I have data for the lipid profile before treatment, 4 weeks, 12 weeks after treatment.
Paired data analyses showed that LDL significantly increased 4 weeks after treatment, and no difference was noted between 4wk and 12 wk.
Could I conclude that the increase will mostly occur in 4 weeks after the treatment starts, and it isn't significant thereafter?
What is a better analysis for the conclusion I want?
Thank you.
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Cheng:
yes, you can, as you can see in the following toy-example:
Code:. use "http://www.stata-press.com/data/r15/nlswork.dta" . xtreg ln_wage i.year Random-effects GLS regression Number of obs = 28,534 Group variable: idcode Number of groups = 4,711 R-sq: Obs per group: within = 0.1058 min = 1 between = 0.0796 avg = 6.1 overall = 0.0724 max = 15 Wald chi2(14) = 3198.67 corr(u_i, X) = 0 (assumed) Prob > chi2 = 0.0000 ------------------------------------------------------------------------------ ln_wage | Coef. Std. Err. z P>|z| [95% Conf. Interval] -------------+---------------------------------------------------------------- year | 69 | .0854251 .0123808 6.90 0.000 .0611592 .1096911 70 | .069889 .0115653 6.04 0.000 .0472215 .0925566 71 | .1196013 .0114272 10.47 0.000 .0972043 .1419983 72 | .1327835 .0117484 11.30 0.000 .109757 .1558099 73 | .1476736 .0113915 12.96 0.000 .1253467 .1700006 75 | .1609048 .0112586 14.29 0.000 .1388385 .1829712 77 | .2207951 .0112687 19.59 0.000 .1987089 .2428814 78 | .2596833 .0115128 22.56 0.000 .2371186 .282248 80 | .267724 .0116586 22.96 0.000 .2448735 .2905745 82 | .2852433 .0113995 25.02 0.000 .2629007 .3075859 83 | .3126372 .0115421 27.09 0.000 .2900152 .3352592 85 | .3653587 .0114383 31.94 0.000 .34294 .3877773 87 | .3813851 .0113703 33.54 0.000 .3590997 .4036706 88 | .4370689 .0113081 38.65 0.000 .4149054 .4592325 | _cons | 1.426677 .0103611 137.70 0.000 1.406369 1.446984 -------------+---------------------------------------------------------------- sigma_u | .36928787 sigma_e | .30294584 rho | .59773703 (fraction of variance due to u_i) ------------------------------------------------------------------------------ . test (69.year=70.year) (69.year=71.year)(70.year=71.year), mtest(bonferroni) ( 1) 69.year - 70.year = 0 ( 2) 69.year - 71.year = 0 ( 3) 70.year - 71.year = 0 Constraint 3 dropped --------------------------------------- | chi2 df p -------+------------------------------- (1) | 1.76 1 0.5547 # (2) | 8.66 1 0.0098 # (3) | 22.55 1 0.0000 # -------+------------------------------- all | 23.45 2 0.0000 --------------------------------------- # Bonferroni-adjusted p-values . -
Sorry that I didn't present my question well.Originally posted by Carlo Lazzaro View Post
My question is:
May I have pairwise comparison results after performing panel data analyses? (wk4 vs wk12, wk4 vs wk24, w12 vs wk24, etc..)
Like the results from post-hoc analyses after performing ANOVA.Leave a comment:
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Cheng:
I fail to get your concern.
if -hausman- outcome pointed you to -re-, this exactly what you have already did (see the results in #4).
I fail also to get what kind of problems you have with the Pregibon test.Leave a comment:
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-hausman- outcome suggests I go -re-.
The results look like those from regression analyses.
I can't tell the LDL increase is only significant between 0-4 week, but not 4-12 weeks, not 4-24 weeks, and not 12-24 weeks, from the results.
What do I miss?
I have problems with -Pregibon test- and will study about it later.
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Cheng:
assuming that -re- specification is the way to go and that you did not detect heteroskedasticity and/or autocorrelation in your data (if that were the case, impose the -robust- option on your standard errors), your conclusion would make sense if your regression model were well specified with only -i.time- as a predictor.
I think you have probably collected other predictors, such as age, geneder and comorbidities of patients enrolled in your study.
If that were the case, I would plug them in the right-hand side of your regression equation and see what happens with your outcome.
Besides, post estimation test play a relevant role in detecting model misspecification.
For instance, you can run the Pregibon test (see references and assumptions under -linktest- esntry in Stata .pdf manual) like in the following toy-example:
As you can see, -hausman- outcome suggests to go -fe-, but the Pregibon test proves the regression model to be misspecified (that may happen for various reasons).Code:. use "http://www.stata-press.com/data/r15/nlswork.dta" (National Longitudinal Survey. Young Women 14-26 years of age in 1968) . quietly xtreg ln_wage age i.year, fe . estimates store fe . quietly xtreg ln_wage age i.year, re . estimates store re *Hausman test* . hausman fe re ---- Coefficients ---- | (b) (B) (b-B) sqrt(diag(V_b-V_B)) | fe re Difference S.E. -------------+---------------------------------------------------------------- age | .0125992 .0137208 -.0011216 .01004 year | 69 | .0748621 .0744312 .0004309 .0098206 70 | .0478697 .0453659 .0025038 .0202541 71 | .0865577 .0819949 .0045629 .0303028 72 | .0856757 .0827461 .0029296 .0402525 73 | .0880069 .0840751 .0039318 .0503357 75 | .0778607 .0707387 .007122 .070056 77 | .108365 .1032639 .0051011 .0900953 78 | .1309518 .1279039 .0030479 .1005435 80 | .1142649 .108871 .0053939 .1202629 82 | .1090451 .098831 .0102141 .1403289 83 | .1211272 .1127655 .0083617 .1502649 85 | .1465637 .1380611 .0085026 .1703831 87 | .1382642 .1264818 .0117824 .1905725 88 | .1799741 .1640382 .0159359 .2042295 ------------------------------------------------------------------------------ b = consistent under Ho and Ha; obtained from xtreg B = inconsistent under Ha, efficient under Ho; obtained from xtreg Test: Ho: difference in coefficients not systematic chi2(15) = (b-B)'[(V_b-V_B)^(-1)](b-B) = 81.61 Prob>chi2 = 0.0000 . quietly xtreg ln_wage age i.year, fe . predict fitted, xb (24 missing values generated) . g sq_fitted=fitted^2 (24 missing values generated) *Pregibon test* . xtreg ln_wage fitted sq_fitted, fe Fixed-effects (within) regression Number of obs = 28,510 Group variable: idcode Number of groups = 4,710 R-sq: Obs per group: within = 0.1086 min = 1 between = 0.0962 avg = 6.1 overall = 0.0845 max = 15 F(2,23798) = 1449.33 corr(u_i, Xb) = 0.0519 Prob > F = 0.0000 ------------------------------------------------------------------------------ ln_wage | Coef. Std. Err. t P>|t| [95% Conf. Interval] -------------+---------------------------------------------------------------- fitted | 4.791882 .4570443 10.48 0.000 3.896046 5.687718 sq_fitted | -1.125657 .1355632 -8.30 0.000 -1.391369 -.8599442 _cons | -3.1774 .3839526 -8.28 0.000 -3.929971 -2.424828 -------------+---------------------------------------------------------------- sigma_u | .40489607 sigma_e | .30248347 rho | .64180514 (fraction of variance due to u_i) ------------------------------------------------------------------------------ F test that all u_i=0: F(4709, 23798) = 8.78 Prob > F = 0.0000 . test sq_fitted ( 1) sq_fitted = 0 F( 1, 23798) = 68.95 Prob > F = 0.0000 .
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[QUOTE=Carlo Lazzaro;n1483220]Cheng:
looking at your outcome tables, what strikes me is the different number of observations between tests perfomed at 4 and 12 week after the treatment start.
I find difficult to get what's your original sample size and why it increased from the the first to the second measurement.
That said, you may want to consider a panel data regression (provided that the mesurements were taken on the same sample od patients):
keep NO LDL LDL_4wk LDL_12wk LDL_SVRCode:xtreg LDL i.week
rename LDL LDL0
rename LDL_4 LDL4
rename LDL_12 LDL12
rename LDL_SVR LDL24
reshape long LDL, i(NO) j(wk)
xtset NO
I think the results mean that LDL values at week4/12/24 are all significantly higher than the baseline.
Can the results tell me if the increase occurs more dramatically at the 4th week, and not after 4 weeks?
As we can see, the coefficient jumps to 14 in 4 weeks, and only slightly climbs to 17 at 24 weeks.
Thank you for your help, Carlo.
Leave a comment:
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Cheng:
looking at your outcome tables, what strikes me is the different number of observations between tests perfomed at 4 and 12 week after the treatment start.
I find difficult to get what's your original sample size and why it increased from the the first to the second measurement.
That said, you may want to consider a panel data regression (provided that the mesurements were taken on the same sample od patients):
As per -hausman- test you can investigate whether -fe- or -re- specification fits you data better.Code:xtreg LDL i.week
Leave a comment:
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Below are the results by paired t test. Thank you for your help.
SVR is 12 week after treatment
LDL is before treatment
4wk is 4 wk after treatment
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