sj-pdf-1-smm-10.1177_09622802221129042 - Supplemental material for Standardization of continuous and categorical covariates in sparse penalized regressions

Supplemental material, sj-pdf-1-smm-10.1177_09622802221129042 for Standardization of continuous and categorical covariates in sparse penalized regressions by Xiang Li, Yong Ma and Qing Pan in Statistical Methods in Medical Research</p

Studies identification, inclusion and exclusion.

<p>Studies identification, inclusion and exclusion.</p

Meta-analysis of the <i>MDM2</i> SNP309 T>G polymorphism on gastric cancer.

a<p>Random-effects model was used when <i>P</i> value for heterogeneity test <0.05; otherwise, fix-effects model was used.</p>b<p><i>P</i> value of Q-test for heterogeneity test.</p

Sample data following Weibull distributions with and as a step function of .

<p>: covariate with 7 distinct values; : number of observations at each value; : step function of with 4 distinct values; : estimated at each value before the implementation of the reduced isotonic regression algorithm; : standard error of the .</p><p>Sample data following Weibull distributions with and as a step function of .</p

Number of steps identified with various event numbers and percent censored.

<p>The combination of “Sample N” and “%censore” is used to yield the targeted number of events in the “Event N” column, repeated 1000 times.</p><p>Number of steps identified with various event numbers and percent censored.</p

Characteristics of literatures included in the meta-analysis.

a<p>HWE, Hardy-Weinberg equilibrium.</p

Identifying Change Points in a Covariate Effect on Time-to-Event Analysis with Reduced Isotonic Regression

<div><p>Isotonic regression is a useful tool to investigate the relationship between a quantitative covariate and a time-to-event outcome. The resulting non-parametric model is a monotonic step function of a covariate <i>X</i> and the steps can be viewed as change points in the underlying hazard function. However, when there are too many steps, over-fitting can occur and further reduction is desirable. We propose a reduced isotonic regression approach to allow combination of small neighboring steps that are not statistically significantly different. In this approach, a second stage, the reduction stage, is integrated into the usual monotonic step building algorithm by comparing the adjacent steps using appropriate statistical testing. This is achieved through a modified dynamic programming algorithm. We implemented the approach with the simple exponential distribution and then its extension, the Weibull distribution. Simulation studies are used to investigate the properties of the resulting isotonic functions. We apply this methodology to the Diabetes Control and Complication Trial (DCCT) data set to identify potential change points in the association between HbA1c and the risk of severe hypoglycemia.</p></div

Begg's funnel plot for publication bias test (GG vs. TT).

<p>Each point represents a separate study for the indicated association. Log[or], natural logarithm of odds ratio. Horizontal line, mean effect size.</p

Forest plot of gastric cancer risk associated with the <i>MDM2</i> SNP309 (GG vs. TT).

<p>The squares and horizontal lines correspond to the study-specific OR and 95% CI. The area of the squares reflects the study-specific weight (inverse of the variance). The diamond represents the summary OR and 95% CI.</p

Precision of parameter estimates with various event numbers and percent censored.

<p>For the mean and mean squared error columns, the first row is the mean and the second row is the mean squared error. Percent and range of censoring is the same as shown in <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0113948#pone-0113948-t002" target="_blank">Table 2</a>.</p><p>Precision of parameter estimates with various event numbers and percent censored.</p