Type:	Package
Depends:	R (≥ 4.0.0),
Imports:	survival (≥ 3.1-12), pROC (≥ 1.16.2), rms (≥ 6.1-0), mice (≥ 3.12.0), mitml (≥ 0.3-7), mitools (≥ 2.4), dplyr (≥ 1.0.2), purrr (≥ 0.3.4), tidyr (≥ 1.1.2), tibble (≥ 3.0.4), stringr (≥ 1.4.0), car (≥ 3.0-10), rlang, magrittr
Suggests:	foreign (≥ 0.8-80), knitr, rmarkdown, testthat (≥ 3.0.0), bookdown, readr
Title:	Data and Statistical Analyses after Multiple Imputation
Version:	0.5.0
Description:	Statistical Analyses and Pooling after Multiple Imputation. A large variety of repeated statistical analysis can be performed and finally pooled. Statistical analysis that are available are, among others, Levene's test, Odds and Risk Ratios, One sample proportions, difference between proportions and linear and logistic regression models. Functions can also be used in combination with the Pipe operator. More and more statistical analyses and pooling functions will be added over time. Heymans (2007) <doi:10.1186/1471-2288-7-33>. Eekhout (2017) <doi:10.1186/s12874-017-0404-7>. Wiel (2009) <doi:10.1093/biostatistics/kxp011>. Marshall (2009) <doi:10.1186/1471-2288-9-57>. Sidi (2021) <doi:10.1080/00031305.2021.1898468>. Lott (2018) <doi:10.1080/00031305.2018.1473796>. Grund (2021) <doi:10.31234/osf.io/d459g>.
Encoding:	UTF-8
LazyData:	true
RoxygenNote:	7.2.0
License:	GPL-2 | GPL-3 [expanded from: GPL (≥ 2)]
URL:	https://mwheymans.github.io/miceafter/
BugReports:	https://github.com/mwheymans/miceafter/issues
VignetteBuilder:	knitr
Config/testthat/edition:	3
NeedsCompilation:	no
Packaged:	2022-10-02 13:09:22 UTC; mwhey
Author:	Martijn Heymans [cre, aut], Jaap Brand [ctb]
Maintainer:	Martijn Heymans <mw.heymans@amsterdamumc.nl>
Repository:	CRAN
Date/Publication:	2022-10-02 13:30:02 UTC

Calculates the Brown-Forsythe test.

Description

bf_test Calculates the Brown-Forsythe test for homogeneity of variance across groups, coefficients, variance-covariance matrix, and degrees of freedom.

Usage

bf_test(y, x, formula, data)

Arguments

Details

The Levene's test centers around means to calculate outcome residuals, the Brown-Forsythe test around the median.

Value

An object containing:

• fstats F-test value, including numerator and denominator degrees of freedom.

• qhat pooled coefficients from fit.

• vcov variance-covariance matrix.

• dfcom degrees of freedom obtained from df.residual.

Author(s)

Martijn Heymans, 2021

See Also

with.milist

Examples

imp_dat <- df2milist(lbpmilr, impvar="Impnr")
ra <- with(imp_dat, expr=bf_test(Pain ~ factor(Carrying)))

Function to check input data for function glm_mi

Description

check_model Function to check input data for function glm_mi

Usage

check_model(
  data,
  formula,
  keep.predictors,
  impvar,
  p.crit,
  method,
  nimp,
  direction,
  model_type
)

Arguments

Details

The basic pooling procedure to derive pooled coefficients, standard errors, 95 confidence intervals and p-values is Rubin's Rules (RR). RR are possible when the model includes continuous or dichotomous variables. When the model includes categorical (> 2 categories) or restricted cubic spline variables multiparameter pooling methods have to be used. These pooling methods are: “D1” (pooling of the total covariance matrix), ”D2” pooling of Chi-square values, “D3” and "D4" pooling Likelihood ratio statistics and “MPR”, pooling of median p-values (MPR rule). Spline regression coefficients are defined by using the rcs function for restricted cubic splines of the rms package. A minimum number of 3 knots as defined under knots is required.

A typical formula object has the form Outcome ~ terms. Categorical variables has to be defined as Outcome ~ factor(variable), restricted cubic spline variables as Outcome ~ rcs(variable, 3). Interaction terms can be defined as Outcome ~ variable1*variable2 or Outcome ~ variable1 + variable2 + variable1:variable2. All variables in the terms part have to be separated by a "+".

Value

The outcome variable, the names of the predictors and name of variable to keep, if defined. For internal use.

Author(s)

Martijn Heymans, 2020

Calculates the c-index and standard error

Description

cindex Calculates the c-index and standard error for logistic and Cox regression models and the degrees of freedom to be further used in function with.milist.

Usage

cindex(formula, data)

Arguments

Value

The c-index, related standard error and complete data degrees of freedom (dfcom) as n-1.

Author(s)

Martijn Heymans, 2021

See Also

with.milist, pool_cindex

Examples

 imp_dat <- df2milist(lbpmilr, impvar="Impnr")
 ra <- with(data=imp_dat,
 expr = cindex(glm(Chronic ~ Gender + Radiation, family=binomial)))

Function to clean variables

Description

Function to clean variables

Usage

clean_P(variable)

Value

"Clean" version of variables. For internal use.

Author(s)

Martijn Heymans, 2020

Fisher z transformation of correlation coefficient

Description

cor2fz Fisher z transformation of correlation coefficient

Usage

cor2fz(r)

Arguments

Value

correlation coefficient on z scale.

Author(s)

Martijn Heymans, 2022

Examples

 cor2fz(r=0.65)

Calculates the correlation coefficient

Description

cor_est Calculates the correlation coefficient and standard error to be used in function with.miceafter.

Usage

cor_est(y, x, data, method = "pearson", se_method = "normal")

Arguments

Details

The basic method to calculate the standard error is by:

se = \sqrt(\frac{1}{n-3})

For the Spearman correlation coefficients se_method "fieller" is calculated as:

se = \sqrt(\frac{1.06}{n-3})

For the Kendall correlation coefficients se_method "fieller" is calculated as:

se = \sqrt(\frac{0.437}{n-4})

Value

The correlation coefficient, standard error and complete data degrees of freedom (dfcom).

Author(s)

Martijn Heymans, 2022

See Also

with.milist, pool_cor

Examples

imp_dat <- df2milist(lbpmilr, impvar="Impnr")
ra <- with(imp_dat, expr=cor_est(y=BMI, x=Age))

Turns a data frame with multiply imputed data into an object of class 'milist'

Description

df2milist Turns a data frame of class 'data.frame', 'tbl_df' or 'tbl' (tibble) into an object of class 'milist' to be further used by 'miceafter::with'

Usage

df2milist(data, impvar, keep = FALSE)

Arguments

Value

an object of class 'milist' (Multiply Imputed Data list)

Author(s)

Martijn Heymans, 2021

Converts F-values into Chi Square values

Description

f2chi convert F to Chi-square values.

Usage

f2chi(f, df_num)

Arguments

Value

The Chi square values.

Author(s)

Martijn Heymans, 2021

Examples

  f2chi(c(5.83, 4.95, 3.24, 6.27, 4.81), 5)

Fisher z back transformation of correlation coefficient

Description

fz2cor Fisher z back transformation of correlation coefficient

Usage

fz2cor(z)

Arguments

Value

correlation coefficient on correlation scale.

Author(s)

Martijn Heymans, 2022

Examples

 fz2cor(z=0.631)

Backward selection of Linear regression models across multiply imputed data.

Description

glm_lm_bw Backward selection of Linear regression models across multiply imputed data using selection methods RR, D1, D2, D4 and MPR. Function is called by glm_mi.

Usage

glm_lm_bw(data, nimp, impvar, Outcome, P, p.crit, method, keep.P)

Arguments

Author(s)

Martijn Heymans, 2021

Forward selection of Linear regression models across multiply imputed data.

Description

glm_lm_fw Forward selection of Linear regression models across multiply imputed data using selection methods RR, D1, D2, D4 and MPR. Function is called by glm_mi.

Usage

glm_lm_fw(data, nimp, impvar, Outcome, P, p.crit, method, keep.P)

Arguments

Author(s)

Martijn Heymans, 2021

Backward selection of Logistic regression models in multiply imputed data.

Description

glm_lr_bw Backward selection of Logistic regression models in multiply imputed data using selection methods RR, D1, D2, D3 and MPR. Function is called by glm_mi.

Usage

glm_lr_bw(data, nimp, impvar, Outcome, P, p.crit, method, keep.P)

Arguments

Author(s)

Martijn Heymans, 2021

Forward selection of Logistic regression models in multiply imputed data.

Description

glm_lr_fw Forward selection of Logistic regression models across multiply imputed data using selection methods RR, D1, D2, D3 and MPR. Function is called by glm_mi.

Usage

glm_lr_fw(data, nimp, impvar, Outcome, P, p.crit, method, keep.P)

Arguments

Author(s)

Martijn Heymans, 2021

Direct Pooling and model selection of Linear and Logistic regression models across multiply imputed data.

Description

glm_mi Pooling and backward or forward selection of Linear and Logistic regression models across multiply imputed data using selection methods RR, D1, D2, D3, D4 and MPR (without use of with function).

Usage

glm_mi(
  data,
  formula = NULL,
  nimp = 5,
  impvar = NULL,
  keep.predictors = NULL,
  p.crit = 1,
  method = "RR",
  direction = NULL,
  model_type = NULL
)

Arguments

Details

The basic pooling procedure to derive pooled coefficients, standard errors, 95 confidence intervals and p-values is Rubin's Rules (RR). However, RR is only possible when the model includes continuous and dichotomous variables. Specific procedures are available when the model also included categorical (> 2 categories) or restricted cubic spline variables. These pooling methods are: “D1” is pooling of the total covariance matrix, ”D2” is pooling of Chi-square values, “D3” and "D4" is pooling Likelihood ratio statistics (method of Meng and Rubin) and “MPR” is pooling of median p-values (MPR rule). Spline regression coefficients are defined by using the rcs function for restricted cubic splines of the rms package. A minimum number of 3 knots as defined under knots is required.

A typical formula object has the form Outcome ~ terms. Categorical variables has to be defined as Outcome ~ factor(variable), restricted cubic spline variables as Outcome ~ rcs(variable, 3). Interaction terms can be defined as Outcome ~ variable1*variable2 or Outcome ~ variable1 + variable2 + variable1:variable2. All variables in the terms part have to be separated by a "+". If a formula object is used set predictors, cat.predictors, spline.predictors or int.predictors at the default value of NULL.

Value

An object of class pmods (multiply imputed models) from which the following objects can be extracted:

• data imputed datasets

• RR_model pooled model at each selection step

• RR_model_final final selected pooled model

• multiparm pooled p-values at each step according to pooling method

• multiparm_final pooled p-values at final step according to pooling method

• multiparm_out (only when direction = "FW") pooled p-values of removed predictors

• formula_step formula object at each step

• formula_final formula object at final step

• formula_initial formula object at final step

• predictors_in predictors included at each selection step

• predictors_out predictors excluded at each step

• impvar name of variable used to distinguish imputed datasets

• nimp number of imputed datasets

• Outcome name of the outcome variable

• method selection method

• p.crit p-value selection criterium

• call function call

• model_type type of regression model used

• direction direction of predictor selection

• predictors_final names of predictors in final selection step

• predictors_initial names of predictors in start model

• keep.predictors names of predictors that were forced in the model

Author(s)

Martijn Heymans, 2021

References

Eekhout I, van de Wiel MA, Heymans MW. Methods for significance testing of categorical covariates in logistic regression models after multiple imputation: power and applicability analysis. BMC Med Res Methodol. 2017;17(1):129.

Enders CK (2010). Applied missing data analysis. New York: The Guilford Press.

Meng X-L, Rubin DB. Performing likelihood ratio tests with multiply-imputed data sets. Biometrika.1992;79:103-11.

van de Wiel MA, Berkhof J, van Wieringen WN. Testing the prediction error difference between 2 predictors. Biostatistics. 2009;10:550-60.

Marshall A, Altman DG, Holder RL, Royston P. Combining estimates of interest in prognostic modelling studies after multiple imputation: current practice and guidelines. BMC Med Res Methodol. 2009;9:57.

Van Buuren S. (2018). Flexible Imputation of Missing Data. 2nd Edition. Chapman & Hall/CRC Interdisciplinary Statistics. Boca Raton.

EW. Steyerberg (2019). Clinical Prediction MOdels. A Practical Approach to Development, Validation, and Updating (2nd edition). Springer Nature Switzerland AG.

http://missingdatasolutions.rbind.io/

Examples

  pool_lr <- glm_mi(data=lbpmilr, formula = Chronic ~ Pain +
  factor(Satisfaction) + rcs(Tampascale,3) + Radiation +
  Radiation*factor(Satisfaction) + Age + Duration + BMI,
  p.crit = 0.05, direction="FW", nimp=5, impvar="Impnr",
  keep.predictors = c("Radiation*factor(Satisfaction)", "Age"),
  method="D1", model_type="binomial")

  pool_lr$RR_model_final

Takes the inverse of a logit transformed value

Description

invlogit Takes the inverse of a logit transformed value

Usage

invlogit(est)

Arguments

Value

back transformed value.

Author(s)

Martijn Heymans, 2021

Examples

 invlogit(est=1.39)

Takes the inverse of logit transformed parameters and calculates the confidence intervals

Description

invlogit_ci Takes the inverse of logit transformed parameters and calculates the confidence interval by using the critical value.

Usage

invlogit_ci(est, se, crit.value)

Arguments

Details

Takes the inverse of logit transformed parameter estimates. The confidence interval is calculated by taking the inverse of est +/- crit.value{1-\alpha/2} * se.

Value

Parameter, critical value and confidence intervals on original scale.

Author(s)

Martijn Heymans, 2021

Examples

 invlogit_ci(est=1.39, se=0.25, crit.value=1.96)

Dataset of 159 Low Back Pain Patients with missing values

Description

A data frame with 159 observations of 15 variables related to low back pain.

Usage

lbp_orig

Format

A data frame with 159 observations on the following 15 variables.

Chronic

dichotomous

Gender

dichotomous

Carrying

categorical

Pain

continuous

Tampascale

continuous

Function

continuous

Radiation

dichotomous

Age

continuous

Smoking

dichotomous

Satisfaction

categorical

JobControl

continuous

JobDemands

continuous

SocialSupport

continuous

Duration

continuous

BMI

continuous

Examples

 data(lbp_orig)
 ## maybe str(lbp_orig)

Survival data of 265 Low Back Pain Patients

Description

A data frame with 10 multiply imputed datasets of 265 observations each on 17 variables related to low back pain.

Usage

lbpmicox

Format

A data frame with 2650 observations on the following 18 variables.

Impnr

a numeric vector

patnr

a numeric vector

Status

dichotomous event

Time

continuous follow up time variable

Duration

continuous

Previous

dichotomous

Radiation

dichotomous

Onset

dichotomous

Age

continuous

Tampascale

continuous

Pain

continuous

Function

continuous

Satisfaction

categorical

JobControl

continuous

JobDemand

continuous

Social

continuous

Expectation

a numeric vector

Expect_cat

categorical

Examples

 data(lbpmicox)
 ## maybe str(lbpmicox)

Data of 159 Low Back Pain Patients

Description

A data frame with 10 multiply imputed datasets of 159 observations each on 17 variables related to low back pain.

Usage

lbpmilr

Format

A data frame with 1590 observations on the following 17 variables.

Impnr

a numeric vector

ID

a numeric vector

Chronic

dichotomous

Gender

dichotomous

Carrying

categorical

Pain

continuous

Tampascale

continuous

Function

continuous

Radiation

dichotomous

Age

continuous

Smoking

dichotomous

Satisfaction

categorical

JobControl

continuous

JobDemands

continuous

SocialSupport

continuous

Duration

continuous

BMI

continuous

Examples

 data(lbpmilr)
 ## maybe str(lbpmilr)

Calculates the Levene's test

Description

levene_test Calculates the Levene's test for homogeneity of variance across groups, model coefficients, the variance-covariance matrix and the degrees of freedom.

Usage

levene_test(y, x, formula, data)

Arguments

Details

The Levene's test centers on group means to calculate outcome residuals, the Brown-Forsythe test on the median.

Value

An object from which the following objects are extracted:

• fstats F-test value, including numerator and denominator degrees of freedom.

• qhat model coefficients.

• vcov variance-covariance matrix.

• dfcom degrees of freedom obtained from df.residual.

Author(s)

Martijn Heymans, 2021

See Also

with.milist, pool_levenetest, bf_test

Examples

imp_dat <- df2milist(lbpmilr, impvar="Impnr")
ra <- with(imp_dat, expr=levene_test(Pain ~ factor(Carrying)))

Turns a list object with multiply imputed datasets into an object of class 'milist'.

Description

list2milist Turns a list with multiply imputed datasets into an object of class 'milist' to be further used by 'with.milist'

Usage

list2milist(data)

Arguments

Value

an object of class 'milist'

Author(s)

Martijn Heymans, 2021

Logit transformation of parameter estimates

Description

logit_trans Logit transformation of parameter estimate and standard error.

Usage

logit_trans(est, se)

Arguments

Details

Function is used to logit transform parameters and standard errors. For the standard error the Delta method is used.

Value

The logit transformed values.

Author(s)

Martijn Heymans, 2021

Turns a 'mice::mids' object into an object of class 'milist' to be further used by 'miceafter::with'

Description

mids2milist Turns a 'mice::mids' object into an object with multiply imputed datasets of class 'milist' to be further used by 'miceafter::with'

Usage

mids2milist(data, keep = FALSE)

Arguments

Value

an object of class 'milist'

Author(s)

Martijn Heymans, 2021

Calculates the odds ratio (OR) and standard error.

Description

odds_ratio Calculates the odds ratio and standard error and degrees of freedom to be used in function with.milist.

Usage

odds_ratio(y, x, formula, data)

Arguments

Details

Note that the standard error of the OR is in fact the standard error of the (natural) log odds ratio.

Value

The odds ratio, related standard error and complete data degrees of freedom (dfcom) as n-2.

Author(s)

Martijn Heymans, 2021

See Also

with.milist, pool_odds_ratio

Examples

imp_dat <- df2milist(lbpmilr, impvar="Impnr")
ra <- with(imp_dat, expr=odds_ratio(Chronic ~ Radiation))

Combines the Chi Square statistics across Multiply Imputed datasets

Description

pool_D2 The D2 statistic to combine the Chi square values across Multiply Imputed datasets.

Usage

pool_D2(dw, v)

Arguments

Value

The pooled chi square values as the D2 statistic, the p-value, the numerator, df1 and denominator, df2 degrees of freedom for the F-test.

Author(s)

Martijn Heymans, 2021

References

Eekhout I, van de Wiel MA, Heymans MW. Methods for significance testing of categorical covariates in logistic regression models after multiple imputation: power and applicability analysis. BMC Med Res Methodol. 2017;17(1):129.

Van Buuren S. (2018). Flexible Imputation of Missing Data. 2nd Edition. Chapman & Hall/CRC Interdisciplinary Statistics. Boca Raton.

Examples

  pool_D2(c(2.25, 3.95, 6.24, 5.27, 2.81), 4)

Pools the Likelihood Ratio tests across Multiply Imputed datasets ( method D4)

Description

pool_D4 The D4 statistic to combine the likelihood ratio tests (LRT) across Multiply Imputed datasets according method D4.

Usage

pool_D4(data, nimp, impvar, fm0, fm1, robust = TRUE, model_type = "binomial")

Arguments

Value

The D4 statistic, the numerator, df1 and denominator, df2 degrees of freedom for the F-test.

Author(s)

Martijn Heymans, 2021

References

Chan, K. W., & Meng, X.-L. (2019). Multiple improvements of multiple imputation likelihood ratio tests. https://arxiv.org/abs/1711.08822

Grund, Simon, Oliver Lüdtke, and Alexander Robitzsch. 2021. “Pooling Methods for Likelihood Ratio Tests in Multiply Imputed Data Sets.” PsyArXiv. January 29. doi:10.31234/osf.io/d459g.

Examples

fm0 <- Chronic ~ BMI + factor(Carrying) +
  Satisfaction + SocialSupport + Smoking
fm1 <- Chronic ~ BMI + factor(Carrying) +
  Satisfaction +  SocialSupport + Smoking +
  Radiation

miceafter::pool_D4(data=lbpmilr, nimp=10, impvar="Impnr",
               fm0=fm0, fm1=fm1, robust = TRUE)

Calculates the pooled Brown-Forsythe test.

Description

pool_levenetest Calculates the pooled F-statistic of the Brown-Forsythe test.

Usage

pool_bftest(object, method = "D1")

Arguments

Value

The (combined) F-statistic, p-value and degrees of freedom.

Author(s)

Martijn Heymans, 2021

References

Eekhout I, van de Wiel MA, Heymans MW. Methods for significance testing of categorical covariates in logistic regression models after multiple imputation: power and applicability analysis. BMC Med Res Methodol. 2017;17(1):129.

Enders CK (2010). Applied missing data analysis. New York: The Guilford Press.

Van Buuren S. (2018). Flexible Imputation of Missing Data. 2nd Edition. Chapman & Hall/CRC Interdisciplinary Statistics. Boca Raton.

See Also

with.milist, bf_test

Examples

imp_dat <- df2milist(lbpmilr, impvar="Impnr")
ra <- with(imp_dat, expr=bf_test(Pain ~ factor(Carrying)))
res <- pool_bftest(ra)
res

Calculates the pooled C-index and Confidence intervals

Description

pool_cindex Calculates the pooled C-index and Confidence intervals.

Usage

pool_cindex(data, conf.level = 0.95, dfcom = NULL)

Arguments

Details

Rubin's Rules are used for pooling. The C-index values are log transformed before pooling and finally back transformed.

Value

The pooled c-index value and the confidence intervals.

Vignettes

https://mwheymans.github.io/miceafter/articles/pooling_cindex.html

Author(s)

Martijn Heymans, 2021

See Also

with.milist, cindex

Examples

 # Logistic Regression
 imp_dat <- df2milist(lbpmilr, impvar="Impnr")
 res_stats <- with(data=imp_dat,
  expr = cindex(glm(Chronic ~ Gender + Radiation,
  family=binomial)))
 res <- pool_cindex(res_stats)
 res

 # Cox regression
 library(survival)
 imp_dat <- df2milist(lbpmicox, impvar="Impnr")
 res_stats <- with(data=imp_dat,
   expr = cindex(coxph(Surv(Time, Status) ~ Pain + Radiation)))
 res <- pool_cindex(res_stats)
 res

Calculates the pooled correlation coefficient and Confidence intervals

Description

pool_cor Calculates the pooled correlation coefficient and Confidence intervals.

Usage

pool_cor(
  data,
  conf.level = 0.95,
  dfcom = NULL,
  statistic = TRUE,
  df_small = TRUE,
  approxim = "tdistr"
)

Arguments

Details

Rubin's Rules are used for pooling. The correlation coefficient is first transformed using Fisher z transformation (function cor2fz) before pooling and finally back transformed (function fz2cor). The test statistic and p-values are obtained using the Fisher z transformation.

Value

An object of class mipool from which the following objects can be extracted:

• cor correlation coefficient

• SE standard error

• t t-value (for confidence interval)

• low_r lower limit of confidence interval

• high_r upper limit of confidence interval

• statistic test statistic

• pval p-value

Author(s)

Martijn Heymans, 2022

See Also

with.milist, cor_est

Examples

 imp_dat <- df2milist(lbpmilr, impvar="Impnr")
 res_stats <- with(data=imp_dat,
  expr = cor_est(y=BMI, x=Age))
 res <- pool_cor(res_stats)
 res

Pools and selects Linear and Logistic regression models across multiply imputed data.

Description

pool_glm Pools and selects Linear and Logistic regression models across multiply imputed data, using pooling methods RR, D1, D2, D3, D4 and MPR (in combination with 'with' function).

Usage

pool_glm(
  object,
  method = "D1",
  p.crit = 1,
  keep.predictors = NULL,
  direction = NULL
)

Arguments

Details

The basic pooling procedure to derive pooled coefficients, standard errors, 95 confidence intervals and p-values is Rubin's Rules (RR). However, RR is only possible when the model includes continuous and dichotomous variables. Multiparameter pooling methods are available when the model also included categorical (> 2 categories) variables. These pooling methods are: “D1” is pooling of the total covariance matrix, ”D2” is pooling of Chi-square values, “D3” and "D4" is pooling Likelihood ratio statistics (method of Meng and Rubin) and “MPR” is pooling of median p-values (MPR rule). For pooling restricted cubic splines using the 'rcs' function of of the rms package, use function 'glm_mi'.

A typical formula object has the form Outcome ~ terms. Categorical variables has to be defined as Outcome ~ factor(variable). Interaction terms can be defined as Outcome ~ variable1*variable2 or Outcome ~ variable1 + variable2 + variable1:variable2. All variables in the terms part have to be separated by a "+".

Value

An object of class mipool (multiply imputed pooled models) from which the following objects can be extracted:

• pmodel pooled model (at last selection step)

• pmultiparm pooled p-values according to multiparameter test method (at last selection step)

• pmodel_step pooled model (at each selection step)

• pmultiparm_step pooled p-values according to multiparameter test method (at each selection step)

• multiparm_final pooled p-values at final step according to pooling method

• multiparm_out (only when direction = "FW") pooled p-values of removed predictors

• formula_final formula object at final step

• formula_initial formula object at final step

• predictors_in predictors included at each selection step

• predictors_out predictors excluded at each step

• impvar name of variable used to distinguish imputed datasets

• nimp number of imputed datasets

• Outcome name of the outcome variable

• method selection method

• p.crit p-value selection criterium

• call function call

• model_type type of regression model used

• direction direction of predictor selection

• predictors_final names of predictors in final selection step

• predictors_initial names of predictors in start model

• keep.predictors names of predictors that were forced in the model

Vignettes

https://mwheymans.github.io/miceafter/articles/regression_modelling.html

Author(s)

Martijn Heymans, 2021

References

Eekhout I, van de Wiel MA, Heymans MW. Methods for significance testing of categorical covariates in logistic regression models after multiple imputation: power and applicability analysis. BMC Med Res Methodol. 2017;17(1):129.

Enders CK (2010). Applied missing data analysis. New York: The Guilford Press.

Meng X-L, Rubin DB. Performing likelihood ratio tests with multiply-imputed data sets. Biometrika.1992;79:103-11.

van de Wiel MA, Berkhof J, van Wieringen WN. Testing the prediction error difference between 2 predictors. Biostatistics. 2009;10:550-60.

Marshall A, Altman DG, Holder RL, Royston P. Combining estimates of interest in prognostic modelling studies after multiple imputation: current practice and guidelines. BMC Med Res Methodol. 2009;9:57.

Van Buuren S. (2018). Flexible Imputation of Missing Data. 2nd Edition. Chapman & Hall/CRC Interdisciplinary Statistics. Boca Raton.

Examples

  dat_list <- df2milist(lbpmilr, impvar="Impnr")
  ra <- with(data=dat_list, expr = glm(Chronic ~ factor(Carrying) + Radiation + Age))
  poolm <- pool_glm(ra, method="D1")
  poolm$pmodel
  poolm$pmultiparm

Calculates the pooled Levene test.

Description

pool_levenetest Calculates the pooled F-statistic of the Levenene test.

Usage

pool_levenetest(object, method = "D1")

Arguments

Value

The (combined) F-statistic, p-value and degrees of freedom.

Vignettes

https://mwheymans.github.io/miceafter/articles/levene_test.html

Author(s)

Martijn Heymans, 2021

References

Eekhout I, van de Wiel MA, Heymans MW. Methods for significance testing of categorical covariates in logistic regression models after multiple imputation: power and applicability analysis. BMC Med Res Methodol. 2017;17(1):129.

Enders CK (2010). Applied missing data analysis. New York: The Guilford Press.

Van Buuren S. (2018). Flexible Imputation of Missing Data. 2nd Edition. Chapman & Hall/CRC Interdisciplinary Statistics. Boca Raton.

See Also

with.milist, levene_test

Examples

library(magrittr)
lbpmilr %>%
   df2milist(impvar="Impnr") %>%
      with(expr=levene_test(Pain ~ factor(Carrying))) %>%
        pool_levenetest(method="D1")

# Same as
imp_dat <- df2milist(lbpmilr, impvar="Impnr")
ra <- with(imp_dat, expr=levene_test(Pain ~ factor(Carrying)))
res <- pool_levenetest(ra, method="D1")

Calculates the pooled odds ratio (OR) and related confidence interval.

Description

pool_odds_ratio Calculates the pooled odds ratio and confidence interval.

Usage

pool_odds_ratio(object, conf.level = 0.95, dfcom = NULL)

Arguments

Value

The pooled OR and confidence intervals.

Author(s)

Martijn Heymans, 2021

See Also

with.milist, odds_ratio

Examples

library(magrittr)
lbpmilr %>%
   df2milist(impvar="Impnr") %>%
     with(expr=odds_ratio(Chronic ~ Radiation)) %>%
       pool_odds_ratio()

# Same as
imp_dat <- df2milist(lbpmilr, impvar="Impnr")
ra <- with(imp_dat, expr=odds_ratio(Chronic ~ Radiation))
res <- pool_odds_ratio(ra)

Calculates the pooled proportion and confidence intervals using an approximate Beta distribution.

Description

pool_prop_nna Calculates the pooled proportion and confidence intervals using an approximate Beta distribution.

Usage

pool_prop_nna(object, conf.level = 0.95)

Arguments

Details

The parameters for the Beta distribution are calculated using the method of moments (Gelman et al. p. 582).

Value

The pooled proportion and the 95% Confidence interval.

Author(s)

Martijn Heymans, 2021

References

Raghunathan, T. (2016). Missing Data Analysis in Practice. Boca Raton, FL: Chapman and Hall/CRC. (paragr 4.6.2)

Andrew Gelman, John B. Carlin, Hal S. Stern, David B. Dunson, Aki Vehtari, Donald B. Rubin. (2003). Bayesian Data Analysis (2nd ed). Chapman and Hall/CRC.

See Also

with.milist, prop_nna

Examples

 imp_dat <- df2milist(lbpmilr, impvar='Impnr')
 ra <- with(imp_dat, expr=prop_nna(Radiation))
 res <- pool_prop_nna(ra)
 res

Calculates the pooled proportion and standard error according to Wald across multiply imputed datasets.

Description

pool_prop_wald Calculates the pooled proportion and standard error according to Wald across multiply imputed datasets and using Rubin's Rules.

Usage

pool_prop_wald(object, conf.level = 0.95, dfcom = NULL)

Arguments

Details

Before pooling, the proportions will be naturally log transformed and the pooled estimates back transformed to the original scale.

Value

The proportion, the Confidence intervals, the standard error and the statistic.

Author(s)

Martijn Heymans, 2021

See Also

with.milist, prop_wald

Examples

imp_dat <- df2milist(lbpmilr, impvar="Impnr")
ra <- with(imp_dat, expr=prop_wald(Radiation ~ 1))
res <- pool_prop_wald(ra)
res

Calculates the pooled single proportion confidence intervals according to Wilson across multiply imputed datasets.

Description

pool_prop_wilson Calculates the pooled single proportion and confidence intervals according to Wald across multiply imputed datasets.

Usage

pool_prop_wilson(object, conf.level = 0.95)

Arguments

Value

The proportion and the 95% Confidence interval according to Wilson.

Author(s)

Martijn Heymans, 2021

References

Anne Lott & Jerome P. Reiter (2020) Wilson Confidence Intervals for Binomial Proportions With Multiple Imputation for Missing Data, The American Statistician, 74:2, 109-115, DOI: 10.1080/00031305.2018.1473796.

See Also

with.milist, prop_wald

Examples

library(magrittr)
lbpmilr %>%
  df2milist(impvar="Impnr") %>%
    with(expr=prop_wald(Radiation ~ 1)) %>%
      pool_prop_wilson()

# Same as
imp_dat <- df2milist(lbpmilr, impvar="Impnr")
ra <- with(imp_dat, expr=prop_wald(Radiation ~ 1))
res <- pool_prop_wilson(ra)

Calculates the pooled difference between proportions and standard error according to Agresti-Caffo across multiply imputed datasets.

Description

pool_propdiff_ac Calculates the pooled difference between proportions and standard error according to Agresti-Caffo across multiply imputed datasets.

Usage

pool_propdiff_ac(object, conf.level = 0.95, dfcom = NULL)

Arguments

Details

For the pooled difference between proportions the difference between proportions according to Wald are used. The Agresti-Caffo difference is used to derive the Agresti-Caffo confidence intervals.

Value

The proportion, the Confidence intervals, the standard error and statistic.

Author(s)

Martijn Heymans, 2021

References

Agresti, A. and Caffo, B. Simple and Effective Confidence Intervals for Proportions and Differences of Proportions Result from Adding Two Successes and Two Failures. The American Statistician. 2000;54:280-288.

Fagerland MW, Lydersen S, Laake P. Recommended confidence intervals for two independent binomial proportions. Stat Methods Med Res. 2015 Apr;24(2):224-54.

See Also

with.milist, propdiff_ac

Examples

imp_dat <- df2milist(lbpmilr, impvar="Impnr")
ra <- with(imp_dat, expr=propdiff_ac(Chronic ~ Radiation))
res <- pool_propdiff_ac(ra)
res

Calculates the pooled difference between proportions and confidence intervals according to Newcombe-Wilson (NW) across multiply imputed datasets.

Description

pool_propdiff_nw Calculates the pooled difference between proportions and confidence intervals according to Newcombe-Wilson (NW) across multiply imputed datasets.

Usage

pool_propdiff_nw(object, conf.level = 0.95)

Arguments

Details

The pool_propdiff_nw function uses information from separate exposure groups. It is therefore important to first use the propdiff_wald function and to set strata = TRUE in that function.

Value

The Proportion and the Confidence intervals according to Newcombe-Wilson.

Author(s)

Martijn Heymans, 2021

References

Yulia Sidi & Ofer Harel (2021): Difference Between Binomial Proportions Using Newcombe’s Method With Multiple Imputation for Incomplete Data, The American Statistician, DOI:10.1080/00031305.2021.1898468

See Also

with.milist, propdiff_wald

Examples

library(magrittr)
lbpmilr %>%
  df2milist(impvar="Impnr") %>%
    with(expr=propdiff_wald(Chronic ~ Radiation, strata = TRUE)) %>%
      pool_propdiff_nw()

# Same as
imp_dat <- df2milist(lbpmilr, impvar="Impnr")
res <- with(imp_dat, expr=propdiff_wald(Chronic ~ Radiation, strata = TRUE))
res <- pool_propdiff_nw(res)

Calculates the pooled difference between proportions and standard error according to Wald across multiply imputed datasets.

Description

pool_propdiff_wald Calculates the pooled difference between proportions and standard error according to Wald across multiply imputed datasets.

Usage

pool_propdiff_wald(object, conf.level = 0.95, dfcom = NULL)

Arguments

Value

The proportion, the Confidence intervals, the standard error and statistic.

Author(s)

Martijn Heymans, 2021

See Also

with.milist, propdiff_wald

Examples

imp_dat <- df2milist(lbpmilr, impvar="Impnr")
ra <- with(imp_dat, expr=propdiff_wald(Chronic ~ Gender))
res <- pool_propdiff_wald(ra)
res

Calculates the pooled risk ratio (RR) and related confidence interval.

Description

pool_risk_ratio Calculates the pooled risk ratio and confidence interval.

Usage

pool_risk_ratio(object, conf.level = 0.95, dfcom = NULL)

Arguments

Value

The pooled RR and confidence intervals.

Author(s)

Martijn Heymans, 2021

See Also

with.milist, risk_ratio

Examples

library(magrittr)
lbpmilr %>%
 df2milist(impvar="Impnr") %>%
   with(expr=risk_ratio(Chronic ~ Radiation)) %>%
     pool_risk_ratio()

# Same as
imp_dat <- df2milist(lbpmilr, impvar="Impnr")
ra <- with(imp_dat, expr=risk_ratio(Chronic ~ Radiation))
res <- pool_risk_ratio(ra)

Rubin's Rules for scalar estimates

Description

pool_scalar_RR Applies Rubin's pooling Rules for scalar estimates

Usage

pool_scalar_RR(
  est,
  se,
  logit_trans = FALSE,
  conf.level = 0.95,
  statistic = FALSE,
  dfcom = NULL,
  df_small = TRUE,
  approxim = "tdistr"
)

Arguments

Details

The t-value is the quantile value of the t-distribution that can be used to calculate confidence intervals according to est_{pooled} +/- t_{1-\alpha/2} * se_{pooled}. When statistic is TRUE the test statistic is calculated as statistic = est{pooled}/se{pooled}. The p-value is than derived using the t-distribution and adjusted degrees of freedom.

Value

A list object from which the following objects are extracted:

• pool_est the pooled parameter value.

• pool_se the pooled standard error value.

• t quantile of the t-distribution (to calculate confidence intervals).

• r the relative increase in variance due to missing data.

• dfcom complete data degrees of freedom.

• v_adj adjusted degrees of freedom (according to Barnard and Rubin 1999)

Author(s)

Martijn Heymans, 2021

Examples

est <- c(0.4, 0.6, 0.8)
se <- c(0.02, 0.05, 0.03)
res <- pool_scalar_RR(est, se, dfcom=500)
res

Calculates the pooled t-test and Confidence intervals

Description

pool_t_test Calculates the pooled t-test, confidence intervals and p-value.

Usage

pool_t_test(object, conf.level = 0.95, dfcom = NULL, statistic = FALSE)

Arguments

Value

An object of class mipool from which the following objects can be extracted:

• Mean diff Difference between means

• SE standard error

• t t-value (for confidence interval)

• low_r lower limit of confidence interval

• high_r upper limit of confidence interval

• statistic test statistic

• pval p-value

Author(s)

Martijn Heymans, 2022

See Also

with.milist, t_test

Examples

 imp_dat <- df2milist(lbpmilr, impvar="Impnr")
 res_stats <- with(data=imp_dat,
  expr = t_test(Pain ~ Gender, var_equal=TRUE, paired=FALSE))
 res <- pool_t_test(res_stats)
 res

Calculates the posterior beta components for a single proportion

Description

prop_nna Calculates the posterior beta components for a single proportion (assuming noninformative prior).

Usage

prop_nna(x, data)

Arguments

Value

The posterior beta components.

Author(s)

Martijn Heymans, 2021

References

Raghunathan, T. (2016). Missing Data Analysis in Practice. Boca Raton, FL: Chapman and Hall/CRC. (paragr 4.6.2)

See Also

with.milist, pool_prop_nna

Examples

 imp_dat <- df2milist(lbpmilr, impvar='Impnr')
 ra <- with(imp_dat, expr=prop_nna(Radiation))

Calculates a single proportion and related standard error according to Wald

Description

prop_wald Calculates a single proportion and related standard error according to Wald and provides degrees of freedom to be used in function with.miceafter.

Usage

prop_wald(x, formula, data)

Arguments

Value

The proportion, standard error and complete data degrees of freedom (dfcom) as n-1.

Author(s)

Martijn Heymans, 2021

See Also

with.milist, pool_prop_wald

Examples

imp_dat <- df2milist(lbpmilr, impvar="Impnr")
ra <- with(imp_dat, expr=prop_wald(Chronic ~ 1))

Calculates the difference between proportions and standard error according to method Agresti-Caffo

Description

propdiff_ac Calculates the difference between proportions and standard error according to method Agresti-Caffo.

Usage

propdiff_ac(y, x, formula, data)

Arguments

Details

As output the differences between proportions according to Agresti-Caffo and Wald are provided. The Agresti-Caffo difference is used in the function pool_propdiff_ac to derive the Agresti-Caffo confidence intervals. For the pooled difference between proportions the difference between proportions according to Wald are used.

Value

The difference between proportions, the standard error according to Agresti-Caffo and complete data degrees of freedom (dfcom) as n-1.

Author(s)

Martijn Heymans, 2021

References

Agresti, A. and Caffo, B. Simple and Effective Confidence Intervals for Proportions and Differences of Proportions Result from Adding Two Successes and Two Failures. The American Statistician. 2000;54:280-288.

Fagerland MW, Lydersen S, Laake P. Recommended confidence intervals for two independent binomial proportions. Stat Methods Med Res. 2015 Apr;24(2):224-54.

See Also

with.milist, pool_propdiff_ac

Examples

imp_dat <- df2milist(lbpmilr, impvar="Impnr")
ra <- with(imp_dat, expr=propdiff_ac(Chronic ~ Radiation))

# same as
ra <- with(imp_dat, expr=propdiff_ac(y=Chronic, x=Radiation))

Calculates the difference between proportions and standard error according to Wald

Description

propdiff_wald Calculates the difference between proportions and standard error according to Wald and degrees of freedom to be used in function with.miceafter.

Usage

propdiff_wald(y, x, formula, data, strata = FALSE)

Arguments

Value

The difference between proportions, standard error and complete data degrees of freedom (dfcom) as n-1.

Author(s)

Martijn Heymans, 2021

See Also

with.milist, pool_propdiff_nw

Examples

imp_dat <- df2milist(lbpmilr, impvar="Impnr")
ra <- with(imp_dat, expr=propdiff_wald(Chronic ~ Radiation))

# proportions in each subgroup
imp_dat <- df2milist(lbpmilr, impvar="Impnr")
ra <- with(imp_dat, expr=propdiff_wald(Chronic ~ Radiation, strata=TRUE))

Calculates the risk ratio (RR) and standard error.

Description

risk_ratio Calculates the risk ratio and standard error.

Usage

risk_ratio(y, x, formula, data)

Arguments

Details

Note that the standard error of the RR is in fact the standard error of the (natural) risk ratio.

Value

The risk ratio, related standard error and complete data degrees of freedom (dfcom) as n-2.

Author(s)

Martijn Heymans, 2021

See Also

with.milist

Examples

imp_dat <- df2milist(lbpmilr, impvar="Impnr")
ra <- with(imp_dat, expr=risk_ratio(Chronic ~ Radiation))

Calculates the one, two and paired sample t-test

Description

t_test Calculates the one, two and paired sample t-test.

Usage

t_test(y, x, formula, data, paired = FALSE, var_equal = TRUE)

Arguments

Details

For all t-tests the dataset must be in long format (i.e. group data under each other). For the paired t-test x and y must have the same length. When variances between groups are unequal, the Welch df correction formula is used and eventually averaged across multiply imputed datasets in the pool_t_test function.

Value

An object containing the following objects are extracted:

• mdiff the mean difference.

• se the standard error.

• dfcom the complete data degrees of freedom.

Author(s)

Martijn Heymans, 2022

See Also

with.milist, pool_t_test

Examples

imp_dat <- df2milist(lbpmilr, impvar="Impnr")
ra <- with(imp_dat, expr=t_test(Pain ~ Gender))

Evaluate an Expression across a list of multiply imputed datasets

Description

with.milist Evaluate an expression in the form of a statistical test procedure across a list of multiply imputed datasets

Usage

## S3 method for class 'milist'
with(data, expr = NULL, ...)

Arguments

Value

The value of the evaluated expression with class mistats 'Multiply Imputed Statistical Analysis'.

Author(s)

Martijn Heymans, 2021