Development and evaluation of risk prediction models in the presence of correlated markers and non-linear associations between markers and outcomes using logistic regression and net benefit analysis

With 6 million pregnancies a year in the US, one of the most prevalent screening tests is prenatal screening for Down syndrome. A woman's risk of carrying an affected fetus is estimated using maternai age and 7 markers. In this thesis, we examine the standard method for estimating a woman's risk which multiplies an a priori risk based on maternai age atone by a likelihood ratio which reflects the increased odds of carrying an affected fetus based on the measured markers. This method ignores the correlations among the individual markers and between the markers and the a priori risk. We show that this assumption of independence among the markers leads to biased estimates of absolute risk. Second, we propose logistic regression analysis as an alternative method for combining the markers. Using simulated datasets, we show that absolute risk estimates from logistic regression have less variability and better calibration than the standard method and perform as well as the standard method in terms of predictive accuracy, producing sensitivities as high as 97% with false positive fractions as low as 2%. Next, we use generalized additive models (GAMs) to assess non-linearity in the relationships between maternai age and the individual markers and risk of carrying an affected fetus. Based on the results of the GAM models, we modified the logistic regression model to account for the non-linear relationships and evaluated this new model on simulated datasets. The modified logistic regression model produced higher sensitivities and lower false positive fractions as compared to the standard method and original logistic model. Finally, we use the novel methods of decision curve and net benefit analyses to compare predictive models across various thresholds for positive screening results. We developed a measure of public health cost that quantifies the number of unnecessary invasive procedures that must be performed to detect one affected pregnancy. Ultimately we find that the logistic regression model is easier to understand and use, performs better than the standard method for estimating a woman's risk of carrying an affected fetus and if implemented would decrease the number of unnecessary invasive procedures performed each year.