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I have survey data, with weights that adjust the sample to be nationally representative, from two time points. There is a binary presence/absence variable. Presence increases from time 1 to time 2. I would like to put a confidence interval around the percentage increase. This would be a risk ratio confidence interval, which is straightforward unweighted. But, I can't find any method for a risk-ratio confidence-interval that allows weighting. Is there any known? An R implementation would be ideal.

As a crude method I have thought of calculating confidence intervals around the proportion at time 1 and proportion at time 2, for which weighted methods do exist (https://onlinelibrary.wiley.com/doi/abs/10.1002/sim.4780131009) and then using ratios between these intervals. But (a) I don't know an R implementation, and (b) I don't know how valid this would be be.

Help much appreciated!

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  • $\begingroup$ Make sure you really want risk ratios. They have multiple drawbacks including (1) a zero-order problem where the ratio varies wildly depending on you take ratios of proportions of presence vs. ratios of proportions of absence and (2) a first-order problem where the ratio must vary as a function of the reference class's risk. On (2) a risk ratio of 2 cannot apply to a base risk > 0.5. You can easily get odds ratios for weighted data using weighted logistic regression depending on how you handle correlations over time. $\endgroup$ – Frank Harrell Jul 14 '19 at 10:47
  • $\begingroup$ @FrankHarrell Thanks for the point, I'm definitely after risk ratio. They have drawbacks but so do odds ratios, especially for a lay audience. Lay audiences general cope better with statements like "the behaviour was twice as common at time 2". $\endgroup$ – Amorphia Jul 16 '19 at 10:49
  • $\begingroup$ I've found over time that it's a mistake to choose a more problematic measure just to please an audience. I always choose the best measure and take time to explain it and to compare with measures they may be more familiar with. $\endgroup$ – Frank Harrell Jul 16 '19 at 11:24
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I've now done it by bootstrapping, where I used the survey weights as sampling probabilities for by bootstrap samples. I'm not 100% certain this is valid but I have a strong hunch that this is probably OK.

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