Specifying models for BACI design

[FTvM]

I have a before-after control-impact (BACI) experimental design for a study to determine impacts of a new highway on black bears. I have 4 data groups based on 2 study phases and 2 study areas: (1) treatment-before highway, (2) treatment-after highway, (3) control-before highway, and (4) control-after highway. I want to test if there was a treatment effect with regard to survival, i.e., did survival on the treatment area decrease more compared with the control area? I am using known-fate models in MARK to estimate survival based on telemetry data of 57 bears, using group variables to assign each bear to 1 of the 4 data groups.

I want to use AIC to test for a treatment effect. IF there is a treatment effect, the model where survival is reduced more on the treatment than the control area should have a lower AIC than models where survival is constant for all 4 data groups, does not change between study phases, etc. I have been able to build all relevant models with one exception: I have not been able to build a model where survival is different for the treatment and control area but where the CHANGE in survival between the 2 study phases is the same for the 2 study areas (which, of course, would not indicate a treatment effect).

The closest I can come to this is a design matrix with a parameter grouping data groups 1 and 2 versus 3 and 4 (i.e., survival on treatment area is different from control area), and an additional parameter to add a constant to data groups 2 and 4 (‘after highway’ study phase). However, once you apply the parameter estimates in the linear model, the resulting estimates of survival, of course, do not reflect a similar change. Can anyone think of a way to ‘force’ the difference in estimates of S to be the same between data groups 1 and 2 vs. 3 and 4?

Thanks,

Frank

[wchallen]

Howdy,

You could also use two groups (control and impact) with capture occasions that occurred both before and after. You can then model the Phi's for differences in survival between the before and after period to see a difference. You could also do this as a single group, but designate control/impact (individual covariates) and before/after using just the design matrix.

While I am generally in favour of AIC rankings, in the case of a BACI design we are interested in estimating differences in survival before/after in the control/impact as well as any interactions. In this case you may want to present the results as 95% CI of the effect estimate or 95% CI of the differences.

Depending on how we generate the design matrix, we can directly estimate most of these quantities.