[Basta-users] Calculating daily mortality rates for models with cont. covariates using estimates

[Fernando Colchero]

Dear Dries,

   Sorry for the late reply. This is certainly an issue we have not yet addressed with the package. Alternatively, you could produce a plot by extracting the information from the coefficients table in the BaSTA output. Here’s an option based on your results:

# Define the Weibull mortality with proportional hazards as:
mort <- function(x, z, b, g) {
	exp(g * z) * (b[1] + b[2] * b[3]^(b[2]) * x^(b[2] - 1))
}

where x is age, z is the SMI value, b is the vector of mortality parameters and g is the vector of proportional hazards parameters.

# Define x (I’m making up this range of ages…):
x <- seq(0.1, 5, 0.1)

# Define the lower and upper bounds of z (these are also made up…):
z <- c(3, 6)

# Extract the b and g parameters:
b <- out$coefficients[1:3, 1]
g <- out$coefficients[4, 1]

# Calculate the corresponding mortalities:
mulow <- mort(x, z[1], b, g)
muup <- mort(x, z[2], b, g)

# Define the range for the y-axis:
ylim <- c(0, max(c(mulow, muup)))

# Plot the results:
plot(x, mulow, col = 1, type = 'l', ylim = ylim)
lines(x, muup, col = 2)
legend('topright', c("Low SMI", "High SMI"), col = c(1, 2),
		lwd = 2)

  Let me know if this is of any help.

Best,

Fernando

Fernando Colchero
Assistant Professor
Department of Mathematics and Computer Science
Max-Planck Odense Center on the Biodemography of Aging

Tlf.               +45 65 50 23 24
Email           colchero at imada.sdu.dk <mailto:colchero at imada.sdu.dk>
Web             www.sdu.dk/staff/colchero <http://www.sdu.dk/staff/colchero>
Pers. web   www.colchero.com <http://www.sdu.dk/staff/colchero>
Adr.              Campusvej 55, 5230, Odense, Dk

University of Southern Denmark

> On 22 Mar 2016, at 11:32, Dries Van de Loock <dries.vandeloock at ugent.be> wrote:
> 
> Dear BaSTA community,
>  
> Thanks to your help and BaSTA, we could statistically confirm some of our expectations on post-fledging survival in a afrotropical passerine <http://lists.r-forge.r-project.org/pipermail/basta-users/2015-October/000131.html>.
>  
> While plotfancybasta() and plot() produce nice graphs for categorical variables, we are looking for a way to visualise the impact of continues covariates on survival of the fledglings.
>  
> More specifically, we fitted a weibull survival curve with makeham shape + mass at fledging (SMI) as a covariate (base model + 1 covariate) and find a negative relation with mortality (CI does not include zero).
>  
> Coefficients:
>           Estimate  StdErr Lower95%CI Upper95%CI SerAutocor UpdateRate PotScaleReduc
> c          0.02704 0.01595   0.009527   0.066033    0.56051     0.2223         1.017
> b0         0.06541 0.06751   0.001576   0.252938    0.38508     0.2605         1.002
> b1         0.90422 0.63824   0.043231   2.358846    0.06547     0.2501         1.001
> gamma.SMI -0.03971 0.01978  -0.083632  -0.006801    0.55284     0.2526         1.003
> pi.1       0.14211 0.01089   0.121642   0.163994    0.03578     1.0000         1.001
>  
> We see two ways to visualise this
> 
> 1. Daily mortality rates over a two month period (y-axis) plotted against time (x-axis) for a discrete number of SMI values. As such, you visualise the mortality shape for a number of SMI values over a two month period.
> 
> 2. The cumulative mortality probabilities (y-axis) after a two month period plotted against SMI (x-axis). We then expect that cumulative mortality probabilities will decrease with increasing SMI.
>  
> To do this, we could use the estimates to calculate (i) the daily mortality rates over a two month period and use these to calculate (ii) the cumulative mortality probabilities after a two month period for a discrete number of SMI values within the measured range (for example : 20, 25,30,35).
> 
>  
> While we successfully calculate daily mortality rates fitting the estimates in the function (b0 * b1 * ((b1 * k)^(b0 - 1))) + c) when no covariates were added to the model, we failed to find a method on how to include the gamma estimate in the function.
> 
>  
> Any help on how we can calculate daily mortality rates for a specific value of the covariate and be able to produce these graphs is highly appreciated.
>  
> Best wishes,
>  
> Dries Van de Loock
> PhD student
> Terrestrial Ecology Unit
> Department of Biology
> Ghent University
> KL Ledeganckstraat 35
> B-9000 Ghent, Belgium
> Phone: +32 (0)9 265 50 39
> http://www.ecology.ugent.be/terec/ <http://www.ecology.ugent.be/terec/>
>  
> 
>  
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