Missing values are a wide spread problem in analyzing large data sets. In the medical domain they are unavoidable and complete analyzing methods fail here. In the paper we give an overview of kinds of missingness and common methods to handle missing values in machine learning algorithms. We introduce the Charité Query Language Toolkit which was developed to find out similar patterns in patient data records with respect to post-kidney-transplant patients. The toolkit uses available case analysis methods combined with a preprocessing of missing values as a compromise of simplicity and functionality.
Missing values are a wide spread problem for analyzing methods, such as machine learning, pattern recognition or data-mining algorithms, in many domains. For medical data sets missing values are unfortunately unavoidable. In a complete case analysis for these data sets all patient records with missing data would excluded. Performing clinical studies only with complete patient data sets lead to a significantly smaller sample size with reduced statistical expressiveness.
Depending of the choosen method for the statistical analysis missing values can restrict the cohort so much that the whole study is endangered.
In the last decades the amount of electronically collected patient data has grown rapidly and the demand of researchers and physicians for the development of analyzing methods and tools for data-sets with missing values is obvious.
In our work, we will describe the different kinds of missing values and follow here
in principle the systematic of Pigott [
Missing values are a common issue when analyzing data in a wide range of research
fields. In the medical domain it seems unavoidable, especially in long-term treatments.
De Goeij et.al. [
MCAR U˝ missing completely at random - is the strongest assumption for missing values of a dataset. The missing of a value neither depends on the observed parameters nor on the unknown value itself. MCAR will not bias the analysis of data, because the missing data has the same distribution as the available data. In medical domain it occurs e.g. if it was forgotten to induce an examination or there were problems in the transmission of laboratory data.
A less strict mechanism is MAR U˝ missing at random. The missing of a value is allowed to be dependent on the observed parameters but not on the missing value itself. In long-term treatment of a patient it happens e.g. if the patient was not motivated to come to a medical control round because he had no health problems.
When adjusting a set of variables, MAR can be avoided by selecting highly correlated variables to be observed.
But clearly, this requires a specialist with domain-specific knowledge. To the third category of missingness belong data where values are not missing at random U˝ NMAR. Here the missing of a value depends on the value itself. E.g. a creatinine value of a kidney transplanted patient was not measured because of rejection and loss of the transplant.
Without evaluating the dataset, no type of missing value can be ruled out. Even worse, each type of missingness can occur in a single dataset where different mechanisms overlay as our instances above show. Furthermore, it is not trivial to find out what kind of missingness applies.
There are several ways to handle missing values in pattern mining and data-analysis
algorithms. Especially in the medical domain there are several studies on different
approaches of dealing with missing values. Van der Heijden et. al. [
All methods are suitable for MCAR data-sets. Furthermore, Single Conditional Mean Imputation, Multiple Imputation, Maximum Likelihood and Pattern-Mixture Model are additional usable for MAR data-sets, but only the last one is practicable for NMAR data-sets. In the following we will introduce in short the handling of missing values for the mentioned methods. 3.1
The easiest way to handle missing values is to delete all cases (rows) that contain missing values. The remaining data will be complete and all methods requiring complete data sets can be applied without further issues. When applying Complete Case analysis (CC) to table 1, the patients 2, 3 and 4 would be discarded. In subsequent operations, only patient 1 would be considered. If the missing values were not missing completely at random, Complete Case analysis will be biased. Unfortunately MCAR applies rarely (see table 2).
Furthermore, the deletion of many cases is not applicable if there are missing values
in almost every case. The loss of information would increase while the significance
decreases [
Available Case analysis (AC), which is sometimes referred to as pair wise deletion,
is less strictly than Complete Case analysis. When analyzing a subset of the observed
variables, all complete cases for that subset are viewed. That means only missing values
are ignored [
The Single Unconditional Mean Imputation (sometimes referred to as single value
imputation) replaces all missing of an observed variable by the mean of the available
values of that variable [
There are several drawbacks of that method: The variance of the imputed variables decreases while the precision is overrated. The results of an unconditional mean imputation will always be biased. This method is rather easily applicable as there is no further information about the dataset required. Adapting this approach to categorical data, the most frequent value of a column is imputed. In order to avoid precision overrating, the unconditional imputation may be extended to analyze columns in order to find the underlying random distribution. The imputation is then based on the columns distribution.
An improvement to unconditional imputation is the conditional imputation method. By linear regression on the conditional (observed) variables with complete data, the missing values are imputed. When considering test B as the condition for test A in table 1, the mean of column A is calculated for all patients where test B is negative (mean = 3.0) and once more for all patients where test B is positive (mean = 1.0). Hence the imputed value for test A of patient 3 would be 3.0. The selection of conditional variables is not trivial. When selecting too many columns, the imputed value may be over fitted. 3.5
In contrast to the previously mentioned single imputation methods, Multiple Imputation (MI) does not calculate a single mean of an observed variable in order to impute a missing value, but creates a set of possible complete data sets. Each imputed parameter is selected by the columns underlying random distribution that was determined by regression. On each complete set the analysis is done. Finally, the results will be brought together. Practical tests show that MI often performs better than CC and AC, especially in the field of nephrology. This holds for MCAR and MAR data as long as the model specification is suitable. An overrated precision is avoided by imputing data several times, while biasing is avoided by applying regression. 3.6
Maximum Likelihood (ML) methods estimate the parameters of the underlying distributions of the observed variables.
To get the most probable parameters, an EM algorithm can be used. If the algorithm
converges, the coefficients with the highest likelihood can be used in linear regression
models [
For pattern-mixture models the missing data mechanism may remain unknown. Instead, a mixture of different patterns describes the missingness in the data set, whereas each pattern describes a subset of the missing values. These patterns support the statistical model and can therefore improve the analysis. Hence pattern mixture models can produce good estimates for data that is MCAR, MAR and NMAR. Unfortunately, creating patterns requires a lot of domain specific knowledge about the data. 4
The Charité Query Language Toolkit was developed to find out similar patterns in patient data records with respect to post-kidney-transplant patients. Physicians should be enabled to find out similar courses of diseases and treatments to infer from it for actual cases.
For the development of a toolkit, it might be disappointing that there is no simple
general purpose method that handles all missing values in each imaginable query, especially
if the data missing mechanism is unknown. Calders et.al. [
The toolkit uses available case analysis methods combined with a preprocessing of missing values as a compromise of simplicity and functionality. It does not focus on creating statistically faultless results. Biased correlations caused by violations of the MCAR-property can be expected and are accepted for that purpose.
When searching for new correlations, the user may not be interested in strong and therefore possibly known rules but in weaker or overlooked associations.
In the design phase of the toolkit, two essential settings have to be done. Firstly, the definition of time slices in order to discretize the time axis is required (see figure 1). In the second step, the definition of norms in order to provide a discretization of the parameters is necessary.
Norm values of parameters can be set in the norms tab (see figure 2). A group of norms for the same parameter was named norm family. This classification is necessary in order to recognize missing values. The norm type depends on the detected parameter as some tests generate qualitative (e.g. HCV, CMV, etc.) and some result in quantitative values (e.g. heart rate, creatinine, etc.). Qualitative norms are simply a mapping of a string value to the norm’s name.
This allows to assign several values to the same category (e.g. weak and positive are both mapped to not negative). Quantitative norms are ranges for numeric parameters that are mapped to the name of a norm (e.g. a creatinine value of 1.2 to 6.0 is mapped to bad).
Norms can be created automatically as well. The database contains references for several parameters that may be loaded. Furthermore, a function calculating quartiles and creating norms by these is available. 5
In our paper we give a survey of kinds of missing values and common methods to handle them in pattern mining algorithms. We introduce the Charité Query Language Toolkit which was configured to work on post-kidney-transplant patient data. Since the data does not differ from other medical domains, the toolkit may be used in other departments as well. Either a separate database is provided or the data is loaded into the current database. Depending on the domain, individual preprocessing plug-ins might be necessary in order to provide proper data transformation abilities.