Dear All,

I have received very few replies about the issue of extrapolating to a much 
larger area (e-mail posted on 24th of january); I would very much 
appreciate hearing more comments on this project, on the whole or on any 
specific point...

thanks in advance

TOPIC: health indicators (traffic injury ones) on a geographical area to be 
extrapolated to the nation-wide level.


CONTEXT:

The local geographical area is a French department (rhône) which is 
equivalent to a large county (this department has1.6 million inhabitants ; 
it is made of a large city (Lyon), its suburbs and a rural area)

Traffic injury indicators are number of road traffic victims, number of 
road traffic victims by injury severity, number of road traffic victims by 
type of injury... Local results are based on a road trauma registry, 
covering all hospitals in the Rhône county (and its close surroundings) ; 
this registry includes all victims from a road crash occurring in the the 
rhône county. We have 8 years of data, with about 10,000 victims par year.

There is a second source of data on road crash victims : police data. They 
are available at the national level, and in each of the 95 counties. 
However they are not satisfactory as they suffer from large under-reporting 
(about 4,500 victims per year in the Rhone county) and they contain no 
medical information such as type of injury, severity of injury (as measured 
by a trauma scale)
this is why we want to extrapolate traffic injury indicators based on the 
rhone county registry to the nation level (France)

(I have mentioned counts and not incidences as traffic injury indicators; 
the reasoning could however be done in terms of incidence rates; the ratio 
between the number of road victims from a crash in the Rhone department in 
year j and the population of the Rhone department in year j is not an 
incidence rate by definition; however it is close to it, as most victims of 
road crashes in a given departement live in that department: 90% for Rhone 
road crashes, which is one of the departments with some amount of traffic 
due to long-distance trips=from outside the department)


METHOD considered:

Following suggestions from collegues in my research unit, I have looked 
into survey methodology : use of auxilairy variable to improve/ « correct » 
the estimator, ratio estimation and more specifically regression estimation

The first idea we had about how to proceed was :
The Rhone county is a non-representative sample of France ; it is biased on 
a number of characteristics, and those at the county-level associated with 
road safety are: urbanisation rate, road types distribution...
By taking these characteristics into account (in survey methodology 
wording, using auxiliary data), we could improve the estimation at the 
national-level.
More specifically, this would consist of :
1) on the police casualty data, model the number of road victims at the 
nation-wide level as a function of the number of road victims in the Rhône 
county and as a function of county characteristics such as urbanisation 
rate, road types distribution, and ...?
2) apply the obtained model on the registry data to get a nation-wide 
picture of the registry

The underlying assumption would be that one can find the appropriate county 
characteristics so that by kind of re-weigthing according to these, one can 
build a good un-biased estimator from a very distorted sample
I am kind of sceptical about that ; I think this is a very strong assumption.

Second strategy (also regression estimation):
1) to model, on the Rhône county data, registry figures (number of road 
victims, by &) as a function of police figures and as a function of bias 
factors found between the two  (this has been studied ; the major ones are: 
injury severity, road user type, single vs. multiple-vehicle crash)
2) apply the obtained model on the national police figures in order to 
obtain a nation-wide picture of the registry

The underlying assumption is that police reporting practice is the same 
all-over France.

The model would be in the framework of Generalized Linear Model : poisson 
regression or negative binomial regression

  What do you think about this way of doing ? any comment, suggestion ?


LITERATURE:

Some literature search was done in Pubmed (2 years ago ; I need to update 
it) ; this has provided some interesting papers but I am surprised I did 
not find more.
The papers I found could be classified under ratio estimation or regression 
estimaton ; they could also be classified according to an epidemiological 
point of view :
1) extrapolation adjusting for confusion factors (regression estimation)
age and sex at least :
Jones, I. E., R. Cannan, et al. (2000). "Distal forearm fractures in New 
Zealand children: annual rates in a geographically defined area." New 
Zealand Medicine Journal 113(1120): 443-5.
Takala, J. (1999). "Global estimates of fatal occupational accidents." 
Epidemiology 10(5): 640-6.

adjusting on several confusion factors:
Frey, C. M., E. J. Feuer, et al. (1994). "Projection of incidence rates to 
a larger population using ecologic variables." Statistics in Medecine 
13(17): 1755-70.
Mariotto, A., R. Capocaccia, et al. (2002). "Projecting SEER cancer 
survival rates to the US: an ecological regression approach." Cancer Causes 
and Control 13(2): 101-11.

2) Extrapolation from a correlated morbibity or from the associated 
mortality (ratio estimation):
I found some in drug addiction :
Gossop, M., J. Strang, et al. (1994). "A ratio estimation method for 
determining the prevalence of cocaine use." Bristish Journal of Psychiatry 
164(5): 676-9.
Kraus, L., P. Kummler, et al. (1999). Methodological guidelines to estimate 
the prevalence of problem drug use on the national level. Lisbon, European 
Monitoring Centre for Drugs and Drug Addiction: 1-47.
Kraus, L., R. Augustin, et al. (2003). "Estimating prevalence of problem 
drug use at national level in countries of the European Union and Norway." 
Addiction 98(4): 471-85.

some in traffic injury :
Hvoslef, H. (1994). Under-reporting of road traffic accidents recorded by 
the police at the international level, OECD-International Road Traffic 
Accident database.
Stutts, J. C., J. E. Williamson, et al. (1988). Hospital records and police 
accidents reports: two sources of information on bicycle-related injuries 
and accidents. 32nd proceedings Association for the Advancement of 
Automative Medicine, Seattle, USA.
James, H. F. (1991). "Under-reporting of road traffic accidents." Traffic 
Engineering and Control 32: 573-583.

3) Extrapolation from a correlated morbibidy or associated mortality AND 
confusion factors (regression estimation):
Jensen, O. M., J. Esteve, et al. (1990). "Cancer in the European Community 
and its member states." European Journal of Cancer 26(11-12): 1167-1256.
Menegoz, F., R. J. Black, et al. (1997). "Cancer incidence and mortality in 
France in 1975-95." European Journal of Cancer Prevention 6(5): 442-466.

As I said I am surprised I did not find more. I mean, isn't extrapolation 
to the nation-wide level an issue for (at least) all regional registries, 
which exist in different areas of health?

I am concerned I may have missed some important papers ; do you know about 
other papers, studies... ?

Also, I was not sure about which keywords to use in doing this literature 
search. I have used:
extrapolation, projection, prediction, (different combinations, with or 
without: ecological regression, incidence, nation-wide/state/area/county...)
Would you suggest other keywords?

I am concerned I may have missed some « field ». For instance I don't know 
anything about spatial epidemiology ; the only bits I have grasped about it 
give me the impression that it does not tackle the issue of extrapolating 
to a larger area; does anyone confirm, or on the contrary has some 
suggestions about what to look for in this field ?

What about other field(s) outside medical statistic ? do you know if 
similar things have been done ?
(maybe I could send this later to all-stat mailing list ; But I am first of 
all interested in receiving comments from people in my field)

Confidence intervals :
none of the papers using regression estimator method has displayed 
confidence intervals... the only solution I see is bootstrap. Any 
suggestion/comment ?

Predictive value of the model:
How do I measure the « goodness of prediction » of the model ? (this is my 
way of calling it as an analogy to « goodness of fit ») I could not find 
any « goodness of prediction » statistic& Is there anything like that ?
The only suggestion I was given by colleagues is to split the rhone county 
data into two sets, one to be used to build a model and the other one on 
which to apply the model and compare the predictions with the observations 
; which criteria do I use to decide whether the predictions are OK ?
Also I am a bit reluctant to do that as I don't have that many data to work 
on (in some categories : higher level of severity, or truck drivers or ...)
any comment, suggestion ?

Further issues :
It can get a bit more complicated :
number of road casualties at the local level : instead of considering the 
observed count in the registry, we could estimate it by capture-recapture 
on the two sources : registry (based on hospitals) and police files, as a 
record-linkage between the two has shown that a number of casualties are 
only found in one source.
This mean an additional level of estimation; how do I take this into account?

Thank you in advance for comments/suggestions on any part of this whole 
project!


Emmanuelle Amoros

Epidemiological Research and Surveillance Unit in Transport, Occupation and 
Environment (UMRESTTE)
French National Institute for Transport and Safety Research (INRETS)

INRETS - UCBL - InVS UMRESTTE
25 Avenue Francois Mitterrand
Case 24
69675 Bron cedex
France

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