Abstract Background Missing data present a challenge to many research projects. The problem is often pronounced in studies utilizing self-report scales, and literature addressing different strategies for dealing with missing data in such circumstances is scarce. The objective of this study was to compare six different imputation techniques for dealing with missing data in the Zung Self-reported Depression scale SDS.
Methods participants from a surgical outcomes study completed the SDS.
The SDS is a 20 question scale that respondents complete by circling a value of 1 to 4 for each question. The sum of the responses is calculated and respondents are classified as exhibiting depressive symptoms when their total score is over Missing values were simulated by randomly selecting questions whose values were then deleted a missing completely at random simulation. Additionally, a missing at random and missing not at random simulation were completed. Six imputation methods compare dealing center then considered; 1 multiple imputation, 2 single regression, 3 individual mean, 4 overall mean, 5 participant's preceding response, and 6 random selection of a value from 1 to 4.
For each method, the imputed mean SDS score compare dealing center standard deviation were compared to the population statistics. The Spearman correlation coefficient, percent misclassified and the Kappa statistic were also calculated. MI produces the most valid imputed values with a high Kappa statistic 0. The individual mean and single regression method produced Kappas in the 'substantial agreement' range 0.
Conclusion Multiple imputation is the most accurate method for dealing with missing data in most of the missind data scenarios we assessed for the SDS.
Imputing the individual's mean is also an appropriate and simple method for dealing with missing data that may be more interpretable to the majority of medical readers. Researchers should consider conducting methodological assessments such as this one when confronted with missing data. The optimal method should balance validity, ease of interpretability for readers, and analysis expertise of the research team.
Dealing with missing data in a multi-question depression scale: a comparison of imputation methods
Peer Review reports Background Missing data are a common challenge in health research, and the problem is often pronounced in studies that use self-report instruments. As part of an outcome study in surgical patients, we measured levels of depression in surgical patients using a validated instrument, the Zung Self-rated Depression Scale SDS Table 1 [ 1 ].
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Among the patients surveyed, did not fully complete the instrument. The quantity of missing data among those subjects occasionally involved only 1 missing response in the entire instrument, with the majority of respondents missing 4 or less compare dealing center. The remaining participants of the study completed all 20 questions of the SDS.
Such missing data scenarios leave researchers with the choice of dropping cases compare dealing center when they have missing responses to some questions, or alternatively, finding an imputation solution to deal with missing information.
Table 1 The Zung Self-rating Depression Scale SDS Full size table To gain insights into how to deal with missing data in such scenarios, we conducted a methodological study for which we selected the subset of participants with complete responses in the above-mentioned study, and simulated missing data scenarios by deleting observations. We then compared 6 methodological approaches to imputing replacement values for the deleted observations and assessed the accuracy of each of the six methods.
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These 6 methodological approaches are described in detail in the Compare dealing compare dealing center section. Five missing data simulations were produced from a complete data set to permit this methodological comparison. We then implemented a deletion binary option dragon pattern that assigned a higher probability of missing data to one particular question, a pattern of missing data that resembles that of our surgical outcome study.
We also considered a scenario where the probability of missing was linked to patient characteristics age and gender. Lastly, a missing not at random simulation was completed by linking the probability of missing one particular question to the response of that question. Our methodological approach and findings will inform researchers who encounter such missing data scenarios in the conduct of health research.
Methods A total of patients seen in the pre-operative assessment clinic of a tertiary care centre in Calgary, Alberta, Canada agreed to participate in the survey portion of a surgical outcomes study.
After informed consent was obtained, participants were given a study package containing an introductory letter and the questionnaires.
All questionnaires were self-reported and returned to the research assistant upon completion. The SDS questionnaire is a 20 question scale for which details are shown in Table 1. Each question is scored between 1 and 4, and a sum of responses is calculated.
A previous version of the Zung SDS included 25 questions with a maximum total score of [ 2 ]. To maintain comparability across the previous and the current version of the SDS instrument, the score from the current version is converted onto a point scale.
Thus, the calculated sum of scores across the 20 questions is converted to a point scale by dividing the sum by 0. Respondents are classified as exhibiting depressive symptoms when their converted score is over As mentioned earlier, patients completed all items of the SDS questionnaire. Missing values were simulated in these complete cases by assigning each observation a number between 0 and 1 randomly selected from the uniform distribution 0,1 ; each number between 0 and 1 has an equal probability of being assigned.
The assigned value was then used to assign missing values to selected observations. Initially, three missing completely at random MCAR scenarios were simulated; the probability of missing is not linked to any other patient characteristics.
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Observations assigned a value of less than 0. For subsequent MCAR simulations the value was increased to 0. Subjects with no deleted values were then removed from the analysis since there is no missing value to impute. This was done to mimic the pattern the missing data seen in our cohort where question 6 was found to be missing approximately twice as often as other questions among the incomplete cases.
This simulation is referred to as the "Q6" simulation. Next, a missing at random MAR simulation was completed; the probability of missing is linked to known patient characteristics.
The probability of an observation being missing was linked to the age and gender of the patient. This association has been demonstrated in the literature with females and those over 65 being more likely to have missing values [ 3 ]. Lastly, a missing not at random simulation was completed MNAR. In this scenario, the probability of missing depends on an unknown patient characteristic.
Thus, the probability of missing questions 6 was linked to the response of question 6 itself an unknown characteristic in real missing data situations. Six methods of imputation were compared: 1 random selection, 2 preceding question, 3 question mean, 4 individual mean 5 single regression and 6 a multiple imputation MI algorithm. Each method is briefly described below: 1 Random Selection The imputed value was a randomly selected value from 1 to 4.
This method was included to compare dealing center an example of an imputation method for which no participant characteristics are considered. Subjects tend to respond at levels consistent with their compare dealing center state throughout the instrument. In such situations, a subject's response to the preceding question could be used as a source of information for determining the missing response. For this method, we replicated the preceding question's response to impute the missing response.
For example, if a participant has a missing value for question 17, the imputed value is the mean calculated from the completed question 17 for the entire cohort.
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The imputed value is the calculated mean of a given subject's complete responses to other questions. If a participant has 2 missing responses, the values are filled with the calculated average of the remaining completed 18 questions. The missing value was considered the outcome variable with all other available data points for an individual used as the predictor variables. Since traditional regression approach would result in a different model for each pattern of missing data, we applied the multiple regression procedure from SAS see below using only one repetition.
The method is based on Rubin's work [ 5 ] that attempts to estimate a missing value with a plausible set of values. The method assumes a multivariate normal distribution and that the missing data are MAR. Compare dealing center resulting statistics appropriately reflect the uncertainty in the data due to missing values. The imputation is carried out in three steps.
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The missing data are filled 5 times generating 5 complete unique data sets. Each data set is analysed separately to calculate a mean, and standard deviation. Then, the results from each analysis are combined to produce an overall mean and standard deviation for each missing value. The missing values are predicted based on a specified list of characteristics that are used as predictors of the missing value s.
In our compare dealing center, the predicting variables used in the MI procedure to predict missing responses were the responses to completed questions. Analysis For each method, the SDS score was calculated first with imputed values, and then with the "true" values, that are known to be true because the missing values are artificially created.
The sample mean and standard deviation SDS scores were compared to the known population statistics the latter derived from the known values prior to creation of missing values. The Spearman correlation coefficient, the percent of patients misclassified as depressive, and the Kappa statistic for dichotomous classification of depression were also calculated for each method.
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All three of these calculated statistics, through differing approaches, represent the level of agreement between the imputed values and the known "true" values. The Spearman correlation coefficient is a non-parametric statistic based on the ranks of the observations.
The Kappa statistic expresses the amount of agreement over and above that expected due to chance alone between the dichotomous assessments of depression present vs. Landis and Koch categorize Kappa into five categories: less than 0.
As the probability of a missing value increases, the compare dealing center number of missing observations per participant increases. The calculated mean for both random selection MI produces the most valid imputed values with the highest Kappa statistic 0. However, notably, the individual mean does produce similar statistics. Both MI and single regression panels E and F show a tight cluster of observations around the line of agreement the diagonal line. Individual mean imputation panel D portrays a slightly more scattered distribution about the agreement line but maintains a fairly tight distribution.
The resulting scatter from the other three methods is compare dealing center dispersed with random selection panel A producing a number of observations that fall far away from the diagonal line. A slight rotation away from the diagonal line of agreement and towards a horizontal line is observed in the question mean imputation panel C.
All the other methods produce scatter patterns that fall about the diagonal line of agreement a straight line with a slope of 1.