Smoothing in occupational cohort studies: an illustration based on penalised splines

• Published in: Occupational and environmental medicine (London, England) Vol. 61; no. 10; pp. 854 - 860
• Main Authors: Eisen, E A, Agalliu, I, Thurston, S W, Coull, B A, Checkoway, H
• Format: Journal Article
• Language: English
• Published: London BMJ Publishing Group Ltd 01.10.2004; BMJ Publishing Group; BMJ; BMJ Publishing Group LTD; BMJ Group
• Subjects: Adult; Aged; Aged, 80 and over; AIC; Akaike’s Information Criterion; Biological and medical sciences; Cohort Studies; Cox regression; Data smoothing; degrees of freedom; Diatomaceous earth; Disease models; Dose response relationship; exposure-response models; GAM; generalised additive model; hazard ratio; Health hazards; Health promotion; Health risks; Humans; Linear regression; Lung cancer; Lung neoplasms; Lung Neoplasms - epidemiology; Male; Medical sciences; Methods; Middle Aged; Miscellaneous; Modeling; Models, Statistical; Mortality; Occupational Diseases - epidemiology; Occupational exposure; Occupational Exposure - adverse effects; Occupational medicine; Original; Outdoor air quality; P-splines; Parametric models; penalised splines; Polynomials; Public health; Public health. Hygiene-occupational medicine; Reference Values; regression diagnostics; relative risk; Risk assessment; Risk Assessment - methods; Risk Factors; Silica; Studies; USA, California; Human; Lung cancer; Regression analysis; Occupational exposure; Statistical study; Modeling; Bronchopulmonary malignant tumor; Spline; Cox model; Cohort study; Risk factor; Graphic method; Occupational medicine
• ISSN: 1351-0711; 1470-7926
• DOI: 10.1136/oem.2004.013136

Aims: To illustrate the contribution of smoothing methods to modelling exposure-response data, Cox models with penalised splines were used to reanalyse lung cancer risk in a cohort of workers exposed to silica in California’s diatomaceous earth industry. To encourage application of this approach, computer code is provided. Methods: Relying on graphic plots of hazard ratios as smooth functions of exposure, the sensitivity of the curve to amount of smoothing, length of the exposure lag, and the influence of the highest exposures was evaluated. Trimming and data transformations were used to down-weight influential observations. Results: The estimated hazard ratio increased steeply with cumulative silica exposure before flattening and then declining over the sparser regions of exposure. The curve was sensitive to changes in degrees of freedom, but insensitive to the number or location of knots. As the length of lag increased, so did the maximum hazard ratio, but the shape was similar. Deleting the two highest exposed subjects eliminated the top half of the range and allowed the hazard ratio to continue to rise. The shape of the splines suggested a parametric model with log hazard as a linear function of log transformed exposure would fit well. Conclusions: This flexible statistical approach reduces the dependence on a priori assumptions, while pointing to a suitable parametric model if one exists. In the absence of an appropriate parametric form, however, splines can provide exposure-response information useful for aetiological research and public health intervention.