Sample
We implemented a factorial experiment within HaBIDS, an online panel to assess preventive behaviour regarding infectious diseases (10,11). In brief, 26,895 individuals (15–69 years old) from four districts in Lower Saxony, Germany were invited, of which 9% participated in the panel. In February 2016, the questionnaire about allocation of scarce medical resources (Additional File 1) was activated; 1,037 participants were still enrolled in HaBIDS at that time.
Of those, 878 individuals participated in this factorial experiment. Compared with the sampling frame (the four districts in Lower Saxony), the participants of this study were older (median age group 50–54 years vs. 40–44 years in the sampling frame), more likely to be female (59.9% vs. 50.0%), more likely to have a university degree (41.8% vs. 13.5%), and more likely to be married (59.0% vs. 46.7%).
Factorial experiment
Participants were presented with a hypothetical resource allocation problem concerning an STI that is spreading in a city. Participants were 1:1 randomly assigned to a scenario where either prevention (vaccination) or treatment (cure) should be distributed.
The description stated that inhabitants differ in how often they change sex partners and how often they have several sex partners at the same time (information corresponding to results from the Natsal study (12)). Participants were randomly assigned to one of 6 combinations, based on a 2 × 3 factorial design (Figure 1): time until death as indicator of severity of the disease (5 years vs. 15 years) × model-based information on expected population-level effects of each allocation scheme (number of the avoided deaths in two versions as described below vs. no information) The two factors were randomized independently from each other.
Participants were asked to choose among the following options for allocation: “random allocation” (i.e., equal treatment), “young individuals first” (i.e., prioritarianism), “promiscuous individuals first” (i.e., utilitarianism in the case of this STI), “individuals with long-lasting partnerships first” (i.e., individual behaviour), or “undecided”. In the scenario “treatment”, an additional option “first come, first served” was given because the waiting-list principle is often applied to (expensive) treatments, but usually not to (non-expensive) vaccinations. We excluded allocation schemes based on instrumental value or monetary contribution because these are not applicable to STI.
For the model-based information on expected population-level effects, there were three options: no information, or one of two versions of information on the effects of the various allocation schemes. The information consisted of a bar chart (Additional File 1): The top bar showed the expected number of deaths in the absence of treatment. Then, for each allocation scheme, a bar showed the expected number of deaths if the treatment was distributed according to this scheme. The expected numbers of deaths were based on the results of a simple compartmental model of the disease dynamics. The two versions of the information differed only in the top bars of the bar chart: One version showed that in the absence of treatment, 10,000 inhabitants would die while the other stated that 20,000 inhabitants would die (Additional File 1). All other numbers of deaths (i.e., all other bars) were equal for both versions, so that in the version with 10,000 deaths the relative differences between various allocation schemes appeared substantially larger, while in the version with 20,000 deaths the various allocation schemes appeared more similar to each other (but more different from the scenario with no treatment).
Sample size
We aimed to investigate any difference in the distribution of the choices of allocation schemes dependent on the randomization factors. We estimated that 500 participants per scenario (i.e., 1,000 participants in total, corresponding to the size of the HaBIDS panel), would allow us to achieve at least 95% power in a chi-squared test if there was a medium or large effect (Cohen’s effect size index (13) w = 0.3 or w = 0.5, respectively).
The 1:1 randomization resulted in 441 participants in the scenario “prevention” (Additional File 2) and 437 participants in the scenario “treatment” (Additional File 3).
Statistical analysis
The influence of each factor on the choice of allocation scheme was investigated with Pearson's chi-squared tests. The factor “model-based information on expected population-level effects” was entered as no information vs. any additional information for the primary analysis. To assess if there was any interaction between the two factors, we investigated the influence of the factor “time until death” on the choice of allocation schemes separately in the subgroups “No info” and “Additional info”.
To investigate if the number of deaths in the event of no treatment influences the choice of allocation scheme by making the differences between them appear larger or smaller, the two versions of the factor “model-based information on expected population-level effects” were analysed with chi-squared tests among the participants who had received any additional information. All analyses were performed with R (14) version 4.0.4.
Qualitative analysis
In a free text field, participants were also asked to give the reason for their choice of allocation scheme within the factorial experiment. These responses were evaluated with a modified and extended structured content analysis according to Mayring (15). They were presented to three independent researchers who developed a category system with subcategories, which was further elaborated with the help of an external researcher. Three researchers, one of whom was not involved in the previous process, applied the category system independently. Intercoder reliability was calculated by using Krippendorff's alpha (16), which indicates the overall match of the three encoders (0 = no match, 1 = perfect match). A consensus was found for any nonmatching categorizations according to pre-established rules by two researchers to determine the final classification. The structured content analysis revealed four categories with a total of eight subcategories (Additional File 4). Krippendorff's alpha among the three encoders was lowest for “condemnation of a particular lifestyle” (0.51) and highest for “minimize risks/number of deaths” (0.83).