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

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

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

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

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

Steps in the Forecasting Process 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 Chapter 2: Quantitatve Methods in Health Care Management Yasar A. Ozcan

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

Method of obtaining opinions of managers and staff 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 Chapter 2: Quantitatve Methods in Health Care Management Yasar A. Ozcan

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

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 (yt = a + bxt) Trend adjusted exponential smoothing Techniques for seasonality Seasonal Variations Indices Technique Chapter 2: Quantitatve Methods in Health Care Management Yasar A. Ozcan

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

Jan Mar May Jul Sep Nov Figure 2.1 Variation Characteristics Seasonal 2005 2004 2003 Jan Mar May Jul Sep Nov Cycle Random Variation Chapter 2: Quantitatve Methods in Health Care Management Yasar A. Ozcan Trend

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

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

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

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) Age Visits 1 5 15908 2 4 15504 3 14272 13174 10022 Chapter 2: Quantitatve Methods in Health Care Management Yasar A. Ozcan

Moving Averages, cont. Solution: The three-period moving average (MA3) for period 6 is F6 = MA3 = (14272+13174+10022) ÷ 3 = 12489.3 Period (t) Age Visits Forecast 1 5 15908 2 4 15504 3 14272 13174 15228 10022 14317 6 12489 Chapter 2: Quantitatve Methods in Health Care Management Yasar A. Ozcan

Moving Averages, cont. MA3 Data MA5 1 2 3 4 5 6 7 8 9 The greater the number of periods in a moving average, the greater the forecast will lag with changes in the data MA3 Data MA5 1 2 3 4 5 6 7 8 9 Chapter 2: Quantitatve Methods in Health Care Management Yasar A. Ozcan

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

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) Age Visits Weights 1 5 15908 2 4 15504 3 14272 0.2 13174 0.3 10022 0.5 6 Chapter 2: Quantitatve Methods in Health Care Management Yasar A. Ozcan

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: F6 = 14272*.2+13174*.3+10022*.5 F6 = 11818. Period (t) Age Visits Weights Forecast 1 5 15908 2 4 15504 3 14272 0.2 13174 0.3 10022 0.5 6 11818 Chapter 2: Quantitatve Methods in Health Care Management Yasar A. Ozcan

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 Ft = Ft-1 + α(At-1 - Ft-1), where, Ft = Forecast for period t Ft-1 = Forecast for period t-1 α = Smoothing constant At-1 = Actual demand or sales in period t-1 Chapter 2: Quantitatve Methods in Health Care Management Yasar A. Ozcan

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. F3 = 15908 + .30(15504-15908) F3 = 15786.8 Smoothing constant α = 0.3 Error Period (t) Actual (Visits) Forecast (Actual – Forecast) 1 15908 -- 2 15504 -404.0 3 14272 15786.8 -1514.8 4 13174 15332.4 -2158.4 5 10022 14684.9 -4662.9 Chapter 2: Quantitatve Methods in Health Care Management Yasar A. Ozcan

Exponential Smoothing, cont. Smoothing constant α = 0.5 Error Period(t) Visits Forecast (Actual – Forecast) 1 15908 -- 2 15504 -404.0 3 14272 15706.0 -1434.0 4 13174 14989.0 -1815.0 5 10022 14081.5 -4059.5 Example 2.5: Using the data from Example 2.1, build forecasts with smoothing constant α = 0.5. Solution: Chapter 2: Quantitatve Methods in Health Care Management Yasar A. Ozcan

Exponential Smoothing, cont. Example 2.6: Using the data from Example 2.1, build forecasts with smoothing constants α = 0.0 and α = 1.0. Solution: Period (t) α = 0.0 Error α = 1.0 Visits Forecast (Actual – Forecast) 1 15908 -- 2 15504 -404.0 3 14272 15908.0 -1636.0 15504.0 -1232.0 4 13174 -2734.0 14272.0 -1098.0 5 10022 -5886.0 13174.0 -3152.0 6   10022.0 Chapter 2: Quantitatve Methods in Health Care Management Yasar A. Ozcan

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 n(åxy) - (åx)(åy) n(åx2) - (åx)2 b = a = åy - båx n Chapter 2: Quantitatve Methods in Health Care Management Yasar A. Ozcan

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

Multi Hospital System Revenues and Profits Data Techniques for Trends 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. Multi Hospital System Revenues and Profits Data Hospital Revenue (x) Profit (y) x*y x2 1 7 0.15 1.05 49 2 0.10 0.2 4 3 6 0.13 0.78 36 0.6 16 5 14 0.25 3.5 196 15 0.27 4.05 225 0.24 3.84 256 8 12 0.20 2.4 144 9 3.78 10 20 0.44 8.8 400 11 0.34 5.1 0.17 1.19 Total 132 2.71 35.29 1796 Chapter 2: Quantitatve Methods in Health Care Management Yasar A. Ozcan

Solution: After calculating yx = 0.0506 + 0.01593x. substitute into the equations [2.5] for a and [2.6] for b, respectively. Hence, the regression line is: yx = 0.0506 + 0.01593x. 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 = 0.0506 + 0.01593(10) = .209903 Multiplying this value by one million, the profit level with $10 million in revenue is found to be $209,903. Chapter 2: Quantitatve Methods in Health Care Management Yasar A. Ozcan

Techniques for Trends n(åty) - (åt)(åy) n(åt2) - (åt)2 b = a = 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(åty) - (åt)(åy) n(åt2) - (åt)2 b = a = åy - båt n Chapter 2: Quantitatve Methods in Health Care Management Yasar A. Ozcan

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

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

Techniques for Seasonality Employing Seasonal Indices in Forecasts Example 2.10: A forecast based on linear regression yields the following trend equation Demand (Yt) = 511.06 + 1.259 t. The forecast of demand for periods 29 through 31 would be: Y29 = 511.06 + 1.259 (29) = 547.6. Y30 = 511.06 +1.259 (30) = 548.8. Y31 = 511.06 + 1.259 (31) = 550.1. 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 1.036. Monthly adjustments to those forecasts are calculated Monthly Adjusted Forecast (t): Forecast * Monthly Index Period 29 (November): 547.6 (0.984) = 538.8. Period 30 (December): 548.9 (0.973) = 534.0. Period 31 (January) : 550.1 (1.036) = 569.9. Chapter 2: Quantitatve Methods in Health Care Management Yasar A. Ozcan

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: 538.8 * (0.972) = 523.7. Tuesday, November: 538.8 * (1.023) = 551.2. Chapter 2: Quantitatve Methods in Health Care Management Yasar A. Ozcan

Errors may be caused by: How accurate are we? Forecast Error equals the actual value minus the forecasted value. Error = Actual – Forecast 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 Chapter 2: Quantitatve Methods in Health Care Management Yasar A. Ozcan

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

Is your forecast accurate? Using data from Example 2.4, SES with α = 0.3, we observe the necessary error calculations in Table below. Period t Smoothing constant α = .3 Error Absolute Error Actual Forecast (Actual – Forecast) |Actual – Forecast| 1 15908 -- 2 15504 -404 404 3 14272 15786.8 -1514.8 1515 4 13174 15332.4 -2158.4 2158 5 10022 14684.9 -4662.9 4662.9 6 13286 Sum Σ 52972 8740.1 Hence, MAD = 8740.1 ÷ 4 = 2185.03, and MAPE = 8740.1 ÷ 52972 = 0.165 or 16.5%. Chapter 2: Quantitatve Methods in Health Care Management Yasar A. Ozcan

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

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

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

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

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