<div dir="ltr">Dear Fernando, <div><br></div><div>many, many thanks for this. It was <i>exactly</i> what I was looking for and will greatly improve our manuscript. </div><div><br></div><div>I have one questions remaining. </div><div><br></div><div>How should I approach this method when wanting to visualise the effect of one continuous variable from a multivariate model both including continuous and one categorical variable with 5 levels ?<br></div><div><br></div><div>- Could I use the weighted average (=average c, b1 and b0 based on cohorts sample sizes) of the mortality estimates ? When just averaging, I have found that the mort rates were far too high as one cohort with just one case had high estimates. </div><div>- Could I just add another term <b>* exp(g * z) </b>to the model for each continuous variable and use the averaged predictor (z) value for the variable I'm not interested in ?</div><div><br></div><div><br></div><div>For example, we have a model : mort ~ LOC + SMI + GS</div><div><br></div><div>GS = groupsize (continuous)</div><div>SMI = mass (continuous, like above example)</div><div>LOC = location (5 levels, sample sizes differ hugely between cohorts)</div><div><br></div><div>When I want to visualise the effect of SMI solely, would this approach be correct : </div><div><br></div><div><font face="monospace, monospace">#define function</font></div><div><div><font face="monospace, monospace">mort <- function(x, z1, z2, b, g) {</font></div><div><font face="monospace, monospace"> exp(g[1] * z1) * exp(g[2] * z2) * (b[1] + b[2] * b[3]^(b[2]) * x^(b[2] - 1))</font></div><div><font face="monospace, monospace">}</font></div><div><font face="monospace, monospace"><br></font></div><div><font face="monospace, monospace"># define values</font></div><div><font face="monospace, monospace">x <- seq(1, 55, 1)</font></div><div><font face="monospace, monospace">z1 <- c(min(covariates$SMI),max(covariates$SMI)) # min and max value of the continuous variable of interest</font></div><div><font face="monospace, monospace">z2 <- mean(covariates$GS) # mean of the continuous variable not interested in to visualise</font></div><div><font face="monospace, monospace"> c <- mean(out$coefficients[c(1:5),1]) # average of the c values of each LOC (c.LOC1, c.LOC2, etc.) (in this example not yet weighted)</font></div><div><font face="monospace, monospace"> b0 <- mean(out$coefficients[c(6:10),1]) # average of the b0 values of each LOC (b0.LOC1, b0.LOC2, etc.) (in this example not yet weighted)</font></div><div><font face="monospace, monospace"> b1 <- mean(out$coefficients[c(11:15),1])</font></div><div><font face="monospace, monospace">b <- c(c,b0,b1)</font></div><div><font face="monospace, monospace">g <- out.SMI$coefficients[c(16:17), 1] # g parameters</font></div><div><font face="monospace, monospace"><br></font></div><div><font face="monospace, monospace"># calculate</font></div><div><font face="monospace, monospace">mumin <- mort(x, z1[1], z2, b, g)</font></div><div><font face="monospace, monospace">mumax <- mort(x, z1[2], z2, b, g)</font></div></div><div><br></div><div><br></div><div>I hope the example and my question are clear. </div><div><br></div><div>Again, many thanks for your time invested in this and I'm looking forward to your reply !</div><div><br></div><div>Dries</div><div><br></div><div class="gmail_extra"><br><div class="gmail_quote">2016-03-26 8:25 GMT+01:00 Fernando Colchero <span dir="ltr"><<a href="mailto:colchero@imada.sdu.dk" target="_blank">colchero@imada.sdu.dk</a>></span>:<br><blockquote class="gmail_quote" style="margin:0px 0px 0px 0.8ex;border-left-width:1px;border-left-color:rgb(204,204,204);border-left-style:solid;padding-left:1ex">
<div style="word-wrap:break-word">
Dear Dries,
<div><br>
</div>
<div> 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:</div>
<div><br>
</div>
<div>
<div>
<div style="margin:0px 0px 0px 4px;font-size:15.1px;font-family:Monaco;color:rgb(6,26,153)">
<span style="color:rgb(79,79,79)"># Define the Weibull mortality with proportional hazards as:</span></div>
<div style="margin:0px 0px 0px 4px;font-size:15.1px;font-family:Monaco;color:rgb(6,26,153)">
<span style="color:rgb(0,0,0)">mort </span><- <span style="color:rgb(195,136,9)">
function</span>(<span style="color:rgb(0,0,0)">x</span>, <span style="color:rgb(0,0,0)">
z</span>,<span style="color:rgb(0,0,0)"> b</span>,<span style="color:rgb(0,0,0)"> g</span>) {</div>
<div style="margin:0px 0px 0px 4px;font-size:15.1px;font-family:Monaco;color:rgb(6,26,153)">
<span style="white-space:pre-wrap"></span>exp(<span style="color:rgb(0,0,0)">g
</span>* <span style="color:rgb(0,0,0)">z</span>) * (<span style="color:rgb(0,0,0)">b</span>[<span style="color:rgb(4,82,24)">1</span>] +
<span style="color:rgb(0,0,0)">b</span>[<span style="color:rgb(4,82,24)">2</span>] *
<span style="color:rgb(0,0,0)">b</span>[<span style="color:rgb(4,82,24)">3</span>]^(<span style="color:rgb(0,0,0)">b</span>[<span style="color:rgb(4,82,24)">2</span>]) *
<span style="color:rgb(0,0,0)">x</span>^(<span style="color:rgb(0,0,0)">b</span>[<span style="color:rgb(4,82,24)">2</span>] -
<span style="color:rgb(4,82,24)">1</span>))</div>
<div style="margin:0px 0px 0px 4px;font-size:15.1px;font-family:Monaco;color:rgb(6,26,153)">
}</div>
<div style="margin:0px 0px 0px 4px;font-size:15.1px;font-family:Monaco;color:rgb(6,26,153)">
<br>
</div>
<div style="margin:0px 0px 0px 4px;font-size:15.1px;font-family:Monaco;color:rgb(6,26,153)">
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.</div>
<div style="margin:0px 0px 0px 4px;font-size:15.1px;font-family:Monaco;color:rgb(6,26,153);min-height:20px">
<br>
</div>
<div style="margin:0px 0px 0px 4px;font-size:15.1px;font-family:Monaco;color:rgb(79,79,79)">
# Define x (I’m making up this range of ages…):</div>
<div style="margin:0px 0px 0px 4px;font-size:15.1px;font-family:Monaco;color:rgb(6,26,153)">
<span style="color:rgb(0,0,0)">x </span><- seq(<span style="color:rgb(4,82,24)">0.1</span>,
<span style="color:rgb(4,82,24)">5</span>,<span style="color:rgb(4,82,24)"> 0.1</span>)</div>
<div style="margin:0px 0px 0px 4px;font-size:15.1px;font-family:Monaco;color:rgb(6,26,153);min-height:20px">
<br>
</div>
<div style="margin:0px 0px 0px 4px;font-size:15.1px;font-family:Monaco;color:rgb(79,79,79)">
# Define the lower and upper bounds of z (these are also made up…):</div>
<div style="margin:0px 0px 0px 4px;font-size:15.1px;font-family:Monaco;color:rgb(6,26,153)">
<span style="color:rgb(0,0,0)">z </span><- c(<span style="color:rgb(4,82,24)">3</span>,<span style="color:rgb(4,82,24)"> 6</span>)</div>
<div style="margin:0px 0px 0px 4px;font-size:15.1px;font-family:Monaco;color:rgb(6,26,153);min-height:20px">
<br>
</div>
<div style="margin:0px 0px 0px 4px;font-size:15.1px;font-family:Monaco;color:rgb(79,79,79)">
# Extract the b and g parameters:</div>
<div style="margin:0px 0px 0px 4px;font-size:15.1px;font-family:Monaco">
b <span style="color:rgb(6,26,153)"><- </span>out<span style="color:rgb(6,26,153)">$</span>coefficients<span style="color:rgb(6,26,153)">[</span><span style="color:rgb(4,82,24)">1</span><span style="color:rgb(6,26,153)">:</span><span style="color:rgb(4,82,24)">3</span><span style="color:rgb(6,26,153)">,
</span><span style="color:rgb(4,82,24)">1</span><span style="color:rgb(6,26,153)">]</span></div>
<div style="margin:0px 0px 0px 4px;font-size:15.1px;font-family:Monaco">
g<span style="color:rgb(6,26,153)"> <- </span>out<span style="color:rgb(6,26,153)">$</span>coefficients<span style="color:rgb(6,26,153)">[</span><span style="color:rgb(4,82,24)">4</span><span style="color:rgb(6,26,153)">,
</span><span style="color:rgb(4,82,24)">1</span><span style="color:rgb(6,26,153)">]</span></div>
<div style="margin:0px 0px 0px 4px;font-size:15.1px;font-family:Monaco;color:rgb(6,26,153);min-height:20px">
<br>
</div>
<div style="margin:0px 0px 0px 4px;font-size:15.1px;font-family:Monaco;color:rgb(79,79,79)">
# Calculate the corresponding mortalities:</div>
<div style="margin:0px 0px 0px 4px;font-size:15.1px;font-family:Monaco;color:rgb(6,26,153)">
<span style="color:rgb(0,0,0)">mulow </span><- mort(<span style="color:rgb(0,0,0)">x</span>,<span style="color:rgb(0,0,0)"> z</span>[<span style="color:rgb(4,82,24)">1</span>],
<span style="color:rgb(0,0,0)">b</span>,<span style="color:rgb(0,0,0)"> g</span>)</div>
<div style="margin:0px 0px 0px 4px;font-size:15.1px;font-family:Monaco;color:rgb(6,26,153)">
<span style="color:rgb(0,0,0)">muup </span><- mort(<span style="color:rgb(0,0,0)">x</span>,<span style="color:rgb(0,0,0)"> z</span>[<span style="color:rgb(4,82,24)">2</span>],
<span style="color:rgb(0,0,0)">b</span>, <span style="color:rgb(0,0,0)">
g</span>)</div>
<div style="margin:0px 0px 0px 4px;font-size:15.1px;font-family:Monaco;color:rgb(79,79,79);min-height:20px">
<br>
</div>
<div style="margin:0px 0px 0px 4px;font-size:15.1px;font-family:Monaco;color:rgb(79,79,79)">
# Define the range for the y-axis:</div>
<div style="margin:0px 0px 0px 4px;font-size:15.1px;font-family:Monaco;color:rgb(6,26,153)">
<span style="color:rgb(0,0,0)">ylim </span><- c(<span style="color:rgb(4,82,24)">0</span>,<span style="color:rgb(4,82,24)">
</span>max(c(<span style="color:rgb(0,0,0)">mulow</span>,<span style="color:rgb(0,0,0)"> muup</span>)))</div>
<div style="margin:0px 0px 0px 4px;font-size:15.1px;font-family:Monaco;color:rgb(79,79,79);min-height:20px">
<br>
</div>
<div style="margin:0px 0px 0px 4px;font-size:15.1px;font-family:Monaco;color:rgb(79,79,79)">
# Plot the results:</div>
<div style="margin:0px 0px 0px 4px;font-size:15.1px;font-family:Monaco">
<span style="color:rgb(6,26,153)">plot(</span>x<span style="color:rgb(6,26,153)">,</span> mulow<span style="color:rgb(6,26,153)">,</span> col
<span style="color:rgb(6,26,153)">=</span> <span style="color:rgb(4,82,24)">
1</span><span style="color:rgb(6,26,153)">,</span><span style="color:rgb(4,82,24)">
</span>type <span style="color:rgb(6,26,153)">= </span><span style="color:rgb(176,22,0)">'l'</span><span style="color:rgb(6,26,153)">,</span><span style="color:rgb(176,22,0)">
</span>ylim <span style="color:rgb(6,26,153)">=</span> ylim<span style="color:rgb(6,26,153)">)</span></div>
<div style="margin:0px 0px 0px 4px;font-size:15.1px;font-family:Monaco;color:rgb(6,26,153)">
lines(<span style="color:rgb(0,0,0)">x</span>,<span style="color:rgb(0,0,0)"> muup</span>,
<span style="color:rgb(0,0,0)">col </span>=<span style="color:rgb(0,0,0)">
</span><span style="color:rgb(4,82,24)">2</span>)</div>
<div style="margin:0px 0px 0px 4px;font-size:15.1px;font-family:Monaco;color:rgb(176,22,0)">
<span style="color:rgb(6,26,153)">legend(</span>'topright'<span style="color:rgb(6,26,153)">,</span>
<span style="color:rgb(6,26,153)">c(</span>"Low SMI"<span style="color:rgb(6,26,153)">,
</span>"High SMI"<span style="color:rgb(6,26,153)">), </span><span style="color:rgb(0,0,0)">col
</span><span style="color:rgb(6,26,153)">= c(</span><span style="color:rgb(4,82,24)">1</span><span style="color:rgb(6,26,153)">,</span><span style="color:rgb(4,82,24)"> 2</span><span style="color:rgb(6,26,153)">),</span></div>
<div style="margin:0px 0px 0px 4px;font-size:15.1px;font-family:Monaco">
<span style="color:rgb(6,26,153)"><span style="white-space:pre-wrap"></span></span>lwd
<span style="color:rgb(6,26,153)">=</span> <span style="color:rgb(4,82,24)">
2</span><span style="color:rgb(6,26,153)">)</span></div>
</div>
<div><br>
</div>
<div> Let me know if this is of any help.</div>
<div>
<div style="color:rgb(0,0,0);font-family:Helvetica;font-size:16px;font-style:normal;font-variant:normal;font-weight:normal;letter-spacing:normal;line-height:normal;text-align:start;text-indent:0px;text-transform:none;white-space:normal;word-spacing:0px">
<br>
Best,</div>
<div style="color:rgb(0,0,0);font-family:Helvetica;font-size:16px;font-style:normal;font-variant:normal;font-weight:normal;letter-spacing:normal;line-height:normal;text-align:start;text-indent:0px;text-transform:none;white-space:normal;word-spacing:0px">
<br>
</div>
<div style="color:rgb(0,0,0);font-family:Helvetica;font-size:16px;font-style:normal;font-variant:normal;font-weight:normal;letter-spacing:normal;line-height:normal;text-align:start;text-indent:0px;text-transform:none;white-space:normal;word-spacing:0px">
Fernando<br>
<br>
</div>
<div style="color:rgb(0,0,0);font-family:Helvetica;font-style:normal;font-variant:normal;font-weight:normal;letter-spacing:normal;line-height:normal;text-align:start;text-indent:0px;text-transform:none;white-space:normal;word-spacing:0px;font-size:12px">
<b>Fernando Colchero</b></div>
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Assistant Professor</div>
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Department of Mathematics and Computer Science</div>
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Max-Planck Odense Center on the Biodemography of Aging</div>
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<b><i><br>
</i></b></div>
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Tlf. <a href="tel:%2B45%2065%2050%2023%2024" value="+4565502324" target="_blank">+45 65 50 23 24</a></div>
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Email <a href="mailto:colchero@imada.sdu.dk" target="_blank">colchero@imada.sdu.dk</a></div>
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Web <a href="http://www.sdu.dk/staff/colchero" target="_blank">www.sdu.dk/staff/colchero</a></div>
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Pers. web <a href="http://www.sdu.dk/staff/colchero" target="_blank">www.colchero.com</a></div>
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<b>University of Southern Denmark</b></div>
</div>
<br>
<div>
<blockquote type="cite"><div><div>
<div>On 22 Mar 2016, at 11:32, Dries Van de Loock <<a href="mailto:dries.vandeloock@ugent.be" target="_blank">dries.vandeloock@ugent.be</a>> wrote:</div>
<br>
</div></div><div><div><div>
<div dir="ltr">
<p class="MsoNormal" style="margin-bottom:0.0001pt"><span lang="EN-GB">Dear BaSTA community,
</span></p>
<div style="margin-bottom:0.0001pt"><span lang="EN-GB"> </span><br>
</div>
<p class="MsoNormal" style="margin-bottom:0.0001pt"><span lang="EN-GB">Thanks to your help and BaSTA, we could statistically confirm some of our expectations on
<a href="http://lists.r-forge.r-project.org/pipermail/basta-users/2015-October/000131.html" target="_blank">
post-fledging survival in a afrotropical passerine</a>. </span></p>
<div style="margin-bottom:0.0001pt"><span lang="EN-GB"> </span><br>
</div>
<p class="MsoNormal" style="margin-bottom:0.0001pt"><span lang="EN-GB">While
<i>plotfancybasta()</i> and <i>plot() </i>produce nice graphs for categorical variables, we are looking for a way to visualise the impact of
<b>continues covariates</b> on survival of the fledglings. </span></p>
<div style="margin-bottom:0.0001pt"><span lang="EN-GB"> </span><br>
</div>
<p class="MsoNormal" style="margin-bottom:0.0001pt"><span lang="EN-GB">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). </span></p>
<div style="margin-bottom:0.0001pt"><span lang="EN-GB"> </span><br>
</div>
<pre style="line-height:10.25pt;background-image:initial;background-repeat:initial"><span lang="EN-GB" style="font-size:8pt;font-family:Courier">Coefficients:</span></pre>
<pre style="line-height:10.25pt;background-image:initial;background-repeat:initial"><span lang="EN-GB" style="font-size:8pt;font-family:Courier"> Estimate StdErr Lower95%CI Upper95%CI SerAutocor UpdateRate PotScaleReduc</span></pre>
<pre style="line-height:10.25pt;background-image:initial;background-repeat:initial"><span lang="EN-GB" style="font-size:8pt;font-family:Courier">c 0.02704 0.01595 0.009527 0.066033 0.56051 0.2223 1.017</span></pre>
<pre style="line-height:10.25pt;background-image:initial;background-repeat:initial"><span lang="EN-GB" style="font-size:8pt;font-family:Courier">b0 0.06541 0.06751 0.001576 0.252938 0.38508 0.2605 1.002</span></pre>
<pre style="line-height:10.25pt;background-image:initial;background-repeat:initial"><span lang="EN-GB" style="font-size:8pt;font-family:Courier">b1 0.90422 0.63824 0.043231 2.358846 0.06547 0.2501 1.001</span></pre>
<pre style="line-height:10.25pt;background-image:initial;background-repeat:initial"><span lang="EN-GB" style="font-size:8pt;font-family:Courier"><span style="background-color:rgb(255,255,0)">gamma.SMI -0.03971 0.01978 -0.083632 -0.006801</span> 0.55284 0.2526 1.003</span></pre>
<pre style="line-height:10.25pt;background-image:initial;background-repeat:initial"><span lang="EN-GB" style="font-size:8pt;font-family:Courier">pi.1 0.14211 0.01089 0.121642 0.163994 0.03578 1.0000 1.001</span></pre>
<div style="margin-bottom:0.0001pt"><span lang="EN-GB"> </span><br>
</div>
<p class="MsoNormal" style="margin-bottom:0.0001pt"><span lang="EN-GB">We see two ways to visualise this</span></p>
<p class="MsoNormal" style="margin-bottom:0.0001pt"><span lang="EN-GB"><br>
</span></p>
<p class="MsoNormal" style="margin-bottom:0.0001pt"><span lang="EN-GB">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. </span></p>
<p class="MsoNormal" style="margin-bottom:0.0001pt"><span lang="EN-GB"><br>
</span></p>
<p class="MsoNormal" style="margin-bottom:0.0001pt"><span lang="EN-GB">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.</span></p>
<div style="margin-bottom:0.0001pt"><span lang="EN-GB"> </span><br>
</div>
<p class="MsoNormal" style="margin-bottom:0.0001pt"><span lang="EN-GB">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).
</span></p>
<p class="MsoNormal" style="margin-bottom:0.0001pt"><span lang="EN-GB"><br>
</span></p>
<div style="margin-bottom:0.0001pt"><span lang="EN-GB"> </span><br>
</div>
<p class="MsoNormal" style="margin-bottom:0.0001pt"><span lang="EN-GB">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. </span></p>
<p class="MsoNormal" style="margin-bottom:0.0001pt"><span lang="EN-GB"><br>
</span></p>
<div style="margin-bottom:0.0001pt"><span lang="EN-GB"> </span><br>
</div>
<p class="MsoNormal" style="margin-bottom:0.0001pt"><span lang="EN-GB">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.
</span></p>
<div style="margin-bottom:0.0001pt"><span lang="EN-GB"> </span><br>
</div>
<p class="MsoNormal" style="margin-bottom:0.0001pt"><span lang="EN-GB">Best wishes,
</span></p>
<div style="margin-bottom:0.0001pt"><span lang="EN-GB"> </span><br>
</div>
<p class="MsoNormal" style="margin-bottom:0.0001pt"><span lang="EN-GB">Dries Van de Loock</span></p>
<p class="MsoNormal" style="margin-bottom:0.0001pt"><span lang="EN-GB">PhD student</span></p>
<p class="MsoNormal" style="margin-bottom:0.0001pt"><span lang="EN-GB">Terrestrial Ecology Unit</span></p>
<p class="MsoNormal" style="margin-bottom:0.0001pt"><span lang="EN-GB">Department of Biology</span></p>
<p class="MsoNormal" style="margin-bottom:0.0001pt"><span lang="EN-GB">Ghent University</span></p>
<p class="MsoNormal" style="margin-bottom:0.0001pt"><span lang="EN-GB">KL Ledeganckstraat 35</span></p>
<p class="MsoNormal" style="margin-bottom:0.0001pt"><span lang="EN-GB">B-9000 Ghent, Belgium</span></p>
<p class="MsoNormal" style="margin-bottom:0.0001pt"><span lang="EN-GB">Phone: <a href="tel:%2B32%20%280%299%20265%2050%2039" value="+3292655039" target="_blank">+32 (0)9 265 50 39</a></span></p>
<p class="MsoNormal" style="margin-bottom:0.0001pt"><span lang="EN-GB"><a href="http://www.ecology.ugent.be/terec/" target="_blank">http://www.ecology.ugent.be/terec/</a></span></p>
<div style="margin-bottom:0.0001pt"><span lang="EN-GB"> </span><br>
</div>
<div style="margin-bottom:0.0001pt"><br>
</div>
<div style="margin-bottom:0.0001pt"><span lang="EN-GB"> </span><br>
</div>
</div></div></div>
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</blockquote>
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</blockquote></div><br></div></div>