusp(y ~ dr, alpha ~ zWB + zAge + mt2fa.PTGENDER + zEduc, beta ~ zWB +zAge + mt2fa.PTGENDER + zEduc, datac)
fit_r <- cusp(y ~ r, alpha ~ zWB + zAge + mt2fa.PTGENDER + zEduc, beta ~ zWB +zAge + mt2fa.PTGENDER + zEduc, datac)
not bad at all for Delay Recall
> summary(fit_dr)
Call:
cusp(formula = y ~ dr, alpha = alpha ~ zWB + zAge + mt2fa.PTGENDER +
zEduc, beta = beta ~ zWB + zAge + mt2fa.PTGENDER + zEduc,
data = datac)
Deviance Residuals:
Min 1Q Median 3Q Max
-3.1117 -0.4991 -0.1005 0.4315 3.3147
Coefficients:
Estimate Std. Error z value Pr(>|z|)
a[(Intercept)] 0.007960 0.020930 0.380 0.703714
a[zWB] 0.508635 0.017192 29.585 < 2e-16 ***
a[zAge] 0.138990 0.013981 9.942 < 2e-16 ***
a[mt2fa.PTGENDERFemale] 0.102236 0.025494 4.010 6.07e-05 ***
a[zEduc] 0.190303 0.013197 14.420 < 2e-16 ***
b[(Intercept)] 0.825442 0.054864 15.045 < 2e-16 ***
b[zWB] -0.235399 0.029643 -7.941 2.01e-15 ***
b[zAge] -0.182519 0.025867 -7.056 1.71e-12 ***
b[mt2fa.PTGENDERFemale] 0.745478 0.047279 15.768 < 2e-16 ***
b[zEduc] 0.125539 0.023628 5.313 1.08e-07 ***
w[(Intercept)] 0.039500 0.011097 3.559 0.000372 ***
w[dr] 1.118457 0.009343 119.717 < 2e-16 ***
---
Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
Null deviance: 8511.4 on 6804 degrees of freedom
Linear deviance: 5443.0 on 6799 degrees of freedom
Logist deviance: NA on NA degrees of freedom
Delay deviance: 4560.9 on 6793 degrees of freedom
R.Squared logLik npar AIC AICc BIC
Linear model 0.2000289 -8896.008 6 17804.02 17804.03 17844.97
Cusp model 0.4672353 -7913.728 12 15851.46 15851.50 15933.36
---
Note: R.Squared for cusp model is Cobb's pseudo-R^2. This value
can become negative.
Chi-square test of linear vs. cusp model
X-squared = 1965, df = 6, p-value = 0
Number of optimization iterations: 38
but worst for Recognition
> summary(r)
Call:
cusp(formula = y ~ r, alpha = alpha ~ zWB + zAge + mt2fa.PTGENDER +
zEduc, beta = beta ~ zWB + zAge + mt2fa.PTGENDER + zEduc,
data = datac)
Deviance Residuals:
Min 1Q Median 3Q Max
-3.1343 -0.8453 -0.2669 0.2033 2.5628
Coefficients:
Estimate Std. Error z value Pr(>|z|)
a[(Intercept)] 0.754786 0.029939 25.211 < 2e-16 ***
a[zWB] 0.445183 0.020237 21.998 < 2e-16 ***
a[zAge] 0.082755 0.017131 4.831 1.36e-06 ***
a[mt2fa.PTGENDERFemale] -0.138675 0.032093 -4.321 1.55e-05 ***
a[zEduc] 0.076295 0.015311 4.983 6.26e-07 ***
b[(Intercept)] 0.898577 0.061474 14.617 < 2e-16 ***
b[zWB] 0.013364 0.030828 0.433 0.664652
b[zAge] 0.041912 0.028325 1.480 0.138959
b[mt2fa.PTGENDERFemale] 0.395628 0.052501 7.536 4.86e-14 ***
b[zEduc] 0.084819 0.025534 3.322 0.000894 ***
w[(Intercept)] 0.641352 0.012443 51.543 < 2e-16 ***
w[r] 0.960657 0.009485 101.286 < 2e-16 ***
---
Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
Null deviance: 6279.2 on 6804 degrees of freedom
Linear deviance: 5963.7 on 6799 degrees of freedom
Logist deviance: NA on NA degrees of freedom
Delay deviance: 5578.1 on 6793 degrees of freedom
R.Squared logLik npar AIC AICc BIC
Linear model 0.1235032 -9206.852 6 18425.70 18425.72 18466.66
Cusp model 0.2913304 -8250.294 12 16524.59 16524.63 16606.49
---
Note: R.Squared for cusp model is Cobb's pseudo-R^2. This value
can become negative.
Chi-square test of linear vs. cusp model
X-squared = 1913, df = 6, p-value = 0
Number of optimization iterations: 44
Notas para Composite Scores
Lo ideal seria hacer script con todos los composites posibles y mirarlo contra los biomarcadores disponibles en adnimerge. Pero cada biomarcador lleva un tipo de procesamiento distinto y cada composite ha de ser definido previamente. Por ejemplo el composite de Delay Recall (drcs) lo construimos a partir de adas.Q4SCORE y neurobat.AVDEL30MIN pero en cada caso hay que definir las variables de partida.
Hay varios biomarcadores en la tabla adnimerge que pueden estar relacionados con los composites neuropsicologicos
> names(adnimerge)
[1] "ORIGPROT" "COLPROT" "RID" "PTID"
[5] "VISCODE" "EXAMDATE" "SITE" "DX.bl"
[9] "AGE" "PTGENDER" "PTEDUCAT" "PTETHCAT"
[13] "PTRACCAT" "PTMARRY" "APOE4" "FDG"
[17] "PIB" "AV45" "CDRSB" "ADAS11"
[21] "ADAS13" "MMSE" "RAVLT.immediate" "RAVLT.learning"
[25] "RAVLT.forgetting" "RAVLT.perc.forgetting" "FAQ" "MOCA"
[29] "EcogPtMem" "EcogPtLang" "EcogPtVisspat" "EcogPtPlan"
[33] "EcogPtOrgan" "EcogPtDivatt" "EcogPtTotal" "EcogSPMem"
[37] "EcogSPLang" "EcogSPVisspat" "EcogSPPlan" "EcogSPOrgan"
[41] "EcogSPDivatt" "EcogSPTotal" "FLDSTRENG" "FSVERSION"
[45] "Ventricles" "Hippocampus" "WholeBrain" "Entorhinal"
[49] "Fusiform" "MidTemp" "ICV" "DX"
[53] "EXAMDATE.bl" "CDRSB.bl" "ADAS11.bl" "ADAS13.bl"
[57] "MMSE.bl" "RAVLT.immediate.bl" "RAVLT.learning.bl" "RAVLT.forgetting.bl"
[61] "RAVLT.perc.forgetting.bl" "FAQ.bl" "FLDSTRENG.bl" "FSVERSION.bl"
[65] "Ventricles.bl" "Hippocampus.bl" "WholeBrain.bl" "Entorhinal.bl"
[69] "Fusiform.bl" "MidTemp.bl" "ICV.bl" "MOCA.bl"
[73] "EcogPtMem.bl" "EcogPtLang.bl" "EcogPtVisspat.bl" "EcogPtPlan.bl"
[77] "EcogPtOrgan.bl" "EcogPtDivatt.bl" "EcogPtTotal.bl" "EcogSPMem.bl"
[81] "EcogSPLang.bl" "EcogSPVisspat.bl" "EcogSPPlan.bl" "EcogSPOrgan.bl"
[85] "EcogSPDivatt.bl" "EcogSPTotal.bl" "FDG.bl" "PIB.bl"
[89] "AV45.bl" "Years.bl" "Month.bl" "Month"
[93] "M"
El problema es que cada uno debe ser analizado de manera distinta. Las variables Ventricles, Hippocampus y WholeBrain deben de alguna manera normalizarse por ICV (revisar Entorhinal, Fusiform y MidTemp) mientras que FDG, PIB y AV45 son variables normalizadas.
library("ADNIMERGE")
library(cusp)
library(psych) #for composite scores
# Let's get the data
tmp_np <- merge(adas, neurobat, by=c("RID", "VISCODE") )
m <- merge(tmp_np, adnimerge, by=c("RID", "VISCODE") )
rm(tmp_np)
# Select data
m$cAGE = m$AGE + m$Years
data <- data.frame(m$WholeBrain, m$ICV, m$cAGE, m$PTGENDER, m$PTEDUCAT, m$AVDEL30MIN, m$Q4SCORE)
datac <- data[complete.cases(data),]
#Z-scores and Composite Scores
datac$zavd = (datac$m.AVDEL30MIN - mean(datac$m.AVDEL30MIN))/sd(datac$m.AVDEL30MIN)
datac$zdr = (mean(datac$m.Q4SCORE) - datac$m.Q4SCORE)/sd(datac$m.Q4SCORE)
datac$zAge = (datac$m.cAGE - mean(datac$m.cAGE))/sd(datac$m.cAGE)
datac$zEduc = (datac$m.PTEDUCAT - mean(datac$m.PTEDUCAT))/sd(datac$m.PTEDUCAT)
gfam <- data.frame(datac$zavd, datac$zdr)
famod <- fa(gfam, scores="regression")
datac$drcs <- famod$scores
# NI biomarker
datac$wb = datac$m.WholeBrain/datac$m.ICV
datac$zwb = (datac$wb - mean(datac$wb))/sd(datac$wb)
#fit to Cusp model
fit <- cusp(y ~ drcs, alpha ~ zwb + zAge + m.PTGENDER + zEduc, beta ~ zwb +zAge + m.PTGENDER + zEduc, datac)
summary(fit)
El resultado no es demasiado bueno para la materia gris
> summary(fit)
Call:
cusp(formula = y ~ drcs, alpha = alpha ~ zwb + zAge + m.PTGENDER +
zEduc, beta = beta ~ zwb + zAge + m.PTGENDER + zEduc, data = datac)
Deviance Residuals:
Min 1Q Median 3Q Max
-3.03128 -0.34504 0.04153 0.68234 3.46997
Coefficients:
Estimate Std. Error z value Pr(>|z|)
a[(Intercept)] -0.495490 0.034268 -14.459 < 2e-16 ***
a[zwb] 0.439670 0.016181 27.172 < 2e-16 ***
a[zAge] 0.084987 0.015421 5.511 3.57e-08 ***
a[m.PTGENDERFemale] 0.335385 0.036312 9.236 < 2e-16 ***
a[zEduc] 0.246808 0.016847 14.650 < 2e-16 ***
b[(Intercept)] 0.707160 0.038400 18.416 < 2e-16 ***
b[zwb] -0.430749 0.019983 -21.556 < 2e-16 ***
b[zAge] -0.263518 0.015366 -17.149 < 2e-16 ***
b[m.PTGENDERFemale] 0.737773 0.041330 17.851 < 2e-16 ***
b[zEduc] 0.121714 0.021839 5.573 2.50e-08 ***
w[(Intercept)] -0.343946 0.012126 -28.364 < 2e-16 ***
w[drcs] 1.144778 0.009349 122.443 < 2e-16 ***
---
Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
Null deviance: 7603.1 on 6754 degrees of freedom
Linear deviance: 4650.8 on 6749 degrees of freedom
Logist deviance: NA on NA degrees of freedom
Delay deviance: 5097.1 on 6743 degrees of freedom
R.Squared logLik npar AIC AICc BIC
Linear model 0.1983602 -8324.282 6 16660.56 16660.58 16701.47
Cusp model 0.3583674 -7877.500 12 15779.00 15779.05 15860.82
---
Note: R.Squared for cusp model is Cobb's pseudo-R^2. This value
can become negative.
Chi-square test of linear vs. cusp model
X-squared = 893.6, df = 6, p-value = 0
Number of optimization iterations: 52
Un poco mejor (no mucho) para los Ventriculos
> summary(fit)
Call:
cusp(formula = y ~ drcs, alpha = alpha ~ zwb + zAge + m.PTGENDER +
zEduc, beta = beta ~ zwb + zAge + m.PTGENDER + zEduc, data = datac)
Deviance Residuals:
Min 1Q Median 3Q Max
-1.96597 -0.34590 0.08371 0.71785 3.30025
Coefficients:
Estimate Std. Error z value Pr(>|z|)
a[(Intercept)] -0.45714 0.02514 -18.184 < 2e-16 ***
a[zwb] -0.37215 0.01895 -19.643 < 2e-16 ***
a[zAge] 0.02568 0.01398 1.837 0.0662 .
a[m.PTGENDERFemale] 0.26724 0.02818 9.484 < 2e-16 ***
a[zEduc] 0.24629 0.01497 16.455 < 2e-16 ***
b[(Intercept)] 0.68135 0.06771 10.063 < 2e-16 ***
b[zwb] 0.04897 0.02989 1.638 0.1013
b[zAge] -0.13237 0.02618 -5.057 4.27e-07 ***
b[m.PTGENDERFemale] 0.71151 0.05476 12.994 < 2e-16 ***
b[zEduc] 0.13563 0.02624 5.169 2.35e-07 ***
w[(Intercept)] -0.28049 0.01186 -23.655 < 2e-16 ***
w[drcs] 1.12939 0.01124 100.486 < 2e-16 ***
---
Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
Null deviance: 7186.9 on 6554 degrees of freedom
Linear deviance: 4853.0 on 6549 degrees of freedom
Logist deviance: NA on NA degrees of freedom
Delay deviance: 4458.2 on 6543 degrees of freedom
R.Squared logLik npar AIC AICc BIC
Linear model 0.1386990 -8315.823 6 16643.65 16643.66 16684.37
Cusp model 0.4315817 -7959.414 12 15942.83 15942.88 16024.28
---
Note: R.Squared for cusp model is Cobb's pseudo-R^2. This value
can become negative.
Chi-square test of linear vs. cusp model
X-squared = 712.8, df = 6, p-value = 0
Number of optimization iterations: 40
Para el hipocampo el lineal es tan bueno como el no lineal
> summary(fit)
Call:
cusp(formula = y ~ drcs, alpha = alpha ~ zwb + zAge + m.PTGENDER +
zEduc, beta = beta ~ zwb + zAge + m.PTGENDER + zEduc, data = datac)
Deviance Residuals:
Min 1Q Median 3Q Max
-3.0590 -0.3649 0.0143 0.5757 3.2717
Coefficients:
Estimate Std. Error z value Pr(>|z|)
a[(Intercept)] -0.5748835 0.0203013 -28.318 < 2e-16 ***
a[zwb] 0.7766157 0.0209173 37.128 < 2e-16 ***
a[zAge] 0.1420567 NA NA NA
a[m.PTGENDERFemale] 0.3207513 NA NA NA
a[zEduc] 0.2969783 0.0005627 527.749 < 2e-16 ***
b[(Intercept)] 0.5155457 NA NA NA
b[zwb] -0.7661551 0.0139140 -55.064 < 2e-16 ***
b[zAge] -0.3060879 0.0196256 -15.596 < 2e-16 ***
b[m.PTGENDERFemale] 0.7437734 0.0132296 56.220 < 2e-16 ***
b[zEduc] 0.1028033 0.0284092 3.619 0.000296 ***
w[(Intercept)] -0.4249690 0.0080047 -53.090 < 2e-16 ***
w[drcs] 1.1575905 0.0062789 184.362 < 2e-16 ***
---
Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
Null deviance: 6826.7 on 5939 degrees of freedom
Linear deviance: 3140.1 on 5934 degrees of freedom
Logist deviance: NA on NA degrees of freedom
Delay deviance: 4303.2 on 5928 degrees of freedom
R.Squared logLik npar AIC AICc BIC
Linear model 0.3836286 -6535.252 6 13082.50 13082.52 13122.64
Cusp model 0.3817421 -6092.774 12 12209.55 12209.60 12289.82
---
Note: R.Squared for cusp model is Cobb's pseudo-R^2. This value
can become negative.
Chi-square test of linear vs. cusp model
X-squared = 885, df = 6, p-value = 0
Number of optimization iterations: 65
Malo para el FDG
> summary(fit)
Call:
cusp(formula = y ~ drcs, alpha = alpha ~ zwb + zAge + m.PTGENDER +
zEduc, beta = beta ~ zwb + zAge + m.PTGENDER + zEduc, data = datac)
Deviance Residuals:
Min 1Q Median 3Q Max
-3.02185 -0.35020 0.05687 0.63803 3.60924
Coefficients:
Estimate Std. Error z value Pr(>|z|)
a[(Intercept)] -0.508309 0.023910 -21.259 < 2e-16 ***
a[zwb] 0.524366 0.014518 36.119 < 2e-16 ***
a[zAge] -0.077225 0.020089 -3.844 0.000121 ***
a[m.PTGENDERFemale] 0.266786 0.007268 36.705 < 2e-16 ***
a[zEduc] 0.210118 0.021580 9.737 < 2e-16 ***
b[(Intercept)] 0.842972 0.015688 53.734 < 2e-16 ***
b[zwb] -0.589807 NA NA NA
b[zAge] -0.124395 0.033468 -3.717 0.000202 ***
b[m.PTGENDERFemale] 0.600601 0.040893 14.687 < 2e-16 ***
b[zEduc] 0.122145 0.034828 3.507 0.000453 ***
w[(Intercept)] -0.426748 0.014152 -30.154 < 2e-16 ***
w[drcs] 1.169788 0.008142 143.666 < 2e-16 ***
---
Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
Null deviance: 3895.6 on 3317 degrees of freedom
Linear deviance: 2026.9 on 3312 degrees of freedom
Logist deviance: NA on NA degrees of freedom
Delay deviance: 2475.7 on 3306 degrees of freedom
R.Squared logLik npar AIC AICc BIC
Linear model 0.2880251 -3890.378 6 7792.755 7792.781 7829.398
Cusp model 0.3869597 -3622.986 12 7269.971 7270.066 7343.257
---
Note: R.Squared for cusp model is Cobb's pseudo-R^2. This value
can become negative.
Chi-square test of linear vs. cusp model
X-squared = 534.8, df = 6, p-value = 0
Number of optimization iterations: 43
Pesimo para el AV45
> summary(fit)
Call:
cusp(formula = y ~ drcs, alpha = alpha ~ zwb + zAge + m.PTGENDER +
zEduc, beta = beta ~ zwb + zAge + m.PTGENDER + zEduc, data = datac)
Deviance Residuals:
Min 1Q Median 3Q Max
-2.77918 -0.53934 -0.09885 0.52564 2.93425
Coefficients:
Estimate Std. Error z value Pr(>|z|)
a[(Intercept)] -0.329897 NA NA NA
a[zwb] -0.509019 0.029985 -16.976 < 2e-16 ***
a[zAge] -0.175968 0.022751 -7.735 1.04e-14 ***
a[m.PTGENDERFemale] 0.492413 0.050822 9.689 < 2e-16 ***
a[zEduc] 0.185683 0.026500 7.007 2.44e-12 ***
b[(Intercept)] 0.149342 NA NA NA
b[zwb] 0.169838 0.006714 25.295 < 2e-16 ***
b[zAge] -0.183744 NA NA NA
b[m.PTGENDERFemale] 0.701522 NA NA NA
b[zEduc] 0.127566 NA NA NA
w[(Intercept)] -0.049160 0.016707 -2.943 0.00326 **
w[drcs] 1.088235 0.010977 99.138 < 2e-16 ***
---
Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
Null deviance: 1649.6 on 1691 degrees of freedom
Linear deviance: 1051.9 on 1686 degrees of freedom
Logist deviance: NA on NA degrees of freedom
Delay deviance: 1403.4 on 1680 degrees of freedom
R.Squared logLik npar AIC AICc BIC
Linear model 0.2448373 -1998.714 6 4009.428 4009.478 4042.030
Cusp model 0.1503419 -2015.754 12 4055.508 4055.693 4120.712
---
Note: R.Squared for cusp model is Cobb's pseudo-R^2. This value
can become negative.
Chi-square test of linear vs. cusp model
X-squared = 34.08, df = 6, p-value = 6.494e-06
Number of optimization iterations: 68
Pero bastante bueno para el PiB
> summary(fit)
Call:
cusp(formula = y ~ drcs, alpha = alpha ~ zwb + zAge + m.PTGENDER +
zEduc, beta = beta ~ zwb + zAge + m.PTGENDER + zEduc, data = datac)
Deviance Residuals:
Min 1Q Median 3Q Max
-1.39747 -0.34765 0.02365 0.61995 2.80434
Coefficients:
Estimate Std. Error z value Pr(>|z|)
a[(Intercept)] -0.41926 0.10606 -3.953 7.71e-05 ***
a[zwb] -0.41509 0.08006 -5.185 2.16e-07 ***
a[zAge] -0.01542 0.06966 -0.221 0.82483
a[m.PTGENDERFemale] 0.01350 0.14087 0.096 0.92365
a[zEduc] 0.15078 0.07280 2.071 0.03835 *
b[(Intercept)] 1.38998 0.24548 5.662 1.49e-08 ***
b[zwb] 0.09861 0.13536 0.729 0.46629
b[zAge] -0.33692 0.11845 -2.844 0.00445 **
b[m.PTGENDERFemale] 0.61578 0.24049 2.561 0.01045 *
b[zEduc] 0.04128 0.12358 0.334 0.73837
w[(Intercept)] -0.49934 0.05477 -9.116 < 2e-16 ***
w[drcs] 1.23598 0.04958 24.928 < 2e-16 ***
---
Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
Null deviance: 297.20 on 217 degrees of freedom
Linear deviance: 154.46 on 212 degrees of freedom
Logist deviance: NA on NA degrees of freedom
Delay deviance: 152.70 on 206 degrees of freedom
R.Squared logLik npar AIC AICc BIC
Linear model 0.2060384 -271.7741 6 555.5482 555.9463 575.8552
Cusp model 0.5180603 -235.4183 12 494.8367 496.3586 535.4506
---
Note: R.Squared for cusp model is Cobb's pseudo-R^2. This value
can become negative.
Chi-square test of linear vs. cusp model
X-squared = 72.71, df = 6, p-value = 1.135e-13
Number of optimization iterations: 34
