How do I 'control for' between cases and controls in survival analysis? I would appreciate some advice concerning the best practice for controlling covariates in KM curve survival analysis. Individuals suffer from headaches and individuals and are sub-grouped by controlling for gender. I am interested in looking at risk of headache relapse in association with a secondary disease.
I have a large number of controls (male and female), both in excess of 100,000 per gender that do not have any secondary disease. The groups just concentrating on Males for clarity are:


*

*1a) Males with a headache and with disease Xd1 (cases) - 6,000 individuals

*1b) Males with a headache and with disease Xd2 (cases) - 4,200 individuals

*1c) Males with a headache and with disease Xd3 (cases) - 1,900 individuals


I am using KM curves to look at headache remission between the two groups, controlled by gender (so that's four subpopulation in total if I consider both male and female cases and controls). 
Should I perform a KM curve over the complete control set of 100,000 individuals (males only) or should I take from that complete control set only 4 randomly selected controls per case, thus a total of 24,000 controls in Xd1, 16,800 in Xd2 and 7600 in Xd3? Therefore my actual numbers will look like:
Ratio consistent of 1:4 (case:control)


*

*2a) Males with a headache and with disease Xd1 (cases) - 6,000 individuals

*2b) Males with a headache and no disease (controls) - 24,000 individuals

*3a) Males with a headache and with disease Xd2 (cases) - 4,200 individuals

*3b) Males with a headache and no disease (controls) - 16,800 individuals

*4a) Males with a headache and with disease Xd3 (cases) - 1,900 individuals

*4b) Males with a headache and no disease (controls) - 7,600 individuals


OR (as before):


*

*2a) Males with a headache and with disease Xd1 (cases) - 6,000 individuals

*2b) Males with a headache and no disease (controls) - 100,000 individuals

*3a) Males with a headache and with disease Xd2 (cases) - 4,200 individuals

*3b) Males with a headache and no disease (controls) - 100,000 individuals

*4a) Males with a headache and with disease Xd3 (cases) - 1,900 individuals

*4b) Males with a headache and no disease (controls) - 100,000 individuals


Thanks
 A: It depends on what you mean by "matching". 
If you just mean "controlling for gender", then it's just as easy to either include gender in a Cox regression model, or stratify treatments and controls by gender and then compare the four Kaplan-Meier curves. If you have a large amount of data, this is what I would recommend as long as all four groups (disease + male, disease + female, etc.) are sufficiently large. In this case, there's no reason not to use all available data. Alternatively, if you wanted to compare several diseases without stratifying your data so much, this could all be fed into a Cox PH model. 
However, sometimes when we talk about "matching", we mean that we are matching several potentially unknown covariates. For example, suppose we are testing a poison oak treatment, and subjects use the treatment on one arm and use nothing on the other. Then we have a matched pairs design (everyone is matched with themselves) and we recognize that we've matched on several variables that we don't even know about (gender, age, etc.). 
It doesn't sound like this is a case in which we have something like a matched pairs design, so I would recommend comparing KM curves between subgroups. 
A: In a case-control study, those with the outcome of interest are the cases and those free of the outcome are controls. In your case, headache relapse defines case/control membership. In your situation disease is an exposure and does not define case or control status. 
You will need a regression technique as @Cliff_AB points out below. If you restrict yourself to KM, you will have to reconcile the many gender and disease-specific curves (gender*n_diseases = 6) in hopes of distilling the effect of disease on headache. Cox’s model will give the gender-adjusted effect of disease in a simpler and more readily interpretable form. You will need to enter disease as a dummy-coded or factor variable to model all three diseases.  
As for ratios, never throw away data! The ratio will not matter given the large amount of data you possess. 
