Influenza Vaccination of Healthcare Workers: Critical Analysis of the Evidence for Patient Benefit Underpinning Policies of Enforcement

Background Four cluster randomized controlled trials (cRCTs) conducted in long-term care facilities (LTCFs) have reported reductions in patient risk through increased healthcare worker (HCW) influenza vaccination. This evidence has led to expansive policies of enforcement that include all staff of acute care hospitals and other healthcare settings beyond LTCFs. We critique and quantify the cRCT evidence for indirect patient benefit underpinning policies of mandatory HCW influenza vaccination. Methods Plausibility of the four cRCT findings attributing indirect patient benefits to HCW influenza vaccination was assessed by comparing percentage reductions in patient risk reported by the cRCTs to predicted values. Plausibly predicted values were derived according to the basic mathematical principle of dilution, taking into account HCW influenza vaccine coverage and the specificity of patient outcomes for influenza. Accordingly, predicted values were calculated as a function of relevant compound probabilities including vaccine efficacy (ranging 40–60% in HCWs and favourably assuming the same indirect protection conferred through them to patients) × change in proportionate HCW influenza vaccine coverage (as reported by each cRCT) × percentage of a given patient outcome (e.g. influenza-like illness (ILI) or all-cause mortality) plausibly due to influenza virus. The number needed to vaccinate (NNV) for HCWs to indirectly prevent patient death was recalibrated based on real patient data of hospital-acquired influenza, with adjustment for potential under-detection (5.2-fold), and using favourable assumptions of HCW-attributable risk (ranging 60–80%). Results In attributing patient benefit to increased HCW influenza vaccine coverage, each cRCT was found to violate the basic mathematical principle of dilution by reporting greater percentage reductions with less influenza-specific patient outcomes (i.e., all-cause mortality > ILI > laboratory-confirmed influenza) and/or patient mortality reductions exceeding even favourably-derived predicted values by at least 6- to 15-fold. If extrapolated to all LTCF and hospital staff in the United States, the prior cRCT-claimed NNV of 8 would implausibly mean >200,000 and >675,000 patient deaths, respectively, could be prevented annually by HCW influenza vaccination, inconceivably exceeding total US population mortality estimates due to seasonal influenza each year, or during the 1918 pandemic, respectively. More realistic recalibration based on actual patient data instead shows that at least 6000 to 32,000 hospital workers would need to be vaccinated before a single patient death could potentially be averted. Conclusions The four cRCTs underpinning policies of enforced HCW influenza vaccination attribute implausibly large reductions in patient risk to HCW vaccination, casting serious doubts on their validity. The impression that unvaccinated HCWs place their patients at great influenza peril is exaggerated. Instead, the HCW-attributable risk and vaccine-preventable fraction both remain unknown and the NNV to achieve patient benefit still requires better understanding. Although current scientific data are inadequate to support the ethical implementation of enforced HCW influenza vaccination, they do not refute approaches to support voluntary vaccination or other more broadly protective practices, such as staying home or masking when acutely ill.

Figure illustrating the effects of a discount coupon for "60%-off" a featured chicken item: Grocery cart example: discount coupon for "60%-off" a featured chicken item: In the above grocery cart example consisting of three $10 chicken items (total value $30), sundry other non-chicken meat (valued at $60), and non-meat items (valued at $210) the all-item grocery bill without the discount coupon is $300.
The chicken items targeted by the "60%-off" coupon represent one third ($30/$90=33%) of overall meat items purchased and a smaller proportion ($30/$300=10%) of the all-item (meat and nonmeat) grocery bill. As additional items against which the chicken coupon has no effect are added to the grocery cart (i.e. as chicken comprises a smaller proportion of the all-item grocery bill), the chicken coupon provides a lower percentage reduction on the total shopping bill.
In accordance with the principle of dilution, the coupon that is effective for 60% reduction off the cost of all three $10 chicken items (i.e. an $18 saving on the total $30 chicken cost) confers a lower 20% reduction in relation to the cost of overall meat items (i.e. $18/$90) and even lower 6% reduction in relation to the all-item grocery bill (i.e. $18/$300).
Percentage reduction also varies with coupon coverage. If the "60%-off" discount coupon were only "good for" a single $10 chicken purchase rather than all three chicken items in the cart, then percentage reductions would be adjusted accordingly in relation to the reduced coupon coverage (by one-third). There would instead be 20% reduction in relation to the total chicken cost (i.e. $6/$30), 7% reduction in relation to overall meat cost (i.e. $6/$90) and 2% reduction in relation to the allitem grocery bill (i.e. $6/$300).

Indication of error based on the principle of dilution
In measuring coupon effects, the percentage reduction must always be proportional to the dilution of the featured item by non-featured items in the grocery cart and to the coverage of featured items by the coupon (e.g. all chicken items or limited to only one or two or some other proportion of all chicken items purchased). Where this is not observed, there is a de facto error.
If at the check-out counter, the cashier takes the "60%-off chicken" coupon that the customer provides, and charges the customer only $120 on a full grocery cart bill originally valued at $300 (a 60% reduction in the all-item grocery cost rather than "60%-off" chicken items) then the customer knows there has been an error.
The customer may be very pleased to accept this error at face value but no matter how many times the cashier or others may insist that this is due to the rebate given by the coupon, the customer would know that it is impossible to legitimately attribute to the coupon. A "60%-off" coupon specific for chicken cannot possibly give "60%-off" the cost of a total grocery bill inclusive of other nonchicken items, and the more that other items contribute to the total grocery bill, the less possible this can be. The effects of the discount coupon specific for a featured product must always decrease as more non-featured items contribute to the grocery bill.

Relevance to influenza vaccine benefit
The same principle of dilution applies in attributing percentage reductions in non-specific outcomes to influenza vaccination. Influenza vaccine is only effective against influenza virus and provides no benefit against other causes of illness or death unrelated to influenza virus. As more non-influenza causes contribute to the outcome considered, the lower must be the percentage reduction attributed to vaccine effects. Where that is not observed, there is a de facto error in claiming vaccine benefits.
In the above example, instead of "chicken" substitute the word "influenza"; instead of "coupon" substitute the word "vaccine"; instead of "overall meat items" substitute the word influenza-like illness (ILI); and instead of "all-item grocery bill" substitute "all-cause mortality" and the same pattern would have to be true.
The percentage reduction from the rebate (coupon or vaccine) must always be higher in relation to the outcome that is specifically targeted (chicken or influenza) and lower as more non-targeted (nonspecific) conditions (all-item groceries or all-cause mortality) are included in summarizing benefit.
In our manuscript, the plausibility of percentage reductions reported in non-specific patient outcomes (i.e. ILI and all-cause mortality) attributed to differences in healthcare worker influenza vaccine coverage are examined in detail based on this universal and basic mathematical principle of dilution.