Binary Outcome, Test for Trend

| Background | Test for Trend | Exercises | References |


This chapter a binomial outcome when the exposure is ordinal (e.g., non-smoker, light-smoker, moderate-smoker, and heavy-smoker). Our goal is to determine whether there is a dose-dependent relations between the exposure and outcome. Data are cross-tabulated to form an R-by-2 table with exposure along rows and disease status along columns. The following notation is used:

Exposure Level Disease + Disease - Odds Ratio
1 a b or1 = 1 (referent)
2 c d or2 = bc/ad
... ... ... ...
R y z orR = yb/az

We are looking for an upward or downward trend in the odds ratios.

Illustrative data example. Suppose data on smoking (disease variable) and socioeconomic status (exposure variable) shows: (Chang et al., 1983):

SEX Smoke + Smoke - Odds Ratio
1 (high) 17 40 referent
2 76 195 or2 = 0.92
3 34 88 or3 = 0.91
4 32 53 or4 = 1.42
5 (low) 20 30 or5 = 1.57

A possible upward trend is seen, especially seen between levels 3 and 5.

Test for Trend

A Mantel-Haenszel extension of the chi-square test for trend (Schlesselman 1982, pp. 203-206) is used to test

H0: no trend in the population
1: trend in the population.

After cross-tabulating the data, this is computed by clicking StatCalc > Chi-square for trend. Output for the illustrative data is:

EpiInfo Version 6               Statcalc                    November 1993

                    Analysis For Linear Trend In Proportions

     Chi Square for                               Exposure
       linear trend :   3.535                        Score       Odds Ratio
     p value        : 0.06010                         1.00             1.00
                                                      2.00             0.92
                                                      3.00             0.91
                                                      4.00             1.42
                                                      5.00             1.57

Under the null hypothesis, the chi-square statistic has a chi-square distribution with 1 degree of freedom. The illustrative example shows c2stat = 3.54 with 1 df, p = .060.


(1) BD1.ZIP .French Case-Control Study of Esophageal Cancer (Breslow & Day, 1980; Tuyns, 1977). Use the data in BD1.REC to determine if there is a dose-response relationship between alcohol (variable ALC) and esophageal cancer (variable ESOPH_CA). Data are cross-tabulated with ANALYSIS and tested with STATCALC.

(2) IUD. Intrauterine Device Use and Infertility (Rosner, 1990, p. 382; Cramer et al., 1985).The table below contains cross-tabulated data from a case-control study on intrauterine device use and infertility. Do these data provide evidence of a dose-response relationship? Justify your response with the appropriate statistics.

(n = 89)
(n = 640)
< 3 10 53
3 - 17 23 200
18 - 35 20 168
36+ 36 219

(3) EAR.ZIP. Otitis Media Clinical Trial (Mandel et al., 1982; Rosner, 1990, p. 68). Data in EAR.REC are based on a clinical trial to determine the efficacy of a 14-day course of cefaclor and amoxicillin in the treatment of otitis media. Test for trend in clearance rates (CLEAR) by AGE.



Breslow, N. E., & Day, N. E.(1980). Statistical Methods in Cancer Research. Volume 1--The Analysis of Case-Control Studies. Lyon: International Agency for Research on Cancer.

Chang, C. L., Selvin, S., Langhauser, C. (1983). Biology and Public Health Statistics: BioEnv 130A. Unpublished course Reader, University of California, Berkeley.

Cramer, D. W., Schiff, I., Schoenbaum, S. C., et al. (1985). Tubal infertility and the intrauterine device. New England Journal of Medicine, 312, 941 - 917.

Mandel, E., Bluestone, C. D., Rockette, H. E., Blatter, M. M., Reisinger, K. S., Wucher, F. P., & Harper, J. (1982). Duration of effusion after antibiotic treatment for acute otitis media: comparison of cefaclor and amoxicillin. Pediatric Infectious Diseases, 1, 310 - 316.

Rosner, B. (1990). Fundamentals of Biostatistics (3rd ed.) Boston: PWS - Kent Publishing.

Schlesselman S. (1982). Case-Control Studies. New York: Oxford, pp. 203-206.

Tuyns, A. J., Péquignot, G., & Jensen, O. M.. (1977). Le cancer de l'oesophage en Ille-et Vilaine en function des niveaux de consommation d'alcool et de tabac. Des risques qui se multiplient. Bull Cancer, 64, 45 - 60.