Statistics for the health sciences 2

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Headshot of Ted Chauvin, PhD · Associate Professor
Ted Chauvin
PhD · Associate Professor
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Headshot of Anne Grossman, MD, FACP · Assistant Professor, Medical Education and Clinical Sciences
Anne Grossman
MD, FACP · Assistant Professor, Medical Education and Clinical Sciences
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  1. Describe some of the basic statistical tests used in health care and explain how to interpret them

Calculate and interpret relative risk and odds ratios using multiple examples

Watch this Osmosis video: Relative and absolute risk

The experimental event rate (EER) is the rate that an event occurs in the experimental group. Control event rate (CER) is the rate that an event occurs in the control group. Absolute risk is the rate of events in the entire population being studied. Relative Risk (RR) is used in a study to compare the likelihood of an event occurring between two groups. Absolute risk increase (ARI) or absolute risk reduction (ARR) is the difference between the EER and the CER and is sometimes referred to as attributable risk.

Watch this Osmosis video: Odds ratio

Odds can be calculated as the number of people with a given outcome divided by the number without. The odds ratio is defined as the ratio of the odds of an event occurring in the presence of an intervention and the odds of an event occurring in the absence of an intervention.

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Question 1

A case-control study is conducted to assess the relationship between indoor tanning and uveal melanoma. A total of 1200 subjects are enrolled in the study. Half of the study participants have uveal melanoma, and half are matched controls. The investigators report that 400 of the patients with melanoma and 360 of the controls had tanned indoors.

Based on these results, which of the following is the best estimate of the odds ratio for uveal melanoma among those who have tanned indoors compared to those who have not?

The odds ratio (OR) measures the strength of association between a given exposure and an outcome of interest. This study aims to measure the association of indoor tanning (exposure) with uveal melanoma (outcome). An OR of 1 indicates no association between the exposure and the outcome, while an odds ratio greater than (or less than) 1 indicates an increased (or decreased) risk of the outcome among exposed individuals. 

Mathematically, we are calculating the ratio of the odds of the given outcome among exposed individuals and the odds of the outcome among unexposed individuals, given as:  

(A/C)/(B/D) or AD/BC
 (400/200)/(360/240) = 2/1.5  = 1.33 = 4/3  

Question 2

A placebo-controlled clinical trial is conducted to assess whether a new oral hypoglycemic agent is more effective than standard therapy. A total of 2000 patients with diabetes mellitus are enrolled and assigned to one of two groups. Half of the study participants are randomly assigned to receive the new drug, and half receive placebo. The investigators report that 100 patients receiving drug and 40 patients receiving placebo experience severe headaches.

Based on these results, which of the following is the best estimate of the attributable risk of the new drug for headaches?

Attributable risk, the amount of the risk for a given outcome (such as a side effect) that can be ascribed to a specific intervention, is calculated as the difference in the risk for that outcome between the interventional and control groups. 

In this study, the risk for severe headaches is 0.04 (40/1000) in the group receiving placebo and 0.10 (100/1000) in the group receiving the new drug.

Question 3

A randomized controlled trial is conducted to evaluate the relationship between the angiotensin converting enzyme inhibitor lisinopril and end-stage renal failure in patients with Type II Diabetes Mellitus. Patients are randomized either to lisinopril (N = 1500) or placebo (N = 1200). The results of the study show that 100 of the patients taking lisinopril developed end-stage renal failure, and 300 of the patients taking the placebo developed end-stage renal failure.

Based on this information, how many cases of end stage renal failure in a group of 600 patients with Type II Diabetes Mellitus could be prevented by treating them with lisinopril?

The attributable risk in this study is the risk in the placebo group, 300 / 1200 = 0.25, minus the risk in the losartan group, 100 / 1500 = 0.0666667. Thus, the attributable risk = 0.25 – 0.0666667 = 0.183333. Therefore, the number needed to treat is 1/0.183333 = 5.454545 patients. This means that for every 5.454545 patients treated, one death will be prevented. For the 600 patients treated, 110 deaths will be prevented. 

Question 4

An observational study in diabetics assesses the role of an increased plasma fibrinogen level on the risk of cardiac events. 130 diabetic patients are followed for 5 years to assess the development of myocardial infarction. In the group of 60 patients with a normal baseline plasma fibrinogen level, 10 develop a myocardial infarction. In the group of 70 patients with a high baseline plasma fibrinogen level, 25 develop a myocardial infarction.

Which of the following is the best estimate of relative risk in patients with a high baseline plasma fibrinogen level compared to patients with a normal baseline plasma fibrinogen level?

The relative risk (RR) or risk ratio is the ratio of the probability of an outcome in an exposed group to the probability of an outcome in an unexposed group.  

RR = (25/70)/(10/60) = 2.143