stride.estimator: STRIDE: Robust powerful mixture models
In tpgarcia/stride: STRIDE: Robust powerful mixture models
Description
Usage
Arguments
Value
Details
References
Examples
Description
STRIDE estimators are nonparametric estimates of the distribution function for mixture data where
the population identifiers are unknown, and the probability of belonging
to a population is known (typically estimated with external data).
The distribution functions are evaluated at
time points tval. All STRIDE estimators can adjust for dynamic landmark prediction. The NPNA,
NPNA_avg and NPNA_wrong estimators can adjust for one
discrete covariate (zz) and one continuous covariate (ww). See details below.
Usage
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stride.estimator(
n,
m,
p,
qvs,
q,
x,
delta,
ww,
zz,
run.NPMLEs,
run.NPNA,
run.NPNA_avg,
run.NPNA_wrong,
run.OLS,
run.WLS,
run.EFF,
run.EMPAVA,
tval,
tval0,
z.use,
w.use,
update.qs,
know.true.groups = FALSE,
true.group.identifier = NULL,
run.prediction.accuracy,
do_cross_validation_AUC_BS
)
Arguments
n
sample size, must be at least 1.
m
number of different mixture proportions, must be at least 2.
p
number of populations, must be at least 2.
qvs
a numeric matrix of size p by m containing all possible
mixture proportions (i.e., the probability of belonging to each population k, k=1,...,p.).
q
a numeric matrix of size p by n containing the
mixture proportions for each person in the sample.
x
a numeric vector of length n containing the observed event times
for each person in the sample.
delta
a numeric vector of length n that denotes
censoring (1 denotes event is observed, 0 denotes event is censored).
ww
a numeric vector of length n containing the values of the continuous
covariate for each person in the sample. Can be NULL.
zz
a numeric vector of length n containing the values of the discrete
covariate for each person in the sample. Can be NULL.
run.NPMLEs
a logical indicator. If TRUE, then the output includes the
estimated distribution function for mixture data based on the type-I and type II nonparametric maximum likelihood
estimators. The type I nonparametric maximum likelihood estimator is referred
to as the "Kaplan-Meier" estimator in Garcia and Parast (2020). Neither the type I nor type II
adjust for covariates.
run.NPNA
a logical indicator. If TRUE, then the output includes the
estimated distribution function for mixture data that accounts for covariates and dynamic
landmarking. This estimator is called "NPNA" in Garcia and Parast (2020).
run.NPNA_avg
a logical indicator. If TRUE, then the output includes the
estimated distribution function for mixture data that averages out over the observed covariates.
This is referred to as NPNA_marg in Garcia and Parast (2020).
run.NPNA_wrong
a logical indicator. If TRUE, then the output includes the
estimated distribution function for mixture data that adjusts for covariates, but
ignores landmarking. This is referred to as NPNA_t_0=0 in Garcia and Parast (2020).
run.OLS
a logical indicator. If TRUE, then the output includes the estimated distribution function
computed using an ordinary least squares influence function. The estimator adjusts for censoring using
inverse probability weighting (IPW), augmented inverse probability weighting (AIPW),
and imputation (IMP). See details in Wang et al (2012). These estimators do not
adjust for covariates.
run.WLS
a logical indicator. If TRUE, then the output includes the estimated distribution function
computed using a weighted least squares influence function. The estimator adjusts for censoring using
inverse probability weighting (IPW), augmented inverse probability weighting (AIPW),
and imputation (IMP). See details in Wang et al (2012). These estimators do not
adjust for covariates.
run.EFF
a logical indicator. If TRUE, then the output includes the estimated distribution function
computed using the efficient influence function based on Hilbert space projection theory results.
The estimator adjusts for censoring using
inverse probability weighting (IPW), augmented inverse probability weighting (AIPW),
and imputation (IMP). See details in Wang et al (2012). These estimators do not
adjust for covariates.
run.EMPAVA
logical indicator. If TRUE, we compute the distribution function for the mixture data
based on an expectation-maximization (EM) algorithm that uses the pool adjacent violators algorithm (PAVA)
from isotone regression to yield a non-negative and monotone estimator. This estimator does not adjust
for covariates. See details in Qing et al (2014).
tval
numeric vector of time points at which the distribution function is evaluated, all values must
be non-negative.
tval0
numeric vector of time points representing the landmark times. All values must be non-negative
and smaller than the maximum of tval.
z.use
numeric vector at which to evaluate the discrete covariate Z at in the estimated distribution function.
The values of z.use must be in the range of the observed zz. Can be NULL.
w.use
numeric vector at which to evaluate the continuous covariate W at in the estimated distribution function.
The values of w.use must be in the range of the observed ww. Can be NULL.
update.qs
logical indicator. If TRUE, the mixture proportions q will be updated. This is currently not implemented.
know.true.groups
logical indicator. If TRUE, then we know the population identifier for each person in the sample.
This option is only used for simulation studies to check prediction accuracy. Default is FALSE.
true.group.identifier
numeric vector of length n denoting the population identifier for each person in the sample.
Default is NULL.
run.prediction.accuracy
logical indicator. If TRUE, then we compute the prediction accuracy measures, including the
area under the receiver operating characteristic curve (AUC) and the Brier Score (BS). Prediction accuracy is only valid
in simulation studies where know.true.groups=TRUE and true.group.identifier is available.
do_cross_validation_AUC_BS
logical indicator. If TRUE, then we compute the prediction accuracy measures, including the
area under the receiver operating characteristic curve (AUC) and the Brier Score (BS) using cross-validation. Prediction accuracy is only valid
in simulation studies where know.true.groups=TRUE and true.group.identifier is available.
Value
stride.estimator returns a list containing
problem: a numeric indicator of errors in the NPNA estimator. If NULL, no error is reported.
Otherwise, there is an error in the computation of the NPNA estimator.
Ft.estimate: a numeric array containing the estimated distribution functions for all methods for all
p populations. The distribution function is evaluated at each tval,
tval0, z.use (if non-NULL), w.use (if non-NULL), and for all p populations.
The dimension of the array is \# of methods by length(tval) by lenth(tval0) by
length(z.use) by length(w.use) by p. If z.use and w.use are NULL,
the dimension of the array is \# of methods by length(tval) by lenth(tval0) by p. The distribution function is only valid for t≥q t_0, so
Ft.estimate shows NA for any combination for which t<t_0.
-
St.estimate: a numeric array containing the estimated distribution functions for all methods
for all m mixture proportion subgroups. The distribution function is evaluated
at each tval, tval0, z.use (if non-NULL), w.use (if non-NULL), and for all m mixture
proportion subgroups.
The dimension of the array is \# of methods by length(tval) by lenth(tval0) by
length(z.use) by length(w.use) by m. If z.use and w.use are NULL,
the dimension of the array is \# of methods by length(tval) by lenth(tval0) by m. The distribution function is only valid for t≥q t_0, so
St.estimate shows NA for any combination for which t<t_0.
Ft.AUC.BS: a numeric array containing the
area under the receiver operating characteristic curve (AUC) and
Brier Score (BS) for the p populations. The dimension of the array is \# of methods by
length(tval) by length(tval0) by 2,
where the last dimension stores the AUC and BS results.
Results for both the estimated distributon functions and prediction
accuracy measures (AUC, BS) are only valid when t≥q t_0, so
arrays show NA for any combination for which t<t_0.
-
St.AUC.BS: a numeric array containing the results are the
area under the receiver operating characteristic curve (AUC) and
Brier Score (BS) for the m mixture proportion groups.
The dimension of the array is \# of methods by
length(tval) by length(tval0) by 2,
where the last dimension stores the AUC and BS results.
Results for both the estimated distributon functions and prediction
accuracy measures (AUC, BS) are only valid when t≥q t_0, so
arrays show NA for any combination for which t<t_0.
Details
We estimate nonparametric distribution functions for mixture data where
the population identifiers are unknown, and the probability of belonging
to a population is known (typically estimated with external data).
The distribution functions are evaluated at
time points tval. All estimators adjust for dynamic landmark prediction.
Dynamic landmark prediction means that the distribution function is computed knowing
that the survival time, T, satisfies T >t_0
where t_0 are the time points in tval0. The NPNA, NPNA_avg,
and NPNA_wrog adjust for one discrete covariate (zz) and one continuous covariate (ww).
References
Garcia, T.P. and Parast, L. (2020). Dynamic landmark prediction for mixture data. Biostatistics, doi:10.1093/biostatistics/kxz052.
Garcia, T.P., Marder, K. and Wang, Y. (2017). Statistical modeling of Huntington disease onset.
In Handbook of Clinical Neurology, vol 144, 3rd Series, editors Andrew Feigin and Karen E. Anderson.
Qing, J., Garcia, T.P., Ma, Y., Tang, M.X., Marder, K., and Wang, Y. (2014).
Combining isotonic regression and EM algorithm to predict genetic risk under monotonicity constraint.
Annals of Applied Statistics, 8(2), 1182-1208.
Wang, Y., Garcia, T.P., and Ma. Y. (2012). Nonparametric estimation for censored mixture data with
application to the Cooperative Huntington's Observational Research Trial. Journal of the American Statistical Association,
107, 1324-1338.
Examples
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# Setup parameters to generate the data
set.seed(1)
censoring.rate <- 40
p <- 2
n <- 2000
m <- 4
simu.setting <- "HD-With-Covariates"
qvs <- qvs.values(p,m)
## generate the data
data.gen <- GenerateData(n,p,m,qvs,censoring.rate,simu.setting)
x <- data.gen$x
delta <- data.gen$delta
q <- data.gen$q
ww <- data.gen$ww
zz <- data.gen$zz
## Estimation procedures to run to estimate F(t|t0,z,w)
update.qs <- FALSE
run.NPMLEs <- TRUE
run.NPNA <- TRUE
run.NPNA_avg <- FALSE
run.NPNA_wrong <- FALSE
run.OLS <- FALSE
run.WLS <- FALSE
run.EFF <- FALSE
run.EMPAVA <- FALSE
## The distribution function we are estimating is F(t|t0,z,w).
tval <- seq(0,80,by=5) ## tval refers to "t" in F(t|t0,z,w)
tval0 <- c(0,20,30,40,50) ##tval0 refers to "t0" in F(t|t0,z,w)
z.use <- c(0,1) ## z.use refers to "z" in F(t|t0,z,w)
w.use <- seq(35,55,by=1) ## w.use refers to "w" in F(t|t0,z,w)
## Setup to compute AUC/BS as in Garcia and Parast (2020). Only for simulated data.
run.prediction.accuracy <- TRUE
do_cross_validation_AUC_BS <- FALSE
know.true.groups <- TRUE
true.group.identifier <- data.gen$true.group.identifier
## Perform the estimation
estimators.out <- stride.estimator(n,m,p,qvs,q,
x,delta,ww,zz,
run.NPMLEs,
run.NPNA,
run.NPNA_avg,
run.NPNA_wrong,
run.OLS,
run.WLS,
run.EFF,
run.EMPAVA,
tval,tval0,
z.use,w.use,
update.qs,
know.true.groups,
true.group.identifier,
run.prediction.accuracy,
do_cross_validation_AUC_BS)
## Show results for the estimates
## estimators.out$Ft.estimate
## estimators.out$St.estimate
## Show results for prediction accuracy AUC and BS measures (only valid for simulated data
## where we know the true.group.identifiers.)
## estimators.out$Ft.AUC.BS
## estimators.out$St.AUC.BS
## NOT RUN
## Do bootstrap variance
#nboot <- 100
#variance.estimation <- TRUE
#varboot <- stride.bootstrap.variance(
# nboot,n,m,p,qvs,q,
# x,delta,ww,zz,
# run.NPMLEs,
# run.NPNA,
# run.NPNA_avg,
# run.NPNA_wrong,
# run.OLS,
# run.WLS,
# run.EFF,
# run.EMPAVA,
# tval,tval0,
# z.use,w.use,
# update.qs,
# know.true.groups,
# true.group.identifer,
# estimator_Ft=estimators.out$Ft.estimate,
# estimator_St=estimators.out$St.estimate,
# AUC_BS_Ft=estimators.out$Ft.AUC.BS,
# AUC_BS_St=estimators.out$St.AUC.BS,
# run.prediction.accuracy,
# do_cross_validation_AUC_BS=FALSE)
## Show results for the bootstrap variances of the estimates
## varboot$Ft.estimate.boot
## varboot$St.estimate.boot
## Show results for the bootstrap variances of the prediction accuracy measures, AUC and BS
## varboot$Ft.AUC.BS.boot
## varboot$St.AUC.BS.boot
tpgarcia/stride documentation built on March 18, 2021, 3:42 p.m.
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Description Usage Arguments Value Details References Examples
Description
STRIDE estimators are nonparametric estimates of the distribution function for mixture data where
the population identifiers are unknown, and the probability of belonging
to a population is known (typically estimated with external data).
The distribution functions are evaluated at
time points tval. All STRIDE estimators can adjust for dynamic landmark prediction. The NPNA,
NPNA_avg and NPNA_wrong estimators can adjust for one
discrete covariate (zz) and one continuous covariate (ww). See details below.
Usage
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 | stride.estimator(
n,
m,
p,
qvs,
q,
x,
delta,
ww,
zz,
run.NPMLEs,
run.NPNA,
run.NPNA_avg,
run.NPNA_wrong,
run.OLS,
run.WLS,
run.EFF,
run.EMPAVA,
tval,
tval0,
z.use,
w.use,
update.qs,
know.true.groups = FALSE,
true.group.identifier = NULL,
run.prediction.accuracy,
do_cross_validation_AUC_BS
)
|
Arguments
n |
sample size, must be at least 1. |
m |
number of different mixture proportions, must be at least 2. |
p |
number of populations, must be at least 2. |
qvs |
a numeric matrix of size |
q |
a numeric matrix of size |
x |
a numeric vector of length |
delta |
a numeric vector of length |
ww |
a numeric vector of length |
zz |
a numeric vector of length |
run.NPMLEs |
a logical indicator. If TRUE, then the output includes the estimated distribution function for mixture data based on the type-I and type II nonparametric maximum likelihood estimators. The type I nonparametric maximum likelihood estimator is referred to as the "Kaplan-Meier" estimator in Garcia and Parast (2020). Neither the type I nor type II adjust for covariates. |
run.NPNA |
a logical indicator. If TRUE, then the output includes the estimated distribution function for mixture data that accounts for covariates and dynamic landmarking. This estimator is called "NPNA" in Garcia and Parast (2020). |
run.NPNA_avg |
a logical indicator. If TRUE, then the output includes the estimated distribution function for mixture data that averages out over the observed covariates. This is referred to as NPNA_marg in Garcia and Parast (2020). |
run.NPNA_wrong |
a logical indicator. If TRUE, then the output includes the estimated distribution function for mixture data that adjusts for covariates, but ignores landmarking. This is referred to as NPNA_t_0=0 in Garcia and Parast (2020). |
run.OLS |
a logical indicator. If TRUE, then the output includes the estimated distribution function computed using an ordinary least squares influence function. The estimator adjusts for censoring using inverse probability weighting (IPW), augmented inverse probability weighting (AIPW), and imputation (IMP). See details in Wang et al (2012). These estimators do not adjust for covariates. |
run.WLS |
a logical indicator. If TRUE, then the output includes the estimated distribution function computed using a weighted least squares influence function. The estimator adjusts for censoring using inverse probability weighting (IPW), augmented inverse probability weighting (AIPW), and imputation (IMP). See details in Wang et al (2012). These estimators do not adjust for covariates. |
run.EFF |
a logical indicator. If TRUE, then the output includes the estimated distribution function computed using the efficient influence function based on Hilbert space projection theory results. The estimator adjusts for censoring using inverse probability weighting (IPW), augmented inverse probability weighting (AIPW), and imputation (IMP). See details in Wang et al (2012). These estimators do not adjust for covariates. |
run.EMPAVA |
logical indicator. If TRUE, we compute the distribution function for the mixture data based on an expectation-maximization (EM) algorithm that uses the pool adjacent violators algorithm (PAVA) from isotone regression to yield a non-negative and monotone estimator. This estimator does not adjust for covariates. See details in Qing et al (2014). |
tval |
numeric vector of time points at which the distribution function is evaluated, all values must be non-negative. |
tval0 |
numeric vector of time points representing the landmark times. All values must be non-negative
and smaller than the maximum of |
z.use |
numeric vector at which to evaluate the discrete covariate Z at in the estimated distribution function.
The values of |
w.use |
numeric vector at which to evaluate the continuous covariate W at in the estimated distribution function.
The values of |
update.qs |
logical indicator. If TRUE, the mixture proportions |
know.true.groups |
logical indicator. If TRUE, then we know the population identifier for each person in the sample. This option is only used for simulation studies to check prediction accuracy. Default is FALSE. |
true.group.identifier |
numeric vector of length |
run.prediction.accuracy |
logical indicator. If TRUE, then we compute the prediction accuracy measures, including the
area under the receiver operating characteristic curve (AUC) and the Brier Score (BS). Prediction accuracy is only valid
in simulation studies where |
do_cross_validation_AUC_BS |
logical indicator. If TRUE, then we compute the prediction accuracy measures, including the
area under the receiver operating characteristic curve (AUC) and the Brier Score (BS) using cross-validation. Prediction accuracy is only valid
in simulation studies where |
Value
stride.estimator returns a list containing
problem: a numeric indicator of errors in the NPNA estimator. If NULL, no error is reported. Otherwise, there is an error in the computation of the NPNA estimator.
Ft.estimate: a numeric array containing the estimated distribution functions for all methods for all
ppopulations. The distribution function is evaluated at eachtval,tval0,z.use(if non-NULL),w.use(if non-NULL), and for allppopulations. The dimension of the array is \# of methods bylength(tval)bylenth(tval0)bylength(z.use)bylength(w.use)byp. Ifz.useandw.useare NULL, the dimension of the array is \# of methods bylength(tval)bylenth(tval0)byp. The distribution function is only valid for t≥q t_0, soFt.estimateshows NA for any combination for which t<t_0.-
St.estimate: a numeric array containing the estimated distribution functions for all methods for all
mmixture proportion subgroups. The distribution function is evaluated at eachtval,tval0,z.use(if non-NULL),w.use(if non-NULL), and for allmmixture proportion subgroups. The dimension of the array is \# of methods bylength(tval)bylenth(tval0)bylength(z.use)bylength(w.use)bym. Ifz.useandw.useare NULL, the dimension of the array is \# of methods bylength(tval)bylenth(tval0)bym. The distribution function is only valid for t≥q t_0, soSt.estimateshows NA for any combination for which t<t_0. Ft.AUC.BS: a numeric array containing the area under the receiver operating characteristic curve (AUC) and Brier Score (BS) for the
ppopulations. The dimension of the array is \# of methods bylength(tval)bylength(tval0)by 2, where the last dimension stores the AUC and BS results.Results for both the estimated distributon functions and prediction accuracy measures (AUC, BS) are only valid when t≥q t_0, so arrays show NA for any combination for which t<t_0.
-
St.AUC.BS: a numeric array containing the results are the area under the receiver operating characteristic curve (AUC) and Brier Score (BS) for the
mmixture proportion groups. The dimension of the array is \# of methods bylength(tval)bylength(tval0)by 2, where the last dimension stores the AUC and BS results.Results for both the estimated distributon functions and prediction accuracy measures (AUC, BS) are only valid when t≥q t_0, so arrays show NA for any combination for which t<t_0.
Details
We estimate nonparametric distribution functions for mixture data where
the population identifiers are unknown, and the probability of belonging
to a population is known (typically estimated with external data).
The distribution functions are evaluated at
time points tval. All estimators adjust for dynamic landmark prediction.
Dynamic landmark prediction means that the distribution function is computed knowing
that the survival time, T, satisfies T >t_0
where t_0 are the time points in tval0. The NPNA, NPNA_avg,
and NPNA_wrog adjust for one discrete covariate (zz) and one continuous covariate (ww).
References
Garcia, T.P. and Parast, L. (2020). Dynamic landmark prediction for mixture data. Biostatistics, doi:10.1093/biostatistics/kxz052.
Garcia, T.P., Marder, K. and Wang, Y. (2017). Statistical modeling of Huntington disease onset. In Handbook of Clinical Neurology, vol 144, 3rd Series, editors Andrew Feigin and Karen E. Anderson.
Qing, J., Garcia, T.P., Ma, Y., Tang, M.X., Marder, K., and Wang, Y. (2014). Combining isotonic regression and EM algorithm to predict genetic risk under monotonicity constraint. Annals of Applied Statistics, 8(2), 1182-1208.
Wang, Y., Garcia, T.P., and Ma. Y. (2012). Nonparametric estimation for censored mixture data with application to the Cooperative Huntington's Observational Research Trial. Journal of the American Statistical Association, 107, 1324-1338.
Examples
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 | # Setup parameters to generate the data
set.seed(1)
censoring.rate <- 40
p <- 2
n <- 2000
m <- 4
simu.setting <- "HD-With-Covariates"
qvs <- qvs.values(p,m)
## generate the data
data.gen <- GenerateData(n,p,m,qvs,censoring.rate,simu.setting)
x <- data.gen$x
delta <- data.gen$delta
q <- data.gen$q
ww <- data.gen$ww
zz <- data.gen$zz
## Estimation procedures to run to estimate F(t|t0,z,w)
update.qs <- FALSE
run.NPMLEs <- TRUE
run.NPNA <- TRUE
run.NPNA_avg <- FALSE
run.NPNA_wrong <- FALSE
run.OLS <- FALSE
run.WLS <- FALSE
run.EFF <- FALSE
run.EMPAVA <- FALSE
## The distribution function we are estimating is F(t|t0,z,w).
tval <- seq(0,80,by=5) ## tval refers to "t" in F(t|t0,z,w)
tval0 <- c(0,20,30,40,50) ##tval0 refers to "t0" in F(t|t0,z,w)
z.use <- c(0,1) ## z.use refers to "z" in F(t|t0,z,w)
w.use <- seq(35,55,by=1) ## w.use refers to "w" in F(t|t0,z,w)
## Setup to compute AUC/BS as in Garcia and Parast (2020). Only for simulated data.
run.prediction.accuracy <- TRUE
do_cross_validation_AUC_BS <- FALSE
know.true.groups <- TRUE
true.group.identifier <- data.gen$true.group.identifier
## Perform the estimation
estimators.out <- stride.estimator(n,m,p,qvs,q,
x,delta,ww,zz,
run.NPMLEs,
run.NPNA,
run.NPNA_avg,
run.NPNA_wrong,
run.OLS,
run.WLS,
run.EFF,
run.EMPAVA,
tval,tval0,
z.use,w.use,
update.qs,
know.true.groups,
true.group.identifier,
run.prediction.accuracy,
do_cross_validation_AUC_BS)
## Show results for the estimates
## estimators.out$Ft.estimate
## estimators.out$St.estimate
## Show results for prediction accuracy AUC and BS measures (only valid for simulated data
## where we know the true.group.identifiers.)
## estimators.out$Ft.AUC.BS
## estimators.out$St.AUC.BS
## NOT RUN
## Do bootstrap variance
#nboot <- 100
#variance.estimation <- TRUE
#varboot <- stride.bootstrap.variance(
# nboot,n,m,p,qvs,q,
# x,delta,ww,zz,
# run.NPMLEs,
# run.NPNA,
# run.NPNA_avg,
# run.NPNA_wrong,
# run.OLS,
# run.WLS,
# run.EFF,
# run.EMPAVA,
# tval,tval0,
# z.use,w.use,
# update.qs,
# know.true.groups,
# true.group.identifer,
# estimator_Ft=estimators.out$Ft.estimate,
# estimator_St=estimators.out$St.estimate,
# AUC_BS_Ft=estimators.out$Ft.AUC.BS,
# AUC_BS_St=estimators.out$St.AUC.BS,
# run.prediction.accuracy,
# do_cross_validation_AUC_BS=FALSE)
## Show results for the bootstrap variances of the estimates
## varboot$Ft.estimate.boot
## varboot$St.estimate.boot
## Show results for the bootstrap variances of the prediction accuracy measures, AUC and BS
## varboot$Ft.AUC.BS.boot
## varboot$St.AUC.BS.boot
|
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