The impact of continous parameters on ordinal outcome by repeat measures anova

[Xiao-Hua Luo]

Dear,
I am trying to analyze the impact of continous parameters on ordinal outcome by repeat measures anova.
The continous parameters (A, B, C) were monitored regularly at different time points (n=5,1 month, 2month, 3,6,12). Ordinal outcome is dead or alive. The sample size is 25.
The continous parameters are not gaussian distribution.
I wonder if we could use repeat measures anova to do so.
Any help will be much appreciated!

Best regards,
Xiao-Hua Luo

[Joseph Coveney]

You can search Statalist's archives for posts where the Linear Probability Model is used with panel data. There are some helpful suggestions among the responses to them, especially with respect to handling the inevitable heteroscedasticity. With continuous predictors, you're liable to get predictions outside the parameter space.

You might want to consider using GEE.

assert inlist(outcome, 0, 1)
xtset patient_id
xtgee outcome c.(A B C) i.time_point, family(binomial) link(logit) vce(bootstrap)

A sample size of 25 is a little lean, but GEE could still give you a check on your ANOVA.

It doesn't matter that your continuous predictors are not normally distributed.

[Xiao-Hua Luo]

Joseph Coveney, thank you for your helpful suggetstions.
I run STATA as you suggested. I have some questions below.

. xtgee outcome c.A i.Time_point,family(binomial) link(logit) vce(bootstrap)
(running xtgee on estimation sample)

Bootstrap replications (50)
----+--- 1 ---+--- 2 ---+--- 3 ---+--- 4 ---+--- 5
xx.x..x.x.x.xxx..x.xx..x...x.....x..x.......x.x... 50

GEE population-averaged model Number of obs = 96
Group variable: id Number of groups = 24
Link: logit Obs per group:
Family: binomial min = 2
Correlation: exchangeable avg = 4.0
max = 5
Wald chi2(5) = 0.48
Scale parameter: 1 Prob > chi2 = 0.9928

(Replications based on 24 clusters in id)
------------------------------------------------------------------------------
| Observed Bootstrap Normal-based
outcome | Coef. Std. Err. z P>|z| [95% Conf. Interval]
-------------+----------------------------------------------------------------
A | .000361 .0006007 0.60 0.548 -.0008162 .0015383
|
Time_point |
2 | -.0077417 .0135367 -0.57 0.567 -.0342732 .0187898
3 | -.0035457 .007602 -0.47 0.641 -.0184454 .011354
6 | -.006197 .0107019 -0.58 0.563 -.0271723 .0147782
12 | -.0094666 .0138959 -0.68 0.496 -.036702 .0177688
|
_cons | -.524852 .2514257 -2.09 0.037 -1.017637 -.0320666
------------------------------------------------------------------------------
Note: One or more parameters could not be estimated in 18 bootstrap replicates;
standard-error estimates include only complete replications.


. xtgee outcome c.B i.Time_point,family(binomial) link(logit) vce(bootstrap)
(running xtgee on estimation sample)
estimates diverging (correlation > 1)
an error occurred when bootstrap executed xtgee
r(430);



So I think GEE may be not proper. I wonder if xtmixed (generalized linear mixed models) would be better in this condition.

. xtmixed outcome c.A i.Time_point
Mixed-effects ML regression Number of obs =	96
Wald chi2(5) =	4.48
Log likelihood = -62.556472 Prob > chi2 =	0.4832
outcome Coef. Std. Err. z P>z [95% Conf.	Interval]
A .0052341 .0025734 2.03 0.042 .0001903	.0102778
Time_point
2 -.1023622 .1506714 -0.68 0.497 -.3976727	.1929484
3 -.0409938 .1519686 -0.27 0.787 -.3388469	.2568592
6 -.0907823 .1480073 -0.61 0.540 -.3808713	.1993068
12 -.1681883 .1688374 -1.00 0.319 -.4991035	.1627269
_cons .1645702 .1462509 1.13 0.260 -.1220763	.4512167
Random-effects Parameters Estimate Std. Err. [95% Conf.	Interval]
sd(Residual) .4642609 .0335051 .4030249	.5348011

. xtmixed outcome c.B i.Time_point
Mixed-effects ML regression Number of obs =	96
Wald chi2(5) =	7.75
Log likelihood = -61.017124 Prob > chi2 =	0.1706
outcome Coef. Std. Err. z P>z [95% Conf.	Interval]
B .4487018 .1649435 2.72 0.007 .1254184	.7719852
Time_point
2 -.0137166 .1448709 -0.09 0.925 -.2976585	.2702252
3 .0000367 .1482301 0.00 1.000 -.290489	.2905624
6 .018825 .1423781 0.13 0.895 -.2602309	.297881
12 -.0353876 .161859 -0.22 0.827 -.3526254	.2818502
_cons .3124012 .1068183 2.92 0.003 .1030412	.5217613
Random-effects Parameters Estimate Std. Err. [95% Conf.	Interval]
sd(Residual) .4568759 .0329722 .396614	.526294

It seems that the results are different in two models. How can I deal with it? Another problem is that how we find out the interaction between these three factors (A, B,C). Could we find out the impact of other random factor involved in this model?

Thanks a lot!


Xiao-Hua Luo

[Joseph Coveney]

It didn't really dawn on me before that the outcome is mortality. You might want to consider using survival data methods instead of repeated-measures ANOVA or xtmixed.

[Xiao-Hua Luo]

It didn't really dawn on me before that the outcome is mortality. You might want to consider using survival data methods instead of repeated-measures ANOVA or xtmixed.

Yes. The outcome is mortality. It would be better to use survival analysis to do, but the paramers of each patient were dynamic, but not a fixed one. I do not think it is a practical to do so. Or anything new has been developed these years? I have no idea. Could we introduce GEE or ANOva into Cox model?
Thx!

[Xiao-Hua Luo]

It didn't really dawn on me before that the outcome is mortality. You might want to consider using survival data methods instead of repeated-measures ANOVA or xtmixed.

If we do not want to consider the effect of surival and just focus on alive or dead, is it possible to use GEE or xtmixed? Which one is better GEE or xtmixed?
Thx!

[Joseph Coveney]

I recommend that you Google discrete time survival for pointers on what you can do. There are several threads on the topic on Statalist, too, that could probably be helpful to you.