## The smartest solution [Bioanalytics]

Ladies and gentlemen,

I present to you the Philadelphia variation: The smartest and most empirical solution to a very, very small (and mainly theoretical?) problem.

Let us apply weights 1/C^z in such a fashion that

And it may make good sense to look at the relative magnitude of residuals since this is what runs pass criteria are based on.

Therefore, here is something to play around with:

Note: the fit is not very good, r squared is rather low, but that is besides the point. You get my drift, I hope.

z then defines the weighting scheme which can be said to give the smallest overall amount of percent-wise prediction error on the calibration curve. Not a bad place to start.

You can modify the idea as you please, perhaps you want to define ObjF via the Ratio and not via the Conc, or perhaps you want to return another type of objective altogether. Various things that don't work include but aren't limited to abs sum of residuals, sum of residuals, and more.

Thank me later.

I present to you the Philadelphia variation: The smartest and most empirical solution to a very, very small (and mainly theoretical?) problem.

Let us apply weights 1/C^z in such a fashion that

*the sum of relative absolute residuals is smallest*. Idea borrowed from ISR.And it may make good sense to look at the relative magnitude of residuals since this is what runs pass criteria are based on.

Therefore, here is something to play around with:

```
Conc=c(1, 2, 4, 8, 20, 50, 100, 150, 200, 300)
```

Ratio=c(0.5303, 0.1074, 0.2092, 0.4121, 0.9886, 2.3197, 5.0343, 7.7656, 10.2105, 14.9564)

ObjF=function(z)

{

w=1/(Conc^z)

M=lm(Ratio ~Conc, weight=w)

return(sum(abs(resid(M)/Conc)))

}

##now let us find the value of z which gives the smallest sum of absolute relative residuals

optimize(ObjF, c(0, 10))

Note: the fit is not very good, r squared is rather low, but that is besides the point. You get my drift, I hope.

z then defines the weighting scheme which can be said to give the smallest overall amount of percent-wise prediction error on the calibration curve. Not a bad place to start.

You can modify the idea as you please, perhaps you want to define ObjF via the Ratio and not via the Conc, or perhaps you want to return another type of objective altogether. Various things that don't work include but aren't limited to abs sum of residuals, sum of residuals, and more.

Thank me later.

—

I could be wrong, but...

Best regards,

ElMaestro

I could be wrong, but...

Best regards,

ElMaestro

### Complete thread:

- Handling BLOQ values (Fisher Info etc.) mittyri 2019-03-16 14:41 [Bioanalytics]
- Handling BLOQ values (Fisher Info etc.) Helmut 2019-03-16 15:39
- The smartest solution ElMaestro 2019-03-16 22:35
- An old solution Helmut 2019-03-16 23:05
- old, obvious? ElMaestro 2019-03-19 08:26

- Example Helmut 2019-03-17 01:56

- An old solution Helmut 2019-03-16 23:05
- ADA example mittyri 2019-03-18 22:20
- My beloved Ada Helmut 2019-03-19 01:34

- The smartest solution ElMaestro 2019-03-16 22:35
- Handling BLOQ values (Fisher Info etc.) Ohlbe 2019-03-17 14:32
- Handling BLOQ values (Fisher Info etc.) nobody 2019-03-18 08:14
- Don’t weight by 1/s² Helmut 2019-03-18 11:19

- Handling BLOQ values (Fisher Info etc.) nobody 2019-03-18 08:14

- Handling BLOQ values (Fisher Info etc.) Helmut 2019-03-16 15:39