Added cumulative hazard

[piever]

This is a refactoring to allow the computation of the Nelson-Aalen estimator with the same machinery set up for Kaplan-Meier. This takes care of point 3 in #5 .

Nelson-Aalen estimates the cumulative hazard. Cumulative hazard H is linked to survival S via the formula:

exp(-H) = S

So it can also be used to estimate the survival. It has the advantage, compared to Kaplan-Meier, that it can be used also to get baseline cumulative hazard of a fitted Cox Model (whereas getting the survival function from a Cox model with Kaplan-Meier is somewhat convoluted in case of simultaneous events)

[ararslan]

Nice refactoring, I like it! Though do you think it will be extensible to cumulative incidence, which also needs to track the number of competing events?

[piever]

Not sure, maybe the best is to add some compute_competing variable defaulting to false and add compute_competing && before the lines that are exclusive to cumulative incidence/estimators that need the number of competing events. Compiler in 0.7 should be smart enough that there is no penalty at all for this right?

[ararslan]

Compiler in 0.7 should be smart enough that there is no penalty at all for this right?

Perhaps, I'm not entirely sure.

One notable difference is that you need the vector of competing events as another argument to the estimating function, so branching on compute_competing won't get us all the way there.

[piever]

Fair enough: It may actually be better to simply duplicate the code...

[ararslan]

Keyword arguments in 0.7 are fast, since they're based on NamedTuples, so I wonder if we could get away with doing something clever hacky, e.g.

function f(time, status; kwargs...)
    if haskey(kwargs, :compete)
        # do stuff
    end
    # more stuff
end

Not sure though.

[ararslan]

Regardless, this refactoring and the addition look good to me.