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Chapter 2: Quantitatve Methods in Health Care Management Yasar A. Ozcan 1 Chapter 2. Forecasting

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Chapter 2: Quantitatve Methods in Health Care Management Yasar A. Ozcan 2 OutlineOutline Why Forecast? Steps in the Forecasting Process Forecasting Approaches –Judgmental – Time Series-- Historical Data – Techniques for Averaging – Techniques for Trend – Techniques for Seasonality –Associative Accuracy and Control of Forecasts Choosing a Forecasting Technique Why Forecast? Steps in the Forecasting Process Forecasting Approaches –Judgmental – Time Series-- Historical Data – Techniques for Averaging – Techniques for Trend – Techniques for Seasonality –Associative Accuracy and Control of Forecasts Choosing a Forecasting Technique

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Chapter 2: Quantitatve Methods in Health Care Management Yasar A. Ozcan 3 Why forecasting is important? Forecasts serve as a basis for planning Enable health care managers to anticipate the future to plan the system and plan the use of that system Forecasting is more than predicting demand It is not an exact science; one must blend experience, judgment, and technical expertise experience, judgment, and technical expertise Forecasts serve as a basis for planning Enable health care managers to anticipate the future to plan the system and plan the use of that system Forecasting is more than predicting demand It is not an exact science; one must blend experience, judgment, and technical expertise experience, judgment, and technical expertise

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Chapter 2: Quantitatve Methods in Health Care Management Yasar A. Ozcan 4 All forecasts have common elements Assumption that past continues into future Errors occur-- actual differs from predicted; presence of randomness Forecasts of group of items (aggregate) tends to be more accurate than individual items (i.e., departmental vs. whole hospital) Forecast accuracy decreases as time horizon increases Assumption that past continues into future Errors occur-- actual differs from predicted; presence of randomness Forecasts of group of items (aggregate) tends to be more accurate than individual items (i.e., departmental vs. whole hospital) Forecast accuracy decreases as time horizon increases

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Chapter 2: Quantitatve Methods in Health Care Management Yasar A. Ozcan 5 Characteristics of a Good Forecast Timely Reliable Accurate Meaningful units ($$’s, visits, discharges, patient days, etc.) Easy to use

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Chapter 2: Quantitatve Methods in Health Care Management Yasar A. Ozcan 6 Step 1 Identify the goal of the forecast Step 2 Establish a time horizon Step 3 Select a forecasting technique Step 4 Conduct the forecast (analyze data) Step 5 Determine its accuracy Step 6 Monitor the forecast Steps in the Forecasting Process

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Chapter 2: Quantitatve Methods in Health Care Management Yasar A. Ozcan 7 What approaches can we use? Judgmental – –Delphi method – –Executive opinions – –Contracts/insurance/HMO/PPO/POS estimates – –Consumer surveys – –Outside opinions – –Opinions of managers/staff Judgmental – –Delphi method – –Executive opinions – –Contracts/insurance/HMO/PPO/POS estimates – –Consumer surveys – –Outside opinions – –Opinions of managers/staff

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Chapter 2: Quantitatve Methods in Health Care Management Yasar A. Ozcan 8 The Delphi Method Method of obtaining opinions of managers and staff Involves circulating a series of questionnaires, each developed from the previous one, to achieve a consensus on an issue (in this case, a forecast) Useful for forecasting technological changes and their impacts Method of obtaining opinions of managers and staff Involves circulating a series of questionnaires, each developed from the previous one, to achieve a consensus on an issue (in this case, a forecast) Useful for forecasting technological changes and their impacts

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Chapter 2: Quantitatve Methods in Health Care Management Yasar A. Ozcan 9 The Delphi Approach, cont. Advantages –More individuals may be engaged than can effectively interact face-to-face –It is important to avoid bandwagon effect –Preserves anonymity of participants Weaknesses –Questions may be ambiguous leading to false consensus –Panel members may change –Studies do not prove that Delphi forecasts are highly accurate –Preserving anonymity removes accountability Advantages –More individuals may be engaged than can effectively interact face-to-face –It is important to avoid bandwagon effect –Preserves anonymity of participants Weaknesses –Questions may be ambiguous leading to false consensus –Panel members may change –Studies do not prove that Delphi forecasts are highly accurate –Preserving anonymity removes accountability

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Chapter 2: Quantitatve Methods in Health Care Management Yasar A. Ozcan 10 Forecasting Approaches, cont. Time series-- identify the behavior of the series by using factors such as trend, seasonality, cycles, irregular variations, and random variations Techniques for averaging Naive forecasts Moving averages (MA) Exponential smoothing –Techniques for trend Linear equations using regression (y t = a + bx t ) Trend adjusted exponential smoothing –Techniques for seasonality Seasonal Variations Indices Technique Time series-- identify the behavior of the series by using factors such as trend, seasonality, cycles, irregular variations, and random variations Techniques for averaging Naive forecasts Moving averages (MA) Exponential smoothing –Techniques for trend Linear equations using regression (y t = a + bx t ) Trend adjusted exponential smoothing –Techniques for seasonality Seasonal Variations Indices Technique

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Chapter 2: Quantitatve Methods in Health Care Management Yasar A. Ozcan 11 Forecasting Approaches, cont. Associative Techniques –Simple linear regression (y = a + bx) –Scatter diagram-- plot data –Correlations Associative Techniques –Simple linear regression (y = a + bx) –Scatter diagram-- plot data –Correlations

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Chapter 2: Quantitatve Methods in Health Care Management Yasar A. Ozcan 12 Jan Mar May Jul Sep Nov Seasonal Variation Seasonal Variation Cycle Random Variation Trend Figure 2.1 Variation Characteristics

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Chapter 2: Quantitatve Methods in Health Care Management Yasar A. Ozcan 13 Averaging Techniques Smooth out fluctuations in time serious because individual highs and lows cancel each other out So, would forecasts based on averages exhibit more or less variability? Smooth out fluctuations in time serious because individual highs and lows cancel each other out So, would forecasts based on averages exhibit more or less variability?

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Chapter 2: Quantitatve Methods in Health Care Management Yasar A. Ozcan 14 Naive Forecasts A naive forecast for any period equals the previous period’s actual value Low cost, easy to prepare, easy to understand, but less accurate forecasts Can be applied to seasonal or trend data A naive forecast for any period equals the previous period’s actual value Low cost, easy to prepare, easy to understand, but less accurate forecasts Can be applied to seasonal or trend data Examples: If last week’s demand was 50 units, the naive forecast for the coming week is 50 units. If seasonal pattern exists, the naive forecast for next January would equal the actual demand for January of this year.

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Chapter 2: Quantitatve Methods in Health Care Management Yasar A. Ozcan 15 Moving Averages where, i = “Age” of data (i=1,2,3...) n = number of periods in moving average A i = actual value with age i Forecast uses a number of the most recent actual data values in generating a forecast

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Chapter 2: Quantitatve Methods in Health Care Management Yasar A. Ozcan 16 Moving Averages Example 2.1: An OB/GYN clinic has the following yearly patient visits, and would like to predict the volume of business for the next year for budgeting purposes. Period (t)AgeVisits

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Chapter 2: Quantitatve Methods in Health Care Management Yasar A. Ozcan 17 Moving Averages, cont. Solution: The three-period moving average (MA 3 ) for period 6 is F 6 = MA 3 = ( ) ÷ 3 = Period (t)AgeVisitsForecast

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Chapter 2: Quantitatve Methods in Health Care Management Yasar A. Ozcan 18 Moving Averages, cont Data MA 5 MA 3 The greater the number of periods in a moving average, the greater the forecast will lag with changes in the data

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Chapter 2: Quantitatve Methods in Health Care Management Yasar A. Ozcan 19 Moving Averages, cont. Easy to compute and understand, but data storage requirements can be high and all values are weighted equally (i.e., in a ten year moving average, each value is given a weight of 1/10, adding up to 1). A weighted average assigns more weight to recent values Easy to compute and understand, but data storage requirements can be high and all values are weighted equally (i.e., in a ten year moving average, each value is given a weight of 1/10, adding up to 1). A weighted average assigns more weight to recent values

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Chapter 2: Quantitatve Methods in Health Care Management Yasar A. Ozcan 20 Using Weighted Values Example: Continuing with Example 2.1; since there is a downward trend in visits and in period 5 there is a sharp decline, a weight of.5 or even higher is justified by the healthcare manager to calculate a weighted average for period 6 Period (t)AgeVisitsWeights

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Chapter 2: Quantitatve Methods in Health Care Management Yasar A. Ozcan 21 Using Weighted Values Solution: In this analysis, a weighted average, using formula [2.2], for the OB/GYN clinic for the period 6 would be: F 6 = 14272* * *.5 F 6 = Solution: In this analysis, a weighted average, using formula [2.2], for the OB/GYN clinic for the period 6 would be: F 6 = 14272* * *.5 F 6 = Period (t)AgeVisitsWeightsForecast

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Chapter 2: Quantitatve Methods in Health Care Management Yasar A. Ozcan 22 Simple Exponential Smoothing Each new forecast is based on the previous forecast plus a percentage of the difference between that forecast the actual value of the series at that point New forecast = Old forecast + α(Actual-Old forecast), where α is a percentage or F t = F t-1 + α(A t-1 - F t-1 ), F t = F t-1 + α(A t-1 - F t-1 ), where, F t = Forecast for period t F t-1 = Forecast for period t-1 F t-1 = Forecast for period t-1 α = Smoothing constant α = Smoothing constant A t-1 = Actual demand or sales in period t-1 A t-1 = Actual demand or sales in period t-1 Each new forecast is based on the previous forecast plus a percentage of the difference between that forecast the actual value of the series at that point New forecast = Old forecast + α(Actual-Old forecast), where α is a percentage or F t = F t-1 + α(A t-1 - F t-1 ), F t = F t-1 + α(A t-1 - F t-1 ), where, F t = Forecast for period t F t-1 = Forecast for period t-1 F t-1 = Forecast for period t-1 α = Smoothing constant α = Smoothing constant A t-1 = Actual demand or sales in period t-1 A t-1 = Actual demand or sales in period t-1

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Chapter 2: Quantitatve Methods in Health Care Management Yasar A. Ozcan 23 Exponential Smoothing, cont. Example 2.4: Using the data from Example 2.1, build forecasts with smoothing constant α = 0.3 Solution: Following the previous example and formula [2.3], we can build forecasts for periods as data become available. F 3 = ( ) F 3 = Example 2.4: Using the data from Example 2.1, build forecasts with smoothing constant α = 0.3 Solution: Following the previous example and formula [2.3], we can build forecasts for periods as data become available. F 3 = ( ) F 3 = Smoothing constant α = 0.3 Error Period (t)Actual (Visits)Forecast(Actual – Forecast)

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Chapter 2: Quantitatve Methods in Health Care Management Yasar A. Ozcan 24 Smoothing constant α = 0.5 Error Period(t)VisitsForecast (Actual – Forecast) Example 2.5: Using the data from Example 2.1, build forecasts with smoothing constant α = 0.5. α = 0.5.Solution: Example 2.5: Using the data from Example 2.1, build forecasts with smoothing constant α = 0.5. α = 0.5.Solution: Exponential Smoothing, cont.

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Chapter 2: Quantitatve Methods in Health Care Management Yasar A. Ozcan 25 Example 2.6: Using the data from Example 2.1, build forecasts with smoothing constants α = 0.0 and α = 1.0. α = 0.0 and α = 1.0.Solution: Example 2.6: Using the data from Example 2.1, build forecasts with smoothing constants α = 0.0 and α = 1.0. α = 0.0 and α = 1.0.Solution: Exponential Smoothing, cont. Period (t) α = 0.0 Error α = 1.0 Error VisitsForecast(Actual – Forecast)VisitsForecast(Actual – Forecast)

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Chapter 2: Quantitatve Methods in Health Care Management Yasar A. Ozcan 26 Techniques for Trends Least squares regression-- minimizes the sum of the squared errors Least squares line: y = a + bx, y = predicted (dependent) variable x = predictor (independent) variable b = slope of data line a = value of y when x = 0 Least squares regression-- minimizes the sum of the squared errors Least squares line: y = a + bx, y = predicted (dependent) variable x = predictor (independent) variable b = slope of data line a = value of y when x = 0 n( xy) - ( x)( y) n( x 2 ) - ( x) 2 b = a = y - b x n

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Chapter 2: Quantitatve Methods in Health Care Management Yasar A. Ozcan 27 Figure 2.9 Linear Regression y x y = a + bx a error ΔyΔy ΔxΔx b =(Δy/Δx), where b>0

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Chapter 2: Quantitatve Methods in Health Care Management Yasar A. Ozcan 28 Techniques for Trends Multi Hospital System Revenues and Profits Data HospitalRevenue (x)Profit (y)x*yx2x Total Example 2.7: A multi-hospital system (MHS) owns 12 hospitals. Revenues (x, or the independent variable) and profits (y, or the dependent variable) for each hospital are given below. Obtain a regression line for the data, and predict profits for a hospital with $10 million in revenues. All figures are in millions of dollars.

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Chapter 2: Quantitatve Methods in Health Care Management Yasar A. Ozcan 29 Solution:Solution: After calculating substitute into the equations [2.5] for a and [2.6] for b, respectively. Hence, the regression line is: y x = x. To predict the profits for a hospital with $10 million in revenue, simply plug 10 in as the value of x in the regression equation: Profit = (10) = Multiplying this value by one million, the profit level with $10 million in revenue is found to be $209,903.

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Chapter 2: Quantitatve Methods in Health Care Management Yasar A. Ozcan 30 Techniques for Trends Linear Regression as a Trend Line y = a + b*t y = predicted (dependent) variable t = predictor (time) variable b = slope of data line a = value of y when x = 0 Linear Regression as a Trend Line y = a + b*t y = predicted (dependent) variable t = predictor (time) variable b = slope of data line a = value of y when x = 0 n( ty) - ( t)( y) n( t 2 ) - ( t) 2 b = a = y - b t n

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Chapter 2: Quantitatve Methods in Health Care Management Yasar A. Ozcan 31 Example 2.8: Referring back to the OB/GYN example, the health care manager can estimate the trend line using regression analysis. Solution: Solution:

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Chapter 2: Quantitatve Methods in Health Care Management Yasar A. Ozcan 32 Techniques for Seasonality Seasonal variations in a data set consistently repeat upward or downward movements of the data values that can be traced to recurrent events. In the additive model, seasonality is expressed as a quantity (example: 5 units), which is added or subtracted from the series average in order to incorporate seasonality. In the multiplicative model, seasonality is expressed as a percentage of the average amount (example: 1.15) Quarterly, Monthly, Daily Indices Technique Seasonal variations in a data set consistently repeat upward or downward movements of the data values that can be traced to recurrent events. In the additive model, seasonality is expressed as a quantity (example: 5 units), which is added or subtracted from the series average in order to incorporate seasonality. In the multiplicative model, seasonality is expressed as a percentage of the average amount (example: 1.15) Quarterly, Monthly, Daily Indices Technique

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Chapter 2: Quantitatve Methods in Health Care Management Yasar A. Ozcan 33 Techniques for Seasonality Employing Seasonal Indices in Forecasts Example 2.10: A forecast based on linear regression yields the following trend equation Demand (Y t ) = t. The forecast of demand for periods 29 through 31 would be: Y29 = (29) = Y30 = (30) = Y31 = (31) = Having forecast the next three months, the healthcare manager needs to incorporate seasonality back into those forecasts. The periods t = 29, 30 and 31 represent the months of November, December and January, respectively, with corresponding monthly indices 0.984, 0.973, and Monthly adjustments to those forecasts are calculated Monthly Adjusted Forecast (t): Forecast * Monthly Index Period 29 (November): (0.984) = Period 30 (December): (0.973) = Period 31 (January) : (1.036) = Employing Seasonal Indices in Forecasts Example 2.10: A forecast based on linear regression yields the following trend equation Demand (Y t ) = t. The forecast of demand for periods 29 through 31 would be: Y29 = (29) = Y30 = (30) = Y31 = (31) = Having forecast the next three months, the healthcare manager needs to incorporate seasonality back into those forecasts. The periods t = 29, 30 and 31 represent the months of November, December and January, respectively, with corresponding monthly indices 0.984, 0.973, and Monthly adjustments to those forecasts are calculated Monthly Adjusted Forecast (t): Forecast * Monthly Index Period 29 (November): (0.984) = Period 30 (December): (0.973) = Period 31 (January) : (1.036) =

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Chapter 2: Quantitatve Methods in Health Care Management Yasar A. Ozcan 34 Techniques for Seasonality Employing Seasonal Indices in Forecasts The next step in adjustment of the forecasted demand would be for daily fluctuations. As was shown in Table 2.4, Heal Me Hospital experiences daily variation in demand. Thus, the monthly index adjusted forecasts should be further adjusted for daily variations. Daily Adjusted Forecast = Monthly Adjusted Forecast (t) * Daily Index For example, for November (period 29), the adjusted forecasts for Monday and Tuesday are: Monday, November: * (0.972) = Tuesday, November: * (1.023) = Employing Seasonal Indices in Forecasts The next step in adjustment of the forecasted demand would be for daily fluctuations. As was shown in Table 2.4, Heal Me Hospital experiences daily variation in demand. Thus, the monthly index adjusted forecasts should be further adjusted for daily variations. Daily Adjusted Forecast = Monthly Adjusted Forecast (t) * Daily Index For example, for November (period 29), the adjusted forecasts for Monday and Tuesday are: Monday, November: * (0.972) = Tuesday, November: * (1.023) =

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Chapter 2: Quantitatve Methods in Health Care Management Yasar A. Ozcan 35 How accurate are we? Errors may be caused by: –An inadequate forecasting model –Irregular variations due to severe weather, shortages or breakdowns, catastrophes, etc. –Forecasting technique may be used improperly –There may be random variations in the data Errors may be caused by: –An inadequate forecasting model –Irregular variations due to severe weather, shortages or breakdowns, catastrophes, etc. –Forecasting technique may be used improperly –There may be random variations in the data Forecast Error equals the actual value minus the forecasted value. Error = Actual – Forecast Forecast Error equals the actual value minus the forecasted value. Error = Actual – Forecast

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Chapter 2: Quantitatve Methods in Health Care Management Yasar A. Ozcan 36 Is your forecast accurate? Mean Absolute Deviation (MAD) Seek lowest of MAD or MAPE for given set of data; also examine historical performance versus responsiveness to current situation. MAD weights all errors evenly. MAPE avoids the problem of interpreting the measure of accuracy relative to the magnitudes of the actual and the forecast values. Mean Absolute Percent Error (MAPE)

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Chapter 2: Quantitatve Methods in Health Care Management Yasar A. Ozcan 37 Period t Smoothing constant α =.3 ErrorAbsolute Error ActualForecast(Actual – Forecast)|Actual – Forecast| Sum Σ Is your forecast accurate? Using data from Example 2.4, SES with α = 0.3, we observe the necessary error calculations in Table below. Hence, MAD = ÷ 4 = , and MAPE = ÷ = or 16.5%.

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Chapter 2: Quantitatve Methods in Health Care Management Yasar A. Ozcan 38 Is your forecast accurate? Controlling forecasts-- set predetermined upper/lower limits for forecast errors Forecasts can be monitored using either a tracking signal or control chart. –Tracking signals show cumulative errors - Control Charts-- set upper and lower limits for individual forecast errors Controlling forecasts-- set predetermined upper/lower limits for forecast errors Forecasts can be monitored using either a tracking signal or control chart. –Tracking signals show cumulative errors - Control Charts-- set upper and lower limits for individual forecast errors

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Chapter 2: Quantitatve Methods in Health Care Management Yasar A. Ozcan 39 Control Chart for Tracking Signal Range of Acceptable Variation Need for Corrective Action -During periods 12 through 15 the tracking signal went beyond the acceptable control limits (down to -5.51), but recovered at period 16 and stayed within acceptable limits after that. -Until period 8 the predicted values were below the actual. That changed from period 9 to period 20, when forecasts were higher than actual data. -At the period 21 a return to under-forecast occurred.

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Chapter 2: Quantitatve Methods in Health Care Management Yasar A. Ozcan 40 So what technique should we use? Factors of importance: –Frequency –Level of aggregation – Type of Model- Errors [MAD, MAPE] –Degree of managerial involvement –Cost per forecast Time horizon considerations-- short, intermediate, or long Factors of importance: –Frequency –Level of aggregation – Type of Model- Errors [MAD, MAPE] –Degree of managerial involvement –Cost per forecast Time horizon considerations-- short, intermediate, or long

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Chapter 2: Quantitatve Methods in Health Care Management Yasar A. Ozcan 41 What makes a forecast a good one? Timeliness Accuracy Meaningful Units ($$’s, visits, etc.) In writing Simple to understand and use Timeliness Accuracy Meaningful Units ($$’s, visits, etc.) In writing Simple to understand and use

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Chapter 2: Quantitatve Methods in Health Care Management Yasar A. Ozcan 42 The End

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