Missing Value Imputation for Accelerometer Data

Description

We present a statistical method for imputing missing values in accelerometer data. The methodology includes both parametric and semi-parametric multiple imputation under the zero-inflated Poisson lognormal model. It also offers several functions to preprocess accelerometer data before imputation. These include detecting wear and non-wear time, selecting valid days and subjects, and generating plots.

Details

Author(s)

Jung Ae Lee <jungae.lee@umassmed.edu>

Maintainer: Jung Ae Lee <jungaeleeb@gmail.com>

References

Lee JA, Gill J (2016). Missing value imputation for physical activity data measured by accelerometer. Statistical Methods and Medical Research.

See Also

mice, pscl

Missing Value Imputation for Accelerometer Data

Description

This function imputes the missing count values generated by the accelerometer. The imputation is performed during the user-defined daytime (9am-9pm as a default). At each minute, the function runs the multiple imputation with chained equations under the assumption of the zero-inflated poisson log-normal distribution.

Usage

accel.impute(PA, label, flag, demo=NA, method = "zipln.pmm", 
time.range = c("09:00","20:59"), K = 3, D = 5, mark.missing = 0, 
thresh = 10000, graph.diagnostic = TRUE, seed = 1234, m = 5, 
maxit = 6, demo.include = FALSE)

Arguments

Value

Note

seed, m, maxit are the input arguments in mice function.

Author(s)

Jung Ae Lee <jungaeleeb@gmail.com>

References

[1] Lee JA, Gill J (2016). Missing value imputation for physical activity data measured by accelerometer. Statistical Methods in Medical Research.
[2] van Buuren S, Groothuis-Oudshoorn K (2011). mice: Multivariate imputations by chained equations in R. Journal of Statistical Software.
[3] Jackman S (2014). pscl: Classes and Methods for R Developed in the Political Science Computational Laboratory. Stanford University. R package version 1.4.6.

Examples

####################################################
# A full example from data filtering to imputation	
####################################################
data(acceldata)    # read data
ls(acceldata)      # This is a list with four matrix objects, PA, label, flag, and demo
d = acceldata

## missing rate
missing.rate(label=d$label, flag=d$flag)$total  # 32 percent

# create missing flag with 60 min criterion
flag60 = create.flag(PA=d$PA, window=60)

## missing rate with flag60
mr = missing.rate(label=d$label, flag=flag60)
mr$total  #28.1 percent

## missing proportion by days
mean(mr$table < 0.1)   # 45.8 percent

# wearing proportion over time 
wear.time.plot(PA=d$PA, label=d$label, flag=flag60)

# data filtering for valid days
valid.days.out = valid.days(PA=d$PA, label=d$label, flag=flag60, wear.hr=8)
ls(valid.days.out)   # list with three matrix objects

# data filtering for valid subjects
x1 = list(PA=d$PA, label=d$label, flag=flag60) # original
x2 = valid.days.out   # output of valid.days()
valid.sub.out = valid.subjects(data1=x1, data2=x2, valid.days=3)
length(unique(valid.sub.out$label[,1]))   # 184 persons 
ls(valid.sub.out)

## missing rate with the filtered data
missing.rate(valid.sub.out$label, valid.sub.out$flag)$total    
# 20.1 percent 

# demographic data for the filtered data
idv= unique(valid.sub.out$label[,1])
matchid = match(idv, d$demo[,1]) 
demo1 = d$demo[matchid, ]

# save the data before imputation
acceldata2 = list(PA=valid.sub.out$PA, label=valid.sub.out$label, flag=valid.sub.out$flag, 
demo=demo1)
# save(acceldata2, file="acceldata2.RData")

################################
# prepare the imputation
library(mice); library(pscl)
data(acceldata2) # load prepared data in this package
# load("acceldata2.RData") # to use the data you saved in previous step.
data = acceldata2

# imputation: test only 10 minutes with semiparametic method  
# accelimp = accel.impute(PA=data$PA, label=data$label, flag=data$flag, 
# demo=data$demo, time.range=c("10:51","11:00"), method="zipln.pmm", D=5) 

# imputation: test only 10 minutes with parametic method  
# accelimp = accel.impute(PA=data$PA, label=data$label, flag=data$flag, 
# demo=data$demo, time.range=c("10:51","11:00"), method="zipln")

# plot 7 days before imputation 
accel.plot.7days(PA=data$PA[1:7, ], label=data$label[1:7, ], flag=data$flag[1:7, ],
 time.range=c("09:00", "20:59"), save.plot=FALSE)

# plot 7 days after imputation
data(accelimp) # load prepared data in this package, or use the data you created above.
accel.plot.7days(PA=accelimp[[1]][1:7, ], label=data$label[1:7, ], flag=data$flag[1:7, ], 
time.range=c("09:00", "20:59"),  save.plot=FALSE)

Daily Activity Plot

Description

Displays an individual's physical activity pattern of a day during one week.

Usage

accel.plot.7days(PA, label, flag, time.range = c("00:00", "23:59"),  
mark.missing = 0, axis.time = TRUE, save.plot = FALSE,  
directory.plot = getwd() )

Arguments

Value

Plot of activity counts with smoothing curve and missing flag.

Author(s)

Jung Ae Lee <jungaeleeb@gmail.com>

References

[1] Lee JA, Gill J (2016). Missing value imputation for physical activity data measured by accelerometer. Statistical Methods in Medical Research.
[2] Ramsay, J. O., Wickham, H., Graves, S., and Hooker, G. (2014). fda: Functional Data Analysis. R package version 2.4.3.

Examples

data(acceldata2) ; data=acceldata2 # read data before imputation	
data(accelimp) # read data after imputation
	
# plot 7 days before imputation 
accel.plot.7days(PA=data$PA[1:7, ], label=data$label[1:7, ], flag=data$flag[1:7, ],
 time.range=c("09:00", "20:59"), save.plot=FALSE)

# plot 7 days after imputation
accel.plot.7days(PA=accelimp[[1]][1:7, ], label=data$label[1:7, ], flag=data$flag[1:7, ], 
time.range=c("09:00", "20:59"), save.plot=FALSE)
	
# save the plot
# setwd("yourfolder")  #--- set the directory to save plot when save.plot=TRUE
# accel.plot.7days(PA=accelimp[[1]], label=data$label, flag=data$flag, 
# time.range=c("09:00", "20:59"),  save.plot=TRUE)

Accelerometer Data Example

Description

Data example from 2003-4 National Health and Nutrition Examination Survey dataset. The dataset is available at the website: http://wwwn.cdc.gov/nchs/nhanes/search/nhanes03_04.aspx. This data example only includes 218 individuals, which gives 1526 daily profiles, from 7176 total participants in the physical activity survey.

Usage

data(acceldata)

Format

List with four matrix objects:

• acceldata$PA: matrix

• acceldata$label: matrix

• acceldata$flag: matrix

• acceldata$demo: matrix

Details

PA

an N by T matrix including activity counts, where N is the total number of daily profiles, and T is the total minutes of a day (N=1526, T=1440).

label

an N by 2 matrix including the labels corresponding to PA matrix. The first column, label[,1], includes the person id, and the second column, label[,2], includes the day label of 1 to 7, indicating Sunday to Saturday.

flag

an N by T matrix with the values of either 1 or 0 which indicating wearing or missing. This matrix can be created from create.flag().

demo

an n by p matrix (or dataframe) where n is the total number of subject (n=218). The first column must include the unique person id, which equals to unique(label[,1]). From the second column to p-th column, one may include the demographic variables of intrest, for example, age, sex, body mass index, and race. These variables will be used as covariates in the imputation model.

Note

This data format is strongly recommended for proceeding the missing value imputation from this package.

Source

http://wwwn.cdc.gov/nchs/nhanes/search/nhanes03_04.aspx

References

[1] Lee JA, Gill J (2016). Missing value imputation for physical activity data measured by accelerometer. Statistical Methods in Medical Research.

Examples

data(acceldata)
ls(acceldata)
dim(acceldata$PA)

Accelerometer Data Example 2

Description

Data example from 2003-4 National Health and Nutrition Examination Survey dataset. This data example includes 184 individuals to give 1288 daily profiles. This only includes valid subjects that have at least three complete days, a subset of acceldata as a result of valid.subjects().

Usage

data(acceldata2)

Format

List with four matrix objects:

• acceldata2$PA: matrix

• acceldata2$label: matrix

• acceldata2$flag: matrix

• acceldata2$demo: matrix

Details

PA

an N by T matrix including activity counts, where N is the total number of daily profiles, and T is the total minutes of a day (N=1288, T=1440).

label

an N by 2 matrix including the labels corresponding to PA matrix. The first column, label[,1], includes the person id, and the second column, label[,2], includes the day label of 1 to 7, indicating Sunday to Saturday.

flag

an N by T matrix with the values of either 1 or 0 which indicating wearing or missing. This matrix can be created from create.flag().

demo

an n by p matrix (or dataframe) where n is the total number of subject (n=184). The first column must include the unique person id, which equals to unique(label[,1]). From the second column to p-th column, one may include the demographic variables of intrest, for example, age, sex, body mass index, and race. These variables will be used as covariates in the imputation model.

Source

http://wwwn.cdc.gov/nchs/nhanes/search/nhanes03_04.aspx

References

[1] Lee JA, Gill J (2016). Missing value imputation for physical activity data measured by accelerometer. Statistical Methods in Medical Research.

See Also

acceldata, valid.subjects

Examples

data(acceldata2)
ls(acceldata2)

Accelerometer Data Example with Imputations

Description

Imputed Data example from 2003-4 National Health and Nutrition Examination Survey dataset. This data example includes 184 individuals to give 1288 daily profiles, as a result of accel.impute().

Usage

data(accelimp)

Format

List with multiple matrix objects. accelimp includes a single dataset a result of accel.impute(..., m=1,...). You may produce multiple datasets by setting m=5 (default).

• accelimp$imp1: matrix

• ...

• accelimp$imp5: matrix

References

[1] Lee JA, Gill J (2016). Missing value imputation for physical activity data measured by accelerometer. Statistical Methods in Medical Research.

See Also

accel.impute

Examples

data(accelimp)
ls(accelimp)

Create a Missing Flag Matrix

Description

Defines the missing interval by detecting consecutive zeros for a while (20 minutes as a default), and create a flag matrix with the binary indicator for wearing vs. nonwearing time.

Usage

create.flag(PA, window = 20, mark.missing = 0)

Arguments

Value

an N by T matrix with the elements of 0 or 1.

Author(s)

Jung Ae Lee <jungaeleeb@gmail.com>

References

[1] Lee JA, Gill J (2016). Missing value imputation for physical activity data measured by accelerometer. Statistical Methods and Medical Research.
[2] Catellier DJ, Hannan PJ, Murray DM, Addy CL, Conway TL, Yang S, Rice JC (2005). Imputation of missing data when measuring physical activity by accelerometry. Medicine and Science in Sports and Exercise; 37 (11 Suppl).

See Also

missing.rate, wear.time.plot.

Examples

data(acceldata)  # read data	
PA = acceldata$PA
	
# create a missing flag matrix with 60 minutes criterion 
flag60 = create.flag(PA, window=60, mark.missing=0)

# create a missing flag matrix with 30 minutes criterion
flag30 = create.flag(PA, window=30, mark.missing=0)
	

Imputation by PMM under ZIP model.

Description

Imputes univariate missing data using the predictive mean matching (PMM) under the zero-inflated Poisson (ZIP) model.

Usage

mice.impute.2l.zip.pmm(y, ry, x, wy=NULL, type, K, D)

Arguments

Value

A vector of length nmis with imputations

Note

This function is called when you set accel.impute(..., method = "zip.pmm"; internally, it then calls mice(..., method="2l.zip.pmm",...).

Author(s)

Jung Ae Lee <jungaeleeb@gmail.com>

References

[1] Lee JA, Gill J (2016). Missing value imputation for physical activity data measured by accelerometer. Statistical Methods in Medical Research.
[2] van Buuren S, Groothuis-Oudshoorn K (2011). mice: Multivariate imputations by chained equations in R. Journal of Statistical Software.
[3] Kleinke K, Reinecke J (2013). Multiple imputation of incomplete zero-infated count data. Statistica Neerlandica.

See Also

mice, accel.impute

Imputation by Bayesian ZIPLN model.

Description

Imputes univariate missing data using Bayesian model under the zero-inflated Poisson Log-normal (ZIPLN) distribution.

Usage

mice.impute.2l.zipln(y, ry, x, wy=NULL, type, K, zs = zs)

Arguments

Value

A vector of length nmis with imputations

Note

This function is called when you set accel.impute(..., method = "zipln"; interally, it then calls mice(..., method="2l.zipln",...).

Author(s)

Jung Ae Lee <jungaeleeb@gmail.com>

References

[1] Lee JA, Gill J (2016). Missing value imputation for physical activity data measured by accelerometer. Statistical Methods in Medical Research.
[2] van Buuren S, Groothuis-Oudshoorn K (2011). mice: Multivariate imputations by chained equations in R. Journal of Statistical Software.
[3] Kleinke K, Reinecke J (2013). Multiple imputation of incomplete zero-infated count data. Statistica Neerlandica.

See Also

mice, accel.impute

Imputation by PMM under ZIPLN model.

Description

Imputes univariate missing data using the predictive mean matching (PMM) under the zero-inflated Poisson Log-normal (ZIPLN) model.

Usage

mice.impute.2l.zipln.pmm(y, ry, x, wy=NULL, type, K, zs = zs, D)

Arguments

Value

A vector of length nmis with imputations

Note

This function is called when you set accel.impute(..., method = "zipln.pmm"; internally, it then calls mice(..., method="2l.zipln.pmm",...).

Author(s)

Jung Ae Lee <jungaeleeb@gmail.com>

References

[1] Lee JA, Gill J (2016). Missing value imputation for physical activity data measured by accelerometer. Statistical Methods in Medical Research.
[2] van Buuren S, Groothuis-Oudshoorn K (2011). mice: Multivariate imputations by chained equations in R. Journal of Statistical Software.
[3] Kleinke K, Reinecke J (2013). Multiple imputation of incomplete zero-infated count data. Statistica Neerlandica.

See Also

mice, accel.impute

Computing Missing Rate

Description

Computes the missing rate from acceleromater data.

Usage

missing.rate(label, flag, mark.missing = 0, time.range = c("09:00", "20:59"))

Arguments

Value

Numeric value of a missing rate between 0 to 1. The output is a list of

Author(s)

Jung Ae Lee <jungaeleeb@gmail.com>

References

[1] Lee JA, Gill J (2016). Missing value imputation for physical activity data measured by accelerometer. Statistical Methods in Medical Research.

See Also

create.flag, wear.time.plot

Examples

## missing rate calculation: uncomment and run the code below
# data(acceldata); attach(acceldata)
# missing.rate(label, flag, mark.missing=0, time.range=c("09:00", "20:59"))$total  

## create missing flag by 60 min criterion
# flag60 = create.flag(PA, window=60, mark.missing=0)
# mr = missing.rate(label, flag60, mark.missing=0, time.range=c("09:00", "20:59"))
# mr$total  #28.1 percent

## missing proportion by days
# mean(mr$table < 0.1)   # 45.8 percent

Select the Valid Days

Description

Selects the complete (valid) days that include sufficient wearing time.

Usage

valid.days(PA, label, flag, wear.hr = 10, time.range = c("09:00", "20:59"), 
mark.missing = 0)

Arguments

Value

List with the updated PA, label and flag matrix objects.

Author(s)

Jung Ae Lee <jungaeleeb@gmail.com>

References

[1] Lee JA, Gill J (2016). Missing value imputation for physical activity data measured by accelerometer. Statistical Methods in Medical Research.

See Also

valid.subjects

Examples

data(acceldata); attach(acceldata) # read data
	
# filtering data for valid days
valid.days.out = valid.days(PA, label, flag, wear.hr=8,  time.range=c("09:00","20:59"))
ls(valid.days.out)

Include or Exclude Subjects by Criteria

Description

Select the subjects that have at least 3 complete days (or other criteria). By such criteria, some complete days are dropped if one has only one or two completed days, although some incomplete days are included if the subject has already three or more complete days.

Usage

valid.subjects(data1, data2, valid.days = 3, valid.week.days = NA, 
valid.weekend.days = NA, mark.missing = 0, keep.7days=TRUE)

Arguments

Value

List with the updated PA, label and flag matrix objects.

Author(s)

Jung Ae Lee <jungaeleeb@gmail.com>

References

[1] Lee JA, Gill J (2016). Missing value imputation for physical activity data measured by accelerometer. Statistical Methods in Medical Research.

See Also

valid.days

Examples

data(acceldata); attach(acceldata) # read original data
	
# filtering data for valid days
valid.days.out = valid.days(PA, label, flag, wear.hr=8,  time.range=c("09:00","20:59"))
ls(valid.days.out)

# filtering data for valid subjects
x1 = list(PA=PA, label=label, flag=flag) # original data
x2 = valid.days.out                                     # output of valid.days()
valid.sub.out = valid.subjects(data1=x1, data2=x2, valid.days=3)
ls(valid.sub.out)	

Proportion of Wearing over Time

Description

Displays the proportion of wearing over time among the daily profiles.

Usage

wear.time.plot(PA, label, flag, mark.missing = 0)

Arguments

Value

Plot with the proportion of wearing in y-axis and the time index in x-axis, also displaying the standard measurement day.

Note

By looking at the plot, we may decide the standard measurement day, which is the time range that exhibits the sufficiently large portion of wearing (60 or 70 percent).

Author(s)

Jung Ae Lee <jungaeleeb@gmail.com>

References

[1] Lee JA, Gill J (2016). Missing value imputation for physical activity data measured by accelerometer. Statistical Methods in Medical Research.
[2] Catellier, D. J., Hannan, P. J., Murray, D. M., Addy, C. L., Conway, T. L., Yang, S., and Rice, J. C. (2005). Imputation of missing data when measuring physical activity by accelerometry. Medicine and Science in Sports and Exercise, 37(11 Suppl).

See Also

missing.rate

Examples

data(acceldata) # read data
ls(acceldata)     # list with four data matrix objects, PA, label, flag, and demo
attach(acceldata)

# plot the proportion of wearing over time
wear.time.plot(PA, label, flag)