International Biometric Society
META-ANALYSIS OF J-SHAPED DOSE-RESPONSE CURVES WITH LIKELIHOOD-BASED ASSIGNMENTS
OF GROUPED EXPOSURE LEVELS
Kunihiko Takahashi1, Hiroyuki Nakao2, Satoshi Hattori3
1
Department of Biostatistics, Nagoya University Graduate School of Medicine, Japan
Center for Public Health Informatics, National Institute of Public Health, Japan
3
Biostatistics Center, Kurume University, Japan
2
In epidemiological studies, it is often necessary to determine the relationship between exposure levels and the risk of disease. Exposure levels are often available in intervals. Also in
meta-analysis to examine the relationship based on aggregated data, we often have to rely
on the summarized data available from research reports with exposure levels in intervals.
One approach is applying regression models describing the relationship and make a summary. When performing a regression analysis of summarized response data that are
grouped into intervals, many researchers use the midpoints as the assigned exposure levels
for each interval. Results of regression analysis with grouped data may be sensitive to the
assignment of the exposure levels. Recently, Takahashi and Tango (2010) proposed a
method for assigning values by applying the likelihood approach, and they showed the procedure can produce a more accurate linear regression coefficient than the typical procedure
which uses the midpoint values.
On the other hand, some studies have reported that the risk of disease has a nonlinear relationship with the exposure level. For example, it is known that the association between alcohol and coronary heart disease or total mortality may be depicted as a J-shaped curve.
Curve-fitting methods based on a fractional polynomial model or a spline model have often
been applied to these nonlinear dose-response associations for regression. Larsson et al.
(2011) discussed that cubic spline regression models may have many advantages over polynomials.
We propose a procedure for assessing nonlinear associations between exposure levels
and the risk of disease from a summarized grouped data, which is based on the assignment
of levels to grouped exposure intervals by applying the likelihood-based assignment procedure. In particular, we focus on the restricted cubic spline model for J-shaped doseresponse curves. Also this procedure can provide the log relative risk on each exposure levels relative to that of 0, even if the level of reference category for reported RRs was not 0.
Numerical illustrations and comparisons based on simulations showed that the proposed
procedure can yield better estimates for curves than those obtained using the typical assignment method based on the midpoints of each interval. And we demonstrate a metaanalysis of J-shaped dose-response curves for the relationship between alcohol consumption and total mortality, based on summarized data which were used in a meta-analysis by
Di Castelnovo et al. (2006).
References:
Takahashi K, Tango T (2010). Assignment of grouped exposure levels for trend estimation
in a regression analysis of summarized data. Statistics in Medicine 29: 2605-2616.
Larsson SC, Orsini N (2011). Coffee consumption and risk of stroke: a dose-response metaanalysis of prospective studies. American Journal of Epidemiology 174(9): 993-1001.
Di Castelnuovo A, Costanzo S, Bagnardi V, Donati MB, Iacoviello L, de Gaetano G (2006).
Alcohol dosing and total mortality in men and women: an updated meta-analysis of 34 prospective studies. Archives of Internal Medicine 499(22): 2437-2445.
International Biometric Conference, Florence, ITALY, 6 – 11 July 2014