Statistical Methods in Medical Research

Cure fraction models are useful to model lifetime data with long-term survivors. We propose a flexible four-parameter cure rate survival model called the log-sinh Cauchy promotion time model for predicting breast carcinoma survival in women who underwent mastectomy. The model can estimate simultaneously the effects of the explanatory variables on the timing acceleration/deceleration of a given event, the surviving fraction, the heterogeneity, and the possible existence of bimodality in the data. In order to examine the performance of the proposed model, simulations are presented to verify the robust aspects of this flexible class against outlying and influential observations. Furthermore, we determine some diagnostic measures and the one-step approximations of the estimates in the case-deletion model. The new model was implemented in the generalized additive model for location, scale and shape package of the R software, which is presented throughout the paper by way of a brief tutorial on its use. The potential of the new regression model to accurately predict breast carcinoma mortality is illustrated using a real data set.

Determining conditional dependence is a challenging but important task in both model building and in applications such as genetic association studies and graphical models. Research on this topic has focused on kernel-based methods or has used categorical conditioning variables because of the challenge of the curse of dimensionality. To overcome this challenge, we propose a class of tests for conditional independence without any restriction on the distribution of the conditioning variables. The proposed test statistic can be treated as a generalized weighted Kendall’s tau, in which the generalized odds ratio is utilized as a weight function to account for the distance between different values of the conditioning variables. The test procedure has desirable asymptotic properties and is easy to implement. We evaluate the finite sample performance of the proposed test through simulation studies and illustrate it using two real data examples.

We introduce flexible robust functional regression models, using various heavy-tailed processes, including a Student t-process. We propose efficient algorithms in estimating parameters for the marginal mean inferences and in predicting conditional means as well as interpolation and extrapolation for the subject-specific inferences. We develop bootstrap prediction intervals (PIs) for conditional mean curves. Numerical studies show that the proposed model provides a robust approach against data contamination or distribution misspecification, and the proposed PIs maintain the nominal confidence levels. A real data application is presented as an illustrative example.

The increase in the popularity of non-inferiority clinical trials represents the increasing need to search for substitutes for some reference (standard) treatments. A new treatment would be preferred to the standard treatment if the benefits of adopting it outweigh a possible clinically insignificant reduction in treatment efficacy (non-inferiority margin). Statistical procedures have recently been developed for treatment comparisons in non-inferiority clinical trials that have multiple experimental (new) treatments. An ethical concern for non-inferiority trials is that some patients undergo the less effective treatments; this problem is more serious when multiple experimental treatments are included in a balanced trial in which the sample sizes are the same for all experimental treatments. With the aim of giving fewer patients the inferior treatments, we propose a response-adaptive treatment allocation scheme that is based on the doubly adaptive biased coin design. The proposed adaptive design is also shown to be superior to the balanced design in terms of testing power.

Hospital-specific electronic health record systems are used to inform clinical practice about best practices and quality improvements. Many surgical centers have developed deterministic clinical decision rules to discover adverse events (e.g. postoperative complications) using electronic health record data. However, these data provide opportunities to use probabilistic methods for early prediction of adverse health events, which may be more informative than deterministic algorithms. Electronic health record data from a set of 9598 colorectal surgery cases from 2010 to 2014 were used to predict the occurrence of selected complications including surgical site infection, ileus, and bleeding. Consistent with previous studies, we find a high rate of missing values for both covariates and complication information (4–90%). Several machine learning classification methods are trained on an 80% random sample of cases and tested on a remaining holdout set. Predictive performance varies by complication, although an area under the receiver operating characteristic curve as high as 0.86 on testing data was achieved for bleeding complications, and accuracy for all complications compares favorably to existing clinical decision rules. Our results confirm that electronic health records provide opportunities for improved risk prediction of surgical complications; however, consideration of data quality and consistency standards is an important step in predictive modeling with such data.

The importance of subgroup analyses has been increasing due to a growing interest in personalized medicine and targeted therapies. Considering designs with multiple nested subgroups and a continuous endpoint, we develop methods for the analysis and sample size determination. First, we consider the joint distribution of standardized test statistics that correspond to each (sub)population. We derive multivariate exact distributions where possible, providing approximations otherwise. Based on these results, we present sample size calculation procedures. Uncertainties about nuisance parameters which are needed for sample size calculations make the study prone to misspecifications. We discuss how a sample size review can be performed in order to make the study more robust. To this end, we implement an internal pilot study design where the variances and prevalences of the subgroups are reestimated in a blinded fashion and the sample size is recalculated accordingly. Simulations show that the procedures presented here do not inflate the type I error significantly and maintain the prespecified power as long as the sample size of the smallest subgroup is not too small. We pay special attention to the case of small sample sizes and attain a lower boundary for the size of the internal pilot study.

Modern medical research relies on multi-institutional collaborations which enhance the knowledge discovery and data reuse. While these collaborations allow researchers to perform analytics otherwise impossible on individual datasets, they often pose significant challenges in the data integration process. Due to the lack of a unique identifier, data integration solutions often have to rely on patient’s protected health information (PHI). In many situations, such information cannot leave the institutions or must be strictly protected. Furthermore, the presence of noisy values for these attributes may result in poor overall utility. While much research has been done to address these challenges, most of the current solutions are designed for a static setting without considering the temporal information of the data (e.g. EHR). In this work, we propose a novel approach that uses non-PHI for linking patient longitudinal data. Specifically, our technique captures the diagnosis dependencies using patterns which are shown to provide important indications for linking patient records. Our solution can be used as a standalone technique to perform temporal record linkage using non-protected health information data or it can be combined with Privacy Preserving Record Linkage solutions (PPRL) when protected health information is available. In this case, our approach can solve ambiguities in results. Experimental evaluations on real datasets demonstrate the effectiveness of our technique.

A binary health outcome may be regressed on covariates using a log link, rather than more typical link functions such as the logit. This allows the exponentiated regression coefficient for each covariate to be interpreted as a relative risk conditional on the remaining covariates. Relative risks are simpler to interpret than the odds ratios which arise with a logit link. There are practical and conceptual challenges in log-link binary regression, mainly due to the requirement that probabilities are less than or equal to 1. Viable probabilities are now usually achieved by the imposition of a constraint on the parameter space, but the log link function is still more work to apply in practice. We propose instead a new smooth link function which is equal to the log up to a cutoff and a linearly scaled logit function above the cutoff. The new approach is conceptually clearer, simpler to implement and generally less biased, and it retains the relative risk interpretation for all but the highest risk individuals. Alternative binary regressions are compared using a simulation study and a diabetic retinopathy dataset.

Classification with a large number of predictors and biomarker discovery become increasingly important in biological and medical research. This paper focuses on performing classification of cardiovascular diseases based on electrocardiogram analysis which deals with many variables and a lot of measurements within variables. We propose an optimal quantile level selection procedure to reduce dimension by characterizing distributions with quantiles and combine with classification tools to produce sensible classification and biomarker discovery results. Simulation and an intensive study of a real data set are performed to illustrate the performance of the proposed method.

Funnel plots are graphical tools to assess and compare clinical performance of a group of care professionals or care institutions on a quality indicator against a benchmark. Incorrect construction of funnel plots may lead to erroneous assessment and incorrect decisions potentially with severe consequences. We provide workflow-based guidance for data analysts on constructing funnel plots for the evaluation of binary quality indicators, expressed as proportions, risk-adjusted rates or standardised rates. Our guidelines assume the following steps: (1) defining policy level input; (2) checking the quality of models used for case-mix correction; (3) examining whether the number of observations per hospital is sufficient; (4) testing for overdispersion of the values of the quality indicator; (5) testing whether the values of quality indicators are associated with institutional characteristics; and (6) specifying how the funnel plot should be constructed. We illustrate our guidelines using data from the Dutch National Intensive Care Evaluation registry. We expect that our guidelines will be useful to data analysts preparing funnel plots and to registries, or other organisations publishing quality indicators. This is particularly true if these people and organisations wish to use standard operating procedures when constructing funnel plots, perhaps to comply with the demands of certification.

The meta-analytic approach is the gold standard for validation of surrogate markers, but has the drawback of requiring data from several trials. We refine modern mediation analysis techniques for time-to-event endpoints and apply them to investigate whether pathological complete response can be used as a surrogate marker for disease-free survival in the EORTC 10994/BIG 1-00 randomised phase 3 trial in which locally advanced breast cancer patients were randomised to either taxane or anthracycline based neoadjuvant chemotherapy. In the mediation analysis, the treatment effect is decomposed into an indirect effect via pathological complete response and the remaining direct effect. It shows that only 4.2% of the treatment effect on disease-free survival after five years is mediated by the treatment effect on pathological complete response. There is thus no evidence from our analysis that pathological complete response is a valuable surrogate marker to evaluate the effect of taxane versus anthracycline based chemotherapies on progression free survival of locally advanced breast cancer patients. The proposed analysis strategy is broadly applicable to mediation analyses of time-to-event endpoints, is easy to apply and outperforms existing strategies in terms of precision as well as robustness against model misspecification.

Couples with diseases associated with the sexual chromosomes, as well as families in countries where the desire for a male is extreme, are interested in influencing the sex of the baby. We propose an original composite likelihood approach to analyse the relation between sex of the newborn and timing of the intercourse which leads to conception. Although there exist numerous works on this relation, only few studies have been carried out on independent datasets to validate the existing theories. Since the sex of the newborn is only known in case of conception, the full likelihood of the data is not easily defined without strong assumptions. A composite likelihood is a pseudo likelihood defined as the product of likelihood functions relative to subsets of the data. In particular, we consider two such likelihoods, one modelling the day-specific probabilities of conception and the other modelling the sex of the newborn given a conception has occurred. The methodology is applied to a dataset from a European fecundability study. The results show no significant dependence of the sex of the newborn on the time of intercourse. The method developed may be applied to other situations when data are affected by selective sampling.

Time-dependent receiver operating characteristic curves allow to evaluate the capacity of a marker to discriminate between subjects who experience the event up to a given prognostic time from those who are free of this event. In this article, we propose an inverse probability weighting estimator of a standardized and weighted time-dependent receiver operating characteristic curve. This estimator provides a measure of the prognostic capacities by taking into account potential confounding factors. We illustrate the robustness of the estimator by a simulation-based study and its usefulness by two applications in kidney transplantation.

Altham (Altham PME. Exact Bayesian analysis of a 2 × 2 contingency table, and Fisher’s “exact” significance test. J R Stat Soc B 1969; 31: 261–269) showed that a one-sided p-value from Fisher’s exact test of independence in a 2 × 2 contingency table is equal to the posterior probability of negative association in the 2 × 2 contingency table under a Bayesian analysis using an improper prior. We derive an extension of Fisher’s exact test p-value in the presence of missing data, assuming the missing data mechanism is ignorable (i.e., missing at random or completely at random). Further, we propose Bayesian p-values for a test of independence in a 2 × 2 contingency table with missing data using alternative priors; we also present results from a simulation study exploring the Type I error rate and power of the proposed exact test p-values. An example, using data on the association between blood pressure and a cardiac enzyme, is presented to illustrate the methods.

Deciding whether two measurement systems agree well enough to be used interchangeably is important in medical and clinical contexts. Recently, the probability of agreement was proposed as an alternative to comparison techniques such as correlation, regression, and the limits of agreement approach, when the systems’ measurement errors are homoscedastic. However, in medical and clinical contexts, it is common for measurement variability to increase proportionally with the magnitude of measurement. In this article, we extend the probability of agreement analysis to accommodate heteroscedastic measurement errors, demonstrating the versatility of this simple metric. We illustrate its use with two examples: one involving the comparison of blood pressure measurement devices, and the other involving the comparison of serum cholesterol assays.

In medical and epidemiologic studies, relative risk is usually the parameter of interest. However, calculating relative risk using standard log-Binomial regression approach often encounters non-convergence. A modified Poisson regression, which uses robust variance, was proposed by Zou in 2004. Although the modified Poisson regression with sandwich variance estimator is valid for the estimation of relative risk, the predicted probability of the outcome may be greater than the natural boundary 1 for the unobserved but plausible covariate combinations. Moreover, the lower and upper bounds of confidence intervals for predicted probabilities could fall out of (0, 1). Chu and Cole, in 2010, proposed a Bayesian approach to overcome this issue. Posterior median was used to get the parameter estimation. However, the Bayesian approach may provide biased estimation, especially when the probability of outcome is high. In this article, we propose an alternative constraint optimization approach for estimating relative risk. Our approach can reach similar or better performance than Bayesian approach in terms of bias, root mean square error, coverage rate, and predictive probabilities. Simulation studies are conducted to demonstrate the usefulness of this approach. Our method is also illustrated by Prospective Registry Evaluating Myocardial Infarction: Event and Recovery data.

The primary goal of a phase I clinical trial in oncology is to evaluate the safety of a novel treatment and identify the maximum tolerated dose, defined as the maximum dose with a toxicity rate below some pre-specified threshold. Researchers are often interested in evaluating the performance of a novel treatment in multiple patient populations, which may require multiple phase I trials if the treatment is to be used with background standard-of-care that varies by population. An alternate approach is to run parallel trials but combine the data through a hierarchical model that allows for a different maximum tolerated dose in each population but shares information across populations to achieve a more accurate estimate of the maximum tolerated dose. In this manuscript, we discuss hierarchical extensions of three commonly used models for the dose–toxicity relationship in phase I oncology trials. We then propose three dose-finding guidelines for phase I oncology trials using hierarchical modeling. The proposed guidelines allow us to fully realize the benefits of hierarchical modeling while achieving a similar toxicity profile to standard phase I designs. Finally, we evaluate the operating characteristics of a phase I clinical trial using the proposed hierarchical models and dose-finding guidelines by simulation. Our simulation results suggest that incorporating hierarchical modeling in phase I dose-escalation studies will increase the probability of correctly identifying the maximum tolerated dose and the number of patients treated at the maximum tolerated dose, while decreasing the rate of dose-limiting toxicities and number of patients treated above the maximum tolerated dose, in most cases.

Agreement is an important concept in medical and behavioral sciences, in particular in clinical decision making where disagreements possibly imply a different patient management. The concordance correlation coefficient is an appropriate measure to quantify agreement between two scorers on a quantitative scale. However, this measure is based on the first two moments, which could poorly summarize the shape of the score distribution on bounded scales. Bounded outcome scores are common in medical and behavioral sciences. Typical examples are scores obtained on visual analog scales and scores derived as the number of positive items on a questionnaire. These kinds of scores often show a non-standard distribution, like a J- or U-shape, questioning the usefulness of the concordance correlation coefficient as agreement measure. The logit-normal distribution has shown to be successful in modeling bounded outcome scores of two types: (1) when the bounded score is a coarsened version of a latent score with a logit-normal distribution on the [0,1] interval and (2) when the bounded score is a proportion with the true probability having a logit-normal distribution. In the present work, a model-based approach, based on a bivariate generalization of the logit-normal distribution, is developed in a Bayesian framework to assess the agreement on bounded scales. This method permits to directly study the impact of predictors on the concordance correlation coefficient and can be simply implemented in standard Bayesian softwares, like JAGS and WinBUGS. The performances of the new method are compared to the classical approach using simulations. Finally, the methodology is used in two different medical domains: cardiology and rheumatology.

Many studies measure the same type of information longitudinally on the same subject at multiple time points, and clustering of such functional data has many important applications. We propose a novel and easy method to implement dissimilarity measure for functional data clustering based on smoothing splines and smoothing parameter commutation. This method handles data observed at regular or irregular time points in the same way. We measure the dissimilarity between subjects based on varying curve estimates with pairwise commutation of smoothing parameters. The intuition is that smoothing parameters of smoothing splines reflect the inverse of the signal-to-noise ratios and that when applying an identical smoothing parameter the smoothed curves for two similar subjects are expected to be close. Our method takes into account the estimation uncertainty using smoothing parameter commutation and is not strongly affected by outliers. It can also be used for outlier detection. The effectiveness of our proposal is shown by simulations comparing it to other dissimilarity measures and by a real application to methadone dosage maintenance levels.

If individual participant data are available from multiple studies or clusters, then a prediction model can be externally validated multiple times. This allows the model’s discrimination and calibration performance to be examined across different settings. Random-effects meta-analysis can then be used to quantify overall (average) performance and heterogeneity in performance. This typically assumes a normal distribution of ‘true’ performance across studies. We conducted a simulation study to examine this normality assumption for various performance measures relating to a logistic regression prediction model. We simulated data across multiple studies with varying degrees of variability in baseline risk or predictor effects and then evaluated the shape of the between-study distribution in the C-statistic, calibration slope, calibration-in-the-large, and E/O statistic, and possible transformations thereof. We found that a normal between-study distribution was usually reasonable for the calibration slope and calibration-in-the-large; however, the distributions of the C-statistic and E/O were often skewed across studies, particularly in settings with large variability in the predictor effects. Normality was vastly improved when using the logit transformation for the C-statistic and the log transformation for E/O, and therefore we recommend these scales to be used for meta-analysis. An illustrated example is given using a random-effects meta-analysis of the performance of QRISK2 across 25 general practices.