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Background Single group data present unique challenges for synthesises of evidence. Proportional meta-analysis is becoming an increasingly common technique employed for the synthesis of single group data. Proportional meta-analysis shares many similarities with the conduct and reporting of comparative, or pairwise, meta-analysis. While robust and comprehensive methods exist detailing how researchers can conduct a meta-analysis that compares two (or more) groups against a common intervention, there is a scarcity of methodological guidance available to assist synthesisers of evidence in the conduct, interpretation, and importance of proportional meta-analysis in systematic reviews. Main body This paper presents an overview targeted to synthesisers of evidence and systematic review authors that details the methods, importance, and interpretation of a proportional meta-analysis. We provide worked examples of how proportional meta-analyses have been conducted in research syntheses previously and consider the methods, statistical considerations, and presentation of this technique. Conclusion This overview is designed to serve as practical guidance for synthesisers of evidence in the conduct of proportional meta-analyses.

Background Interrupted time series analysis is increasingly used to evaluate the impact of large-scale health interventions. While segmented regression is a common approach, it is not always adequate, especially in the presence of seasonality and autocorrelation. An Autoregressive Integrated Moving Average (ARIMA) model is an alternative method that can accommodate these issues. Methods We describe the underlying theory behind ARIMA models and how they can be used to evaluate population-level interventions, such as the introduction of health policies. We discuss how to select the shape of the impact, the model selection process, transfer functions, checking model fit, and interpretation of findings. We also provide R and SAS code to replicate our results. Results We illustrate ARIMA modelling using the example of a policy intervention to reduce inappropriate prescribing. In January 2014, the Australian government eliminated prescription refills for the 25 mg tablet strength of quetiapine, an antipsychotic, to deter its prescribing for non-approved indications. We examine the impact of this policy intervention on dispensing of quetiapine using dispensing claims data. Conclusions ARIMA modelling is a useful tool to evaluate the impact of large-scale interventions when other approaches are not suitable, as it can account for underlying trends, autocorrelation and seasonality and allows for flexible modelling of different types of impacts.

Background Medical practitioners use survival models to explore and understand the relationships between patients’ covariates (e.g. clinical and genetic features) and the effectiveness of various treatment options. Standard survival models like the linear Cox proportional hazards model require extensive feature engineering or prior medical knowledge to model treatment interaction at an individual level. While nonlinear survival methods, such as neural networks and survival forests, can inherently model these high-level interaction terms, they have yet to be shown as effective treatment recommender systems. Methods We introduce DeepSurv, a Cox proportional hazards deep neural network and state-of-the-art survival method for modeling interactions between a patient’s covariates and treatment effectiveness in order to provide personalized treatment recommendations. Results We perform a number of experiments training DeepSurv on simulated and real survival data. We demonstrate that DeepSurv performs as well as or better than other state-of-the-art survival models and validate that DeepSurv successfully models increasingly complex relationships between a patient’s covariates and their risk of failure. We then show how DeepSurv models the relationship between a patient’s features and effectiveness of different treatment options to show how DeepSurv can be used to provide individual treatment recommendations. Finally, we train DeepSurv on real clinical studies to demonstrate how it’s personalized treatment recommendations would increase the survival time of a set of patients. Conclusions The predictive and modeling capabilities of DeepSurv will enable medical researchers to use deep neural networks as a tool in their exploration, understanding, and prediction of the effects of a patient’s characteristics on their risk of failure.

Background Missing data may seriously compromise inferences from randomised clinical trials, especially if missing data are not handled appropriately. The potential bias due to missing data depends on the mechanism causing the data to be missing, and the analytical methods applied to amend the missingness. Therefore, the analysis of trial data with missing values requires careful planning and attention. Methods The authors had several meetings and discussions considering optimal ways of handling missing data to minimise the bias potential. We also searched PubMed (key words: missing data; randomi*; statistical analysis) and reference lists of known studies for papers (theoretical papers; empirical studies; simulation studies; etc.) on how to deal with missing data when analysing randomised clinical trials. Results Handling missing data is an important, yet difficult and complex task when analysing results of randomised clinical trials. We consider how to optimise the handling of missing data during the planning stage of a randomised clinical trial and recommend analytical approaches which may prevent bias caused by unavoidable missing data. We consider the strengths and limitations of using of best-worst and worst-best sensitivity analyses, multiple imputation, and full information maximum likelihood. We also present practical flowcharts on how to deal with missing data and an overview of the steps that always need to be considered during the analysis stage of a trial. Conclusions We present a practical guide and flowcharts describing when and how multiple imputation should be used to handle missing data in randomised clinical.

Background When applying secondary analysis on published survival data, it is critical to obtain each patient’s raw data, because the individual patient data (IPD) approach has been considered as the gold standard of data analysis. However, researchers often lack access to IPD. We aim to propose a straightforward and robust approach to obtain IPD from published survival curves with a user-friendly software platform. Results Improving upon existing methods, we propose an easy-to-use, two-stage approach to reconstruct IPD from published Kaplan-Meier (K-M) curves. Stage 1 extracts raw data coordinates and Stage 2 reconstructs IPD using the proposed method. To facilitate the use of the proposed method, we developed the R package IPDfromKM and an accompanying web-based Shiny application. Both the R package and Shiny application have an “all-in-one” feature such that users can use them to extract raw data coordinates from published K-M curves, reconstruct IPD from the extracted data coordinates, visualize the reconstructed IPD, assess the accuracy of the reconstruction, and perform secondary analysis on the basis of the reconstructed IPD. We illustrate the use of the R package and the Shiny application with K-M curves from published studies. Extensive simulations and real-world data applications demonstrate that the proposed method has high accuracy and great reliability in estimating the number of events, number of patients at risk, survival probabilities, median survival times, and hazard ratios. Conclusions IPDfromKM has great flexibility and accuracy to reconstruct IPD from published K-M curves with different shapes. We believe that the R package and the Shiny application will greatly facilitate the potential use of quality IPD and advance the use of secondary data to facilitate informed decision making in medical research.

Background In systematic reviews and meta-analysis, researchers often pool the results of the sample mean and standard deviation from a set of similar clinical trials. A number of the trials, however, reported the study using the median, the minimum and maximum values, and/or the first and third quartiles. Hence, in order to combine results, one may have to estimate the sample mean and standard deviation for such trials. Methods In this paper, we propose to improve the existing literature in several directions. First, we show that the sample standard deviation estimation in Hozo et al.’s method (BMC Med Res Methodol 5:13, 2005) has some serious limitations and is always less satisfactory in practice. Inspired by this, we propose a new estimation method by incorporating the sample size. Second, we systematically study the sample mean and standard deviation estimation problem under several other interesting settings where the interquartile range is also available for the trials. Results We demonstrate the performance of the proposed methods through simulation studies for the three frequently encountered scenarios, respectively. For the first two scenarios, our method greatly improves existing methods and provides a nearly unbiased estimate of the true sample standard deviation for normal data and a slightly biased estimate for skewed data. For the third scenario, our method still performs very well for both normal data and skewed data. Furthermore, we compare the estimators of the sample mean and standard deviation under all three scenarios and present some suggestions on which scenario is preferred in real-world applications. Conclusions In this paper, we discuss different approximation methods in the estimation of the sample mean and standard deviation and propose some new estimation methods to improve the existing literature. We conclude our work with a summary table (an Excel spread sheet including all formulas) that serves as a comprehensive guidance for performing meta-analysis in different situations.

Background Missing data are common in statistical analyses, and imputation methods based on random forests (RF) are becoming popular for handling missing data especially in biomedical research. Unlike standard imputation approaches, RF-based imputation methods do not assume normality or require specification of parametric models. However, it is still inconclusive how they perform for non-normally distributed data or when there are non-linear relationships or interactions. Methods To examine the effects of these three factors, a variety of datasets were simulated with outcome-dependent missing at random (MAR) covariates, and the performances of the RF-based imputation methods missForest and CALIBERrfimpute were evaluated in comparison with predictive mean matching (PMM). Results Both missForest and CALIBERrfimpute have high predictive accuracy but missForest can produce severely biased regression coefficient estimates and downward biased confidence interval coverages, especially for highly skewed variables in nonlinear models. CALIBERrfimpute typically outperforms missForest when estimating regression coefficients, although its biases are still substantial and can be worse than PMM for logistic regression relationships with interaction. Conclusions RF-based imputation, in particular missForest, should not be indiscriminately recommended as a panacea for imputing missing data, especially when data are highly skewed and/or outcome-dependent MAR. A correct analysis requires a careful critique of the missing data mechanism and the inter-relationships between the variables in the data.

Background Projection of future cancer incidence is an important task in cancer epidemiology. The results are of interest also for biomedical research and public health policy. Age-Period-Cohort (APC) models, usually based on long-term cancer registry data (> 20 yrs), are established for such projections. In many countries (including Germany), however, nationwide long-term data are not yet available. General guidance on statistical approaches for projections using rather short-term data is challenging and software to enable researchers to easily compare approaches is lacking. Methods To enable a comparative analysis of the performance of statistical approaches to cancer incidence projection, we developed an R package (incAnalysis), supporting in particular Bayesian models fitted by Integrated Nested Laplace Approximations (INLA). Its use is demonstrated by an extensive empirical evaluation of operating characteristics (bias, coverage and precision) of potentially applicable models differing by complexity. Observed long-term data from three cancer registries (SEER-9, NORDCAN, Saarland) was used for benchmarking. Results Overall, coverage was high (mostly > 90%) for Bayesian APC models (BAPC), whereas less complex models showed differences in coverage dependent on projection-period. Intercept-only models yielded values below 20% for coverage. Bias increased and precision decreased for longer projection periods (> 15 years) for all except intercept-only models. Precision was lowest for complex models such as BAPC models, generalized additive models with multivariate smoothers and generalized linear models with age x period interaction effects. Conclusion The incAnalysis R package allows a straightforward comparison of cancer incidence rate projection approaches. Further detailed and targeted investigations into model performance in addition to the presented empirical results are recommended to derive guidance on appropriate statistical projection methods in a given setting.

Background With progress on both the theoretical and the computational fronts the use of spline modelling has become an established tool in statistical regression analysis. An important issue in spline modelling is the availability of user friendly, well documented software packages. Following the idea of the STRengthening Analytical Thinking for Observational Studies initiative to provide users with guidance documents on the application of statistical methods in observational research, the aim of this article is to provide an overview of the most widely used spline-based techniques and their implementation in R. Methods In this work, we focus on the R Language for Statistical Computing which has become a hugely popular statistics software. We identified a set of packages that include functions for spline modelling within a regression framework. Using simulated and real data we provide an introduction to spline modelling and an overview of the most popular spline functions. Results We present a series of simple scenarios of univariate data, where different basis functions are used to identify the correct functional form of an independent variable. Even in simple data, using routines from different packages would lead to different results. Conclusions This work illustrate challenges that an analyst faces when working with data. Most differences can be attributed to the choice of hyper-parameters rather than the basis used. In fact an experienced user will know how to obtain a reasonable outcome, regardless of the type of spline used. However, many analysts do not have sufficient knowledge to use these powerful tools adequately and will need more guidance.

Background Researchers often misinterpret and misrepresent statistical outputs. This abuse has led to a large literature on modification or replacement of testing thresholds and P -values with confidence intervals, Bayes factors, and other devices. Because the core problems appear cognitive rather than statistical, we review some simple methods to aid researchers in interpreting statistical outputs. These methods emphasize logical and information concepts over probability, and thus may be more robust to common misinterpretations than are traditional descriptions. Methods We use the Shannon transform of the P -value p , also known as the binary surprisal or S -value s  = −log 2 ( p ), to provide a measure of the information supplied by the testing procedure, and to help calibrate intuitions against simple physical experiments like coin tossing. We also use tables or graphs of test statistics for alternative hypotheses, and interval estimates for different percentile levels, to thwart fallacies arising from arbitrary dichotomies. Finally, we reinterpret P -values and interval estimates in unconditional terms, which describe compatibility of data with the entire set of analysis assumptions. We illustrate these methods with a reanalysis of data from an existing record-based cohort study. Conclusions In line with other recent recommendations, we advise that teaching materials and research reports discuss P -values as measures of compatibility rather than significance, compute P -values for alternative hypotheses whenever they are computed for null hypotheses, and interpret interval estimates as showing values of high compatibility with data, rather than regions of confidence. Our recommendations emphasize cognitive devices for displaying the compatibility of the observed data with various hypotheses of interest, rather than focusing on single hypothesis tests or interval estimates. We believe these simple reforms are well worth the minor effort they require.