**| 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 |
or_{1} = 1 (referent) |

2 | c |
d |
or_{2} = bc/ad |

... | ... | ... | ... |

R |
y |
z |
or_{R} = 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 | or_{2} = 0.92 |

3 | 34 | 88 | or_{3} = 0.91 |

4 | 32 | 53 | or_{4} = 1.42 |

5 (low) | 20 | 30 | or_{5} = 1.57 |

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

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

*H*_{0}: no trend in the population

H_{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 c^{2}_{stat} = 3.54 with 1 *df*, *p* = .060.

**(1) BD1.ZIP .**

**(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.

IUD Use (months) |
Cases ( n = 89) |
Controls ( 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.