A new Annals of Internal Medicine article describes a study that compares two employer-sponsored financial incentive programs for promoting weight loss among obese employees. I first read about the article at the Pacific Standard. The study design is a randomized controlled prospective trial. The two programs are as follows:

1. Program 1. Obese employees are given a monthly weight loss goal. If the goal is reached, the participant receives $100, otherwise the employer keeps the money. This is called the individual incentive.
2. Program 2. Obese employees are organized into groups of five, and each participant is given a montly weight loss goal. A sum of $500 dollars is evenly split among those participants who achieve their monthly weight loss goal. In the event that no participant achieves their montly goal, the employer keeps the incentive money. This is called the group incentive.

The researchers found that the group incentive was associated with greater average weight loss than the individual incentive. This result is especially interesting from a psychological perspective, but I was most drawn to the issue of cost. I found it odd that the authors focused on the fact that "both designs used the same up-front allocation of resources". Presumably, this is to argue that the second program was more effective at no additional up-front cost. For example, the authors write: "Similar to that in the individual-incentive group, the up-front allocation of incentives for meeting weight-loss goals was $100 per participant per month (totaling $21 000)." But, the authors later write that, over a 24 week period: "Mean earnings were $514.70 (SD, $522.60) in the group-incentive group and $128.60 (SD, $165.50) in the individual-incentive group (mean between-group difference, $386.10 [CI, $201.00 to $571.30]; P < 0.001)." Hence, it's clear that the second program is more expensive, as one might expect. It's also a little odd that the study consisted mostly of women (89%). The allocation of race/ethnicity was also somewhat imbalanced. I like that the authors used confidence intervals throughout to summarize the differences in average weight loss (and incentive earnings) between groups. They also used p-values, but I think this was unnecessary. The authors used multiple imputation for missing weights at 24 and 36 weeks. I've always had trouble accepting multiple imputation of outcomes, because the imputation depends so heavily on the method and model used for imputation. In the appendix, the authors write that weight was imputed "adjusting for incentive group, age, sex, race, education, household income, baseline weight, importance of controlling weight, and confidence in controlling weight". No additional details are given about the model, although the software used to implement the method is listed (SAS PROC MI and MIANALYZE). Finally, I felt this senctence was incomplete: "To maintain the type I error rate while testing the 3 hypotheses of primary interest, we used a Bonferroni correction to define an α of 0.0167 as our threshold for statistical significance." The authors neglected that this approach attempts to control the familywise type I error rate. This is an important omission.