BMR 617: Statistical Techniques for the Biomedical Sciences

Relative and Attributable Risks

Recall how to classify relationships between two variables.

When we look at relationships between two variables, one variable will be the response variable while the other will be an explanatory variable.

Each variable will either be categorical (C) or quantitative (Q).

Therefore, we have four possibilities:

Categorical explanatory variable, quantitative response : C-Q
Categorical explanatory variable, categorical response : C-C
Quantitative explanatory variable, quantitative response : Q-Q
Quantitative explanatory variable, categorical response : Q-C

Understanding which of these cases you are in goes a long way to determining the analysis and presentation of the data.

Pfizer-BioNTech severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) vaccine trial

Pfizer developed a mRNA vaccine, BNT162b2, for SARS-CoV-2.

They reported the outcomes from a Phase 3 clinical trial to the FDA on December 10, 2020 (https://www.fda.gov/media/144246/download).

In this clinical trial, 18,198 participants received the vaccine, and 18,325 received a placebo (see Table 12).

Each participant received two doses in each case, which were 21 days apart.

Subjects were evaluated to determine if they became infected with SARS-CoV-2 within 7 days of the second dose.

Variables in the Pfizer-BioNTech SARS-CoV-2 vaccine clinical trial

What is the response variable in this trial?

Fever

Wheezing cough

SARS-CoV-2 status

Flu-like symptoms

Incorrect

We hypothesize that while this symptom may actually be a response from the vaccine being tested, it may or may not be directly related to the main test being targeted by this clinical trial.

Correct

Is the response variable quantitative(Q) or categorical?

Categorical Response Variable

Quantitative Response Variable

Incorrect

SARS-CoV-2 status is either "Infected (Positive)" or "Not Infected (Negative)," which are categories, not quantitative measured values.

Correct. "SARS-CoV-2 status" is a categorical response variable for this clinical trial with possible values ("levels") "Infected (Positive)" or "Not Infected (Negative)."

What is/are the explanatory variable(s) in this trial?

Age and Sex

Treatment

Race

Socio-economic status

Incorrect

While this may indirectly affect the response variable, for this clinical trial, most of the cases and controls have been matched for this variable.

Incorrect

While these may indirectly affect the response variable, for this clinical trial, most of the cases and controls have been matched for these variables.

Correct. "Treatment" is the important categorical explanatory variable for this clinical trial with possible values "vaccine" or "placebo."

Since both explanatory and response variables are categorical, this is an example of a “C-C” case or relationship.

The aim of the study is to see if treatment affects SARS-CoV-2 status.

Pfizer-BioNTech BNT162b2 clinical trial design: discussion

The primary outcome for the trial was SARS-CoV-2 status seven days after the second dose.

Why do you think this outcome (particularly the time period) was chosen?
What are the pros and cons of choosing this as the primary outcome?
Are there any mitigating factors to any of the cons?

Pfizer-BioNTech BNT162b2 clinical trial results

Of the 18325 subjects receiving the placebo, 162 were infected with SARS-CoV-2 within a week of the second dose.

Of the 18198 subjects receiving the vaccine, 8 were infected with SARS-CoV-2 within a week of the second dose.

Data for "C-C" type studies are usually presented in a contingency table.

		Treatment
		Placebo	Vaccine	Total
SARS-CoV-2 status	Infected	162	8	170
SARS-CoV-2 status	Not Infected	18163	18190	36353
	Total	18325	18198	36523

Summarizing contingency table data

There are a number of measures of interest from the contingency table data.

For a randomized trial such as this, we can measure the risk for each treatment group.

The risk is the number with the “bad” outcome, out of the total.

The risk for the placebo group is 162/18325 = 0.00884038 = 0.88404%.

What is the risk for the vaccine group?

8/18190 = 0.0004398 = 0.04398%

8/18198 = 0.00043961 = 0.04396%

170/36523 = 0.0046546 = 0.46546%

170/36353 = 0.00467637 = 0.46764%

Incorrect

Check again. The risk is the number with the "bad" outcome, out of the total.

Correct

Relative Risk

The relative risk is the risk in one group as a ratio of the risk in the other group.

The relative risk for the vaccine group (compared to the placebo group) is 0.0004396/0.0088404 = 0.049726 = 4.9726%

So those who received the vaccine have only about 5% of the risk of those who received the placebo.

This is essentially the statement that Pfizer made that the vaccine is 95% effective.

Attributable risk

The attributable risk is the difference in risk between the two groups

So the attributable risk for the placebo group is 0.88404% - 0.04396% = 0.84%.

If you are in the placebo group (i.e., if you don’t get the vaccine), you have a 0.884% chance of getting SARS-CoV-2 in the four-week timespan represented by the study.

Of that 0.884% risk, 0.84% is attributable to the fact that you did not receive the vaccine.

Note that this is not readily interpretable in this case.

The attributable risk over a more realistic timeline is likely much higher.

Number Needed to Treat

The number needed to treat (NNT) is, in this case, the number of people who need to be vaccinated to prevent one person getting infected with SARS-CoV-2 in the time span of the trial.

NNT is the reciprocal of attributable risk

In this case, NNT = 1/0.84% = 1/0.0084 = 119.

Note that this is really over a very short time span. The number needed to treat to prevent one person being infected over a more realistic time span is likely much smaller.

In March 2021, approximately 220,000 people in WV had been vaccinated.
This represents about 1848 people saved from infection per four-week time span since vaccination.
At a mortality rate of ~2%, it had saved at least 37 lives.

As of January 30, 2022, approximately 1,006,201 people in WV had been vaccinated.
This represents about 8453 people saved from infection per four-week time span since vaccination.
At a mortality rate of ~2%, this had saved at least 169 lives.