Related Experiment Video
Updated: Jun 15, 2026
10:46
A Method of Trigonometric Modelling of Seasonal Variation Demonstrated with Multiple Sclerosis Relapse Data
Published on: December 9, 2015
Modelling continuous exposures with a 'spike' at zero: a new procedure based on fractional polynomials
Patrick Royston1, Willi Sauerbrei, Heiko Becher
1Hub for Trials Methodology Research, MRC Clinical Trials Unit and University College London, 222 Euston Road, London NW1 2DA, UK. pr@ctu.mrc.ac.uk
Statistics in Medicine
|March 2, 2010
Summary
This study introduces an extended fractional polynomial method to model dose-response relationships when a portion of subjects are unexposed. The new statistical approach improves modeling for continuous exposures like alcohol or occupational hazards.
Area of Science:
- Epidemiology
- Biostatistics
- Statistical Modeling
Background:
- Estimating dose-response functions for continuous exposures is crucial in epidemiology.
- A common challenge is handling datasets where a proportion of subjects remain unexposed.
Purpose of the Study:
- To extend the fractional polynomial method for dose-response modeling to accommodate a proportion of unexposed subjects.
- To develop a statistical procedure for effectively modeling continuous exposures with an unexposed fraction.
Main Methods:
- An extension of the fractional polynomial method incorporating a binary variable for the unexposed fraction.
- A two-stage procedure to assess the necessity of the binary variable and/or the continuous exposure function.
- Application to multivariable situations and illustration with three diverse datasets.
Main Results:
- The proposed procedure yielded differing results across three datasets.
- In one case, only the binary variable was significant; in others, both the binary variable and fractional polynomial functions were required.
- The selected functions included monotonic and non-monotonic (with a minimum) forms; confounder adjustment had minimal impact in one instance.
Conclusions:
- The novel procedure offers a valuable enhancement for dose-response modeling in the presence of an unexposed fraction.
- The method is practical, easily implemented using standard statistical software.
Related Concept Videos
01:11Sampling Continuous Time Signal
In signal processing, a continuous-time signal can be sampled using an impulse-train sampling technique, followed by the zero-order hold method. Impulse-train sampling involves the use of a periodic impulse train, which consists of a series of delta functions spaced at regular intervals determined by the sampling period. When a continuous-time signal is multiplied by this impulse train, it generates impulses with amplitudes corresponding to the signal's values at the sampling points.
In the...
In the...
01:14Parametric Survival Analysis: Weibull and Exponential Methods
Parametric survival analysis models survival data by assuming a specific probability distribution for the time until an event occurs. The Weibull and exponential distributions are two of the most commonly used methods in this context, due to their versatility and relatively straightforward application.
Weibull Distribution
The Weibull distribution is a flexible model used in parametric survival analysis. It can handle both increasing and decreasing hazard rates, depending on its shape parameter...
Weibull Distribution
The Weibull distribution is a flexible model used in parametric survival analysis. It can handle both increasing and decreasing hazard rates, depending on its shape parameter...
01:16Basic Discrete Time Signals
The unit step sequence is defined as 1 for zero and positive values of the integer n. This sequence can be graphically displayed using a set of eight sample points, showing a step function starting from n=0 and remaining constant thereafter.
The unit impulse or sample sequence is mathematically expressed as zero for all n values except at n=0, where it is one. The unit impulse sequence, denoted by δ(n), is the first difference of the unit step sequence, while the unit step sequence u(n) is the...
The unit impulse or sample sequence is mathematically expressed as zero for all n values except at n=0, where it is one. The unit impulse sequence, denoted by δ(n), is the first difference of the unit step sequence, while the unit step sequence u(n) is the...
01:22Basic Continuous Time Signals
Basic continuous-time signals include the unit step function, unit impulse function, and unit ramp function, collectively referred to as singularity functions. Singularity functions are characterized by discontinuities or discontinuous derivatives.
The unit step function, denoted u(t), is zero for negative time values and one for positive time values, exhibiting a discontinuity at t=0. This function often represents abrupt changes, such as the step voltage introduced when turning a car's...
The unit step function, denoted u(t), is zero for negative time values and one for positive time values, exhibiting a discontinuity at t=0. This function often represents abrupt changes, such as the step voltage introduced when turning a car's...
01:26Exponential Equations for Modeling Growth
Exponential models are essential for describing rapid, multiplicative changes in natural systems, such as population growth. When a population doubles at regular intervals, the process can be modeled using a suitable base. For instance, a bacterial culture that doubles every three hours follows the model n(t)=n0⋅2t/3, where n(t) is the population at the time t.A more general model uses the natural base e, especially for continuous growth. This takes the form n(t)=n0⋅ert, where r is the relative...
01:29Introduction to Exponential Functions
Exponential functions are fundamental in modeling dynamic processes where the rate of change is proportional to the current value. Defined by f(x) = bx, where b is a positive constant not equal to one, they form the basis for describing processes of growth and decay depending on whether the base b is greater than or less than one.Exponential models describe situations where change occurs at a rate proportional to the current amount. These include phenomena such as bacterial proliferation,...