I have some data that span several years: 2006-2010. I have run logistic regression to model the data. For the whole dataset, I get a 95% confidence interval for the odds ratio of a parameter of interest of
(0.34 - 0.47 )
indicating a very significant effect. However, for each individual year, with the same model specification, the confidence intervals are:
2006: (0.78 - 1.94) (not significant) 2007: (0.61 - 0.93) 2008: (0.63 - 0.90) 2009: (0.92 - 1.30) (not significant) 2010: (0.88 - 1.33) (not significant)
How can I reconcile that the confidence interval for the whole dataset is below the confidence intervals for all the individual years ? I'm guessing that it is to do with the sample sizes - bigger sample sizes leading to lower p values: I think I get the maths behind this, but I can't get the intuition behind it.
In response to the answers by Michael and Peter, I am providing more information.
The model is:
- death is binary
- treatment is binary - whether treatment A or treatment B was given. This is the parameter of interest that I have given confidence intervals for (which I obtained by exponentiating the CIs for the estimate +/- 1.96xSE )
- age is age in years
- imd is a socioeconomic status index for the patient
- smoking is categorical and has several levels pertaining to the patients smoking status.
- clinicals is a set of clinical measures such as heartrate, blood pressure
- drugs is the a set of binary covariates indicating whether a particular drug was given
- comorbidites is a set of binary covariates indicating whether the patient is suffering from certain conditions: eg asthma, diabetes
In the overall model I have not included year as a covariate - the same model formula was used for the subsetted data and the whole data.
There is no problem with collinearity between the continuous variables but I am less sure about associations between the categorical variables. I think this could be a problem but I don't know how to tackle it - I tried some chi-square tests but nothing was independent from anything else (I thought that might be due to the sample size - according to my teacher it doesn't make sense that asthma would be collinear with diabetes for instance)
After further comments by Michael I am now giving some more info....The ratio of treatment A/B has changed a lot over the period - it was a new treatment in 2006 and hardly used, but is now the treatment of choice:
2006: 555 out of 11,505 2007: 2,810 out of 12,307 2008: 5,669 out of 13,243 2009: 9,111 out of 14,654 2010: 12,368 out of 15,573
Overall: 30,643 out of 92,767
The death rate has not changed much (around 7% throughout)