## 90% confidence interval for R_dnm [Study Assessment]

Dear Detlew,

Sorry. It seems I didn't explain it clearly. My SAS code is almost the same as yours:

I just take the output and calculated some of the numbers according to Smith's article to reproduce his result.

This gives (Smith's reported value in blue):

Those are slope and its 90% CI, and the corresponding criteria calculated with dose ratio r = 10 and θ

where R_dnm is the one I used previously, since Smith mentioned in the article that each mean PK was calcuated as

Rdnm is the same thing but calculated with your code which is the one I use now since it's equivalent to previous one but much shorter. I guess that my explanation in previous post with this regard is not clear so I added both of them here.

The last 2 are predicted geometric mean PK values at the dose levels of 25 and 250, as given in the 1st column in Table 2 in Smith's article. These 2nd part of the result are not really necessary to judge dose proportionality (though roh1 and roh2 are useful to know) but as I said, I prefer to reproduce all results as kind of "validation".

By the way, Helmut, I don't know how to make a table (e.g. with 1 row) with heading here so I manually entered all values above; also, I copy/paste greek letter from elsewhere. Is there any helper section with BBCode for special symble and greek letters and table making? I vaguely recall there used to be a section with BBcode examples but couldn't find it now.

❝ Could you please give a detailed example for what you did here?

Sorry. It seems I didn't explain it clearly. My SAS code is almost the same as yours:

`PROC MIXED DATA = smith METHOD = ML;`

CLASS subj ;

MODEL lcmax = ldose / DDFM=SATTERTHWAITE CL ALPHA = 0.1 ;

RANDOM INTERCEPT / SUBJECT = subj;

ODS OUTPUT solutionf = out1;

RUN;

I just take the output and calculated some of the numbers according to Smith's article to reproduce his result.

```
PROC SQL;
```

CREATE TABLE result AS

SELECT

d2.estimate AS beta1,

d2.lower AS beta1_l,

d2.upper AS beta1_u,

1 + LOG(0.8)/LOG(10) AS dpcrit_l,

1 + LOG(1.25)/LOG(10) AS dpcrit_u,

1.25**(1/MAX(1-d2.lower, d2.upper-1)) AS roh1,

1.25**(1/MAX(d2.lower-1, 1-d2.upper)) AS roh2,

EXP(d3.estimate + d2.estimate*LOG(250))/EXP(d3.estimate + d2.estimate*LOG(25)) * (25/250) AS R_dnm,

10**(d2.estimate-1) AS Rdnm,

10**(d2.lower-1) AS Rdnm_l,

10**(d2.upper-1) AS Rdnm_u,

EXP(d3.estimate + d2.estimate*(LOG(25))) AS dosepred_l,

EXP(d3.estimate + d2.estimate*(LOG(250))) AS dosepred_h

FROM out1 AS d2, out1 AS d3

WHERE UPCASE(d2.effect) EQ "LDOSE" AND

UPCASE(d3.effect) EQ "INTERCEPT";

SELECT * FROM result;

QUIT;

This gives (Smith's reported value in blue):

`beta1: 0.7615 (0.7615)`

beta1_l: 0.6789 (0.679)

beta1_u: 0.8441 (0.844)

dpcrit_l: 0.90309 (0.903)

dpcrit_u: 1.09691 (1.097)

Those are slope and its 90% CI, and the corresponding criteria calculated with dose ratio r = 10 and θ

_{L}and θ_{U}of 0.8 and 1.25, respectively. The rest are for information purpose only.`roh1: 2.003428 (2.0)`

roh2: 4.183885 (4.2)

R_dnm: 0.577402 (0.577)

Rdnm: 0.577402 (0.577)

Rdnm_l: 0.477381 (0.477)

Rdnm_u: 0.698378 (0.698)

dosepred_l: 80.92991 (80.9)

dosepred_h: 467.2906 (467)

where R_dnm is the one I used previously, since Smith mentioned in the article that each mean PK was calcuated as

`exp(beta_0 + beta1*ln(dose)`

). R_dnm is dose-normalised mean ratio, hence the long line in `PROC SQL:`

`EXP(d3.estimate + d2.estimate*LOG(250))/EXP(d3.estimate + d2.estimate*LOG(25)) * (25/250)`

.Rdnm is the same thing but calculated with your code which is the one I use now since it's equivalent to previous one but much shorter. I guess that my explanation in previous post with this regard is not clear so I added both of them here.

The last 2 are predicted geometric mean PK values at the dose levels of 25 and 250, as given in the 1st column in Table 2 in Smith's article. These 2nd part of the result are not really necessary to judge dose proportionality (though roh1 and roh2 are useful to know) but as I said, I prefer to reproduce all results as kind of "validation".

By the way, Helmut, I don't know how to make a table (e.g. with 1 row) with heading here so I manually entered all values above; also, I copy/paste greek letter from elsewhere. Is there any helper section with BBCode for special symble and greek letters and table making? I vaguely recall there used to be a section with BBcode examples but couldn't find it now.

—

All the best,

Shuanghe

All the best,

Shuanghe

### Complete thread:

- Dose Proportionality and Variance AngusMcLean 2016-05-11 16:55 [Study Assessment]
- More information, please Helmut 2016-05-12 14:34
- More information, please AngusMcLean 2016-05-13 16:40
- Setup in Phoenix/WinNonlin Helmut 2016-05-14 02:26
- Setup in Phoenix/WinNonlin AngusMcLean 2016-05-14 18:54
- Setup in Phoenix/WinNonlin Helmut 2016-05-15 14:47
- Setup in Phoenix/WinNonlin AngusMcLean 2016-05-15 15:17
- Phoenix 64 Warning Helmut 2016-05-15 15:56
- Phoenix 64 Warning AngusMcLean 2016-05-15 20:11
- OT: imperial vs. metric units Helmut 2016-05-16 16:26

- Phoenix 64 Warning AngusMcLean 2016-05-15 20:11
- Setup in Phoenix/WinNonlin ElMaestro 2016-05-15 20:54
- Setup in Phoenix/WinNonlin AngusMcLean 2016-05-15 22:30

- Phoenix 64 Warning Helmut 2016-05-15 15:56

- Setup in Phoenix/WinNonlin AngusMcLean 2016-05-15 15:17

- Setup in Phoenix/WinNonlin Helmut 2016-05-15 14:47
- Setup in Phoenix/WinNonlin AngusMcLean 2016-05-16 21:00
- NCSS vs. PHX/WNL vs. SAS Helmut 2016-05-17 01:50
- NCSS vs. PHX/WNL vs. SAS - Validation? mittyri 2016-05-18 08:23
- Diagnostics ElMaestro 2016-05-18 09:20
- Diagnostics: R and Phoenix Helmut 2016-05-18 15:14
- Diagnostics: R zizou 2016-05-22 19:07
- Diagnostics: R Helmut 2016-05-23 01:22
- SASian potpourri d_labes 2016-05-24 12:02
- Compilation Helmut 2016-05-24 14:27
- REML or not d_labes 2016-05-24 16:33
- complete or not Helmut 2016-05-24 16:57

- Compilation AngusMcLean 2016-05-26 16:46
- doubts about NCSS Helmut 2016-05-26 19:13
- Doubts about NCSS zizou 2016-05-26 23:38

- doubts about NCSS Helmut 2016-05-26 19:13
- Compilation AngusMcLean 2016-05-28 00:51
- Kenward-Roger? Helmut 2016-05-28 15:59

- 90% confidence interval for R_dnm Shuanghe 2019-01-04 17:45
- 90% confidence interval for R_dnm d_labes 2019-01-05 14:01
- Visualizing lmer and limits mittyri 2019-01-06 17:00
- Visualizing lmer and limits Shuanghe 2019-01-07 11:05
- Visualizing lmer and limits d_labes 2019-01-07 15:08
- Visualizing lmer and limits mittyri 2019-01-13 23:53

- 90% confidence interval for R_dnm Shuanghe 2019-01-07 10:53
- 90% confidence interval for R_dnm d_labes 2019-01-07 15:17
- 90% confidence interval for R_dnmShuanghe 2019-01-07 17:11
- 90% confidence interval for R_dnm d_labes 2019-01-07 18:24
- offtop: greek letters and tables mittyri 2019-01-08 00:19
- OT: greek letters and symbols Helmut 2019-02-02 16:04

- 90% confidence interval for R_dnmShuanghe 2019-01-07 17:11

- 90% confidence interval for R_dnm d_labes 2019-01-07 15:17

- Visualizing lmer and limits mittyri 2019-01-06 17:00

- 90% confidence interval for R_dnm d_labes 2019-01-05 14:01

- REML or not d_labes 2016-05-24 16:33

- Compilation Helmut 2016-05-24 14:27

- SASian potpourri d_labes 2016-05-24 12:02

- Diagnostics: R Helmut 2016-05-23 01:22

- Diagnostics: R zizou 2016-05-22 19:07

- Diagnostics: R and Phoenix Helmut 2016-05-18 15:14
- Smith’s paper Helmut 2016-05-18 14:44
- Smith’s paper d_labes 2019-01-05 15:00

- Diagnostics ElMaestro 2016-05-18 09:20

- NCSS vs. PHX/WNL vs. SAS - Validation? mittyri 2016-05-18 08:23

- NCSS vs. PHX/WNL vs. SAS Helmut 2016-05-17 01:50

- Setup in Phoenix/WinNonlin AngusMcLean 2016-05-14 18:54

- Setup in Phoenix/WinNonlin Helmut 2016-05-14 02:26

- More information, please AngusMcLean 2016-05-13 16:40

- More information, please Helmut 2016-05-12 14:34