Median Absolute Percentage Error Research Articles

Finding the most accurate method to measure head circumference for fetal weight estimation

ObjectiveAccurate measurement of fetal head biometry is important for fetal weight estimation (FWE) and is therefore an important prognostic parameter for neonatal morbidity and mortality and a valuable tool for determining the further obstetric management. Measurement of the head circumference (HC) in particular is employed in many commonly used weight equations. The aim of the present study was to find the most accurate method to measure head circumference for fetal weight estimation. Study designThis prospective study included 481 term pregnancies. Inclusion criteria were a singleton pregnancy and ultrasound examination with complete fetal biometric parameters within 3 days of delivery, and an absence of structural or chromosomal malformations. Different methods were used for ultrasound measurement of the HC (ellipse-traced, ellipse-calculated, and circle-calculated). As a reference method, HC was also determined using a measuring tape immediately after birth. FWE was carried out with Hadlock formulas, including either HC or biparietal diameter (BPD), and differences were compared using percentage error (PE), absolute percentage error (APE), limits of agreement (LOA), and cumulative distribution. ResultsThe ellipse-traced method showed the best results for FWE among all of the ultrasound methods assessed. It had the lowest median APE and the narrowest LOA. With regard to the cumulative distribution, it included the largest number of cases at a discrepancy level of ±10%. The accuracy of BPD was similar to that of the ellipse-traced method when it was used instead of HC for weight estimation. ConclusionDifferences between the three techniques for calculating HC were small but significant. For clinical use, the ellipse-traced method should be recommended. However, when BPD is used instead of HC for FWE, the accuracy is similar to that of the ellipse-traced method. The BPD might therefore be a good alternative to head measurements in estimating fetal weight.

Reliability of estimated glomerular filtration rate in patients treated with platinum containing therapy

Estimates of glomerular filtration rate (eGFR) are widely used when administering nephrotoxic chemotherapy. No studies performed in oncology patients have shown whether eGFR can safely substitute a measured GFR (mGFR) based on a marker method. We aimed to assess the validity of four major formulas based on PCr (Cockcroft-Gault, MDRD, Wright and CKD-EPI) in comparison to mGFR in an oncology setting. Patients included had disseminated germ cell cancer and received conventional chemotherapy: bleomycin, etoposide and cisplatin. The mGFR of the patients was compared to all estimates with focus on bias (median percentage error), precision (median absolute percentage error) and accuracy (p10 and p30). The precision of carboplatin dosage based on eGFR was calculated. Data on mGFR, eGFR, and PCr were available in 390 patients, with a total of ∼ 1,600 measurements. Median PCr and mGFR synchronically decreased after chemotherapy, yielding high bias and low precision of most estimates. Post-chemotherapy, bias ranged from -0.2% (MDRD after four cycles) to 33.8% (CKD-EPI after five cycles+), precision ranged from 11.6% (MDRD after four cycles) to 33.8% (CKD-EPI after five cycles+) and accuracy (p30) ranged from 37.5% (CKD-EPI after five cycles+) to 86.9% (MDRD after four cycles). Although MDRD appeared acceptable after chemotherapy because of high accuracy, this equation underestimated GFR in all other measurements. Before and years after treatment, Cockcroft-Gault and Wright offered best results. Precision of carboplatin dosage was low. In conclusion, bias, precision and accuracy were unacceptable in all equations due to a synchronous decrease of PCr and mGFR during chemotherapy.

Validation of a Body-Worn Accelerometer to Measure Activity Patterns in Octogenarians

ObjectiveTo determine the validity of a triaxial body-worn accelerometer for detection of gait and postures in people aged >80 years. DesignParticipants performed a range of activities (sitting, lying, walking, standing) in both a controlled and a home setting while wearing the accelerometer. Activities in the controlled setting were performed in a scripted sequence. Activities in the home setting were performed in an unscripted manner. Analyzed accelerometer data were compared against video observation as the reference measure. SettingIndependent-living and long-term-care retirement village. ParticipantsOlder people (N=22; mean age ± SD, 88.1±5y) residing in long-term-care and independent-living retirement facilities. InterventionsNot applicable. Main Outcome MeasuresThe level of agreement between video observation and the accelerometer for the total duration of each activity, and second-by-second correspondence between video observation and the accelerometer for each activity. ResultsThe median absolute percentage errors between video observation and the accelerometer were <1% for locomotion and lying. The absolute percentage errors were higher for sitting (median, −22.3%; interquartile range [IQR], −62.8% to 10.7%) and standing (median, 24.7%; IQR, −7.3% to 39.6%). A second-by-second analysis between video observation and the accelerometer found an overall agreement of ≥85% for all activities except standing (median, 56.1%; IQR, 34.8%–81.2%). ConclusionsThis single-device accelerometer provides a valid measure of lying and locomotion in people aged >80 years. There is an error of approximately 25% when discriminating sitting from standing postures, which needs to be taken into account when monitoring longer-term habitual activity in this age group.

A New Algorithm of Parameter Estimation for the Logistic Equation in Modeling CO2Emissions from Fossil Fuel Combustion

CO2emissions from fossil fuel combustion have been considered as the most important driving factor of global climate change. A complete understanding of the rules of CO2emissions is warranted in modifying the climate change mitigation policy. The current paper advanced a new algorithm of parameter estimation for the logistic equation, which was used to simulate the trend of CO2emissions from fossil fuel combustion. The differential equation of the transformed logistic equation was used as the beginning of the parameter estimation. A discretization method was then designed to input the observed samples. After minimizing the residual sum of squares and letting the summation of the residual be equal to 0, the estimated parameters were obtained. Finally, this parameter estimation algorithm was applied to the carbon emissions in China to examine the simulation precision. The error analysis indicators mean absolute percentage error (MAPE), median absolute percentage error (MdAPE), maximal absolute percentage error (MaxAPE), and geometric mean relative absolute error (GMRAE) all showed that the new algorithm was better than the previous ones.

Sonographic Weight Estimation in Fetuses with Congenital Diaphragmatic Hernia

To determine the accuracy of sonographic weight estimation (WE) for fetuses with congenital diaphragmatic hernia (CDH), and to assess whether certain sonographic models perform better than others in cases of CDH. In a retrospective, multicenter cohort study, the accuracy of WE in fetuses with CDH (n = 172) was evaluated using eight sonographic models and was compared with a control group of fetuses without malformations (n = 172). Each fetus underwent ultrasound examination with complete biometric parameters within 7 days of delivery. The accuracy of the different formulas was compared using means of percentage errors (MPE), medians of absolute percentage errors (MAPE), and proportions of estimates within 10 % of actual birth weight. Fetuses with CDH had a significantly lower abdominal circumference (AC) in comparison with the control group (293.6 vs. 312.0 mm, p < 0.001). All of the formulas tested in fetuses with CDH, except for the Siemer equation (the only model that does not incorporate any abdominal measurements), showed significantly lower (more negative) MPEs, larger MAPEs, and smaller proportions of estimates within 10 % of actual birth weight in comparison with the control group. The accuracy of sonographic WE in fetuses with CDH is significantly poorer than in fetuses without malformations, principally because of a larger systematic error due to artificially small AC measurements. The development of new, specific models derived from fetuses with CDH could improve the accuracy of WE for infants with this condition.

Evaluation of glomerular filtration rate estimation by Cockcroft–Gault, Jelliffe, Wright and Modification of Diet in Renal Disease (MDRD) formulae in oncology patients

The aim was to evaluate the accuracy of Cockcroft-Gault, Jelliffe, Wright and Modification of Diet in Renal Disease (MDRD) formulae as a substitute for the gold standard measure of glomerular filtration rate (GFR) using chromium 51 EDTA. Retrospective analysis of GFR measurements in oncology patients from a University Teaching Hospital over 3 years was carried out. Bias and precision of estimates of GFR were compared with measured GFR. Six hundred and sixty patients with measured GFR (median 90 ml/min, range 23-179 ml/min) were identified. Cockcroft-Gault produced the smallest bias (median percentage error -1.4%) and highest precision (median absolute percentage error 14.0%) and was the most accurate for carboplatin dosing. For patients>30% over their ideal body weight (IBW), using IBW+30% in the Cockcroft-Gault formula was more precise than using actual body weight or IBW. The Wright formula was most accurate for patients aged 70+years and patients with a body mass index (BMI)≥30 but overestimated GFR when GFR<50 ml/min. When measured GFR is unavailable, we advise estimating GFR using the Cockcroft-Gault formula and using IBW+30% for patients weighing>30% over their IBW. If the GFR is ≥50 ml/min and the patient is >70 years and/or BMI≥30, the Wright formula gives the best estimate of GFR.

What are the limits of accuracy in fetal weight estimation with conventional biometry in two‐dimensional ultrasound? A novel postpartum study

Commonly used formulae for fetal weight estimation, including combinations of several biometric parameters, lack accuracy despite efforts to improve them. This study aimed to investigate the limits of fetal weight estimation based on conventional biometric parameters on two-dimensional (2D) ultrasound by developing and evaluating new weight equations using postpartum biometric parameters. This was a prospective multicenter study including 628 singleton pregnancies at term. Inclusion criteria were healthy newborns with no physical or chromosomal malformations. Postpartum measurement of head circumference, abdominal circumference and thigh length was performed. Six 'best-fit' formulae were derived using forward regression analysis in a formula-finding group (n = 419), and their accuracy was compared with birth weight in an evaluation group (n = 209) using percentage error, absolute percentage error, limits of agreement and the proportion of weight estimations falling within a discrepancy level of ± 10%. The new formulae showed no systematic error, with SD for the percentage error between 7.42 and 8.77 and no significant differences between median absolute percentage errors (4.84-5.71). They included 74.6-81.3% of neonates within a discrepancy level of 10%. With regard to the 95% limits of agreement, weight estimates were within a range of about ± 500 g. These results show that a good sonographic weight formula has the following features: no systematic error, an SD of about 7% and inclusion of 80% of cases within a discrepancy level of 10%. The study indicates that the current accuracy of fetal weight estimation with conventional biometric parameters by 2D ultrasound has reached its limits. Further improvement will probably only be achieved through new approaches in ultrasonography.

Pharmacodynamic modeling of propofol-induced tidal volume depression in children

This investigation aimed to develop a pediatric pharmacodynamic model of propofol-induced tidal volume depression towards an ultimate goal of developing a dosing schedule that would preserve spontaneous breathing following a loading dose of propofol. Fifty two ASA 1 and 2 children aged 6-15year presenting for gastrointestinal endoscopy were enrolled. Subjects were administered a loading dose of 4mg/kg of propofol intravenously at a constant infusion rate determined by a randomization schedule. Respiratory parameters including tidal volume, respiratory rate, minute volume, and end-tidal CO(2) were recorded at 5s intervals. Using the predicted plasma concentration, based on the Paedfusor pharmacokinetic model, propofol-induced tidal volume depression was modeled by 3 different approaches (2-stage, pooled, and mixed effects) and results were compared using prediction residual, median percentage errors, median absolute percentage errors, and root-mean-squared normalized errors. The effects of age and body weight as covariates were examined. Respiratory rate and end-tidal CO(2) did not show clear dependence on the predicted plasma concentration. The pharmacodynamic models for tidal volume derived from different modeling approaches were highly consistent. The 2-stage, pooled, and mixed effects approaches yielded k(e0) of 1.06, 1.24, and 0.72min(-1); γ of 1.10, 0.83, and 0.93; EC50 of 3.18, 3.44, and 3.00mcg/ml. Including age and body weight as covariates did not significantly improve the predictive performance of the models. A pediatric pharmacodynamic model of propofol-induced tidal volume depression was developed. Models derived from 3 different approaches were shown to be consistent with each other; however, the individual pharmacodynamic parameters exhibited significant inter-individual variability without strong dependence on age and body weight. This would suggest the desirability of adapting the pharmacodynamic model to each subject in real time.

In Vitro Models of the Fetal Lung

Three-dimensional (3D) sonography is an established volumetric method in gynecology and obstetrics. The aim of this study was to investigate the variability of 3D sonographic measurements and their accuracy in comparison with magnetic resonance imaging (MRI) for assessing fetal lung volume using in vitro lung models. Twenty-three in vitro lung models with randomly defined volumes ranging from 1 to 60 mL were made from gelatin with plastic sheaths, manually molded into the shape of fetal lungs. The models were measured using 3D sonography and MRI. The 3D sonographic volumes were calculated using the rotational technique with angles of 6° and 30°. Multiplanar T2-weighted sequences were used for the MRI measurements. The percentage error and absolute percentage error were calculated for each method, and intraobserver and interobserver variability in 3D sonographic measurements was assessed with intraclass correlation coefficients (ICCs). Agreement between calculated and real volumes using the limits of agreement method was also evaluated. The ICCs for the rotation angles indicated very good intraobserver and interobserver variability (6°, 0.995 and 0.996; 30°, 0.997 and 0.985). No systematic errors were observed in the mean percentage errors for 3D sonographic measurements or MRI volumetry. The lowest median absolute percentage error (1.76) was obtained with MRI volumetry, significantly lower than the values for sonography (6°, 5.00; P < .001; 30°, 5.49; P < .001). There were no significant differences in absolute percentage errors between the rotation angles (P = .82) and no significant differences in limits of agreement between 3D sonography and MRI (6°, P = .76; 30°, P = .39). Three-dimensional sonographic volumetry was almost as accurate as MRI in this in vitro model and can be regarded as a good alternative method. Further research is needed to confirm these findings in vivo and to assess the prognostic value in fetuses with lung hypoplasia (eg, congenital diaphragmatic hernias).

Influence of Different Rotation Angles in Assessment of Lung Volumes by 3-Dimensional Sonography in Comparison to Magnetic Resonance Imaging in Healthy Fetuses

Three-dimensional (3D) sonographic volumetry is established in gynecology and obstetrics. Assessment of the fetal lung volume by magnetic resonance imaging (MRI) in congenital diaphragmatic hernias has become a routine examination. In vitro studies have shown a good correlation between 3D sonographic measurements and MRI. The aim of this study was to compare the lung volumes of healthy fetuses assessed by 3D sonography to MRI measurements and to investigate the impact of different rotation angles. A total of 126 fetuses between 20 and 40 weeks' gestation were measured by 3D sonography, and 27 of them were also assessed by MRI. The sonographic volumes were calculated by the rotational technique (virtual organ computer-aided analysis) with rotation angles of 6° and 30°. To evaluate the accuracy of 3D sonographic volumetry, percentage error and absolute percentage error values were calculated using MRI volumes as reference points. Formulas to calculate total, right, and left fetal lung volumes according to gestational age and biometric parameters were derived by stepwise regression analysis. Three-dimensional sonographic volumetry showed a high correlation compared to MRI (6° angle, R(2) = 0.971; 30° angle, R(2) = 0.917) with no systematic error for the 6° angle. Moreover, using the 6° rotation angle, the median absolute percentage error was significantly lower compared to the 30° angle (P < .001). The new formulas to calculate total lung volume in healthy fetuses only included gestational age and no biometric parameters (R(2) = 0.853). Three-dimensional sonographic volumetry of lung volumes in healthy fetuses showed a good correlation with MRI. We recommend using an angle of 6° because it assessed the lung volume more accurately. The specifically designed equations help estimate lung volumes in healthy fetuses.

Two‐stage vs mixed‐effect approach to pharmacodynamic modeling of propofol in children using state entropy

To compare the population pharmacodynamic (PD) models of propofol in children derived using two-stage and mixed-effect modeling approaches. Fifty-two ASA 1 and 2 children aged 6-15 years presenting for gastrointestinal endoscopy were administered a loading dose of 4 mg·kg(-1) of propofol intravenously at an infusion rate determined by a randomization schedule. Using the plasma concentration predicted by the Paedfusor pharmacokinetic (PK) model, the propofol effect on state entropy (SE) was modeled using the two-stage and the mixed-effect modeling approaches, and the final population PD models were compared with each other in terms of their prediction performance, using median percentage and absolute percentage errors as well as mean absolute weighted error as metrics. The effects of age and body weight as prospective covariates were examined. The final population models were comparable with each other; the two-stage and the mixed-effect approaches resulted in a k(e0) of 2.38 and 2.66 min(-1), γ of 5.29 and 5.68, and EC(50) of 4.73 and 4.84 μg·ml(-1), respectively. The bootstrap estimates of the PD parameters were mean (SD) k(e0) = 2.38 (0.10), γ = 5.30 (0.30), and EC(50) = 4.73 (0.14). The PD parameters did not exhibit dependence on age and body weight. The parameters reported in this study in children were different from their adult counterparts reported in previous studies. Models derived using different mathematical approaches produced consistent model parameters. By virtue of its relative computational efficiency, the two-stage approach can serve as an attractive alternative to the mixed-effect approach in situations where data are not sparse.

Comparison of Different Sonographic Methods to Determine Fetal Abdominal Circumference

Purpose: In modern obstetric management, accurate estimation of fetal weight is an important prognostic parameter of neonatal morbidity and mortality, and a valuable tool for determining further treatment. Fetal abdominal measurements, mostly abdominal circumference (AC), are not only included in the majority of commonly used weight equations, but also have the greatest impact on weight estimation. This therefore underlines the importance of accurate determination of the AC. The aim of our study was to evaluate which method for AC calculation is the most accurate one and thereby gives the best results for fetal weight estimation. Materials and Methods: This prospective study included 239 term pregnancies. Inclusion criteria were a singleton pregnancy and ultrasound examination with complete fetal biometric parameters within 3 days of delivery, and absence of structural or chromosomal malformations. For calculation of the sonographic AC, three different methods were used. As a reference method, AC of the infant was determined immediately after birth. The accuracy of fetal weight estimation was determined for all of these methods of AC measurement using a commonly used weight equation. Differences were compared by using percentage error (PE), absolute percentage error (APE), limits of agreement (LOA) and cumulative distribution. Results: The ellipse region-of-interest (ROI) method showed the best results of all sonographic methods. For estimating fetal weight, it had the lowest median APE of the sonographic methods and the lowest SD of the PE, as well as the narrowest LOA. Regarding the cumulative distribution, ellipse ROI technique included the most cases at all discrepancy levels (5, 10, 15, and 20%). Conclusion: Accurate measurement of fetal AC is important for good fetal weight estimation. The differences between the three techniques were small; however, there was a significant advantage when using the ellipse ROI method.

Modeling the glucose regulatory system in extreme preterm infants

Background Premature infants represent a significant proportion of the neonatal intensive care population. Blood glucose homeostasis in this group is often disturbed by immaturity of endogenous regulatory systems and the stress of their condition. Hypo- and hyperglycemia are frequently reported in very low birth weight infants, and more mature infants often experience low levels of glycemia. A model capturing the unique fundamental dynamics of the neonatal glucose regulatory system could be used to develop better blood glucose control methods. Methods A metabolic system model is adapted from adult critical care to the unique physiological case of the neonate. Integral-based fitting methods were used to identify time-varying insulin sensitivity and non-insulin mediated glucose uptake profiles. The clinically important predictive ability of the model was assessed by assuming insulin sensitivity was constant over prediction intervals of 1, 2 and 4 h forward and comparing model-simulated versus actual clinical glucose values for all recorded interventions. The clinical data included 1091 glucose measurements over 3567 total patient hours, along with all associated insulin and nutritional infusion data, for N = 25 total cases. Ethics approval was obtained from the Upper South A Regional Ethics Committee for this study. Results The identified model had a median absolute percentage error of 2.4% [IQR: 0.9–4.8%] between model-fitted and clinical glucose values. Median absolute prediction errors at 1-, 2- and 4-h intervals were 5.2% [IQR: 2.5–10.3%], 9.4% [IQR: 4.5–18.4%] and 13.6% [IQR: 6.3–27.6%] respectively. Conclusions The model accurately captures and predicts the fundamental dynamic behaviors of the neonatal metabolism well enough for effective clinical decision support in glycemic control. The adaptation from adult to a neonatal case is based on the data from the literature. Low prediction errors and very low fitting errors indicate that the fundamental dynamics of glucose metabolism in both premature neonates and critical care adults can be described by similar mathematical models.

Biomass measurements and relationships with Landsat‐7/ETM+ and JERS‐1/SAR data over Canada's western sub‐arctic and low arctic

Information on biomass distribution is needed to estimate GHG emissions and removals from land use changes in Canada's north for UNFCCC reporting. This paper reports aboveground biomass measurements along the Dempster Highway transect in 2004, and around Yellowknife and the Lupin Gold Mine in 2005. The measured aboveground biomass ranges are 10–100 t ha−1 for woodlands, 1–100 t ha−1 for shrub sites, and 0.5–10 t ha−1 for grass/herbs sites. The root mean squared error (RMSE) of measurements is 21%, and the median absolute percentage error (MedAPE) is 14%. The combination of JERS backscatter and Landsat TM4/TM5 gives the best biomass equation for the Dempster Highway transect, with r 2 = 0.72 when using a one‐step approach (i.e. using all points) and 0.78 when using a two‐step approach (i.e. stratifying data into three classes: grass, shrub, and woodlands). The two‐step approach reduces the MedAPE from 53% to 33%. The validation against Yellowknife & Lupin data indicates that the equations have good transferability. The improvement of two‐step approach over the one‐step approach, however, is not significant for the validation dataset, suggesting that the one‐step approach is as good as the two‐step approach when applied over areas outside where the equations are developed. The relationships and error analysis of this study, as well as the final estimate of GHG emission/removal over Canada's north have been incorporated into Canada's 2006 UNFCCC report.

BidAnalyzer: A Method for Estimation and Selection of Dynamic Bidding Models

Online reverse auctions generate real-time bidding data that could be used via appropriate statistical estimation to assist the corporate buyer's procurement decision. To this end, we develop a method, called BidAnalyzer, which estimates dynamic bidding models and selects the most appropriate of them. Specifically, we enable model estimation by addressing the problem of partial observability; i.e., only one of N suppliers' bids is realized, and the other (N-1) bids remain unobserved. To address partial observability, BidAnalyzer estimates the latent price distributions of bidders by applying the Kalman filtering theory. In addition, BidAnalyzer conducts model selection by applying multiple information criteria. Using empirical data from an automotive parts auction, we illustrate the application of BidAnalyzer by estimating several dynamic bidding models to obtain empirical insights, retaining a model for forecasting, and assessing its predictive performance in out-of-sample. The resulting one-step-ahead price forecast is accurate up to 2.95% median absolute percentage error. Finally, we suggest how BidAnalyzer can serve as a device for price discovery in online reverse auctions.

Prediction of hemodynamic changes towards PEEP titrations at different volemic levels using a minimal cardiovascular model

A cardiovascular system model and parameter identification method have previously been validated for porcine experiments of induced pulmonary embolism and positive end-expiratory pressure (PEEP) titrations, accurately tracking all the main hemodynamic trends. In this research, the model and parameter identification process are further validated by predicting the effect of intervention. An overall population-specific rule linking specific model parameters to increases in PEEP is formulated to predict the hemodynamic effects on arterial pressure, pulmonary artery pressure and stroke volume. Hemodynamic changes are predicted for an increase from 0 to 10 cmH 2O with median absolute percentage errors less than 7% (systolic pressures) and 13% (stroke volume). For an increase from 10 to 20 cmH 2O median absolute percentage errors are less than 11% (systolic pressures) and 17% (stroke volume). These results validate the general applicability of such a rule, which is not pig-specific, but holds over for all analyzed pigs. This rule enables physiological simulation and prediction of patient response. Overall, the prediction accuracy achieved represents a further clinical validation of these models, methods and overall approach to cardiovascular diagnosis and therapy guidance.

Development of a Clinical Type 1 Diabetes Metabolic System Model andin SilicoSimulation Tool

The goal of this study was to develop a system model of type 1 diabetes for the purpose of in silico simulation for the prediction of long-term glycemic control outcomes. The system model was created and identified on a physiological cohort of virtual type 1 diabetes patients (n = 40). Integral-based identification was used to develop (n = 40) insulin sensitivity profiles. The n = 40 insulin sensitivity profiles provide a driving input for virtual patient trials using the models developed. The identified models have a median (90% range) absolute percentage error of 1.33% (0.08-7.20%). The median (90% range) absolute error was 0.12 mmol/liter (0.01-0.56 mmol/liter). The model and integral-based identification of SI captured all patient dynamics with low error, which would lead to more physiological behavior simulation. A simulation tool incorporating n = 40 virtual patient data sets to predict long-term glycemic control outcomes from clinical interventions was developed based on a physiological type 1 diabetes metabolic system model. The overall goal is to utilize this model and insulin sensitivity profiles to develop and optimize self-monitoring blood glucose and multiple daily injection therapy.

Errors of intravenous fluid infusion rates in medical inpatients

Prescriptions for intravenous (i.v.) fluids in hospitals may not be closely adhered to. This study prospectively examined whether prescribed i.v. fluids are administered at the correct rate. During a four-week period, the i.v. infusion rates in patients requiring continuous i.v. fluids and cared for by a single medical team in a district hospital were studied. The periods over which i.v. crystalloid fluid bags were administered were compared with the time prescribed. Of a total 207 bags, 53 (26%) were correctly administered at the prescribed rate (percentage error 10% to -10%), 138 bags (67%) were infused too slowly and 16 bags (8%) were infused too fast. Overall, the median (interquartile range) absolute percentage error (positive or negative) for all infused bags was 23% (9.7-50). Thirty-nine per cent of bags were infused accurately when a metered pump was used, compared to 21% of bags infused accurately when a metered pump was not used (p < 0.01). Marked inaccuracies in i.v. fluid infusion rates are common, and do not seem to be perceived by staff as important. Metered pumps improve accuracy. Increased awareness of such errors, and the routine use of metered pumps should help improve the accuracy of i.v. fluid infusion rates.

Forecasting telecommunications data with linear models

For telecommunication companies to successfully manage their business, companies rely on mapping future trends and usage patterns. However, the evolution of telecommunications technology and systems in the provision of services renders imperfections in telecommunications data and impinges on a company's’ ability to properly evaluate and plan their business. International Telecommunication Union (ITU) Recommendation E.507 provides a selection of econometric models for forecasting these trends. However, no specific guidance is given. This paper evaluates whether simple extrapolation techniques in Recommendation E.507 can generate accurate forecasts. Standard forecast error statistics—mean absolute percentage error (MAPE), median absolute percentage error and percentage better—show the ARIMA, Holt and Holt-D models provide better forecasts than a random walk and other linear extrapolation methods.

Decomposition by causal forces: a procedure for forecasting complex time series

Causal forces are a way of summarizing forecasters' expectations about what will happen to a time series in the future. Contrary to the common assumption for extrapolation, time series are not always subject to consistent forces that point in the same direction. Some are affected by conflicting causal forces; we refer to these as complex time series. It would seem that forecasting these time series would be easier if one could decompose the series to eliminate the effects of the conflicts. We hypothesized that a time series could be effectively decomposed when (1) uncertainty is high, (2) forecasters can use domain knowledge to decompose the problem such that different forces can be identified for two or more component series, (3) the causal forces imply trends that differ in direction, and (4) it is possible to obtain forecasts for each component that are more accurate than the forecast for the global series. Forecast accuracy for the components can be assessed by testing how well they can be forecast on early hold-out data. When such data are not available, historical variability may be an adequate substitute. We tested decomposition by causal forces on 12 complex annual time series for automobile accidents, airline accidents, personal computer sales, airline revenues, and cigarette production. The length of these series ranged from 16 years for airline revenues to 56 years for highway safety data. We made forecasts for one to ten horizons, obtaining 800 forecasts through successive updating. For nine series in which the conditions were completely or partially met, the forecast error (median absolute percentage error, MdAPE) was reduced by more than half. For three series in which the conditions were not met, decomposition by causal forces had little effect on accuracy.