Testing For The Presence Or Absence Of A Specific Dis 902372

Testing For The Presence Or Absence Of A Specific Disease Medical Con

Testing for the presence or absence of a specific disease, medical condition, or illegal drug is common. The results of these tests are never as simple as they appear to be on many TV shows and movies. As patients become more and more critical consumers of medical information from their doctors, they must be aware of the quantitative and statistical reasoning that lurks behind the reported facts and figures. For example, if a medical test is reported as “95% accurate” and you get a “positive” result, what is the chance that you actually have that medical condition? In this lab, you will explore the results of medical tests.

The story that we use is for a made-up disease, but the statistics involved are what medical professionals use to evaluate such tests. Here are some definitions that you will need: False positive (FP): when a patient receives an incorrect positive test result for a disease but the patient does not have the disease. False negative (FN): when a patient receives an incorrect negative test result for a disease but the patient does have the disease. True positive (TP): when a patient receives a correct positive result (does have the disease). True negative (TN): when a patient receives a correct negative test result (does not have the disease).

Sensitivity: the probability that a test correctly produces a positive test result when the patient does have the disease. Specificity: the probability that a test correctly produces a negative test result when the patient does not have the disease. A new, faster, cheaper test (we’ll call it CHEAP) has been developed to diagnose a fairly common disease called SpringFeverItis (SFI). The SFI virus causes people to daydream, miss work and school, wear skin-bearing clothing, and spend excessive amounts of time in the sun. The manufacturers of this CHEAP test claim that it is 95% effective in detecting when a person has the SFI virus.

This new test will be compared to the “gold standard” test (which we will consider to be perfectly accurate), a time-consuming and expensive test for SFI. When a patient is said to be SFI-positive, we mean that the time-consuming and expensive test has determined a patient to be SFI-positive. Assume a simple random sample of 100 people is selected to be tested. Using the time-consuming and expensive test, it is determined that 32 of them have SFI, but the CHEAP test only found 30 of these. Similarly, CHEAP reported a “negative” result to only 61 of the 68 SFI-negative people.

Paper For Above instruction

Testing for the presence or absence of a specific disease involves understanding the accuracy and reliability of diagnostic tests. Medical diagnostics are crucial tools in disease management, but interpreting their results requires a solid grasp of statistical concepts such as sensitivity, specificity, and predictive values. This paper explores these concepts in the context of a hypothetical disease, SpringFeverItis (SFI), and evaluates the effectiveness of a new, inexpensive diagnostic test called CHEAP.

To analyze the performance of the CHEAP test, we begin by constructing a classification table based on the data provided. In a sample of 100 individuals, 32 are confirmed to have SFI through the gold standard test, which is considered perfectly accurate. Among these, the CHEAP test correctly identified 30 as positive, resulting in 2 false negatives. Conversely, of the remaining 68 individuals without SFI, CHEAP correctly identified 61 as negative, leading to 7 false positives.

Using these data, we can compute the counts of true positives (TP), false negatives (FN), true negatives (TN), and false positives (FP). The counts are as follows: TP = 30, FN = 2, TN = 61, FP = 7. These counts form the basis for calculating various diagnostic measures. Sensitivity, or the true positive rate, is critical because it reflects the test's ability to identify those with the disease. It is calculated as TP / (TP + FN) = 30 / (30 + 2) ≈ 93.75%. Specificity, the true negative rate, measures how well the test identifies those without the disease, calculated as TN / (TN + FP) = 61 / (61 + 7) ≈ 89.71%.

The percentage of all patients who received a positive CHEAP test result includes both true positives and false positives. It is computed as (TP + FP) / total = (30 + 7) / 100 = 37%. This is a marginal percentage, as it considers all tests without conditioning on disease status.

Furthermore, the proportion of false negatives among all patients tested is FN / total = 2 / 100 = 2%, which is a marginal percentage representing the proportion of actual cases missed by the test.

To address the question of a positive CHEAP test result’s reliability, we calculate the positive predictive value (PPV), which is the probability that a person actually has SFI given they tested positive. PPV = TP / (TP + FP) = 30 / (30 + 7) ≈ 81.08%. This is a conditional percentage, as it depends on a positive test result.

From this, we can interpret that a positive test has roughly an 81% chance of correctly indicating SFI presence. This statistic should reassure the patient’s parents somewhat, but it also indicates the possibility of false alarms. In practical terms, they should consider further testing or consulting with healthcare professionals for confirmation before making any decisions or expressing concern about the diagnosis.

Sensitivity, which is the probability that the test correctly identifies those with the disease, is approximately 93.75%, a measure of the test's ability to detect true cases. High sensitivity reduces the chance of false negatives, which is vital in diseases where missing a diagnosis can be dangerous.

Statistically, to evaluate whether the CHEAP test’s results are associated with actual SFI status, a chi-squared test of independence can be performed. The hypotheses are: H0 (null hypothesis): There is no association between test results and actual disease status; H1 (alternative hypothesis): There is an association. Using SPSS software, the chi-squared test computes a test statistic and p-value, which determine whether the observed associations are statistically significant at the 1% level of significance.

If the p-value obtained is less than 0.01, we reject H0 and conclude that there is a significant association between the test results and actual SFI status, indicating that the CHEAP test is informative. Conversely, a high p-value suggests little to no association, implying the test’s poor predictive capacity.

Per the principles of statistical testing, it is appropriate to perform a chi-squared test here because the data are categorical, and the sample size is sufficiently large to meet assumptions for the chi-squared approximation. The test helps quantify the strength of the association between test results and the actual disease status.

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