This trial
Its aim was to see if calcium supplementation starting before conception reduced pre-eclampsia in late pregnancy. So the main analytical issue was that some (as it turned out, many) women would not get pregnant, so would not be at risk of pre-eclampsia.
In the paper they restricted the analyses to those women who were randomised, became pregnant, and reached 20 weeks gestation, which resulted in a lot of women not being in the final analysis; 1355 were randomised but only 579 were included in the analysis. Main problem is that with so many exclusions we donāt have any guarantee that the randomised groups are stil comparable; conception and early pregnancy loss could be related to the intervention.
The most obvious alternative, analysing the groups as randomised, doesnāt seem ideal either - so what would be the best way to proceed with the analysis of this and similar trials? [I have my own ideas but very interested to see what others would recommend as Iāve never seen this issue really nailed down]
Essentially the same problem crops up in other contexts e.g. neonatal outcomes after interventions in pregnancy, but it seems particularly severe in this trial because of the large numbers excluded.
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Without having any experience on pregnancy research (other than one project on opioid exposure and its relationship to birth of children with opiod withdrawal syndrome), my first thought is that one should condition only on initiation of pregnancy, and to state as an explicit assumption that Ca supplements do not change the likelihood of pregnancy. A supplemental analysis could relate treatment to time until pregnancy (censoring for those not becoming pregnant). For the primary analysis, women not reaching 20w gestation would be counted as a treatment failure, which could be one level of a multi-level ordinal outcome scale. How many women would be included in that case?
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The losses before pregnancy are listed as (in the CONSORT diagram):
did not conceive: calcium 149 placebo 167
lost to follow-up before conception 157/163
withdrew 41/27
and in addition early pregnancy loss 27/27
and a few lost during pregnancy/termination/discontinued 6/10
So an extra complication there; presumably we donāt know that the ālost to follow up before conceptionā women did not actually conceive, so thereās an unknown amount of missing data on pregnancy outcomes.
This trial came up in the context of a query about how to include these data in a systematic review. Not straightforward.
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very interesting. Also the issue with compliance: was the >80% compliance prespecified? i canāt imagine that they didnāt anticipate all of these issues beforehand: they would have identified the āfull analysis setā as per ich e9? but instead they define an itt pop? and they know the % of PE to expect. Then itās an issue of statistica power, thorough follow-up etc. I canāt help but think it would have been a much better trial if run by the industry ā¦!
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Would looking at the effect in the principal strata of those women who got pregnant under either treatment be an option? The original reference would be https://www.ncbi.nlm.nih.gov/pubmed/11890317, but there is currently a lot of research going on in this area, partly sparked by the ICH E9 addendum mentioning āprincipal stratificationā as one strategy to deal with intercurrent events. I guess it boils down how much you can model conception with baseline variables.
Recent papers are https://arxiv.org/abs/1809.03741 or https://arxiv.org/abs/1806.08807
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Thanks for sharing these references! I am thinking about this exact issue quite a lot at the moment, since I work primarily in reproductive medicine and there is a lot of interest in the effects of treatments on babies.
Eric Tchetgen Tchetgen has done a bunch of work on this: https://onlinelibrary.wiley.com/doi/pdf/10.1002/sim.6181
I think the suitability of this approach depends on whether or not you think the survivor average causal effect is a) based on reasonable assumptions and b) something anyone would really want to know.
Iām still working out whether or not I believe a). For b), I think it might depend on whether you are trying to answer a biological question or a more pragmatic one? In relation to the latter, have heard the objection that you have no idea who the always-survivors are going to be, so difficult to turn it into treatment advice. Seems more reasonable to talk of the biological effect of a treatment however. In reproductive medicine, the distinction comes down to (I think) saying ābecause of your characteristics, if any treatment gives you a baby, it will be low birthweight (say)ā on the one hand, and saying āthis intervention has had a physiological effect such that it has made your baby low birthweightā on the other. Really important to think about what question we are really interested in answering.
I am currently doing some simulations to work out the impact of this in plausible scenarios. It may not matter much in practice. If it does, the question is how to deal with it? One approach is to try to adjust for common causes of birth and birthweight (as numbersman77 said). Another I am toying with is using a selection model to jointly model birth and birthweight, using randomisation to identify. This should (?) mop up some of the unmeasured common causes of birth and birthweight, but requires an assumption to be made about the distribution of the unmeasured variables. And probably also requires some other assumptions I havenāt worked out yet!
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