Confidence Intervals in Healthcare Administration

Confidence Intervals in Healthcare Administration

Discussion: Confidence Intervals in Healthcare Administration

Healthcare administration leaders are asked to make evidence-based decisions on a daily basis. Sometimes, these decisions involve high levels of uncertainty, as you have examined previously. Other times, there are data upon which evidence-based analysis might be conducted.

This week, you will be asked to think of scenarios where building and interpreting confidence intervals (CIs) would be useful for healthcare administration leaders to conduct a two-sided hypothesis test using fictitious data.

For example, Ralph is a healthcare administration leader who is interested in evaluating whether the mean patient satisfaction scores for his hospital are significantly different from 87 at the .05 level. He gathers a sample of 100 observations and finds that the sample mean is 83 and the standard deviation is 5. Using a t-distribution, he generates a two-sided confidence interval (CI) of 83 +/- 1.984217 *5/sqrt(100). The 95% CI is then (82.007, 83.992). If repeated intervals were conducted identically, 95% should contain the population mean. The two-sided hypothesis test can be formulated and tested just with this interval. Ho: Mu = 87, Ha: Mu<>87. Alpha = .05. If he assumes normality and that population standard deviation is unknown, he selects the t-distribution. After constructing a 95% CI, he notes that 87 is not in the interval, so he can reject the null hypothesis that the mean satisfaction rates are 87. In fact, he has an evidence-based analysis to suggest that the mean satisfaction rates are not equal to (less than) 87.

For this Discussion, review the resources for this week, and consider how a CI might be used to support hypothesis testing in a healthcare scenario.

By Day 3

Post a description of a healthcare scenario where a CI might be used, and then complete a fictitious two-sided hypothesis test using a CI and fictitious data.

Discussion

Continue the Discussion and respond to 2 of your colleagues in one or more of the following ways:

Each Colleagues 250 words or more (Colleague 1 250 words, Colleague 2 250 words, Total 500 words):

· Ask a probing question, substantiated with additional background information, evidence, or research.

· Share an insight from having read your colleagues’ postings, synthesizing the information to provide new perspectives.

· Offer and support an alternative perspective, using readings from the classroom or from your own research in the Walden Library.

· Validate an idea with your own experience and additional research.

· Make a suggestion based on additional evidence drawn from readings or after synthesizing multiple postings.

· Expand on your colleagues’ postings by providing additional insights or contrasting perspectives based on readings and evidence.

Colleague 1

Forty respondents complete a survey. Each was asked how much of a monthly premium increase they could absorb before leaving their current health care insurance. The sample responses are given as:

The mean of this sample is 47.23, with a standard deviation of 10.05. Moving one standard deviation to the left would incorporate an additional 34.1% of the population. Assuming a normal distribution, the maximized retention level with an increase in premiums would not necessarily occur at the mean itself. Exact estimations regarding the profitability of various options cannot be given without knowledge of current premium rates and total population size; however, a premium increase below the observed mean in this population would likely be most beneficial to the company in terms of minimizing risks maximizing revenue.

When determining a confidence interval for this population, it is necessary to remember that the internal must be one-sided. Determining what percentage of individuals would remain with the current insurance plan with a selected premium increase involves the z-score and greater use of the known features of the normal distribution. For a one-sided ninety percent confidence interval, the corresponding z-score is approximately -1.29, meaning the line would need to be drawn 1.29 standard deviations to the left of the mean to retain ninety percent of the population.

Reference:

Johnson, R. & Bhattacharyya, G. (2009). Statistics: Principles and Methods. New York: Wiley

Colleague 2

Medical Providers use evidence-based medicine when completing some type of decision making for practicing (Shreffler and Huecker, 2021). A scenario where a CI can be used in healthcare is with the estimation of cancer rates in the United States with cancers and the death rates. The width of a confidence interval depends on the amount of inconsistency in the data. Causes of variability include the primary circumstance of cancer as well as doubt about when cancer is identified and diagnosed, when a death from cancer happens, and when the data about the cancer are sent to the registry or the state health department (Centers for Disease Control and Prevention, 2021). The sample below is at random to show a more accurate finding of cancer rates in 120 people and in any given year, when large numbers of a particular cancer are diagnosed or when large numbers of cancer patients die, the effects of random variability are small compared with the large numbers, and the confidence interval will be narrow.

Sample Size: 120 people

Sample Mean: 60.5

Standard Deviation: 1.98

The two-sided confidence interval of 60.5 +/-1.98

The 95% Confidence Interval is (59.0019,60.891)

The total means the number of randomly selected patients that were being diagnosed with cancer and the death rates thereafter. With rare cancers, however, the rates are small and the chance occurrence of more or fewer cases or deaths each year can markedly affect those rates. The average amount of people show that a 95% Confidence interval is appropriate and estimation on the number of individuals that have cancer, and the death rates will be wide to indicate uncertainty or instability in the cancer rate.

Reference

Centers for Disease Control and Prevention. (8 June 2021). United States Cancer Statistics:

Confidence Intervals. Retrieved from https://www.cdc.gov/cancer/uscs/technical_notes/stat_methods/confidence.htm

Shreffler J, Huecker MR (2021). Hypothesis Testing, P Values, Confidence Intervals, and

Significance. In: StatPearls. Treasure Island (FL): StatPearls Publishing

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