Summary
- I calculated zinc supplementation during colds is worth it for an annual net income above 6.85 k$.
- Taking cheap supplements of debatable benefits may be worth it sometimes, but not always. I would like to see a greater focus on cost-benefit analyses to determine the break-even conditions.
Methods and results
Overview
Here are my calculations.
I calculated zinc supplementation during colds is worth it for an annual net income above 6.85 k$. I estimated this from the ratio between:
- An annual cost of zinc supplementation during colds of 12.4 $.
- A relative increase in the annual net income due to zinc supplementation of 0.181 %.
Relative increase in the annual net income due to zinc supplementation
I calculated zinc supplementation of 134 mg/d during colds decreases their duration by 0.750 d/cold. I got this from a weighted mean between:
- My prior of 0 days.
- An estimate of 2.25 days from Wang et al. (2020). “Based on pooled results from the 6 studies,36,38–42 cold duration was estimated to be reduced by 2.25 days (95% CI: −3.39, −1.12) when zinc lozenges used to manage cold, compared with a placebo (Figure 3)”.
I used weights of 2/3 and 1/3 for my prior and empirical estimate. I obtained the reference dose of 134 mg/d from the mean between estimates for the daily doses of the 6 relevant studies analysed in Wang et al. (2020).
I guess I have 3.5 colds per year. So I concluded the aforementioned zinc supplementation would spare me 2.63 days with a cold per year.
I speculated the effect of zinc supplementation is proportional to the logarithm of 1 plus the daily dose of zinc in g. So I inferred my prospective zinc supplementation of 100 mg/d decreases the duration of colds 75.7 % as much as the aforementioned dosage, thus sparing me 1.99 days with a cold per year.
I supposed having a cold has an effect equivalent to decreasing my net income by 1/3 of the net income regarding the period with the cold. This implies my prospective zinc supplementation gives me 0.662 extra days of net income per year, which amounts to an increase in the annual income of 0.181 %.
Annual cost of zinc supplementation during colds
A supplement of zinc I could take costed 6.54 $/g on 23 March 2025. For my daily dose of 0.1 g, which corresponds to 4 capsules, the daily cost of the supplement is 0.654 $.
I estimated taking the supplement costs me 10 s each day. I took 40 s to take the last 4 of 5 supplements after my lunch on 3 March 2025. I am interested in the time saved by taking one less supplement, so the longer time required to take the 1st does not matter. I assumed losing 1 h has a cost of 20 $. So I ended up with a cost of spending time taking the supplement of 0.0556 $/d.
The above lead to a daily cost of 0.710 $. 92.2 % comes from the supplement, and 7.83 % from the time taking it.
I guess my colds last 5 d/cold, which means 17.5 days per year with a cold. This translates into an annual cost of zinc supplementation during colds of 12.4 $/year.
Discussion
Taking cheap supplements of debatable benefits may be worth it sometimes, but not always. I would like to see a greater focus on cost-benefit analyses to determine the break-even conditions.
