Moderna has announced encouraging preliminary results for their COVID-19 vaccine. In this post, I assess the available data and explain what the vaccine’s effectiveness really means. I also look at Moderna’s experimental design and examine how it incorporates statistical procedures and concepts that I discuss throughout my blog posts and books.
These concepts include experimental designs, random assignment, power and sample size considerations, controlling the false positive error rate, and the directional nature of the hypotheses being tested, amongst others.
My goal is to provide a scientist’s view of how researchers designed this experiment, analyzed the data, and obtained the results.
Importantly, this COVID-19 vaccine is showing promising results earlier than anticipated. I’ll cover the reasons why the study was able to obtain these results early and safely.
Pfizer reportedly has a vaccine that uses similar technology and has a similar effectiveness. In this post, I primarily look at Moderna’s COVID-19 vaccine. However, much of the discussion also applies to Pfizer’s COVID-19 vaccine.
COVID-19 mRNA Vaccines
Vaccines teach your immune system to recognize an infection more quickly than it would naturally, allowing you to start fighting the virus before it replicates widely. Most vaccines work by introducing either a dead or weakened virus that your immune system detects and creates antibodies for. These antibodies render viruses harmless.
Moderna and Pfizer used new technology to create an mRNA (messenger RNA) COVID-19 vaccine. This type of vaccine inserts mRNA that contains the code for your body to create the distinctive spike protein on the surface of the SARS-CoV-2 virus. Your immune system detects this protein and makes the antibody for it. If the real virus enters your system, it will have this spike protein, and the antibodies that your immune system is already producing will know to attack it immediately.
Because the mRNA creates only the spike and not the rest of the virus, there is no possibility that this vaccine can infect you.
While the creation of this new type of vaccine appears rapid, there have already been many years of development put into the mRNA vaccine platform that laid the groundwork for creating these COVID-19 vaccines.
Moderna’s COVE Phase 3 Study
The technology behind Moderna’s COVID-19 vaccine (aka candidate vaccine mRNA-1273) is new, but its experimental design uses the tried and true approach for experiments involving medications. This is a large-scale randomized study that uses blinding, a placebo, and stratification. Let’s take a look at these aspects of the experiment.
Sampling Considerations and Characteristics
In inferential statistics, the goal is to use a sample to learn about populations. Scientific studies always use inferential statistics. Why? Scientists don’t want to understand how well the vaccine (in this case) works in just their relatively small group of participants. They need to generalize the results to the larger population. Using inferential statistics, scientists can learn whether the vaccine will work in the population at large and estimate its effectiveness.
The sample must represent the target populations for which the scientists want to generalize the results. With this in mind, Moderna intentionally recruited a representative sample of racial and ethnic minority participants in the study. The sample includes a mix of younger low risk, younger higher risk, and older at-risk participants.
The study uses a stratified random sample. Stratification ensures that each stratum, or subgroup, has sufficient representation within the sample so analysts can assess each of these subgroups. For this study, the scientists want to determine both the vaccine’s effectiveness and safety for these strata.
In this study, there are three strata:
- ≥ 65 years.
- < 65 years and at increased risk for COVID-19 complications (“at risk”).
- < 65 years “not at risk” for COVID-19 complications.
Moderna calculates risk using the subjects’ relevant medical history. Their experimental plan calls for at least 25-40% of participants to be either ≥ 65 years of age or < 65 years of age and at risk.
This approach allows scientists to evaluate vaccine effectiveness and safety using a racially, ethnically, medically, and age-diverse sample. Furthermore, analysts can determine whether efficacy and safety change across these groups.
COVID-19 Vaccine Experimental Design
The experimental design has two arms, the treatment and control groups.
- Treatment: Receives one intramuscular (IM) injection of 100 micrograms (ug) mRNA-1273 on Day 1 and Day 29.
- Control: Receives one IM injection of saline solution on Day 1 and Day 29 (placebo).
The experimental design calls for approximately 30,000 participants and randomly assigns them to either the treatment or control group, split equally between the two groups. The study uses “blinding”—neither the researchers nor participants know their group membership. Blinding helps prevent conscious or unconscious biases in an experiment. These biases can affect care, attitudes, assessments, and ultimately the final results.
The random assignment is crucial because it allows the study to determine whether the vaccine causes a reduction in the number of COVID-19 infections. Randomization helps avoid the problems associated with correlation not implying causation. If the scientists used a non-random process for assigning subjects to the experimental groups, that process might explain the results at the end rather than the vaccine itself!
For more information about randomization, read my post about using random assignment in experiments.
Related post: Control Groups in Experiments
Experimental Definition of COVID-19 Infections
Because this experiment assesses the vaccine’s effectiveness for reducing the number of COVID-19 infections, it has a rigorous, operational definition for what counts as an infection. This study assesses only symptomatic COVID-19 cases.
To count as a COVID-19 infection in this experiment, the participant must experience:
- At least TWO of the following systemic symptoms: Fever (≥ 38ºC), chills, myalgia, headache, sore throat, new olfactory, and taste disorder(s).
- OR at least ONE of the following respiratory symptoms: cough, shortness of breath, or difficulty breathing.
- OR have clinical or radiographical evidence of pneumonia.
AND the participant must have at least one NP swab, nasal swab, or saliva sample (or respiratory sample, if hospitalized) positive for SARS-CoV-2 by RT-PCR.
In short, the subject must have symptoms plus a positive test result.
Power and Sample Size Analysis for the COVID-19 Vaccine’s Effectiveness
In statistics, we talk about the statistical power of the design. Power is the probability that a hypothesis test will detect an effect in a sample when that effect exists in the population. Bear in mind that, because we’re working with samples, an effect in the population might not be evident in a random sample drawn from that population. Obviously, you want to avoid a false negative like that! Hence, it’s crucial to perform a power and sample size analysis before the study.
For more information, read my post about power and sample size analysis.
The primary metric in this experiment is vaccine effectiveness. The researchers want to determine whether this vaccine is effective in reducing COVID-19 infections. I’ll discuss vaccine effectiveness in more detail in later sections.
During the initial power and sample size analysis, the scientists estimated a sample size and devised an experimental design allowing the study to have a good chance of detecting vaccine effectiveness.
Specifically, the researchers used a planning value of 60% effectiveness for their power analysis. They estimated that 151 COVID-19 cases would yield a 90% chance of rejecting the null hypothesis if the vaccine is at least 60% effective in the population.
Statistical Analysis of the COVID-19 Vaccine Data
Let’s look at their plans for the statistical analyses and then we’ll move on to a discussion about the preliminary results and vaccine effectiveness.
The statistical hypotheses for this study are the following:
- Null: Vaccine effectiveness is ≤ 30%.
- Alternative: Vaccine effectiveness is > 30%.
The test is one-sided test, hence the greater than and less than signs in the hypotheses. This test determines whether vaccine effectiveness in the population is greater than 30%. You’ll remember that the analysts used a planning value of 60% effectiveness in the power analysis. However, that is the effect’s point estimate. The lower bound of the confidence interval incorporates a margin of error below the point estimate. The analysts estimate that a point estimate of 60% equates to a lower bound of 30%.
The study will produce significant results if the lower CI bound is greater than 30%.
Type of Regression Analysis for the Vaccine Study
To analyze the COVID-19 vaccine data, statisticians will use a stratified Cox proportional hazard regression model to assess the magnitude of the difference between treatment and control groups using a one-sided 0.025 significance level.
Analysts frequently use this type of model in medical settings to evaluate the reduction in risk associated with a treatment while incorporating patient characteristics and risk factors. By including these other relevant factors, the model can control for the other variables and avoid confounding, which occurs when another factor actually causes the observed treatment effect. Additionally, analysts can include interaction terms to determine whether vaccine effectiveness varies by these factors. For example, is vaccine effectiveness lower in older people?
Vaccine effectiveness is a hazard ratio, making this a great type of regression model to assess it. More on vaccine effectiveness in the results sections! Learn more about Hazard Ratios.
Interim Assessments and Mitigating the Risk of False Positives (Type I Errors)
In this experiment, a Type I error occurs when the statistical analysis produces statistically significant results but the vaccine is not effective in the population. This type of false positive is dangerous because it indicates the vaccine is effective against COVID-19 when it is not. Fortunately, the experimental design incorporates several statistical methods that mitigate this risk.
In clinical studies like this one, clinicians like to assess interim data. If the test produces significant results before the experiment ends, they can use the treatment earlier than otherwise. In this study, analysts evaluate the data at several points while accumulating COVID-19 cases over time. However, when you assess the data multiple times, it increases the Type I error rate (false positives).
Fortunately, this experiment uses the O’Brien-Fleming approach to control the Type I error rate so that it does not increase due to the multiple assessments. This method controls the false positive rate so that it equals the significance level. It is similar in concept to using post hoc tests for ANOVA that control the error rate for multiple comparisons between groups. In this scenario, the O’Brien-Fleming method controls the error rate to account for multiple data assessments.
The study also uses a significance level of 0.025 for their one-sided test. This value is lower than the standard significance level of 0.05 and it reduces the Type I/false positive error rate. Presumably, they’ve lowered the significance level to counteract the problem of increased false positives in the direction of interest with one-tailed tests.
Moderna’s COVID-19 vaccine (and Pfizer’s) produced statistically significant results during an interim analysis. Fortunately, their design allows them to assess the results early without increasing the false positive risk. Consequently, their vaccine will likely receive emergency use authorization in the United States and elsewhere earlier than if they had to wait until the study’s end.
Statistical Results: COVID-19 Vaccine Effectiveness and Safety Interim Analysis
The full data and analyses are currently unavailable, but we can evaluate their interim analysis report. Moderna (and Pfizer) are still assessing the data and will present their analyses to Federal agencies in December 2020.
Moderna reports that in the approximately 30,000 subjects, there were the following counts of COVID-19 cases:
- Vaccine: 5 (0 severe)
- Control: 90 (11 severe)
Both groups should have approximately the same number of participants. There are about 30,000 subjects, and the researchers split them evenly between the two groups. While attrition rates were likely a bit unequal, the group sizes should be roughly equal with about 15,000 in each. Using a simple visual assessment, you can see that the vaccine group had many fewer cases and no severe COVID-19 cases.
COVID-19 Effectiveness in Detail
Let’s see how analysts use these counts to calculate vaccine effectiveness! As I mentioned earlier, vaccine effectiveness is a hazard ratio. Typically, hazard ratios in medical studies are the probability of an event occurring in the treatment group divided by the probability of the event in the control group. Vaccine effectiveness calculations subtract the hazard ratio from one, as shown below:
As the numerator of the ratio decreases relative to the denominator, the value of that ratio decreases. Because we’re subtracting the ratio from 1, a smaller ratio produces a value close to 1 or 100%. For this study, a smaller probability in the numerator relative to the denominator indicates that the vaccine reduces COVID-19 infections. Just by looking at the numbers, we know this is true.
Now, let’s use the reported number of cases and an estimated sample size of 15,000 per group to calculate vaccine effectiveness!
The Data Safety and Monitoring Board (DSMB) also reported that these findings are statistically significant. Statistical significance indicates the data favor the theory that this effect exists in the population. In other words, we have reason to believe that using the vaccine on people outside the experimental sample will reduce the prevalence of COVID-19 infections in the overall population.
Moderna is still collecting safety data. Before the FDA can approve the vaccine, it must be demonstrably safe and effective. As of now, the DSMB reports that participants tolerate the vaccine well, and it did not identify any significant safety concerns. The most common side effects are typical for vaccinations: pain at the injection site, fatigue, and aching muscles and joints.
How this COVID-19 Vaccine Study Obtained Early Results
I showed how using the O’Brien-Fleming method allowed the experimenters to assess the data early without increasing the false positive rate. That was instrumental for being able to produce these significant results at this interim point.
The higher than expected vaccine effectiveness also plays a role. The study’s analysts used a planning value of 60% effectiveness for the power and sample size calculations. However, the actual effectiveness is much higher at 94.5%. This higher value is easier for the hypothesis test to detect.
Additionally, the study planned to assess the data at intervals defined by the number of cases in their sample. Because COVID-19 is spreading faster in communities than expected, the study obtained these prespecified case counts earlier than anticipated. While this faster spread is unfortunate, it has a silver lining. It allowed these vaccine studies to prove their effectiveness more quickly.
In short, the analytical procedures, higher effectiveness, and the rapid community spread of COVID-19 allowed this study to demonstrate that the vaccine is effective earlier than initially anticipated.
For an interesting comparison to flu vaccinations, read my post about the effectiveness of flu shots!
Moderna’s Phase 3 COVE Study of mRNA-1273 website with study protocol documentation