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_posts/2018-09-13-calculating-half-life.md

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+---
+layout: post
+title: "Calculating half-life"
+description: ""
+category: [Consulting]
+tags: [regression, pigs, random effect]
+---
+{% include JB/setup %}
+
+## Problem description
+
+Half-life of drug in SCID, pigs that have no immune system. 
+A total of 6 SCID pigs and 8 SCID pigs in 3 litters where the first litter 
+was bottle fed and the latter two were nursed. The first litter has 2 SCID pigs
+and 2 non-SCID pigs. 
+
+Main scientific question is whether there is a difference in half-life between 
+SCID and non-SCID pigs. 
+
+Approach 1) Currently modeling the log of the amount of drug and calculating the half-life.
+Then fitting another model for the calculated half-life using SCID and litter
+as fixed effects.
+
+Approach 2) Separately fitting a mixed effect model on the log of the amount of drug and 
+including SCID, time, and SCID x time as fixed effects and a random effect for 
+pig. 
+
+Client question is "How are these models the same/different?"
+
+
+## Consulting response
+
+Approach 2) has a common slope for all pigs. 
+If a random coefficient for time by pig is included in Approach 2), 
+it gets closer to the first approach. 
+
+We would suggest modeling the logarithm of the drug amount using 
+litter, SCID, time, and SCID x time as fixed affects and (time|pig) as a random
+effect.
+
+The main quantity of interest to answer the scientific question of interest is 
+the coefficient for the SCID x time interaction which determines if there is 
+a difference in degradation, on average, between the SCID and non-SCID pigs. 
+It may be of interest to calculate the slope (coefficient for time) for both 
+SCID and non-SCID pigs along with their confidence intervals. Then to interpret
+the half-life, use the equation halflife = ln(2)/slope to calculate the point
+estimate and confidence interval for the halflife. 
+
+

_posts/2018-09-13-drill-hole-element-relationship.md

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+---
+layout: post
+title: "Drill hole element relationship"
+description: ""
+category: [Consulting]
+tags: [regression, variable selection]
+---
+{% include JB/setup %}
+
+## Problem description
+
+Samples of rock that contain gold (Au) and a number of other elements including 
+calcium (Ca). Ca is censored into the range 10^-4 to 10^4 and samples are both
+above and below this amount.
+
+There is one drill hole with 500 samples within it. 
+
+There are 49 predictors. 
+
+Main question is the relationship between gold and each of the other elements.
+
+
+## Consulting response
+
+Ask a lot more questions about what the goal of the analysis is.
+Possible approaches include principle components analysis, partial least 
+squares, other variable selection approaches. 
+