How often does correlation=causation?
"Choosing between randomised and non-randomised studies: a systematic review", Britton et al 1998 http://www.journalslibrary.nihr.ac.uk/__data/assets/pdf_file/0009/64827/FullReport-hta2130.pdf (summary: http://www.ncbi.nlm.nih.gov/pmc/articles/PMC1126943/?report=classic ):
"This review explored those issues related to the process of randomisation that may affect the validity of conclusions drawn from the results of RCTs and non-randomised studies.
...Previous comparisons of RCTs and non-randomised studies: Eighteen papers that directly compared the results of RCTs and prospective non-randomised studies were found and analysed. No obvious patterns emerged; neither the RCTs nor the non-randomised studies consistently gave larger or smaller estimates of the treatment effect. The type of intervention did not appear to be influential, though more comparisons need to be conducted before definite conclusions can be drawn.
7 of the 18 papers found no [statistically-]significant differences between treatment effects from the two types of study. 5 of these 7 had adjusted results in the non-randomised studies for baseline prognostic differences. The remaining 11 papers reported [statistically-significant] differences which are summarised in Table 3.
7 studies obtained differences in the same direction but of significantly different magnitude. In 3, effect sizes were greater in the RCTs.
...However, the evidence reviewed here is extremely limited. It suggests that adjustment for baseline differences in arms of non-randomised studies will not necessarily result in similar effect sizes to those obtained from RCTs."
"Choosing between randomised and non-randomised studies: a systematic review", Britton et al 1998 http://www.journalslibrary.nihr.ac.uk/__data/assets/pdf_file/0009/64827/FullReport-hta2130.pdf (summary: http://www.ncbi.nlm.nih.gov/pmc/articles/PMC1126943/?report=classic ):
"This review explored those issues related to the process of randomisation that may affect the validity of conclusions drawn from the results of RCTs and non-randomised studies.
...Previous comparisons of RCTs and non-randomised studies: Eighteen papers that directly compared the results of RCTs and prospective non-randomised studies were found and analysed. No obvious patterns emerged; neither the RCTs nor the non-randomised studies consistently gave larger or smaller estimates of the treatment effect. The type of intervention did not appear to be influential, though more comparisons need to be conducted before definite conclusions can be drawn.
7 of the 18 papers found no [statistically-]significant differences between treatment effects from the two types of study. 5 of these 7 had adjusted results in the non-randomised studies for baseline prognostic differences. The remaining 11 papers reported [statistically-significant] differences which are summarised in Table 3.
7 studies obtained differences in the same direction but of significantly different magnitude. In 3, effect sizes were greater in the RCTs.
...However, the evidence reviewed here is extremely limited. It suggests that adjustment for baseline differences in arms of non-randomised studies will not necessarily result in similar effect sizes to those obtained from RCTs."