Pattern discovery from patient controlled analgesia demand behavior

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Pattern discovery from patient controlled analgesia demand behavior

Yuh-Jyh Hu

a,b,n

, Tien-Hsiung Ku

c

a

Department of Computer Science, National Chiao Tung University, 1001 Tashuei Rd., Hsinchu, Taiwan

b

Institute of Biomedical Engineering, National Chiao Tung University, 1001 Tashuei Rd., Hsinchu, Taiwan

c_{Department of Anesthesia, Changhwa Christian Hospital, Changhwa, Taiwan}

a r t i c l e

i n f o

Article history: Received 9 January 2012 Accepted 7 August 2012

Keywords:

Patient controlled analgesia Pain management PCA demand Behavioral pattern Clustering

a b s t r a c t

Unlike previous research on patient controlled analgesia, this study explores patient demand behavior over time. We apply clustering methods to disclose demand patterns among patients over the first 24 h of analgesic medication after surgery. We consider demographic, biomedical, and surgery-related data in statistical analyses to determine predictors for patient demand behavior, and use stepwise regression and Bayes risk analysis to evaluate the influence of demand pattern on analgesic requirements. We identify three demand patterns from 1655 patient controlled analgesia request log files. Statistical tests show correlations of gender (p¼ .0022), diastolic blood pressure (p ¼.025), surgery type (p ¼.0028), and surgical duration (po.0095) with demand patterns. Stepwise regression and Bayes risk analysis show demand pattern plays the most important role in analgesic consumption prediction (p ¼ 0.E þ0). This study suggests analgesia request patterns over time exist among patients, and clustering can disclose demand behavioral patterns.

1. Introduction

Pain is one of the most commonly reported postoperative symptoms [1]. It is a highly personal experience inﬂuenced by multiple factors, including sensitivity to pain, age, genetics, physical status, and psychological factors[2–4]. With the progress of medical science, people gradually became aware of the impor-tance of pain management.

PCA (patient controlled analgesia) is a delivery system for pain medication that makes effective and ﬂexible pain treatments possible by allowing patients to adjust the dosage of analgesics themselves within a preset range of therapy based on therapeutic and toxic effect. According to research [5,6], PCA is one of the most effective techniques for postoperative analgesia and is widely used in hospitals for the management of postoperative pain, especially for major surgeries. Most research on postoperative pain management is limited to evaluating the correlation of patient characteristics, such as demographic attributes, biomedical variables, and psychological states, with postoperative pain intensity or analgesic requirement. Several studies have identiﬁed the preoperative predictive factors for postoperative pain and analgesic consumption in various patient groups of different genders, ages, or psychological states [7–11]. However, none of these studies analyzed continual patient demand behavior throughout the PCA therapy. Time-series data analysis is a

common practice in various research fields. For example, in the study of sleep in patients with insomnia, time-series data derived from sleep diaries were used to compute conditional probabilities of having insomnia[12]; in biology, a temporal map of fluctuations in mRNA expression of 112 genes during central nervous system development in rats provides a temporal gene expression fingerprint of spinal cord development [13]. Few studies of PCA examined patient demand behavior and its relationship to analgesic drug use [14,15]. We hypothesize that patient demand behavior over time provides different and useful information in PCA administration that is missing in the preoperative factors analyzed earlier.

Our study, unlike previous research, focuses on continual analgesia demand behavior during the postoperative PCA medi-cation. The current study explores and characterizes patient demand behavior. Patient demand behavior is represented by a series of PCA requests over time. We discover distinct and conserved demand patterns from the time-series data and iden-tify the signiﬁcant patient factors that inﬂuence demand beha-vior. In addition, we compare the predictors for PCA demand behavior and analgesic requirements and evaluate the contribu-tion of demand pattern to analgesic consumpcontribu-tion prediccontribu-tion.

2. Materials and methods 2.1. Subjects and statistical tools

The study was conducted from 2005 to 2010 with the approval of Changhwa Christian Hospital (CCH) Institutional Review Board Contents lists available atSciVerse ScienceDirect

journal homepage:www.elsevier.com/locate/cbm

Computers in Biology and Medicine

n

Corresponding author at: National Chiao Tung University, Department of Computer Science, 1001 University Rd., Hsinchu 300, Taiwan.

Tel.: þ886 35731795.

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in Changhwa, Taiwan. Abbott Pain Management Provider (Abbott Lab Chicago, IL, USA) was used for patient controlled analgesia. Instructions were reviewed with patients before initiating PCA therapy. Each patient record contained attributes such as basic health status, age, gender, weight, department code, doctor ID, PCA control parameters, and amount of anesthetic used during different time intervals. Because not all the attributes are relevant to our study or have correct values, after consulting the anesthe-tists, we discarded irrelevant attributes such as doctor ID and department code before further investigation. We divide the attributes used in analysis into three categories: (a) patient demographic attributes, (b) biomedical attributes, and (c) operation-related attributes. Their values are either categorical or numeric. The attribute descriptions are shown in Table 1. All the statistical analyses were performed using the Statistical Package for the Social Science 10.0 (SPSS Inc. Chicago, IL, USA). 2.2. Analysis of PCA demand behavior

Given the PCA demand frequency within each unit of time, we can represent each patient’s PCA demand proﬁle as a time course, as illustrated inFig. 1. The X-axis represents the 24 h time line, and the Y-axis indicates the number of PCA demand requests in a

particular hour. By applying clustering algorithms to the time courses, we identified different patient groups. Patients in the same group are expected to demonstrate similar demand beha-vior; in contrast, demand behavior of patients in different groups is different. For example,Fig. 1shows three patient groups, each consisting of two patients with similar demand patterns, and the demand patterns were different among different groups. In practice, we first transform the demand frequency into a sample standard score (i.e., z-score) to normalize the frequency variance in all units of time. This normalization step is to mitigate the influence of large variance on clustering. After normalization, each patient’s PCA demand profile is represented by a vector of which each element is a normalized PCA demand frequency in a unit of time.

We use k-medoids algorithms[16,17] to partition the patients into clusters according to their demand behavior. In the current study, we use Euclidean distance to measure the similarity between two PCA demand proﬁle vectors. A medoid is a real data point that has the minimum average distance from all other points in the same cluster. Unlike the k-means algorithm[18], k-medoids mitigates the effect of outliers on the resulting proto-types and ensures that all the resulting clusters are non-empty

[19]. To ﬁnd the appropriate number of clusters, we perform a series of k-medoids clustering algorithm with the value of k varying from 2 to K, a user-speciﬁed maximum number of clusters.

We generate bootstrap samples from the dataset by random sampling wit‘h replacement [20]. We run k-medoids on the sample to obtain a clustering solution. From B pairs of bootstrap samples from the original data, we produce B pairs of clustering results. Given two clustering solutions C1 and C2 from a pair of

bootstrap samples, we obtain two partitions of the original data by assigning each observation to the nearest medoid. The number of clusters is determined by reproducibility and stability[21]. If the number of clusters is correct, it is more likely that k-medoids clustering of the bootstrap samples all converges to the real medoids, and reproduce the same partition of the original data. Even if not all clustering results converge to the same medoids, it is well anticipated that the converged medoids will be in the proximity of the real medoids of the clusters, and thus produce stable partitions. We use the adjusted Rand Index[22]to measure the similarity between the two partitions. To determine if the

Table 1

Summary of patient attributes.

Attribute name Description Number Mean7sd

Demographic:

Gender Patient’s gender 986(F)/669(M) –

Age Patient’s age – 56.9715.8

Weight(kg) Patient’s weight – 63.0712.6

Biomedical:

sbp (mmHG) Systolic blood pressure – 135.8722.6 dbp (mmHG) Diastolic blood pressure – 69.4713.8

Pulse(beats/min) Heart rate – 81.0715.4

ASA class*

1: Healthy

2: Mild systemic disease 184(1)/837(2)/634(3) – 3: Major systemic disease

OP related: op_type**

Surgery type: 1 8 107(1)/126(2)/411(3) – 127(4)/427(5)/109(6)212(7)/136(8)

ans_type SA: spinal anesthesia GA: general anesthesia 1470(GA)/185(SA) –

op_time(hr) Surgical duration – 4.272.6

Urgency E: emergency surgery R: regular surgery 136(E)/1519(R) –

n

ASA class is the commonly used preoperative index of physical status deﬁned by American Society of Anesthesiologists.

nn

1: intrathoracic, 2: upper intra-abdominal, 3: lower intra-abdominal, 4: laminectomy, 5: major joints, 6: limbs, 7: head & neck, 8: others.

Fig. 1. An illustrative example of PCA demand patterns. Each curve represents the distribution of PCA demand frequency for a patient in 24 h. The X-axis indicates the 24 h time line (1 h to 24 h). The Y-axis represents the number of demand requests in a particular hour.

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partition of the original data is reproduced, or assess how stable a partition is, we compare the adjusted Rand Index values of the B pairs of bootstrapped partitions.

By iterating the value of k from 2 to K and repeating the same procedure, we obtain different distributions of the adjusted Rand Index values. First, we perform analysis of variance (ANOVA) to determine whether significant statistical evidence existed to show that at least two adjusted Rand Index means differed. Then, we conduct sequential t-tests corrected for multiple comparisons to identify a significant gap between successive differences in bootstrapped adjusted Rand Index values. The most significant jump indicates the most likely number of clusters in the original data.

2.3. Investigation of PCA demand behavioral inﬂuence on analgesic consumption

After identifying the PCA demand patterns using the k-medoids algorithm and bootstrapped stability tests, we examine the association between demand patterns and the patient attri-butes listed inTable 1. We run chi-square tests for the depen-dence of the demand behavior on those patient attributes, and we conduct ANOVA tests to compare the attribute values among different patient groups according to demand patterns. For all the analyses, a level is set at 0.05 for statistical signiﬁcance.

Little research explores the relationship between PCA demand patterns and PCA analgesic consumption. We apply stepwise linear regression to compare demographic, biomedical, opera-tion-related, and PCA demand behavioral influences on PCA analgesic consumption. The criterion for inclusion or elimination of patient attributes is that a patient attribute would be included if its partial regression coefficient is significant at the

a

¼0.05 level or eliminated if it is not. To further evaluate the individual effect of PCA demand pattern on analgesic consumption, we perform stepwise regression only on patient demographic, bio-medical, and surgery-related attributes. We compare the R2_and

adjusted R2 _{before and after removing demand patterns. A}

sub-stantial drop in R2 _{and adjusted R}2 _{indicates that the demand}

patterns play a significant role in predicting analgesic consump-tion. In addition, by discretizing PCA dose into ordinal values (e.g., high, medium, and low), we can define a PCA dose classifica-tion problem [7]. In classification problems, the action ai is

interpreted as the decision that the class is ci. Supposing action

aiis taken and the true class is cj, the decision is correct if i¼j;

otherwise, it is incorrect. We naturally seek a decision rule that minimizes the error rate. Based on the Bayes decision rule, we try to find a decision rule that minimizes the overall risk R[23]. To evaluate the effect of PCA demand behavior on ordinal PCA dose classification, we compute the Bayes risk associated with PCA demand patterns and compare it with other Bayes risks asso-ciated with different patient attributes. Because the patient attribute types are mixed, we dichotomize the values of contin-uous attributes such as weight into categories. Thus, the overall risk associated with attribute x is defined as:

R ¼Xn_{k ¼ 1}Rðai9xkÞ pðxkÞ

where n is the number of categorical values of x. The minimum overall risk is the Bayes risk, deﬁned as (seeAppendices): Rn

¼Xn

k ¼ 1ðargmin i

½1pðci9xkÞÞ pðxkÞ

By comparing the Bayes risks of the patient attributes and PCA demand patterns, we examine their inﬂuences on the PCA dose prediction errors; the lower the Bayes risk of a factor, the more this factor contributed to classiﬁcation accuracy.

3. Results

A total of 5432 PCA log files were collected at Changhwa Christian Hospital from 2005 to 2010. The size of a log file on the PCA device is limited by the Abbott’s hardware design. New log data overwrites the old data when the size reaches its limit. To maintain the consistency, the study focused on the demand behavior of the first 24 h PCA medication, and characterized demand patterns based on the first 24 h PCA requests. After discarding those oversized and thus overwritten incomplete log files, we obtained 4632 PCA log files. Of these patients, 2425 were excluded from our study because of missing values in demo-graphic, biomedical, or surgery-related attributes. Moreover, 552 patients whose PCA medication was administered less than 24 h were also removed because the demand behavior analysis was performed over the first 24 h. Our study included 1655 partici-pants after data preprocesses. Their attribute values are summar-ized inTable 1.

3.1. Identiﬁcation of PCA demand patterns

We performed bootstrap sampling with replacement on the 1655 patient records and generated 100 pairs of samples. In the current study, we set the maximum number of clusters to be 6. Varying k from 2 to 6, we ran k-medoids on the bootstrap samples and calculated their adjusted Rand Index values. We performed ANOVA and sequential t-tests (with Bonferroni correction) on the adjusted Rand Index groups. The test results are presented in

Tables 2 and 3. The ANOVA rejected the null hypothesis that no difference among the adjusted Rand Index means existed. It suggested that one clustering result was more stable and appro-priate than the others. From the sequential t-test results, we observed a signiﬁcant gap between k¼3 and k¼4. The mean of the adjusted Rand Index of the four cluster partitions dropped by 0.12, with p{:000001. It indicated that when k¼3, the clustering result was the most stable. We thus selected k ¼3 as the number of clusters and identiﬁed three PCA patient groups by maximizing the demand behavior similarity among the patients in each group. The group size is 91, 1205, and 359, respectively. Patients in the same group showed a similar demand pattern that was different

Table 2

ANOVA test on different clustering results.

Clusters Adjusted RI mean (sd) F-value p-value

2 0.81(0.14) – –

3 0.74(0.14) – –

4 0.62(0.14) – –

5 0.56(0.12) – –

6 0.50(0.11) – –

ANOVA test – 91.66 o o.00001 Based on the low p-value, we rejected the null hypothesis that there was no difference among these clustering solutions.

Table 3

Sequential t-test for successive differences in adjusted Rand Index (ARI) means. Number of clusters Adjusted RI (ARI) mean

difference t-value p-value 3 vs. 2 0.07 3.63 .00037 4 vs. 3 0.12 5.55 {:000001 5 vs. 4 0.06 3.32 .0011 6 vs. 5 0.06 4.00 .00009 A signiﬁcant drop in ARI from 3-cluster clustering to 4-cluster clustering ðp{:000001Þ suggested 3-cluster clustering was the most stable clustering solution.

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among different groups. Fig. 2 presents the average demand pattern of each group. The X-axis represents the 24 h time line, and the Y-axis is the normalized standard score (z-score) of the PCA demand frequency in a particular hour.

3.2. Association between patient attributes and PCA demand patterns

Different PCA demand patterns deﬁne different patient groups. We identify three demand patterns from 1655 patients and produce three patient groups. The chi-square test was performed to test the dependence of the patient groups on the categorical patient attributes inTable 1, for example, gender, ASA class, and surgery type. ANOVA was used to compare the differences in weight, age, blood pressure, pulse, and surgical duration among different patient groups. Table 4 shows the results of the chi-square and ANOVA tests. We observed statistically signiﬁcant differences among PCA demand pattern groups in gender, dia-stolic blood pressure, surgery type, and surgical duration, respec-tively. The student t-test for differences between means was performed with Bonferroni correction (

a

/N ¼0.016). The results indicates that Demand Pattern 1 (shown inFig. 2) is associated with shorter surgical duration than the other two patterns (p¼.0012; p¼ .008), and Demand Pattern 2 is more associated with lower diastolic blood (p ¼.05) than Pattern 3 (p¼ .09), but

shows no significant difference from Pattern 1 (p¼ .91). In con-trast, age, systolic blood pressure, and urgency show only a weak association with PCA demand behavior. No significant difference in weight (p ¼.47) or pulse (p¼.43) is found among demand pattern groups. In addition, no significant statistical evidence is found to reject or accept the hypothesis that the ASA class (p ¼.37) and the type of anesthesia (p ¼.36) are independent of PCA demand pattern.

3.3. Influence of PCA demand behavior on analgesic consumption Multivariate stepwise linear regression was used to identify major factors influencing PCA analgesic consumption. All demo-graphic, biomedical, and surgery-related attributes and PCA demand patterns were included for regression analysis. We find that PCA demand pattern plays the most significant role in predicting PCA analgesic consumption. The other major factors at the

a

¼0.05 level are weight, age, surgical type, urgency, and anesthesia type, as presented inTable 5. To validate further the individual effect of PCA demand pattern on analgesic consump-tion, we performed stepwise regression only on patient demo-graphic, biomedical, and surgery-related attributes. Three factors are selected at the

a

¼0.05 level, as shown inTable 6. They are weight, age, and surgical type, in the order selected. The R2_and

adjusted R2 _{are 0.05651 and 0.05479, respectively. Compared}

Fig. 2. PCA demand patterns discovered from 1655 subjects. Three patterns are identiﬁed from 1655 PCA patient-demand log ﬁles. Ninety-one patients’ PCA demand behavior matches Pattern 1, 1205 patients’ demand behavior matches Pattern 2, and 359 patients’ demand behavior matches Pattern 3. The X-axis indicates the 24 h time line (1 h to 24 h). The Y-axis represents the normalized standard score (z-score) of the PCA demand frequency in a particular hour.

Table 4

Chi-square and ANOVA tests on patient attributes and demand patterns. Attribute name Chi-square p-value (df*

) ANOVA p-value Demographic Gender 0.0022(2) – Age – 0.12 Weight – 0.47 Biomedical sbp – 0.15 dbp – 0.025 Pulse – 0.44 ASA class 0.37(4) – OP-related op_type 0.0028(14) – ans_type 0.36(2) – op_time – 0.0095 Urgency 0.18(2) – n df: degree of freedom. Table 5

Results of stepwise regression analysis of PCA analgesic consumption. Predicting PCA analgesic consumption.

Factor attribute Betann

Bya SEzb p-value R2 Adjusted R2 Step 1 PCA demand pattern 0.36 3.65 0.23 0.E þ 0 0.13 0.13 Step 2 PCA demand pattern 0.36 3.61 0.23 0.E þ 0 0.15 0.15 Weight 0.15 0.061 0.0089 1.77E 11 Step 3 PCA demand pattern 0.36 3.62 0.23 0.E þ 0 0.17 0.17 Weight 0.16 0.065 0.0089 3.88E 13 op_type 0.13 0.33 0.057 1.64E 8 Step 4 PCA demand pattern 0.36 3.60 0.22 0.E þ 0 0.18 0.18 Weight 0.15 0.059 0.0089 3.16E 11 op_type 0.12 0.31 0.057 4.36E 8 Age 0.12 0.037 0.0071 2.67E 7 Step 5 PCA demand pattern 0.36 3.61 0.22 0.E þ 0 0.19 0.18 Weight 0.15 0.059 0.0089 4.41E 11 op_type 0.12 0.30 0.057 2.17E 7 Age 0.12 0.039 0.0072 7.77E 8 Urgency 0.047 0.86 0.41 0.037 Step 6 PCA demand pattern 0.36 3.60 0.22 0.E þ 0 0.19 0.18 Weight 0.15 0.059 0.0089 5.39E 11 op_type 0.12 0.31 0.058 7.23E 8 Age 0.13 0.042 0.0074 1.15E 8 Urgency 0.049 0.89 0.41 0.030 ans_type 0.046 0.73 0.37 0.049 nn

Beta is standardized coefﬁcient.

ya

B is unstandardized coefﬁcient.

zb

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with the results (R2_{¼0.18761 and adjusted R}2_{¼0.18465) in} Table 5, it is clear that PCA demand pattern makes a signiﬁcant contribution to analgesic consumption prediction.

We partitioned the 1655 patients into three classes based on the analgesic consumptions within 24 h after PCA was made available. The sizes of the classes are approximately equal, and they correspond to low, medium, and high doses. A summary of the three classes is given inTable 7. We computed the Bayes risk for each patient attribute and PCA demand pattern in analgesic consumption classification. As seen in Table 8, PCA demand pattern incurs the least Bayes risk in classification, which suggests that PCA demand pattern has more influence on analgesic con-sumption prediction than the other patient attributes.

4. Discussion

Cluster analysis has been widely used in various applications. In biology, it can help biologists categorize genes or proteins with similar functionality into families or derive a hierarchical organi-zation [24]. In business, it helps market analysts identify dis-tinctive groups in their customer databases and characterize customer groups according to purchasing patterns [25]. Many clustering algorithms have been developed. In general, they can be classiﬁed into methods such as partitioning methods, hier-archical methods, density-based methods, model-based methods, and constraint-based methods[19,26].

The choice of algorithms depends on the type of data and the goal of applications. Different clustering algorithms have different advantages and limitations. As a means of data exploration and characterization, various clustering methods could be applied to disclose different properties embedded in the data. The objectives of this study are to advocate the importance of demand behavior analysis for PCA administration and to propose using clustering methods to characterize patient demand proﬁles. By applying a k-medoids partitioning method, we discovered different PCA demand patterns in the study participants. Each participant was associated with only one demand pattern. Other clustering algo-rithms could be applied to identify different types of patterns to address different medical meanings.

The demographic, biomedical, and surgery-related predictors for analgesic consumption are not necessarily a predictor for PCA demand pattern, though a relationship between analgesia requirements and demand behavior exists. Several studies have discovered a significant correlation between age and the dose of opioid required in the postoperative period[4,27–29]. For exam-ple, Gagliese et al. and Chang et al. both observed that age was significantly negatively correlated with morphine consumption in their studies[11,30]. However, our study only indicated a weak correlation of age with PCA demand patterns. As mentioned in previous studies, possible causes of the discrepancy in the results could be lack of understanding or misuse of PCA by older and younger patients [8], and a difference in pain sensitivity to morphine between young and elderly patients should be con-sidered in the correlation analysis [31]. More specific studies should be restricted to a narrower age range such as 20 to 60 years, and pain intensity should be included in the correlation modeling to alleviate the limitation of a simple two-variable (age and morphine dose) model.

Chang et al. found that weight was a significant determinant of total PCA requirements in their study of 1308 patients[3]. Like-wise, body mass was found to be a significant predictor for pain in the post-anesthesia care unit in Chung et al.’s study among ambulatory surgical patients [1]. Nevertheless, like some other studies that reported no correlation between analgesic consump-tion and patient weight[8,32,33], our results did not show any significant association between the PCA demand pattern and patient weight. The mean weights of the three demand pattern groups are 61.5 kg, 63.0 kg, and 63.3 kg, respectively. They are all close to the mean weight of the total number of study partici-pants, which is 63.0 kg, showing no significant difference.

The relationship of gender with postoperative pain and analgesic consumption varies among different studies. In Chia et al.’s study of 2298 patients, women consumed significantly less morphine using PCA in the first three postoperative days than men[8]. In contrast, in Cepeda et al.’s study, women experienced more intense pain and had a larger morphine consumption than men[34]; in addition, Chang et al. found no significant correlation between gender and morphine consumption[30]. We found that gender was a significant correlate of PCA demand behavior. This concurred with Chia et al.’s report that gender was an important

Table 6

Results of stepwise regression analysis of PCA analgesic consumption without demand patterns.

Predicting PCA analgesic consumption. Factor attribute Betann

Bya SEzb p-value R2 Adjusted R2 Step 1 Weight 0.16 0.064 0.0096 3.52E 11 0.026 0.026 0.5 Step 2: Weight 0.15 0.058 0.0096 1.84E 9 0.042 0.041 Age 0.13 0.040 0.0077 1.94E 11 0.5 Step 3: Weight 0.16 0.063 0.0096 8.28E 11 0.057 0.055 Age 0.12 0.039 0.0076 4.78E 7 op_type 0.12 0.31 0.061 5.38E 7 nn

Beta is standardized coefﬁcient.

ya_{B is unstandardized coefﬁcient.} zb_{SE is standard error of B.}

Table 7

Summary of PCA dose classes.

Symbolic PCA dose Low Medium High Dose mean7sd (mg) 2.0671.01 5.4571.10 12.1974.36 Number of patients 549 565 541

Table 8

The Bayes risks associated with patient attributes. Attribute name Bayes risk Demographic Gender 0.656 Age 0.633 Weight 0.629 Biomedical sbp 0.743 dbp 0.508 Pulse 0.657 ASA class 0.643 OP-related op_type 0.598 ans_type 0.659 op_time 0.657 urgency 0.655 PCA demand pattern 0.449 The lowest Bayes risk of demand pattern indicated its greatest contribution to classiﬁcation.

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predictor of postoperative morphine requirement [8]. The chi-square test indicated that signiﬁcantly more females than expected demonstrated PCA Demand Pattern 1 (see Fig. 2) in our study. Because Demand Pattern 1 indicates an early sharp increase of PCA requests, it suggests that PCA dosage for the ﬁrst 3 h could be increased for the female patients whose character-istics match those in the Demand Pattern 1 group to increase their satisfaction.

We found a signiﬁcant association between PCA demand pattern and surgical type as well as surgical duration. These ﬁndings agreed with the lessons learned from pain management

[35,36] and previous studies of PCA consumption [11,30]. For example, in Gagliese et al.’s study of 123 younger patients [11], gynecological/urological surgery was significantly inversely asso-ciated with morphine intake, and the surgical duration was significantly positively associated with morphine intake. Never-theless, some other studies failed to show any correlation between analgesic consumption and surgical sites or duration[4,8,9]. This inconsistency may be due to the different classifications of surgery; for example, the number of surgical types considered in previous studies was smaller than ours. The chi-square test showed that among those patients revealing Demand Pattern 1, significantly more patients than expected had abdominal surgery, but in contrast, among those patients showing Demand Pattern 2, the number of patients receiving abdominal surgery was significantly smaller than expected. The student t-tests revealed that the surgical duration of patients in the Demand Pattern 1 group was significantly shorter than that in the other two pattern groups.

Some researchers have derived predictive models of analgesic requirements or postoperative pain from regression analyses

[8,10,11]. Although they identified several positive preoperative correlates, such as age and gender, their coefficients of determi-nation were small, and in some cases, no significant predictors were found. For example, in an analysis of the first 6 h of intravenous patient controlled analgesia required in the ward, no predictors were found to meet

a

¼0.05 level[9]. This suggests that predictive factors other than demographic, physiological, and surgical attributes are present that have not been analyzed. We included PCA demand pattern in the multivariate stepwise regression analysis to compare the influence of these factors on PCA consumption prediction. Our results show that PCA demand pattern play the most significant role in predicting analgesic consumption. It increases the value of coefficient of determina-tion from 0.057 to 0.19. In the framework of classificadetermina-tion, we discretized the analgesic consumption into a number of symbolic values, such as low, medium, and high. Instead of a numeric value, we aimed to predict a symbolic value of analgesic con-sumption because this indicator is sufficiently expressive for anesthetists to recognize an abnormality in PCA medications. The Bayes risk analysis indicates that PCA demand pattern causes the least risk in PCA consumption classification. This result is consistent with the findings in the stepwise regression analysis. The stepwise regression analysis and the Bayes risk analysis both demonstrate a significant relationship between PCA demand behavior and analgesic consumption; nevertheless, their predic-tors are not all the same. Surgery type is a significant predictor for both PCA demand behavior and analgesic consumption. Although age and urgency are found to correlate with analgesic consump-tion significantly, they only show weak associaconsump-tion with PCA demand pattern. Furthermore, our study indicates significant gender-related differences in PCA demand pattern, but gender is ruled out in the multivariate regression analysis for PCA require-ment prediction. These conflicting results may be attributed to different medical meanings of demand behavior and analgesic consumption or to other correlated factors that have not been examined in our studies, such as psychosocial factors.

There are a number of limitations in our current study. First, though the patient records have been carefully reviewed, the PCA data used in our analyses were not guaranteed to be free of errors. A small amount of noisy data could occur due to human errors in data entry or misuse of PCA devices by patients. They were not recognized or resolved in the data preprocess. To mitigate the effect of data noise, we used bootstrap replications to ensure the reproducibility and stability of clustering solutions, and statistically significant results were obtained. However, data cleaning is still a crucial step before any form of data exploration, including cluster-ing, and results of this type should be applied with caution within the imitations of clustering algorithms. Second, most previous studies of PCA were conducted on Western patients. Little research focuses on Eastern people such as Taiwanese patients[8,30]. The discrepancy in the analysis results or conclusions might be attri-butable to the impact of different sociocultural origins. Third, our current study of PCA demand behavior is based on the first 24 h of PCA therapy after surgery. Shorter or longer periods of PCA medication may contain different demand behavioral patterns. Distinct and conserved demand patterns among patients over various lengths of PCA therapy are likely to correlate with different regularities in postoperative pain relief and patient satisfaction. Information of this type may be useful for predicting analgesic requirements and postoperative pain. Last, as a retrospective study, the surveyed variables were not under control, and the medical meanings of the correlation between demand patterns and demo-graphic, biomedical, or surgery-related predictors were still unclear. In conclusion, we advocate the analysis of PCA demand behavior. To demonstrate its feasibility and significance, in our current study we used clustering algorithms to identify demand patterns. The stability and reproducibility of the clustering solu-tion have been verified by repeated random bootstrap sampling, an idea similar to that of Monti et al.[37]. The results suggest that PCA demand behavioral patterns exist over time among patients. They are correlated with specific demographic, biomedical, or surgery-related attributes, and have influence on analgesic con-sumption. Other clustering-based methods and alternative approaches are applicable to the study of PCA demand patterns. In particular, various methods have been developed to address the issue of stability in clustering, and to identify consensus clustering. They measure and characterize stability differently. For examples, some assess the stability based on the consensus across multiple subsampling[37], and others focus on the con-sistency in the partitions produced by different clustering algo-rithms[38]. These approaches to consensus clustering have been applied to integrating diverse viral gene expression data for further exploration[39], or to evaluating the appropriateness of a previously proposed classification of breast cancer gene expres-sion data[40]. To our best knowledge, this study is the first to introduce an analysis of time-series data derived from PCA demand log files. We have used a clustering method to analyze the 24 h PCA demand profile of 1655 patients. The advantages of a clustering-based approach to data analysis are that it is adaptable to change and helps extract crucial properties that distinguish different data groups. Unlike the application of consensus cluster-ing in earlier works[39,40], our cluster-based study is currently focused on discovering the conserved PCA demand behavioral patterns in different patient groups because the classification of PCA demand behavior is unavailable, and we have only one data source at CCH. A larger-scale and more detailed analysis based on multiple approaches is in progress. We plan to submit these patterns to the department of anesthesia of Changhwa Christian Hospital. After the classification of PCA demand behavior has been determined based on medical knowledge, we can next use the consensus clustering methods to further evaluate the sig-nificance of the demand patterns we have identified.

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Conﬂict of interests statement No competing interests declared.

Acknowledgments

This work was partially supported by National Science Council, Taiwan (NSC 100-2221-E-009-146, NSC99-2218-E-009-002). Thanks go to Shin-Ru Wu and Yu-Ming Tsao for processing the patient records and the manuscript.

Appendices

Based on the Bayes decision rule, we ﬁnd a decision rule that minimizes the overall risk R.

R ¼ Z

Rðai9xÞ pðxÞdx

where x is a patient’s attribute values, p(x) is the probability of x, and R(ai9x) is risk of taking action aiwith patient attribute value x.

Rðai9xÞ ¼

Xm

j ¼ 1

l

ðai9cjÞ Pðcj9xÞ

where

l

(ai9cj) is the loss incurred by taking action aiwith the true

class cj.

To minimize overall risk, we compute the conditional risk R(ai9x) for each possible decision, i ¼ 1 m, and then select the

action ai, of which R(ai9x) is minimum. The resulting minimum

overall risk is called the Bayes risk Rn

[26]. Assuming that all errors are equally costly, we deﬁne the loss function as the zero-one loss function:

l

ðai9cjÞ ¼

0 i ¼ j

1 iaj i,j ¼ 1 m (

with this loss function, the conditional risk function becomes R(ai9x)¼1p(ci9x). By discretizing continuous patient attributes

into categorical ones, we can redeﬁne the overall risk of the attribute x as

R ¼Xn

k ¼ 1Rðai9xkÞ pðxkÞ

where xkis a legal categorical value of x, and n is the total number

of categorical values of x. The Bayes risk is Rn ¼Xn k ¼ 1ðargmin i ½1pðci9xkÞÞ pðxkÞ: References

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