A simple-to-use method incorporating genomic markers into prostate cancer risk prediction tools facilitated future validation

Grill, Sonja; Fallah, Mahdi; Leach, Robin J.; Thompson, Ian M.; Hemminki, Kari; Ankerst, Donna P.

doi:10.1016/j.jclinepi.2015.01.006

Cited by 8 publications

(12 citation statements)

References 60 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…If B is a binary variable, the logistic regression approximation in Section 3 does not hold and the approximate relationship in equation is not applicable. However, by Bayes theorem, there is a relationship equation connecting Pr( Y =1| X ),Pr( Y =1| X , B ) and f ( B | X , Y ) (Grill et al ., ; Satten and Kupper, ):

\frac{Pr (Y = 1 | X, B)}{Pr (Y = 0 | X, B)} = \frac{f (B | X, Y = 1)}{f (B | X, Y = 0)} \frac{Pr (Y = 1 | X)}{Pr (Y = 0 | X)} .

Thus, when B is binary, we need to define a model for B | X , Y instead of a model for B | X . Assume that

logit false{Pr (B = 1 | X, Y) false} = {normalΣ}_{j = 0}^{p} ϕ_{j} {boldX}_{j} + ϕ_{p + 1} Y

.…”

Section: Statistical Approaches When B Is Binarymentioning

confidence: 99%

“…If B is a binary variable, the logistic regression approximation in Section 3 does not hold and the approximate relationship in equation (6) is not applicable. However, by Bayes theorem, there is a relationship equation connecting Pr.Y = 1|X/, Pr.Y = 1|X, B/ and f.B|X, Y/ (Grill et al, 2015;Satten and Kupper, 1993):…”

Section: The Approximate Relationship Equation When B Is Binarymentioning

confidence: 99%

“…They then multiplied the Gail risk estimate and the multiplicative risk score to give a combined risk score. Grill et al (2015) proposed a simple method of incorporating new markers via Bayes theorem. They updated the posterior odds of developing cancer based on both standard risk factors and new markers by using the likelihood ratio incorporating dependence between the two sets of risk factors to adjust the prior odds of developing cancer based on standard risk alone.…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Informing a Risk Prediction Model for Binary Outcomes with External Coefficient Information

Cheng

Taylor

et al. 2018

Journal of the Royal Statistical Society Series C: Applied Statistics

View full text Add to dashboard Cite

Summary. We consider a situation where there is rich historical data available for the coefficients and their standard errors in an established regression model describing the association between a binary outcome variable Y and a set of predicting factors X, from a large study. We would like to utilize this summary information for improving estimation and prediction in an expanded model of interest, Y|X, B. The additional variable B is a new biomarker, measured on a small number of subjects in a new dataset. We develop and evaluate several approaches for translating the external information into constraints on regression coefficients in a logistic regression model of Y|X, B. Borrowing from the measurement error literature we establish an approximate relationship between the regression coefficients in the models Pr(Y = 1|X, β), Pr(Y = 1|X, B, γ) and E(B|X, θ) for a Gaussian distribution of B. For binary B we propose an alternate expression. The simulation results comparing these methods indicate that historical information on Pr(Y = 1|X, β) can improve the efficiency of estimation and enhance the predictive power in the regression model of interest Pr(Y = 1|X, B, γ). We illustrate our methodology by enhancing the High-grade Prostate Cancer Prevention Trial Risk Calculator, with two new biomarkers prostate cancer antigen 3 and TMPRSS2:ERG.

show abstract

\frac{Pr (Y = 1 | X, B)}{Pr (Y = 0 | X, B)} = \frac{f (B | X, Y = 1)}{f (B | X, Y = 0)} \frac{Pr (Y = 1 | X)}{Pr (Y = 0 | X)} .

Thus, when B is binary, we need to define a model for B | X , Y instead of a model for B | X . Assume that

logit false{Pr (B = 1 | X, Y) false} = {normalΣ}_{j = 0}^{p} ϕ_{j} {boldX}_{j} + ϕ_{p + 1} Y

.…”

Section: Statistical Approaches When B Is Binarymentioning

confidence: 99%

Section: The Approximate Relationship Equation When B Is Binarymentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Informing a Risk Prediction Model for Binary Outcomes with External Coefficient Information

Cheng

Taylor

et al. 2018

Journal of the Royal Statistical Society Series C: Applied Statistics

View full text Add to dashboard Cite

show abstract

“…A special case of the LR approach defined previously, described, for example, in , and used by to update a prostate cancer model with genetic information, is to assume that the new marker Z is independent of X in cases and non‐cases, and therefore,

{LR}_{Y} ((), Z | boldX) = \frac{P (Z | Y = 1, boldX)}{P (Z | Y = 0, boldX)} = \frac{P (Z | Y = 1)}{P (Z | Y = 0)} = {LR}_{Y} ((), Z) .

When case‐control data are used for updating, and the outcome is rare, then if X is independent of Z in the general population, X and Z are also independent in cases and controls, as shown, for example, in . The assumption of independence of X and Z in the general population is somewhat weaker than assuming independence conditional on outcome.…”

Section: Estimating An Updated Risk Prediction Model Rxzmentioning

confidence: 99%

“…Estimating Y (Z| ) based on fitting separate models for cases (Y = ) and non-cases (Y = ) For P(Z| ) in the exponential family, and assuming rare disease, Equations (12) and (13) show that the same general exponential form holds for P(Z| , Y), Y = 0, 1. Thus, we can separately estimate the numerator and the denominator of LR Y (Z| ) in Equation (7) by fitting two different models to the new data set, one to cases (Y = 1) and one to controls (Y = 0).…”

Section: Joint Estimation Of Y (Z| )mentioning

confidence: 99%

Comparison of approaches for incorporating new information into existing risk prediction models

Grill

Ankerst

Gail

et al. 2016

Statistics in Medicine

Self Cite

View full text Add to dashboard Cite

We compare the calibration and variability of risk prediction models that were estimated using various approaches for combining information on new predictors, termed 'markers', with parameter information available for other variables from an earlier model, which was estimated from a large data source. We assess the performance of risk prediction models updated based on likelihood ratio (LR) approaches that incorporate dependence between new and old risk factors as well as approaches that assume independence ('naive Bayes' methods). We study the impact of estimating the LR by (i) fitting a single model to cases and non-cases when the distribution of the new markers is in the exponential family or (ii) fitting separate models to cases and non-cases. We also evaluate a new constrained maximum likelihood method. We study updating the risk prediction model when the new data arise from a cohort and extend available methods to accommodate updating when the new data source is a case-control study. To create realistic correlations between predictors, we also based simulations on real data on response to antiviral therapy for hepatitis C. From these studies, we recommend the LR method fit using a single model or constrained maximum likelihood. Copyright © 2016 John Wiley & Sons, Ltd.

show abstract

Synthetic data method to incorporate external information into a current study

Taylor

Cheng

et al. 2019

Can J Statistics

View full text Add to dashboard Cite

We consider the situation where there is a known regression model that can be used to predict an outcome, Y, from a set of predictor variables X. A new variable B is expected to enhance the prediction of Y. A dataset of size n containing Y,X and B is available, and the challenge is to build an improved model for Y|X,B that uses both the available individual level data and some summary information obtained from the known model for Y|X. We propose a synthetic data approach, which consists of creating m additional synthetic data observations, and then analyzing the combined dataset of size n + m to estimate the parameters of the Y|X,B model. This combined dataset of size n + m now has missing values of B for m of the observations, and is analyzed using methods that can handle missing data (e.g., multiple imputation). We present simulation studies and illustrate the method using data from the Prostate Cancer Prevention Trial. Though the synthetic data method is applicable to a general regression context, to provide some justification, we show in two special cases that the asymptotic variances of the parameter estimates in the Y|X,B model are identical to those from an alternative constrained maximum likelihood estimation approach. This correspondence in special cases and the method's broad applicability makes it appealing for use across diverse scenarios. The Canadian Journal of Statistics 47: 580–603; 2019 © 2019 Statistical Society of Canada

show abstract

A simple-to-use method incorporating genomic markers into prostate cancer risk prediction tools facilitated future validation

Cited by 8 publications

References 60 publications

Informing a Risk Prediction Model for Binary Outcomes with External Coefficient Information

Informing a Risk Prediction Model for Binary Outcomes with External Coefficient Information

Comparison of approaches for incorporating new information into existing risk prediction models

Synthetic data method to incorporate external information into a current study

Contact Info

Product

Resources

About