![]() ![]() Some authors suggested including variables into the common model that appear in at least 3 out of 5 (60%) of the model, and pool these coefficients. The variable selection algorithm may easily produce different models for different imputed data sets. Such pooling is usually straightforward, but introduces complexities if automatic variable selection strategies are applied. MI proceeds by applying the complete-data analysis to each imputed data set, followed by pooling the results into a final estimate. The spread between the imputed values reflects the uncertainty about the missing data. MI replaces each missing values by two or more imputations. Multiple imputation (MI) accounts for the uncertainty caused by the missing data, and when properly done, MI provides correct statistical inferences. Single imputation, such as mean imputation or imputation based on linear regression, leads to incorrect statistical tests because the complete-data analysis does not account for uncertainty created by the fact that data are missing. As the amount of incomplete cases can rapidly increase with the number of variables considered, this strategy is wasteful of costly collected data. The default strategy is to eliminate all incomplete cases from the analysis. The presence of missing data is a frequently encountered problem in the development of prognostic models. This study therefore set outs to develop a prognostic model from incomplete data. Discarding these prognostic variables would undermine the validity of the models. As some variables were measured in only one or two studies, merging the studies resulted in high percentages of missing values for these data. Patients with low back pain were enrolled in each study, and similar baseline and follow-up information was measured. This study aims to investigate the variable selection process in a prognostic model for high risk patients using merged data from three different studies. From a prevention perspective, it is necessary to identify as early as possible the patients that are at high risk for developing chronic low back pain and long-term disability. The development of chronic low back pain is an important societal problem. The new procedure of combining MI with bootstrapping for variable selection, results in multivariable prognostic models with good performance and is therefore attractive to apply on data sets with missing values. ![]() We recommend to account for both imputation and sampling variation in sets of missing data. When MI and bootstrapping were combined at the range of 0% (full model) to 90% of variable selection, bootstrap corrected c-index values of 0.70 to 0.71 and slope values of 0.64 to 0.86 were found. We found that the effect of imputation variation on the inclusion frequency was larger than the effect of sampling variation. The discriminative and calibrative abilities of prognostic models developed by the four methods were assessed at different inclusion levels. the proportion of times that the variable appeared in the model. Variables were selected based on the inclusion frequency of each prognostic variable, i.e. We used four methods to investigate the influence of respectively sampling and imputation variation: MI only, bootstrap only, and two methods that combine MI and bootstrapping. Among the outcome and prognostic variables data were missing in the range of 0 and 48.1%. In our prospective cohort study we merged data from three different randomized controlled trials (RCTs) to assess prognostic variables for chronicity of low back pain. We developed and tested a methodology combining MI with bootstrapping techniques for studying prognostic variable selection. Multiple imputation (MI) accounts for imputation uncertainty that allows for adequate statistical testing. Missing data is a challenging problem in many prognostic studies. ![]()
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