The Continuum of Care
Subacute Care Case Study
1-
On page 138 on your ebook, you will find the Case Study entitled: Subacute Care Case Study.
In reference to this case, please consider the following:
- How can subacute care meet the needs of such different patients as David and Joyce?
- Should both be included in a single care category, or should different levels of care be created for them?
- Is subacute care really a response to patient needs, or is it a way of increasing financing for providers? (NOTE: This question applies to the overall system, but applying it to the case will assist you in seeing the implications for those using the system.)
PG 138
Summary
Subacute care is one of the fastest-growing sectors of health care. It is developing faster than it can learn the rules by which it should play, and it keeps experimenting with new and different ideas and approaches. New models and players keep appearing on the scene. Payers, regulators, and policy makers are trying to keep up with it and, like any parent, are trying to keep it from injuring itself. However, they are finding it difficult to stay ahead of this exciting, but sometimes unruly, model they have created.
Subacute care has developed into a useful, productive model for caring. The growth years have been difficult, but the very fact that it is a new care segment and is ill defined and poorly regulated leaves room for innovation and creativity. The competition from different provider groups and from within those groups is already resulting in some outstanding examples of good care and good management.
Accrediting agencies such as the Joint Commission, CARF International, and NCQA have moved with relative speed to create standards for subacute care and are using measures based primarily on outcomes, as opposed to structure and process measures. Government regulators have not followed suit, at least at this time, but are looking for structures to manage this setting. They will need this if subacute care is to survive as a distinct and viable segment of the healthcare continuum.
The past several years have been exciting and challenging for all involved with subacute care. The next few years will see refinement and enhancements to this care setting.
Subacute Care Case Study
This case involves two people. Both have been admitted to subacute care units following stays in an acute hospital; however, they are different in many ways, as is the type of care they receive. They are used here to demonstrate some of the differences in the segment of the continuum known as subacute care.
David is 17 years old. He was injured in an automobile accident several months ago. Suffering multiple fractures and some internal injuries, he has been in a hospital for several weeks. While his initial injuries have largely healed, with the help of several operations, he still faces a long, difficult period of rehabilitation. It is for that rehabilitation, as well as monitoring of his overall condition, that he has been transferred to a subacute care unit.
Joyce is 67 years old. She has a long history of heart trouble and was admitted to the hospital following her last massive heart attack. That attack, coming on top of her already weakened heart condition, has left her in a semi-comatose state. Her breathing is assisted by a mechanical ventilator, and she must be fed and medicated intravenously.
The subacute unit to which David was sent is known as a general subacute unit. It is operated by, and in conjunction with, a multilevel nursing facility. Joyce, on the other hand, was admitted to a chronic subacute care unit, operated by the hospital from which she was transferred. The difference between the two units is primarily the conditions they treat and the type of staff and equipment needed to do what they each do best.
Both began their journey through subacute care with an assessment by multidisciplinary teams from the subacute units to which they were being transferred. Those assessments identified physical, medical, and mental conditions and developed individual care plans designed to best achieve the outcome goals identified for them. Because David appeared to need physical rehabilitation, his assessment team was heavily weighted with therapists of one type or another, while Joyce’s assessment team was much more nursing oriented.
David’s outcome goal is to be able to return to his home and eventually back to school. The assessment team estimates that he will regain nearly all, if not all, his previous functional independence. To achieve that, he requires intensive rehabilitation, including physical and occupational therapy. His care team is headed by a physiatrist and will focus on those therapies, although his medical condition will be watched.
Joyce’s prognosis is not nearly as clear. The team assessing her agreed that she is unlikely to ever improve and sets a goal of maintaining her condition as well as possible until her death, something that is not likely to be that far distant. She does not need rehabilitation, although staff in the unit do some maintenance range-of-motion exercises with her to keep her physical condition from deteriorating. She does, however, require much more intensive nursing care and monitoring than does David and will be cared for under the watchful eye of a cardiologist.
Another difference, based on expected outcomes, is that David will receive close follow-up care after he is discharged to his home. He will probably continue some of his therapy on an outpatient basis and will be tested periodically to make sure he has not regressed in his quest for functional independence. Joyce, unfortunately, will not have that option.
While the probable results of their subacute care are expected to be so different, Joyce and David have a common reason for being transferred to those units: Their care needs are too high for them to be treated at lower levels, such as nursing facilities or at home, but they do not need acute hospital care. A secondary, but very important, factor contributing to those transfers is the cost of care. David is covered by a managed care plan to which his parents belong. Joyce is eligible for Medicare. Both payment sources want to give them the best care they can, but at the lowest possible cost.
Thus, these two people in such different situations both find themselves in subacute units, between hospital and nursing facility care levels. It is a kind of care that suits them both well. Until only a few years ago, David would have stayed in the hospital for many months, at an unnecessarily high cost. Joyce might have remained in the hospital also, but because she was unconscious and was going to die anyway, it is more than likely that she would have ended up in a nursing facility unprepared to provide her with the care she should have had.
2-Statistical Applications
Qustions to be answered are uploaded
4.2. Defining Standard Deviation and Variance
The standard deviation is the most commonly used and the most important measure of variability. Standard deviation uses the mean of the distribution as a reference point and measures variability by considering the distance between each score and the mean.
In simple terms, the standard deviation provides a measure of the standard, or average, distance from the mean, and describes whether the scores are clustered closely around the mean or are widely scattered.
Although the concept of standard deviation is straightforward, the actual equations tend to be more complex. Therefore, we begin by looking at the logic that leads to these equations. If you remember that our goal is to measure the standard, or typical, distance from the mean, then this logic and the equations that follow should be easier to remember.
Step 1
The first step in finding the standard distance from the mean is to determine the deviation, or distance from the mean, for each individual score. By definition, the deviation for each score is the difference between the score and the mean.
A deviation score is often represented by a lowercase letter x.
For a distribution of scores with μ
, if your score is
, then your deviation score is
If your score is
, then your deviation score is
Notice that there are two parts to a deviation score: the sign (+ or −) and the number. The sign tells the direction from the mean—that is, whether the score is located above (+) or below (−) the mean. The number gives the actual distance from the mean. For example, a deviation score of −6 corresponds to a score that is below the mean by a distance of 6 points.
Step 2
Because our goal is to compute a measure of the standard distance from the mean, the obvious next step is to calculate the mean of the deviation scores. To compute this mean, you first add up the deviation scores and then divide by N. This process is demonstrated in the following example.
Example 4.1
We start with the following set of
scores. These scores add up to
, so the mean is μ
. For each score, we have computed the deviation.
Note that the deviation scores add up to zero. This should not be surprising if you remember that the mean serves as a balance point for the distribution. The total of the distances above the mean is exactly equal to the total of the distances below the mean Example 3.3 . Thus, the total for the positive deviations is exactly equal to the total for the negative deviations, and the complete set of deviations always adds up to zero.
Because the sum of the deviations is always zero, the mean of the deviations is also zero and is of no value as a measure of variability. Specifically, the mean of the deviations is zero if the scores are closely clustered and it is zero if the scores are widely scattered. (You should note, however, that the constant value of zero is useful in other ways. Whenever you are working with deviation scores, you can check your calculations by making sure that the deviation scores add up to zero.)
Step 3
The average of the deviation scores will not work as a measure of variability because it is always zero. Clearly, this problem results from the positive and negative values canceling each other out. The solution is to get rid of the signs (+ and -). The standard procedure for accomplishing this is to square each deviation score. Using the squared values, you then compute the mean squared deviation, which is called variance.
Note that the process of squaring deviation scores does more than simply get rid of plus and minus signs. It results in a measure of variability based on squared distances. Although variance is valuable for some of the inferential statistical methods covered later, the concept of squared distance is not an intuitive or easy to understand descriptive measure. For example, it is not particularly useful to know that the squared distance from New York City to Boston is 26,244 miles squared. The squared value becomes meaningful, however, if you take the square root. Therefore, we continue the process one more step.
Step 4
Remember that our goal is to compute a measure of the standard distance from the mean. Variance, which measures the average squared distance from the mean, is not exactly what we want. The final step simply takes the square root of the variance to obtain the standard deviation, which measures the standard distance from the mean.
Figure 4.2 shows the overall process of computing variance and standard deviation. Remember that our goal is to measure variability by finding the standard distance from the mean. However, we cannot simply calculate the average of the distances because this value will always be zero. Therefore, we begin by squaring each distance, then we find the average of the squared distances, and finally we take the square root to obtain a measure of the standard distance. Technically, the standard deviation is the square root of the average squared deviation. Conceptually, however, the standard deviation provides a measure of the average distance from the mean.
Figure 4.2
Details
The calculation of variance and standard deviation.
Although we still have not presented any formulas for variance or standard deviation, you should be able to compute these two statistical values from their definitions. The following example demonstrates this process.
Example 4.2
We will calculate the variance and standard deviation for the following population of
scores:
Remember that the purpose of standard deviation is to measure the standard distance from the mean, so we begin by computing the population mean. These five scores add up to
so the mean is μ
. Next, we find the deviation (distance from the mean) for each score and then square the deviations. Using the population mean μ
, these calculations are shown in the following table.
For this set of
scores, the squared deviations add up to 40. The mean of the squared deviations, the variance, is
, and the standard deviation is
.
You should note that a standard deviation of 2.83 is a sensible answer for this distribution. The five scores in the population are shown in a histogram in Figure 4.3 so that you can see the distances more clearly. Note that the scores closest to the mean are only 1 point away. Also, the score farthest from the mean is 5 points away. For this distribution, the largest distance from the mean is 5 points and the smallest distance is 1 point. Thus, the standard distance should be somewhere between 1 and 5. By looking at a distribution in this way, you should be able to make a rough estimate of the standard deviation. In this case, the standard deviation should be between 1 and 5, probably around 3 points. The value we calculated for the standard deviation is in excellent agreement with this estimate.
Figure 4.3
Details
A frequency distribution histogram for a population of
scores. The mean for this population is μ
. The smallest distance from the mean is 1 point and the largest distance is 5 points. The standard distance (or standard deviation) should be between 1 and 5 points.
Making a quick estimate of the standard deviation can help you avoid errors in calculation. For example, if you calculated the standard deviation for the scores in Figure 4.3 and obtained a value of 12, you should realize immediately that you have made an error. (If the biggest deviation is only 5 points, then it is impossible for the standard deviation to be 12.)
The following example is an opportunity for you to test your understanding by computing variance and standard deviation yourself.
Example 4.3
Compute the variance and standard deviation for the following set of
scores: 12, 0, 1, 7, 4, and 6. You should obtain a variance of 16 and a standard deviation of 4. Good luck.
Because the standard deviation and variance are defined in terms of distance from the mean, these measures of variability are used only with numerical scores that are obtained from measurements on an interval or a ratio scale. Recall from Chapter 1 that these two scales are the only ones that provide information about distance; nominal and ordinal scales do not. Also, recall from Chapter 3 that it is inappropriate to compute a mean for ordinal data and it is impossible to compute a mean for nominal data. Because the mean is a critical component in the calculation of standard deviation and variance, the same restrictions that apply to the mean also apply to these two measures of variability. Specifically, the mean, standard deviation, and variance should be used only with numerical scores from interval or ratio scales of measurement.
Learning Check
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Standard deviation is probably the most commonly used value to describe and measure variability. Which of the following accurately describes the concept of standard deviation?
- SHOW ANSWER
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the average distance between one score and another
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the average distance between a score and the mean
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the total distance from the smallest score to the largest score
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one half of the total distance from the smallest score to the largest score
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What is the variance for the following set of scores? 2, 2, 2, 2, 2
- SHOW ANSWER
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0
-
2
-
4
-
5
-
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Which of the following values is the most reasonable estimate of the standard deviation for the set of scores in the following distribution? (It may help to imagine or sketch a histogram of the distribution.)
- SHOW ANSWER
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0
-
1
-
3
-
5
4.3. Measuring Variance and Standard Deviation for a Population
The concepts of standard deviation and variance are the same for both samples and populations. However, the details of the calculations differ slightly, depending on whether you have data from a sample or from a complete population. We first consider the formulas for populations and then look at samples in Section 4.4.
The Sum of Squared Deviations (SS)
Recall that variance is defined as the mean of the squared deviations. This mean is computed exactly the same way you compute any mean: first find the sum, and then divide by the number of scores.
The value in the numerator of this equation, the sum of the squared deviations, is a basic component of variability, and we will focus on it. To simplify things, it is identified by the notation SS (for sum of squared deviations), and it generally is referred to as the sum of squares.
You need to know two formulas to compute SS. These formulas are algebraically equivalent (they always produce the same answer), but they look different and are used in different situations.
The first of these formulas is called the definitional formula because the symbols in the formula literally define the process of adding up the squared deviations:
(4.1)
μ
To find the sum of the squared deviations, the formula instructs you to perform the following sequence of calculations:
-
Find each deviation score μ
.
-
Square each deviation score, μ
.
-
Add the squared deviations.
The result is SS, the sum of the squared deviations. The following example demonstrates using this formula.
Example 4.4
We will compute SS for the following set of
scores. These scores have a sum of
, so the mean is μ
. The following table shows the deviation and the squared deviation for each score. The sum of the squared deviation is
.
Although the definitional formula is the most direct method for computing SS, it can be awkward to use. In particular, when the mean is not a whole number, the deviations all contain decimals or fractions, and the calculations become difficult. In addition, calculations with decimal values introduce the opportunity for rounding error, which can make the result less accurate. For these reasons, an alternative formula has been developed for computing SS. The alternative, known as the computational formula, performs calculations with the scores (not the deviations) and therefore minimizes the complications of decimals and fractions.
(4.2)
The first part of this formula directs you to square each score and then add the squared values,
. In the second part of the formula, you find the sum of the scores,
, then square this total and divide the result by N. Finally, subtract the second part from the first. The use of this formula is shown in Example 4.5 with the same scores that we used to demonstrate the definitional formula.
Example 4.5
The computational formula is used to calculate SS for the same set of
scores we used in Example 4.4. Note that the formula requires the calculation of two sums: first, compute
, and then square each score and compute
. These calculations are shown in the following table. The two sums are used in the formula to compute SS.
Note that the two formulas produce exactly the same value for SS. Although the formulas look different, they are in fact equivalent. The definitional formula provides the most direct representation of the concept of SS; however, this formula can be awkward to use, especially if the mean includes a fraction or decimal value. If you have a small group of scores and the mean is a whole number, then the definitional formula is fine; otherwise, the computational formula is usually easier to use.
Final Formulas and Notation
In the same way that sum of squares, or SS, is used to refer to the sum of squared deviations, the term mean square, or MS, is often used to refer to variance, which is the mean squared deviation.
With the definition and calculation of SS behind you, the equations for variance and standard deviation become relatively simple. Remember that variance is defined as the mean squared deviation. The mean is the sum of the squared deviations divided by N, so the equation for the population variance is
Standard deviation is the square root of variance, so the equation for the population standard deviation is
There is one final bit of notation before we work completely through an example computing SS, variance, and standard deviation. Like the mean μ
, variance and standard deviation are parameters of a population and are identified by Greek letters. To identify the standard deviation, we use the Greek letter sigma (the Greek letter s, standing for standard deviation). The capital letter sigma
has been used already, so we now use the lowercase sigma,
, as the symbol for the population standard deviation. To emphasize the relationship between standard deviation and variance, we use
as the symbol for population variance (standard deviation is the square root of the variance). Thus,
(4.3)
(4.4)
Earlier, in Examples 4.4 and 4.5, we computed the sum of squared deviations for a simple population of
scores (1, 0, 6, 1) and obtained
. For this population, the variance is
and the standard deviation is
Learning Check
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What is the value of SS, the sum of the squared deviations, for the following population of
scores? Scores: 1, 4, 6, 1
- SHOW ANSWER
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0
-
18
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54
-
-
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Each of the following is the sum of the scores for a population of
scores. For which population would the definitional formula be a better choice than the computational formula for calculating SS.
- SHOW ANSWER
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-
-
-
-
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What is the standard deviation for the following population of scores? Scores: 1, 3, 7, 4, 5
- SHOW ANSWER
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20
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5
-
4
-
2
-
-
-