Trend tests for the evaluation of exposure-response relationships in epidemiological exposure studies

One possibility for the statistical evaluation of trends in epidemiological exposure studies is the use of a trend test for data organized in a 2 × k contingency table. Commonly, the exposure data are naturally grouped or continuous exposure data are appropriately categorized. The trend test should be sensitive to any shape of the exposure-response relationship. Commonly, a global trend test only determines whether there is a trend or not. Once a trend is seen it is important to identify the likely shape of the exposure-response relationship. This paper introduces a best contrast approach and an alternative approach based on order-restricted information criteria for the model selection of a particular exposure-response relationship. For the simple change point alternative H1 : π1 = ...= πq <πq+1 = ... = πk an appropriate approach for the identification of a global trend as well as for the most likely shape of that exposure-response relationship is characterized by simulation and demonstrated for real data examples. Power and simultaneous confidence intervals can be estimated as well. If the conditions are fulfilled to transform the exposure-response data into a 2 × k table, a simple approach for identification of a global trend and its elementary shape is available for epidemiologists.

[1]  Kazuo Anraku,et al.  An information criterion for parameters under a simple order restriction , 1999 .

[2]  Ludwig A. Hothorn,et al.  Trend Tests for Dichotomous Endpoints with Application to Carcinogenicity Studies , 1997 .

[3]  Y. Nishiwaki,et al.  Lack of Relationship between Occupational Exposure to Carbon Disulfide and Endocrine Dysfunction: A Six‐year Cohort Study of the Japanese Rayon Workers , 2003, Journal of occupational health.

[4]  M. Pike,et al.  Problems involved in including women with simple hysterectomy in epidemiologic studies measuring the effects of hormone replacement therapy on breast cancer risk. , 1998, American journal of epidemiology.

[5]  W. Härdle,et al.  Does male age affect the risk of spontaneous abortion? An approach using semiparametric regression. , 2003, American journal of epidemiology.

[6]  Chihiro Hirotsu,et al.  Use of cumulative efficient scores for testing ordered alternatives in discrete models , 1982 .

[7]  E. A. Cheeseman.  Principles of Medical Statistics, 9th edition , 1972 .

[8]  D. A. Williams,et al.  The comparison of several dose levels with a zero dose control. , 1972, Biometrics.

[9]  W. Schull,et al.  Cataract in atomic bomb survivors based on a threshold model and the occurrence of severe epilation. , 1996, Radiation research.

[10]  S. Greenland.  A meta-analysis of coffee, myocardial infarction, and coronary death. , 1993, Epidemiology.

[11]  P. Rosenbaum.  Does a dose-response relationship reduce sensitivity to hidden bias? , 2003, Biostatistics.

[12]  Leo Breiman,et al.  Bagging Predictors , 1996, Machine Learning.

[13]  T. Raghunathan,et al.  Caffeine Intake in Relation to the Risk of Primary Cardiac Arrest , 1997, Epidemiology.

[14]  S. Peddada,et al.  Tests for Order Restrictions in Binary Data , 2001, Biometrics.

[15]  W J Schull,et al.  Threshold for radiation-related severe mental retardation in prenatally exposed A-bomb survivors: a re-analysis. , 1996, International journal of radiation biology.

[16]  Williams Da,et al.  The comparison of several dose levels with a zero dose control. , 1972 .

[17]  J Benichou,et al.  A comparison of several methods to test for the existence of a monotonic dose–response relationship in clinical and epidemiological studies , 2001, Statistics in medicine.

[18]  D. Waltner-Toews,et al.  Exposure assessment in investigations of waterborne illness: a quantitative estimate of measurement error , 2006, Epidemiologic perspectives & innovations : EP+I.

[19]  C. Holmes,et al.  Generalized monotonic regression using random change points , 2003, Statistics in medicine.

[20]  A. Andersen,et al.  Exposure to different forms of nickel and risk of lung cancer. , 2002, American journal of epidemiology.

[21]  Adolfo Figueiras,et al.  Exposure to residential radon and lung cancer in Spain: a population-based case-control study. , 2002, American journal of epidemiology.

[22]  Chihiro Hirotsu,et al.  Changepoint Analysis as a Method for Isotonic Inference , 2002 .

[23]  Alvan R. Feinstein,et al.  Principles of Medical Statistics , 2001 .

[24]  The penalty for assuming that a monotone regression is linear , 1987 .

[25]  M. Schell,et al.  The Reduced Monotonic Regression Method , 1997 .

[26]  Ludwig A. Hothorn,et al.  An exact Cochran-Armitage test for trend when dose-response shapes are a priori unknown , 1999 .

[27]  J. Benichou,et al.  An alternative test for trend in exposure-response analysis. , 1998, Journal of exposure analysis and environmental epidemiology.

[28]  Frank Bretz,et al.  Evaluation of Animal Carcinogenicity Studies: Cochran‐Armitage Trend Test vs. Multiple Contrast Tests , 2000 .

[29]  Berthold Lausen,et al.  Maximally Selected Rank Statistics for Dose-Response Problems , 2002 .

[30]  S. Heymsfield,et al.  Epidemiology of sarcopenia among the elderly in New Mexico. , 1998, American journal of epidemiology.

[31]  C. Xiong,et al.  On detecting change in likelihood ratio ordering , 2002 .

[32]  F. T. Wright,et al.  Order restricted statistical inference , 1988 .

[33]  L. Hothorn,et al.  Approximate Simultaneous Confidence Intervals for Multiple Contrasts of Binomial Proportions , 2008, Biometrical journal. Biometrische Zeitschrift.

[34]  Georgia Salanti,et al.  Tests for Trend in Binary Response , 2003 .

[35]  J. Olsen,et al.  Residence near high voltage facilities and risk of cancer in children. , 1993, BMJ.

[36]  T. Hothorn,et al.  Simultaneous Inference in General Parametric Models , 2008, Biometrical journal. Biometrische Zeitschrift.

[37]  F. Flamigni,et al.  Dose‐dependent suppression of serum prolactin by cabergoline in hyperprolactinaemia: a placebo controlled, double blind, multicentre study , 1992, Clinical endocrinology.

[38]  Roberto Pastor-Barriuso,et al.  Transition models for change‐point estimation in logistic regression , 2003, Statistics in medicine.

[39]  S. Ruberg,et al.  Detecting dose response with contrasts. , 2000, Statistics in medicine.

[40]  Anthony J. Hayter,et al.  Multiple comparison procedures based on the maximal component of the cumulative chi-squared statistic , 1992 .

[41]  Ludwig A Hothorn,et al.  Multiple Comparisons and Multiple Contrasts in Randomized Dose-Response Trials—Confidence Interval Oriented Approaches , 2006, Journal of biopharmaceutical statistics.

[42]  Frank Bretz,et al.  Statistical Analysis of Monotone or Non-monotone Dose–Response Data from In Vitro Toxicological Assays , 2003, Alternatives to laboratory animals : ATLA.

[43]  S. de Sanjosé,et al.  Regular use of hair dyes and risk of lymphoma in Spain. , 2005, International journal of epidemiology.

[44]  A. Agresti,et al.  The analysis of contingency tables under inequality constraints , 2002 .

[45]  Keith J. Worsley,et al.  On the Likelihood Ratio Test for a Shift in Location of Normal Populations , 1979 .

[46]  H. Akaike.  A new look at the statistical model identification , 1974 .

[47]  A. B. Hill,et al.  Principles of Medical Statistics , 1950, The Indian Medical Gazette.

[48]  Limin Peng,et al.  Model selection under order restriction , 2002 .

[49]  Frank Bretz,et al.  On Multiple Comparisons in R ∗ , 2004 .

[50]  M. Thun,et al.  Coffee consumption, gender, and Parkinson's disease mortality in the cancer prevention study II cohort: the modifying effects of estrogen. , 2004, American journal of epidemiology.

[51]  P Royston,et al.  The use of fractional polynomials to model continuous risk variables in epidemiology. , 1999, International journal of epidemiology.

[52]  S Greenland,et al.  Avoiding power loss associated with categorization and ordinal scores in dose-response and trend analysis. , 1995, Epidemiology.

[53]  Tarone Re,et al.  The relation between score tests and approximate UMPU tests in exponential models common in biometry. , 1983 .

[54]  Chihiro Hirotsu,et al.  Simultaneous confidence intervals based on one-sided max t test , 2000 .

[55]  Frank Bretz,et al.  Detecting dose–response using contrasts: asymptotic power and sample size determination for binomial data , 2002, Statistics in medicine.

[56]  C. Redmond,et al.  Occupationally Related Cancer Risk Among Coke Oven Workers: 30 Years of Follow-Up , 1995, Journal of occupational and environmental medicine.

[57]  D. Weed,et al.  The practice of causal inference in cancer epidemiology. , 1996, Cancer epidemiology, biomarkers & prevention : a publication of the American Association for Cancer Research, cosponsored by the American Society of Preventive Oncology.

[58]  J. Benichou,et al.  Tests for Monotonic Trend from Case‐Control Data: Cochran‐Armitage‐Mantel Trend Test, Isotonic Regression and Single and Multiple Contrast Tests , 2004 .