3-level survival model

[Rakkoo Chung]

Hello. I am using StataIC-10. I've submitted a paper to a journal, and a reviewer wants me to specify a 3-level model, but I don't know how. I have reviewed papers, books, Stata manuals and this forum, but I couldn't find the answer. Would you please help me?

I use stcox on cross-national data between 1945 and 2000. I'd like to test the factors of regime transition from autocracy to democracy. There are about 140 countries each year on average. I stratify them on regions. My command is:

stset dura, f(event) id(id)
stcox llngnp lindust un wsp demrp demgp, strata(region) cluster(country) efron

Because a country can experience the event multiple times, robust standard errors are calculated by clustering on country. The hazards functions are stratified on region. Covariates include log of GNP, level of industrialization, and UN membership for each country in each year, UN membership for each country, the level of democracy for each region in each year, and the level of democracy for the world in each year.

The journal reviewer says, "The combination of a discrete-time survival model with contextual variables at two higher levels of analysis (region-year and year) implies that a three level model is necessary: country-years (level 1) nested within region-years (level 2) nested within years (level 3). Or one could use a cross-classified model (country-years are cross-nested within regions and years)."

Would you please help specify a 3-level model?

Any comment is appreciated. Thank you very much in advance.
Rakkoo

[Carlo Lazzaro]

chungrak (please, as per FAQ re-register with your full name and surname. Just click on the Contact us button, bottom right of the scren page):
- provided that reviewer's request of an explicit nested survival model is correct, you should consider a survey desing in your Cox model (please, see -help survey-), something like:

svy: stcox llngnp lindust un wsp demrp demgp, strata(region) cluster(country) efron

- as far as years are concerned, you can add dummies among the predictors (please, see - help fvvarlist -). If appropriate, you might also want to consider to model time explicitly by switching to a parametric regression model, such as a Weibull one (please, see - help streg-);
- for more on survival analysis with Stata I would point you to http://www.stata.com/bookstore/survi...ion/index.html.

Kind regards,
Carlo

[Stephen Jenkins]

I second Carlo's remarks requesting you to re-register. However, I have different thoughts from him regarding how to meet your reviewers' requests. Carlo refers to continuous time survival models (of which the Cox PH model is an example), but the reviewer refers to discrete time models, and you have data in which the survival times are grouped into years. The reviewer is pointing you towards not only discrete time modelling, but also multilevel/hierarchical modelling (note the references to nesting etc) and hence random effects (or 'mixture' model approaches). If you had Stata 13, you could fit such a model using meglm with the appropriate family and link function (e.g. binomial and cloglog). How you would implement this in Stata 10, I don't know -- there isn't a user-written program that I am aware of. So, what can you do? One option would be to do what the reviewer seeks, but use some other software, perhaps runmlwin for Stata (on SSC) to call routines in MLwiN? Or maybe HLM (which I have never used). Otherwise, I think you're going to have to convince the reviewer that some form of cluster robust approach (perhaps combined with stratification) is also a way to go. You would need to think carefully about what you cluster on (year? region-year combination? what?) [Simply applying svy: is probably not the way ahead, in my opinion.] Whatever, the reviewer's multilevel model approach is not the only way to deal with hierarchical data, especially if the level-2 (or level-3) variances are not of intrinsic interest.

[Rakkoo Chung]

Let me first apologize for my profile. I submitted a request for the suggested change in my profile. Now my full name appears.

Thank you so very much for your advice and comments. Yes, I've been studying those commands you suggested. I hope I can find a solution.

Rakkoo

[Steve Samuels]

I suspect that there is a literature on this kind of problem, but I'm not familiar with it, so bear that in mind. I agree with Stephen about the need for discrete analysis instead of Cox.

If, like me, you are unsure of what the reviewer was asking for, I suggest that you request that f the reviewer supply references for the requested analyses.

Grouped or discrete data can have problems, if > 1 transition to and from autocracy can take place in a year's time; this could result as a duration zero or of one year, depending on the dates. I also would expect that some of your l predictors are time-varying and that they include information on events in other countries.

Three-way?

I am guessing that the editor was asking for a model in which calendar year is a predictor, though it is likely to be correlated with time-varying covariates. The remedy, to me, is not a multi-level model with "year" as a random effect, as presumably requested by the reviewer, but rather addition calendar-year indicators & interactions. There may not be enough events to fit just the 54 indicator variables for the years 1945-2000, but five-year groups or, perhaps, spline functions should be sufficient. (I use a rule of thumb that you need 10 events per covariate.)

How many regions are there? If there are relatively few, region is a poor, candidate for a higher-level random effect in a multi-level model. Also, such a model ordinarily requires some strong assumptions about the distributions of the random effects., As Carlo suggests, I would add indicator variables for region, possibly interacting with time. . These might well be highly correlated with the region-level variables in the model, so, like calendar time, some care is needed.

[Carlo Lazzaro]

Dear All,
to my real shame I was captured by the Stata code on -stcox- and missed the substantive detail of discreteness in Rakkoo's regression model.
Hence, I second Stephen and Steve's comments about considering a discrete time models.
Rakkoo (and me, too) can find some relief from survival analysis headaches at https://www.iser.essex.ac.uk/resourc...sis-with-stata that at least one of the previous authoritative contributors knows very well.

Kind regards,
Carlo

[Steve Samuels]

A change of mind: You have one region-specific covariate, regional-level of democracy. If you simply added indicators for region, as I recommended, you would badly bias standard errors for that "contextual" covariate. As Stephen points out, some kind of multi-level model would be required to properly analyze such covariates. However Bryan and Jenkins (Stephen!), 2013, have shown that for logistic regression you would need at least 30 regions for reliable estimates (Bryan and Jenkins, 2013, page 2). (In their paper, individuals are the lowest level units and they are nested in countries.) So you in somewhat of a bind if you have very few regions. Bryan and Jenkins describe a two-step procedure that might help, one regression for country-specific covariates (including interaction with region & time, if sample size permits) and a second for the the region-specific covariate. You have a similar problem for for the world-level democracy covariate; as that will be the same for all countries in each year. However, "year" is a strange candidate for a higher-level unit in a multi-level analysis, because neither countries nor regions are "nested" within year. Again, I would recommend a two-step approach.


Reference:
Bryan, M. L., & Jenkins, S. P. (2013). Regression analysis of country effects using multilevel data: A cautionary tale (No. 7583). IZA Discussion Paper.

http://www.econstor.eu/bitstream/104...0/1/dp7583.pdf

[Rakkoo Chung]

Thank you all so very much for your comments on my model. I have carefully reviewed your suggestions and some other materials. Now I am almost decided on the following three solutions:

(1) As Steve suggests, I am going to replace the global variable with different ones that are measured at the regional (or similar) level.
(2) As Carlo suggests, I am going to fit Weibull models.
(3) As Stephen suggests, I am going to convince the journal reviewer that Cox models with clustering and stratification are appropriate.

Yes, I am going to use both Cox and Weibull models, instead of discrete-time models. I've been thinking about your common suggestion of discrete-time models, but I am sure that continuous-time models should work fine with the yearly cross-national data. Plus, Cox and Weibull models have merits.

I am pretty sure that Cox and Weibull models work well. I could convince you of my solutions rather quickly if I provided some examples. Let me summarize eight papers that employ event history analysis for the survival of or the transition to democracy. These papers are published in peer-reviewed journals between 1995 and 2011. Only one uses logit models. Among the other seven, two use Cox models, three use Weibull models, and the other two use both Cox and Weibull models.

Please let me know if you are not convinced. Again, thanks a lot!

Rakkoo

p.s. Eight papers that employ event history analysis for democratic transition and/or survival:
- Gasiorowski, Mark J. 1995. "Economic Crisis and Political Regime Change: An Event History Analysis." The American Political Science Review. 89(4): 882-897.
- Pevehouse, Jon C. 2002. "With a Little Help from My Friends? Regional Organizations and the Consolidation of Democracy." American Journal of Political Science. 46(3): 611-626.
- Bernhard, Michael, Timothy Nordstrom and Christopher Reenock. 2001. "Economic Performance, Institutional Intermediation, and Democratic Survival." The Journal of Poiltics. 63(3): 775-803.
- Feng, Yi and Paul J. Zak. 1999. "The Determinants of Democratic Transitions." The Journal of Conflict Resolution. 43(2): 162-177.
- Reenock, Christopher, Michael Bernhard and David Sobek. 2007. "Regressive Socioeconomic Distribution and Democratic Survival." International Studies Quarterly. 51: 677-699.
- Reiter, Dan. 2001. "Does Peace Nurture Democracy?" The Journal of Politics. 63(3): 935-948.
- Lai, Brian and Ruth Melkonian-Hoover. 2005. "Democratic Progress and Regress: The Effect of Parties on the Transitions of States to and Away from Democracy." Political Research Quarterly. 58(4): 551-564.
- Tzelgov, Eitan. 2011. "Communist Successor Parties and Government Survival in Central Eastern Europe." European Journal of Political Research. 50: 530-558.