psfmi_lr Pooling and backward or forward selection of Logistic regression
models in multiply imputed data using selection methods RR, D1, D2, D3 and MPR.
psfmi_lr( data, formula = NULL, nimp = 5, impvar = NULL, Outcome = NULL, predictors = NULL, cat.predictors = NULL, spline.predictors = NULL, int.predictors = NULL, keep.predictors = NULL, nknots = NULL, p.crit = 1, method = "RR", direction = NULL )
Data frame with stacked multiple imputed datasets. The original dataset that contains missing values must be excluded from the dataset. The imputed datasets must be distinguished by an imputation variable, specified under impvar, and starting by 1.
A formula object to specify the model as normally used by glm. See under "Details" and "Examples" how these can be specified. If a formula object is used set predictors, cat.predictors, spline.predictors or int.predictors at the default value of NULL.
A numerical scalar. Number of imputed datasets. Default is 5.
A character vector. Name of the variable that distinguishes the imputed datasets.
Character vector containing the name of the outcome variable.
Character vector with the names of the predictor variables. At least one predictor variable has to be defined. Give predictors unique names and do not use predictor name combinations with numbers as, age2, gender10, etc.
A single string or a vector of strings to define the categorical variables. Default is NULL categorical predictors.
A single string or a vector of strings to define the (restricted cubic) spline variables. Default is NULL spline predictors. See details.
A single string or a vector of strings with the names of the variables that form an interaction pair, separated by a “:” symbol.
A single string or a vector of strings including the variables that are forced in the model during predictor selection. All type of variables are allowed.
A numerical vector that defines the number of knots for each spline predictor separately.
A numerical scalar. P-value selection criterium. A value of 1 provides the pooled model without selection.
A character vector to indicate the pooling method for p-values to pool the total model or used during predictor selection. This can be "RR", D1", "D2", "D3" or "MPR". See details for more information. Default is "RR".
The direction of predictor selection, "BW" means backward selection and "FW" means forward selection.
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
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 included continuous or 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” 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.
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.
Martijn Heymans, 2020
pool_lr <- psfmi_lr(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")#>#> #>#>pool_lr$RR_model_final#> $`Final model` #> term estimate std.error statistic #> 1 (Intercept) -4.709498778 1.43056951 -3.292044710 #> 2 Pain 1.000998071 0.17550142 5.703646588 #> 3 Radiation 1.290636824 1.09101880 1.182964787 #> 4 Age -0.015400069 0.02511643 -0.613147208 #> 5 factor(Satisfaction)2 0.006745828 0.72630877 0.009287825 #> 6 factor(Satisfaction)3 -2.245109289 1.28811308 -1.742944248 #> 7 Radiation:factor(Satisfaction)2 -1.112425071 1.29072002 -0.861863964 #> 8 Radiation:factor(Satisfaction)3 -0.328027439 1.69820886 -0.193160834 #> df p.value OR lower.EXP upper.EXP #> 1 121.39346 1.302896e-03 0.009009292 0.0005305503 0.1529871 #> 2 86.27941 1.612718e-07 2.720996221 1.9196231945 3.8569134 #> 3 30.54412 2.459495e-01 3.635100740 0.3922493500 33.6876464 #> 4 102.60849 5.411357e-01 0.984717906 0.9368661635 1.0350137 #> 5 94.66955 9.926090e-01 1.006768633 0.2380619605 4.2576440 #> 6 23.29136 9.453270e-02 0.105915964 0.0073877578 1.5184839 #> 7 40.99328 3.937762e-01 0.328760726 0.0242557883 4.4559927 #> 8 19.52844 8.488278e-01 0.720343254 0.0207352364 25.0247643 #>