University Statistics Report: Forecasting Methods in Healthcare

This report delves into various statistical forecasting methods, specifically focusing on their application within the healthcare sector. The report begins by outlining five distinct forecasting techniques: change of average, confidence interval, average change of percentage, moving average method, and exponential smoothing. Each method is explained in detail, including the steps involved in its implementation and the formulas used. The report then discusses the importance of forecasting in healthcare, highlighting its role in predicting demand, allocating resources, and minimizing risks. It compares different forecasting mechanisms used in an outpatient clinic and emergency department visits. The report then applies these methods to a case study involving healthcare service data, calculating predictions using moving average, confidence intervals, and exponential smoothing. Finally, the report analyzes the results, comparing the outcomes of different methods and offering insights into their suitability for forecasting in healthcare. The report references multiple research papers and books to support the findings.

Running head: STATISTICS
Statistics
University Name
Student Name
Authors’ Note

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Table of Contents
Solution to Answer 1:.................................................................................................................2
Solution to Question 2:...............................................................................................................6
Solution to Question 3:...............................................................................................................7
Solution to Question 4:.............................................................................................................12
References................................................................................................................................14

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Solution to Answer 1:
Varied steps involved in the procedure of carrying out forecasting are hereby mentioned
below:
Explanation of the 1st Method: Change of Average
The first as well as foremost step involved in forecasting is particularly plotting the definite
data prior to any application of any technique of prediction mechanisms. Based on the
plotting of the specific data, a definite trend can be witnessed. Essentially, the mechanisms of
the average change can necessarily be illustrated using the following steps explained herein
below:
Stage 1 refers to computation of the change/alteration every month
Stage 2 refers to computation of average alteration every month
Stage 3 refers to computation of the specific mid-point of the acquired data. In case if the
total number of data is particularly even in number, then in that case, the mid point can be
determined by the formula (n+1)/2, in which “n” stands for the total number of data.
However, in case if the total number of data is essentially odd in number, then in that case,
the mid-point can be ascertained by using the formula: n/2 (Mead, 2017).
Stage 4 indicates towards computation of the forecast for specified or given month. This can
be enumerated by the formula:
Average visits per month + (Average change per month) X (mid-point of the data)
Explanation of the 2nd Method: Confidence Interval

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Confidence interval refers to a mechanism that presents a specific level of interval for the
prediction (Mertler & Reinhart, 2016). In this case, the prediction is founded on confidence
interval of particularly 95%. In itself, confidence interval of 95% is presented as average
amount ±1.96 x (SD) standard deviation]
Stage 1 of this method includes computation of the mean as well as standard deviation
Stage 2 of this particular method refers to ascertainment of the confidence interval
(that is 95% Confidence Interval = average visits ± 1.96 X (SD) standard deviation of total
visits
Explanation of the 3rd Method: Average change of percentage
This specific method is on the groundwork of calculation of percentage change of average.
Various steps involved in this process are hereby mentioned below:
Step 1 refers to change from prior methods and thereafter divided by the value obtained from
the prior method (Mertler & Reinhart, 2016)
Step 2 includes enumeration of the percentage alteration
Step 3 refers to enumeration of average of change in percentage
Finally Step 4 indicates towards determination of the forecasted figure. This forecasted figure
is calculated by using the following formula:
Latest Month+ Average change in percentage X Most Current Month
Explanation of the 4th Method: Moving Average Method
There is need to make use of historical data using moving average. Various steps involved in
the process of enumeration of moving average method include the following:

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Step 1 refers to calculation of the predicted figure for the month of November of the year
2008 as per the example. Therefore, there is need to include data from November of the year
2007 till the period of October of the year 2008
Step 2 involves selection of a specific period. Fundamentally, the period might be between
two months to 6 months
Step 3 indicates towards calculation of moving average of n period, for instance, at the time
when the n is equal to 2 , then it is feasible to enumerate number of visits to hospital of the
prior month and thereafter divide the same by the value of the n (that is to say 2). Essentially,
this is the predicted figure for the month
Step 4 refers to enumeration of forecast error (abbreviated as FE). Calculation of forecasted
error involves subtraction of actual of the particular month from the predicted figure of them
month.
Step 5 indicates towards calculation of the total sum of the forecasted error (Mertler &
Reinhart, 2016). Basically, this can be referred to as the absolute deviation also simply
indicated as AD.
Step 6 involves calculation of the mean absolute deviation of the data
Step 7 refers to comparison of the figure on mean absolute deviation and selection of the
lowest value of the mean absolute deviation
Step 8 involves prediction or forecast based on the n period of the mean absolute deviation.
In case if n (that is the number of period =4), then the average amount of the past 4 months
reflects the forecast/prediction) of this month.
Explanation of the 5th Method: Exponential Smoothing

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This specific method exponential smoothing utilizes the formula hereby mentioned below:
In this, F stands for the forecast for the following month
O stands for the observed figure for the most current period
Ft-1 stands for the predicted or forecasted figure of the current period
SC stands for the smoothing constant
In essence, the smoothing constant needs to be ascertained by means of trial as well as error
method. Therefore, the process of utilizing multiple constants of smoothing can aid in
lessening the overall error and assist in providing a superior forecast.
Steps involved in carrying out the process are hereby mentioned below:
Step 1 indicates towards calculation of the forecasted error founded on multiple constants of
smoothing.
Step 2 involves calculation of the mean absolute deviation (MAD) and thereafter comparison
of the same. In this case, the lowest MAD can be thereafter chosen. Essentially, this might
perhaps be the best one.
Step 3 refers to selection of smoothing constant that is necessarily the next higher one.
Step 4 indicates towards fraction that can again be divided and the above procedure can again
be continued (Mertler & Reinhart, 2016).
Step 5 refers to selection of the smoothing constants that provides the lowest Mean Absolute
Deviation (MAD)

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Step 6 indicates towards forecast for the entire month that is carried out by the formula
utilizing the best of the smoothing constant
Solution to Question 2:
Forecasting can be considered to be a specific tool in particularly the sector of Healthcare.
Fundamentally, this mechanism helps diverse providers of healthcare service in the process
of carrying out predictions and undertaking fitting dimensions to minimize risks and handle
several demands. Essentially, forecasts in the segment of healthcare can prove to be
beneficial at the time when they are able to deliver timely warning that in turn can help in
undertaking remedial steps (Manly & Alberto, 2016). Remedial actions can be undertaken for
delivering potential demand as well as allocation of resource. In itself, there are different
mechanisms are utilized in the process of forecasting health. Comparison was carried out
between six different mechanisms of forecasting time series in particularly an outpatient
clinic.
The outcome of the data reflected an enhanced forecast with sequencing data in time series
with normal day clustering (Mertler & Reinhart, 2016). Diverse categories of analysis of time
series models were necessarily utilized for predicting different emergency department visit. It
was thereby discovered that time series model can necessarily be utilized for the purpose of
predicting arrival in department for paediatrics (Mertler & Reinhart, 2016).
Mead (2017) applied regression founded models of forecasting for predicting arrivals in
different emergency department. Essentially, their evaluation reflected the fact that analysis
of regression was an important mechanism for handling different needs for forecasting. In
essence, this replicated the fact that the data need to be updated to arrive at a superior
prediction.

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In essence, the world health organization published in their bulletin predicts worldwide
shortage of particularly physicians. Therefore, it can be hereby observed that methods of
forecasting can be specifically utilized at diverse stages of the entire Healthcare system.
Solution to Question 3:
Use of method 1 (Moving Average)
A specific plot is drawn on the total number of individuals at the health care service between
the year 2005 and year 2008. It can be hereby observed during the period 2006 to 2008, the
total number of individuals at the health care service has necessarily diminished particularly
during Jun mainly before showing again an increasing trajectory (Meeker & Escobar, 2014).
Table 1: Reflecting Average Change

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Based on the calculation presented above, it can be hereby mentioned that the predicted value
for the visits during the period November is equal to addition of average number of visits plus
the average of the alteration multiplied by the mid point value. Therefore, the average change
mechanism predicts the number of visits dutring November to be equal to 34.3
Use of Method 2: (Confidence Interval)

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For 95% confidence interval, both the upper limit as well as lower limit can be calculated as
presented below:
Based on the above mentioned method, it can be said that the predicted figure for the total
number of visits will range between 20.68 – 47.92
Use of the third Method: Average Change in Percentage
Based on the particular method, it can be said that the forecasted figure for the period of
November of the year 2008 would be as follows:
Therefore, based on the calculated figure, it can be hereby said that the forecasted figure for
the period of November stands at 40.48

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Use of 4th Method: Moving Average
The data selected for the current study is between November of the year 2007 to October of
the the year 2008. The table below presents the calculation of moving average and considers
n to lioe between 2 to 6
Based on the calculations presented above, it can be hereby said that the lowest MAD is
particularly for n equal to 2. Therefore, the prediction for the period of November of the year
2008 shall necessarily be the average figure of the prior two months.

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So, the predicted figure for the period of November of the year 2008 stands at 38.
Use of 5th Method: Exponential Smoothing’
As the mechanism of exponential smoothing utilizes the mechanism of moving average,
therefore data for the period of November of the year 2007 to October of the year 2008 has
been hereby selected. In this case, the values of forecast utilizing smoothing constants are
necessarily 0.1, 0.3, 0.5 as well as 0.9. Thereafter, the mean abdsolute deviation is calculated.
It can be hereby observed that at the time when the value of forecast is equal to 0.7, the
lowest MAD stands at (5.17). After that, the next higher value of MAD is equal to 5.23 for
the specific forecast value of essentially 0.5. Further, MAD is again enumerated for different
values of forecast such as 0.5 and 0.55, 0.6 and 0.66. It can be hereby witnessed that the
lowest value of MAD stands at 5.11 for the particular predicted value of 0.6. Thus, the
prediction for the period November 2008 is
Solution to Question 4:
If we observe the chart for the past 4 years, an increase in the total number of visits can be
observed in the year 2005 as well as the year 2007 from the month October to particularly
November. However, the same is said to decline during the year 2006.
Again, if we observe the outcomes acquired from confidence interval prediction, it can be
hereby be said that prediction presented a range between 20.68-47.92. Essentially, these
ranges can be considered to be very broad ranges.