Statistical transformation and the interpretation of inpatient glucose control data from the intensive care unit

Abstract

Glucose control can be problematic in critically ill patients. We evaluated the impact of statistical transformation on interpretation of intensive care unit inpatient glucose control data. Point-of-care blood glucose (POC-BG) data derived from patients in the intensive care unit for 2011 was obtained. Box-Cox transformation of POC-BG measurements was performed, and distribution of data was determined before and after transformation. Different data subsets were used to establish statistical upper and lower control limits. Exponentially weighted moving average (EWMA) control charts constructed from April, October, and November data determined whether out-of-control events could be identified differently in transformed versus nontransformed data. A total of 8679 POC-BG values were analyzed. POC-BG distributions in nontransformed data were skewed but approached normality after transformation. EWMA control charts revealed differences in projected detection of out-of-control events. In April, an out-of-control process resulting in the lower control limit being exceeded was identified at sample 116 in nontransformed data but not in transformed data. October transformed data detected an out-of-control process exceeding the upper control limit at sample 27 that was not detected in nontransformed data. Nontransformed November results remained in control, but transformation identified an out-of-control event less than 10 samples into the observation period. Using statistical methods to assess population-based glucose control in the intensive care unit could alter conclusions about the effectiveness of care processes for managing hyperglycemia. Further study is required to determine whether transformed versus nontransformed data change clinical decisions about the interpretation of care or intervention results.

Keywords: diabetes; hospital; hyperglycemia; inpatient; statistical process control.

Figure 1.

Nontransformed versus transformed ICU glucose data sets for example 1. Probability plot (top panel) and exponentially weighted moving average control chart (bottom panel) of nontransformed and transformed intensive care unit point-of-care blood glucose data sets from April 2011, used in example 1. Population mean of the nontransformed data set is denoted by μ; SD is denoted by σ; Box–Cox transformation parameter is denoted by λ. The decrease in the χ² test statistic from 59 430.6 to 557.6 demonstrates improvement in the normal distribution characteristics of the transformed data. Transformed data are in natural logarithm (ln) form. Control limits represent 3 × SD, commonly referred to as 3-σ limits, above and below the mean. Circled areas represent samples exceeding upper or lower control limits, suggesting the occurrence of an out-of-control process. See text for interpretation of control chart findings.

Figure 2.

Nontransformed versus transformed ICU glucose data sets for example 2. Probability plot (top panel) and exponentially weighted moving average control chart (bottom panel), of nontransformed and transformed intensive care unit point-of-care blood glucose data sets from October 2011, used in example 2. Population mean of the nontransformed data set is denoted by μ; SD is denoted by σ; Box–Cox transformation parameter is denoted by λ. The decrease in the χ² test statistic from 71 307.8 to 1100.0 demonstrates improvement in the normal distribution characteristics of the transformed data. Transformed data are in natural logarithm (ln) form. Control limits represent 3 × SD, commonly referred to as 3-σ limits, above and below the mean. Circled areas represent samples exceeding upper or lower control limits, suggesting the occurrence of an out-of-control process. See text for interpretation of control chart findings.

Figure 3.

Nontransformed versus transformed ICU glucose data sets for example 3. Probability plot (top panel) and exponentially weighted moving average control chart (bottom panel), of nontransformed and transformed intensive care unit point-of-care blood glucose data sets from November 2011, used in example 3. Population mean of the nontransformed data set is denoted by μ; SD is denoted by σ; Box–Cox transformation parameter is denoted by λ. The decrease in the χ² test statistic from 35 882.0 to 181.6 demonstrates improvement in the normal distribution characteristics of the transformed data. Transformed data are in natural logarithm (ln) form. Control limits represent 3 × SD, commonly referred to as 3-σ limits, above and below the mean. Circled areas represent samples exceeding upper or lower control limits, suggesting the occurrence of an out-of-control process. See text for interpretation of control chart findings.