arXiv subjects

Madan G. Kundu

Publications and source records attributed to Madan G. Kundu.

4 recordsLinked to original sources

arXiv2021

An introduction to the determination of the probability of a successful trial: Frequentist and Bayesian approaches

Determination of posterior probability for go-no-go decision and predictive power are becoming increasingly common for resource optimization in clinical investigation. There are vast published literature on these topics; however, the terminologies are not consistently used across the literature. Further, there is a lack of consolidated presentation of various concepts of the probability of success. We attempted to fill this gap. This paper first provides a detailed derivation of these probability of success measures under the frequentist and Bayesian paradigms in a general setting. Subsequently, we have presented the analytical formula for these probability of success measures for continuous, binary, and time-to-event endpoints separately. This paper can be used as a single point reference to determine the following measures: (a) the conditional power (CP) based on interim results, (b) the predictive power of success (PPoS) based on interim results with or without prior distribution, and (d) the probability of success (PoS) for a prospective trial at the design stage. We have discussed both clinical success and trial success. This paper's discussion is mostly based on the normal approximation for prior distribution and the estimate of the parameter of interest. Besides, predictive power using the beta prior for the binomial case is also presented. Some examples are given for illustration. R functions to calculate CP and PPoS are available through the LongCART package. An R shiny app is also available at https://ppos.herokuapp.com/.

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arXiv2020

Impact of the adjustment of stratification factors on time-to-event analyses

In a stratified clinical trial design with time to event end points, stratification factors are often accounted for the log-rank test and the Cox regression analyses. In this work, we have evaluated the impact of inclusion of stratification factors on the power of the stratified log-rank test and have compared the bias and standard error in HR estimate between multivariate and stratified Cox regression analyses through simulation. Results from our investigation suggests that both failing to consider stratification factor in presence of their prognostic effect and stratification with smaller number of events may substantially reduce the power of the log-rank test. Further, the HR estimate from the multivariate Cox analysis is more accurate and precise compared to the stratified Cox analysis. Our findings point towards the necessity of evaluating the impact of stratification factors on the time to event analyses at the time of study design which is presently not a norm.

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arXiv2016

Surrogacy of progression free survival for overall survival in metastatic breast cancer studies: meta-analyses of published studies

Purpose: PFS is often used as a surrogate endpoint for OS in metastatic breast cancer studies. We have evaluated the association of treatment effect on PFS with significant HR$_{OS}$ (and how this association is affected by other factors) in published prospective metastatic breast cancer studies. Methods: A systematic literature search in PubMed identified prospective metastatic breast cancer studies. Treatments effects on PFS were determined using hazard ratio (HR$_{PFS}$), increase in median PFS ($Δ$MED$_{PFS}$) and % increase in median PFS (%$Δ$MED$_{PFS}$). Diagnostic accuracy of PFS measures (HR$_{PFS}$, $Δ$MED$_{PFS}$ and %$Δ$MED$_{PFS}$) in predicting significant HR$_{OS}$ was assessed using receiver operating characteristics (ROC) curves and classification trees approach. Results: Seventy-three cases (i.e., treatment to control comparisons) from 64 individual publications were identified for the analyses. Of these, 16 cases reported significant treatment effect on HR$_{OS}$ at 5% level of significance. Median number of deaths reported in these cases were 156. Area under the ROC curve (AUC) for diagnostic measures as HR$_{PFS}$, $Δ$MED$_{PFS}$ and %$Δ$MED$_{PFS}$ were 0.69, 0.70 and 0.75, respectively. Classification tree results identified %$Δ$MED$_{PFS}$ and number of deaths as diagnostic measure for significant HR$_{OS}$. Only 7.9\% (3/39) cases with $Δ$MED$_{PFS}$ shorter than 48.27\% reported significant HR$_{OS}$. There were 7 cases with $Δ$MED$_{PFS}$ of 48.27\% or more and number of deaths reported as 227 or more -- of these 5 cases reported significant HR$_{OS}$. Conclusion: %$Δ$MED$_{PFS}$ was found as better diagnostic measure for significant HR$_{OS}$. Our analysis results also suggest that consideration of total number of deaths may further improve its diagnostic performance.

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arXiv2014

Longitudinal Functional Models with Structured Penalties

This paper addresses estimation in a longitudinal regression model for association between a scalar outcome and a set of longitudinally-collected functional covariates or predictor curves. The framework consists of estimating a time-varying coefficient function that is modeled as a linear combination of time-invariant functions but having time-varying coefficients. The estimation procedure exploits the equivalence between penalized least squares estimation and a linear mixed model representation. The process is empirically evaluated with several simulations and it is applied to analyze the neurocognitive impairment of HIV patients and its association with longitudinally-collected magnetic resonance spectroscopy curves.

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