key: cord-1010051-x79p4mgl
authors: Tentori, K.; Passerini, A.; Timberlake, B.; Pighin, S.
title: The misunderstanding of vaccine efficacy
date: 2021-07-27
journal: Soc Sci Med
DOI: 10.1016/j.socscimed.2021.114273
sha: f4202aa37835ea8e52e0230e2c056a99d06d96f9
doc_id: 1010051
cord_uid: x79p4mgl

Although the efficacies of vaccines against SARS-CoV-2, i.e., the virus that causes Covid-19, have been publicized and praised, and although they are assumed to encourage vaccine compliance, little is known about how well these figures are understood by the general public. Our study aims to fill this gap by investigating whether laypeople have an adequate grasp of what vaccine efficacy means and, if not, which misconceptions and consequences are the most common. To this end, we carried out three online behavioral experiments involving 1800 participants overall. The first, exploratory experiment, with a sample of 600 UK participants, allowed us to document by means of both an open-ended question and a multiple-choice question, a common misinterpretation of the efficacy of SARS-CoV-2 vaccines as the non-incidence rate among the vaccinated. We formally demonstrated that this error leads to a systematic overestimation of the probability of individuals who are vaccinated developing Covid-19. The second experiment confirmed the prevalence of this misinterpretation in a new sample of 600 UK and Italian participants, by means of a slightly different multiple-choice question that included more response options. Finally, in a third experiment, involving another 600 UK and Italian participants, we investigated the behavioral implications of the documented error and showed that it might undermine the general positive attitude toward vaccines as well as the intention to get vaccinated. On the whole, the results of this study reveal a general misunderstanding of vaccine efficacy that may have serious consequences for the perceived benefits of SARS-CoV-2 vaccines and, thus, the willingness to be vaccinated.

The protective effect of a vaccine is typically expressed in both scientific and popular dissemination contexts as vaccine efficacy (VE) . VE is computed based on the results of a double-blind, randomized, controlled trial in which half the subjects receive the vaccine, while the other half receive a placebo. Both groups are followed prospectively to determine their attack rates, and VE is then defined as the percentage reduction in the attack rate among vaccinated compared to unvaccinated individuals under these ideal circumstances, which corresponds to the relative risk reduction among the vaccinated as compared to the unvaccinated: 1 where ARU and ARV indicate the attack rates among unvaccinated and vaccinated groups, respectively, while RR is the relative risk of developing the disease for vaccinated compared to unvaccinated subjects.

The VE ranges from 0% (when ARV = ARU, indicating the vaccine is completely ineffective) to 100%

(when ARV = 0, indicating that the vaccine eliminates the risk entirely). For example, the efficacy of the 4 These figures are much greater than the FDA's stated acceptable threshold 5 and received enthusiastic scientific 6 and popular media coverage. 7, 8 The main questions of our study are whether the information conveyed by VE is well-understood by the general public and, if not, what the implications of possible errors are. Our concerns regarding the comprehension of VE stem from the consideration that its non-obvious meaning has often been misrepresented in mainstream and trade media, as illustrated in the following examples from Reuters and Vox (but see also 9 ,10 ):

J o u r n a l P r e -p r o o f respect: as formally demonstrated in the following section, they both imply a systematic underestimation of the benefits provided by vaccination.

To appreciate the implication of misunderstanding VE as P(not-D|V) (i.e., 1 -ARV), first consider the available data on mRNA-1273 and BNT162b2 vaccines. As stated, their VEs have been reported as 94.05%

and 95.03%, respectively, while P(not-D|V) is 99.93% for the mRNA-1273 vaccine and 99.96% for the BNT162b2 vaccine. These values indicate that, if VE is confused with the non-incidence rate among vaccinees, the attack rate of the vaccinated is overestimated by an order of magnitude: from less than 0.1% to 5-6%. Importantly, such an overestimation is not a peculiarity of the two vaccines considered. Here, we demonstrate that VE is always smaller than P(not-D|V), except for two (vanishingly rare) limit cases, in which they are equal. As illustrated, the gap between 1 -ARV and VE is maximal for small values of ARU, that is, in all (common) situations in which the incidence of a condition is rather low. Moreover, for any fixed value of ARU, the difference increases with greater ARV, that is, the less efficacious the vaccine, the greater J o u r n a l P r e -p r o o f the difference.

The left plot reports the difference between 1 -ARV and VE as a function of ARU, with each curve representing a different value of ARV (from 1% to 50%). The right plot reports the difference between 1 -ARV and VE as a function of ARV, with each curve representing a different value of ARU (again from 1% to 50%). In all cases ARV is assumed never to exceed ARU.

Let us now consider the possible confusion of VE with P(not-D|V&E). In what follows, we show that P(not-D|V&E), even if it is always smaller than 1 -ARV (except for one limit case, in which they are equal), is always larger than VE (again, except for one limit case, in which they are equal).

If everybody is exposed to the virus (i.e., P(E) = 1), then P(not-D|V&E) = 1 -ARV, otherwise (i.e., P(E) < 1), P(not-D|V&E) < 1 -ARV. If all unvaccinated individuals exposed to the virus develop the disease (i.e., P(E) = ARU), then P(not-D|V&E) = VE, otherwise (i.e., P(E) > ARU), P(not-D|V&E) > VE.

Therefore, the misunderstanding of VE as P(not-D|V&E) is simply a less-extreme version of the error of misunderstanding VE as P(not-D|V), in that both imply a systematic overestimation of the probability of developing Covid-19 among vaccinated individuals.

In this section, we report the details of two behavioral experiments, which, in both UK and Italian samples, confirmed a pervasive confusion of VE with the rate of individuals who do not develop Covid-19 among those vaccinated.

Online data collection was carried out December 10-18, 2020, through Prolific Academic (http://prolific.ac), one of the most popular and reliable crowdsourcing platforms for behavioral research. 15 There were no time limits on task completion, and the average response time was less than 2 minutes.

Participants received 0.63 British pounds, which guarantees an hourly rate in line with the Prolific compensation policy.

We recruited 600 UK residents, all native speakers of English. This sample was well-suited to the study due to their native language and their residence in one of the only countries that had begun mass vaccination at the time, as well as because the UK contingent on Prolific constitutes a particularly representative crosssection of the population, as compared to the cohorts of other countries on the platform (e.g. Italy or the USA reporting a complex definition such as that of VE. Therefore, to see whether participants were at least able to recognize the correct definition when they encountered it, we presented half with a list of response J o u r n a l P r e -p r o o f options, including a concise, though precise, formal definition of VE (i.e., the third option in the above list).

The response options comprised our target error-in the variant that could be quantified and, therefore, that could reasonably be the outcome of a clinical trial (i.e., VE as 1 -ARV)-as well as three other incorrect alternatives (for their formalizations, see Table 2 ). Notably, two of the incorrect options (four and five in the above list) refer to a comparison between experimental ("the vaccinated individuals") and control ("the unvaccinated individuals") groups, which served as a check as to whether a reference to this prerequisite of a controlled clinical trial would draw more responses that included this key component of the correct answer.

Four independent judges reviewed and coded each response to the open-ended question. Agreement was above 95%, and disagreements were solved via discussion (they concerned only a few incorrect answers, and whenever the evaluation was not unanimous, the statement was classified as "other error"). The results of classification are reported in Table 1 ; an example for each class of answer and additional classification criteria are outlined in the Appendix. Overall, the amount of correct answers or answers that expressed at least a correct intuition (even if not fully detailed) was notably low: 1% (95% CI, 0% to 2%). Another 1% (95% CI, 0% to 2%) of answers were classified as "mixed," because they contained a correct intuition (e.g., a reference to risk reduction with respect to a control group) but were nevertheless vague and/or included one or more errors. As expected, the great majority of wrong answers (77%; 95% CI, 72% to 82%) perpetrated the target error. More specifically, out of these answers, 79% (95% CI, 74% to 84%) were compatible with both variants of the error detailed in the previous section; 12% (95% CI, 8% to 16%) indicated a misinterpretation of VE as P(not-D|V), i.e., 1 -ARV; while the remaining 9% (95% CI, 5% to 13%), a misinterpretation of VE as P(not-D|V&E); for examples, see the Appendix. Errors other than the target error did not match any of the options from the multiple-choice task; they amounted to 5% (95% CI, 3% to 7%) of responses and did not form any identifiable patterns. The remaining answers were classified J o u r n a l P r e -p r o o f as reiterations (13%; 95% CI, 9% to 17%) or generic comments (3%; 95% CI, 1% to 5%). Of the 17 participants who had participated in a medical trial, two provided an answer that was classified as "mixed,"

one as a "comment," and the remaining 14 as the target error. A different distribution of responses was observed among participants with a higher (i.e., graduate degree and above) versus lower education level (i.e., less than a graduate degree), ꭓ 2 (7, N = 300) = 21.11, p = .004. Specifically, participants with a lower education level provided a greater number of answers that were classified as "reiteration or vague," compared to participants with a higher education level (21% vs. 5%, respectively, p < .001), but no difference was observed in either the number of "correct" answers (1% vs. 2%, respectively, p > .05) or target errors (72% vs. 77%, respectively, p > .05). No significant difference was observed between males and females (p > .05).

Non-incidence rate among vaccinated individuals (i.e., the two variants of the target error) 231* 77* Reiterations or vague answers (i.e., responses that re-state the question or that address only a quality or capacity of the vaccine without implying an effect on people) 37 13

Comments (i.e., responses that express opinions rather than answer the question) 9 3

Other errors (i.e., incorrect responses that differ from the error above and/or are confused) 15 5 Mixed answers (i.e., responses that suggest a correct intuition but are imprecise and/or contain additional errors) 4 1

Correct responses (i.e., responses aligned with the correct definition, even if not fully detailed) 4 1

Total 300 100 * Of the 231 answers classified as the target error, 27 clearly mentioned P(not-D|V); 22 clearly indicated P(not-D|V&E); while for the remaining 182 answers, both interpretations were possible.

The results of the multiple-choice question are reported in Frequencies and percentages for the multiple-choice options (bolded as in the presented text), with corresponding formulas (not included in the presented text).

The 

The second experiment was designed to replicate and extend the results of the first by polling a different population of participants, as well as by excluding the possibility that selections of the target error option in the multiple-choice question of Experiment 1 were boosted by the fact that it was the shortest-available option.

Online data collection was carried out April 29 -May 4, 2021, through Prolific Academic (http://prolific.ac). As with previous experiments, there were no time limits on task completion, and participants received 0.63 British pounds compensation. The average response time was 3 minutes.

We recruited a new sample of 600 participants: 300 UK residents, and 300 Italian residents, all native J o u r n a l P r e -p r o o f speakers of English or Italian, respectively. The mean age of participants was 32 years (SD = 12. 

Participants were presented with the following prompt:

In a rigorous clinical study, scientists found that a vaccine for Covid-19 has an efficacy of 90%.

Please think about how you believe scientists arrived at this figure until the next page appears.  Other (if you select this option, you will be asked to specify your answer)

Compared to the multiple-choice task of Experiment 1, three changes were introduced. First, an interval of 30 seconds was imposed between the appearance of the initial statement about the VE and the subsequent question and response options. This was intended to allow participants to independently consider the meaning of VE before seeing the response options. Second, the question and the response options were rephrased from the present tense, using the past instead, in order to emphasize that the efficacy figure   described was the result of a clinical trial. Finally, and most importantly, two new incorrect options were added to the six previously employed. This was designed to check for, and possibly to eliminate, a potential response bias in the multiple-choice task of Experiment 1, in which the target error was also the shortest statement. The two new options (the second and third from the bottom in the above list) had lengths comparable to that of the target error and, as with all the other options in the list, could technically be computed from the data of a phase 3 clinical trial (in that they are directly quantifiable from ARU and ARV).

The results of Experiment 2 are reported in Table 4 . Overall, the correct option was selected by 8% (95% significantly greater than chance, z = 12.4, p < .001) was the percentage of individuals who did not develop Covid-19 among those vaccinated (i.e., the target error, 1 -ARV). (Chance was set at 14% to account for seven detailed, alternative options.) As in Experiment 1, the second-(23%; 95% CI, 20% to 26%) and the third-most-frequent (20%; 95% CI, 17% to 23%) errors comprised, respectively, the option that outlines the difference between the rate of individuals who did not develop and who did develop Covid-19 among those vaccinated (the second option in the above list), and the option detailing the difference between the difference in the rates of vaccinated individuals who did not and who did develop Covid-19 and the difference in the rates of unvaccinated individuals who did not and who did develop Covid-19 (the fifth and longest option in the above list). The proportion of selection of each of these two options was also greater than chance (z = 6.1, p < .001, and z = 4, p < .001, for the second-and third-most-frequent errors, respectively); nevertheless, they were both selected less often than the target error (z = -2.85, p < .01 and z = -4.2, p < .001, respectively). The two new options referring to the percentage of individuals who were vaccinated among those who did not develop Covid-19, and to the percentage of individuals who were not vaccinated among those who did develop Covid-19 were selected by 8% (95% CI, 6% to 10%) and 1%

(95% CI, 1% to 2%) of participants, respectively.

No significant difference in the distribution of responses was observed between UK and Italian participants, ꭓ 2 (7, N = 600) = 12.50, p = .085, among participants with a different vaccination status, ꭓ 2 (28, N = 600) = 32.73, p = .246, between participants with higher and lower education levels, ꭓ 2 (7, N = 600) = 4.28, p = .747, between participants who had participated in a medical trial and those who had not, ꭓ 2 (7, N = 600) = 6.10, p = .528, nor between males and females, ꭓ 2 (7, N = 600) = 13.95, p = .872. (25) The difference between the percentages of individuals who did not and who did develop Covid-19 among those vaccinated minus the difference between the percentages of individuals who did not and who did develop Covid-19 among those not vaccinated In this section, we present the results of a third empirical investigation, which illustrates, in terms of vaccine acceptance, the potential implications of the misinterpretation of VE documented in Experiments 1 and 2.

Specifically, we compared, in samples of UK and Italian participants, the behavioral intention to receive a vaccine for a hypothetical new variant of the SARS-CoV-2 virus, as well as the attitude toward such a vaccine, when vaccine benefits were conveyed either with VE or with the corresponding non-incidence rate among vaccinees, i.e., 1 -ARV. For an illustration, see Figure 2 .

Based on the results of Experiments 1 and 2, our prediction was that, by misinterpreting VE as 1 -ARV, participants would underestimate vaccine benefits (at least for non-negligible values of ARV), and that, consequently, the presentation of the benefits in terms of VE rather than 1 -ARV would be associated with a weaker intention to receive the vaccine, as well as with a less-positive attitude toward the vaccine.

J o u r n a l P r e -p r o o f

Online data collection was carried out April 30 -May 5, 2021, through Prolific Academic (http://prolific.ac). Again, there were no time limits on task completion, and participants received 0.63

British pounds compensation. The average response time was 2 minutes.

We recruited a new sample of 600 participants: 296 UK residents and 304 Italian residents, all native speakers of English or Italian, respectively. The mean age of participants was 34 years (SD = 12.9), ranging from 18 to 77 years (2 participants did not declare their ages). As in Experiment 2, the UK sample was found to be significantly older than the Italian sample (Mage = 40, SD = 13.5 vs. Mage = 27, SD = 8.1, t(596)=14.48, p < .001). Across countries, females constituted 47% (50% and 44% in the UK and Italian samples, respectively), and 51% of participants had either an undergraduate or graduate degree (54% and 47% in the UK and Italian samples, respectively). As in Experiment 2, the samples recruited in the two countries differed in SARS-CoV-2 vaccination status: 52% of UK participants versus 11% of Italian participants had already received at least one dose of the vaccine, while the percentages of those unvaccinated who intended to receive the vaccine were 37% and 80%, respectively, with less than 6% of participants selecting each of the following responses: undecided, unable or unwilling to receive the vaccine.

This experiment employed a 2 x 2 (information type: VE vs. 1 -ARV; ARV level: 2% vs. 8%) betweensubjects design. All participants were presented with the following scenario: We employed an extremely high incidence rate (ARU = 20%) to encourage participants to think of this hypothetical variant of SARS-CoV-2 as a major threat. As a consequence, for the difference between VE and 1 -ARV to span a wide-enough range, ARV also had to be unusually high (from 2% to 8%). Note, however, that as shown in Figure 1 , similar differences can be found for lower values of ARU and, consequently, ARV.

In accordance with the experimental condition, participants were then presented with one of the following messages: Participants responded on an 11-point scale anchored by "definitely no" (0) and "definitely yes" (10), so that higher scores indicated greater intention to receive the vaccine. The middle point was labelled as "unsure" (6) . 

To test the hypothesis that information type and ARV level affected participants' behavioral intentions, we ran an ANOVA including the two factors as independent variables, with age, gender, education level, 007, ηp 2 = .01). As revealed by the significant interaction effect, again, the difference between the two information types was relevant when ARV was 8% but not when it was 2% (see Figure 3 ). Overall, the results of Experiment 3 indicated that, for both the UK and the Italian participants, vaccine benefits presented in terms of 1 -ARV rather than VE were associated with a greater intention to receive the vaccine and a more-positive attitude toward it when the ARV level was 8% but not when it was 2%.

Because ARU = 20% in our scenarios, these two cases correspond to a difference between 1 -ARV and VE of 32% and 8%, respectively. As shown in the left panel of Figure 1 , appreciable differences between 1 -ARV and VE can also be obtained with lower values of ARV whenever they are associated with lower values of ARU. For example, in a more likely scenario in which ARU = 5%, then an ARV = 2% would mean a difference between 1 -ARV and VE of 38%. 

Scientists and health authorities agree that mass vaccination against Covid-19 offers the most promising strategy by which to reduce deaths and, ultimately, to bring the pandemic under control. 18, 19 Yet they also warn that incidence of the disease will be lowered only if a substantial portion of the population is inoculated. [20] [21] [22] With this objective in mind, serious concerns have emerged from a number of recent studies 23-26 that indicate a vaccine acceptance rate far too low to achieve herd immunity. Vaccine hesitancy is a complex phenomenon that depends on various factors, including socio-cultural, political, and economic considerations. [27] [28] [29] In the case of SARS-CoV-2 vaccination, the major determinants of uncertainty or unwillingness to vaccinate have been reported to belong to the confidence domain, that is, a lack of trust in the safety and benefits of vaccines. 25, 26, [30] [31] [32] In our study, we considered only the perception of benefits and, more specifically, the public's understanding of VE, and we did not explore concerns about vaccine safety, itself a multifaceted issue that might well both interact with the perceived efficacy and heavily affect vaccine uptake. across countries, whose participants differed at least in native language, vaccination status and mean age.

We also formally demonstrated that the misunderstanding of VE as 1 -ARV leads to a systematic undervaluation of the personal safety benefits of the vaccine. Accordingly, in Experiment 3, we showed that this may significantly undermine the general positive attitude toward new vaccines, as well as the intention to get vaccinatedeven in individuals who have already accepted or have decided to accept a current SARS-CoV-2 vaccination, as have some participants in our experiment. It is worth highlighting that The finding that people routinely misunderstand statistical information about the benefits of various screening tests and treatments, including vaccination, is not new. In particular, it is well-known that laypeople, and even health professionals, tend to evaluate more favorably benefits expressed in terms of relative, rather than absolute, risk reductions, since they appear to be larger. [33] [34] [35] This effect has been shown to depend on the size, availability and intelligibility of the baseline risk (e.g., 36, 37 ) , and can be considered an expression of a more general tendency to discount prior probability information (base rate fallacy 38, 39 ).

The error documented in this study, however, is of a different, more substantial stripe. Indeed, when asked to interpret a relative risk reduction (VE), our participants not only failed to normalize the difference between the incidence in the control and treatment groups by the baseline risk, but, as noted in the Results section, they disregarded the incidence in the control group entirely. In this respect, the persistence of the error in the multiple-choice context is particularly striking, given that the corresponding option was one of few available that did not mention unvaccinated individuals. Also remarkable is that the second-most-frequent error in both Experiments 1 and 2, was the selection of the other option that referred exclusively to vaccinated individuals.

The result that laypeople tend to ignore the role and importance of a control group in vaccine testingeven those who have participated in a controlled clinical trial and would presumably be more mindful of this factoris a noteworthy result unto itself. By focusing on the experimental group (i.e. vaccinees) alone, laypeople appear to disregard the importance of having a term of comparison (i.e. non-vaccinees) in order to draw any reliable conclusion about the intervention (i.e. the vaccination). Such neglect of a prerequisite for a rigorous medical investigation may well affect the perceived reliability of its conclusions. Indeed, the apparent lack of basic understanding of how interventions are related to health outcomes precludes distinguishing causal evidence from other categories of empirical evidence, or even non-scientific opinions. Importantly, we are left with the question of why laypeople confuse VE with the non-incidence rate among the vaccinated. An exhaustive explanation of this error is beyond the scope of this paper, in which we limit deliberation to a general consideration and a suggestion. Although there is no doubt that such confusion is an error, the interest in 1 -ARV is not altogether misplaced, in that it represents a piece of information about individual risk that is not expressed by VE alone. Consider, for illustrative purposes, two vaccines that reduce, with the same efficacy VE1 = VE2 = 60%, the incidence of two syndromic diseases, which have broadly different incidences ARU1 = 0.25% and ARU2 = 25%. These values would correspond to 1 -ARV1 = 99.9% and 1 -ARV2 = 90%, respectively. It would appear entirely rational for an individual, in pursuit of precautionary behavior, to be interested in discriminating between these two cases, i.e., in knowing whether her probability of developing the disease when vaccinated is on the order of 0.1% or 10%.

J o u r n a l P r e -p r o o f

P(not-D|V&E) = 1 -P(D|V&E) by additivity

D|V&E) = 1 -P(D&E|V)/P(E|V) by the chain rule of probability

D|V) since exposure to the virus is a necessary condition for developing the disease

P(E) given the assumption of comparability of groups in double blind placebo-controlled trials

Field evaluation of vaccine efficacy

Vaccine epidemiology: efficacy, effectiveness, and the translational research roadmap

Efficacy and safety of the mRNA-1273 SARS-CoV-2 vaccine

Safety and efficacy of the BNT162b2 mRNA Covid-19 vaccine

Development and Licensure of Vaccines to Prevent COVID-19: Guidance for Industry

Wonderful news to wake up to': U.K. greenlights Pfizer's COVID-19 vaccine

Covid vaccine: First 'milestone' vaccine offers 90% protection

Pfizer's Early Data Shows Vaccine Is More Than 90% Effective

) 10. The Conversation. How effective does a COVID-19 coronavirus vaccine need to be to stop the pandemic? A new study has answers

Explainer: Will COVID-19 vaccines protect us? Does efficacy equal effectiveness?

Covid-19 vaccine efficacy results are not enough

What does 95% COVID-19 vaccine efficacy really mean

The Lancet Infectious Diseases. An exceptional vaccination policy in exceptional circumstances

Prolific. ac-A subject pool for online experiments

Acceptability of the H1N1 vaccine among older adults: the interplay of message framing and perceived vaccine safety and efficacy

The role of message framing in promoting MMR vaccination: Evidence of a loss-frame advantage

Ensuring global access to COVID-19 vaccines

What you need to know about a COVID-19 vaccine. Answers to the most common questions about coronavirus vaccine development

The reproductive number of COVID-19 is higher compared to SARS coronavirus

A future vaccination campaign against COVID-19 at risk of vaccine hesitancy and politicisation

COVID-19): Herd immunity, lockdowns and COVID-19

Attitudes towards vaccines and intention to vaccinate against COVID-19: Implications for public health communication

Acceptability of a COVID-19 vaccine among adults in the United States: How many people would get vaccinated?

COVID-19 vaccination intention in the UK: Results from the COVID-19 Vaccination Acceptability Study (CoVAccS), a nationally representative cross-sectional survey

Vaccine hesitancy in the era of COVID-19

Measuring trust in vaccination: A systematic review

Understanding vaccine hesitancy around vaccines and vaccination from a global perspective: a systematic review of published literature

Vaccine hesitancy: Definition, scope and determinants

Influences on attitudes regarding potential COVID-19 vaccination in the United States

A proactive approach for managing COVID-19: The importance of understanding the motivational roots of vaccination hesitancy for SARS-CoV2

The use of the health belief model to assess predictors of intent to receive the COVID-19 vaccine and willingness to pay

Using alternative statistical formats for presenting risks and risk reductions

Communicating relative risk changes with baseline risk: presentation format and numeracy matter

Breast cancer screening pamphlets mislead women

Communicating relative risk changes with baseline risk: presentation format and numeracy matter

Laypersons' understanding of relative risk reductions: randomised cross-sectional study

On the psychology of prediction

Public's understanding of swab test results for SARS-CoV-2: an online behavioral experiment during the April 2020 lockdown

Field evaluation of vaccine efficacy

Additional criteria (open-ended question, Experiment1) No distinction was made between numerically equivalent expressions articulating: -single-case

The vaccine works in 90% of cases, it doesn't work in 10% of people"), a single positive outcome type

The vaccine works on 90 out of 100 people") or as targeting infection, disease, or transmission

90% of people who received the vaccine did not get Covid-19"), or in present/future tenses the effectiveness of the vaccine

Target error Compatible with both interpretations "It will work for 90% of the people that are vaccinated" P(not-D|V) "90% of people vaccinated do not show symptoms of Covid-19" P(not-D|V&E) "Out of 100 vaccinated people exposed to Covid-19, 90 people will not contract the disease"Reiterations or vague answers "It is mostly successful"Comments "90 isn't good enough, medicine needs to be 99.9"Other errors "It stops 90% from dying"Mixed answers "90% of the people that receive the vaccine will be protected from contracting coronavirus compared to a group that is not vaccinated"Correct responses "The number of people diagnosed with Covid-19 is reduced by 90% in the vaccinated group compared to the control group"