Malaria transmission in arid and semi-arid regions of Kenya such as Baringo County, is seasonal and often influenced by climatic factors. Unravelling the relationship between climate variables and malaria transmission dynamics is therefore instrumental in developing effective malaria control strategies. The main aim of this study was to describe the effects of variability of rainfall, maximum temperature and vegetation indices on seasonal trends of malaria in selected health facilities within Baringo County, Kenya. Climate variables sourced from the International Research Institute (IRI)/Lamont-Doherty Earth Observatory (LDEO) climate database and malaria cases reported in 10 health facilities spread across four ecological zones (riverine, lowland, mid-altitude and highland) between 2004 and 2014 were subjected to a time series analysis. A negative binomial regression model with lagged climate variables was used to model long-term monthly malaria cases. The seasonal Mann–Kendall trend test was then used to detect overall monotonic trends in malaria cases. Malaria cases increased significantly in the highland and midland zones over the study period. Changes in malaria prevalence corresponded to variations in rainfall and maximum temperature. Rainfall at a time lag of 2 months resulted in an increase in malaria transmission across the four zones while an increase in temperature at time lags of 0 and 1 month resulted in an increase in malaria cases in the riverine and highland zones, respectively. Given the existence of a time lag between climatic variables more so rainfall and peak malaria transmission, appropriate control measures can be initiated at the onset of short and after long rains seasons.

In low-dimensional data and within the framework of a classical linear regression model, we intend to compare variable selection methods and investigate the role of shrinkage of regression estimates in a simulation study. Our primary aim is to build descriptive models that capture the data structure parsimoniously, while our secondary aim is to derive a prediction model. Simulation studies are an important tool in statistical methodology research if they are well designed, executed, and reported. However, bias in favor of an “own” preferred method is prevalent in most simulation studies in which a new method is proposed and compared with existing methods. To overcome such bias, neutral comparison studies, which disregard the superiority or inferiority of a particular method, have been proposed. In this paper, we designed a simulation study with key principles of neutral comparison studies in mind, though certain unintentional biases cannot be ruled out. To improve the design and reporting of a simulation study, we followed the recently proposed ADEMP structure, which entails defining the aims (A), data-generating mechanisms (D), estimand/target of analysis (E), methods (M), and performance measures (P). To ensure the reproducibility of results, we published the protocol before conducting the study. In addition, we presented earlier versions of the design to several experts whose feedback influenced certain aspects of the design. We will compare popular penalized regression methods (lasso, adaptive lasso, relaxed lasso, and nonnegative garrote) that combine variable selection and shrinkage with classical variable selection methods (best subset selection and backward elimination) with and without post-estimation shrinkage of parameter estimates.

Variable selection is important for developing accurate and interpretable prediction models. While classical and penalized methods are widely used, few simulation studies provide meaningful comparisons. This study compares their predictive performance and model complexity in low-dimensional data. Three classical methods (best subset selection, backward elimination, and forward selection) and four penalized methods (nonnegative garrote (NNG), lasso, adaptive lasso (ALASSO), and relaxed lasso (RLASSO)) were compared. Tuning parameters were selected using cross-validation (CV), Akaike information criterion (AIC), and Bayesian information criterion (BIC). Classical methods performed similarly and produced worse predictions than penalized methods in limited-information scenarios (small samples, high correlation, and low signal-to-noise ratio (SNR)), but performed comparably or better in sufficient-information scenarios (large samples, low correlation, and high SNR). Lasso was superior under limited information but was less effective in sufficient-information scenarios. NNG, ALASSO, and RLASSO outperformed lasso in sufficient-information scenarios, with no clear winner among them. AIC and CV produced similar results and outperformed BIC, except in sufficient-information settings, where BIC performed better. Our findings suggest that no single method consistently outperforms others, as performance depends on the amount of information in the data. Lasso is preferred in limited-information settings, whereas classical methods are more suitable in sufficient-information settings, as they also tend to select simpler models.

The fit of a regression model to new data is often worse due to overfitting. Analysts use variable selection techniques to develop parsimonious regression models, which may introduce bias into regression estimates. Shrinkage methods have been proposed to mitigate overfitting and reduce bias in estimates. Post‐estimation shrinkage is an alternative to penalized methods. This study evaluates effectiveness of post‐estimation shrinkage in improving prediction performance of full and selected models. Through a simulation study, results were compared with ordinary least squares (OLS) and ridge in full models, and best subset selection (BSS) and lasso in selected models. We focused on prediction errors and the number of selected variables. Additionally, we proposed a modified version of the parameter‐wise shrinkage (PWS) approach named non‐negative PWS (NPWS) to address weaknesses of PWS. Results showed that no method was superior in all scenarios. In full models, NPWS outperformed global shrinkage, whereas PWS was inferior to OLS. In low correlation with moderate‐to‐high signal‐to‐noise ratio (SNR), NPWS outperformed ridge, but ridge performed best in small sample sizes, high correlation, and low SNR. In selected models, all post‐estimation shrinkage performed similarly, with global shrinkage slightly inferior. Lasso outperformed BSS and post‐estimation shrinkage in small sample sizes, low SNR, and high correlation but was inferior when the opposite was true. Our study suggests that, with sufficient information, NPWS is more effective than global shrinkage in improving prediction accuracy of models. However, in high correlation, small sample sizes, and low SNR, penalized methods generally outperform post‐estimation shrinkage methods.

Penalized regression methods are widely used for variable selection. Non-negative garrote (NNG) was one of the earliest methods to combine variable selection with shrinkage of regression coefficients, followed by lasso. About a decade after the introduction of lasso, adaptive lasso (ALASSO) was proposed to address lasso’s limitations. ALASSO has two tuning parameters ($\lambda$ and $\gamma$), and its penalty resembles that of NNG when $\gamma =1$, though NNG imposes additional constraints. Given ALASSO’s greater flexibility, which may increase instability, this study investigates whether NNG provides any practical benefit or can be replaced by ALASSO. We conducted simulations in both low- and high-dimensional settings to compare selected variables, coefficient estimates, and prediction accuracy. Ordinary least squares and ridge estimates were used as initial estimates. NNG and ALASSO ($\gamma =1$) showed similar performance in low-dimensional settings with low correlation, large samples, and moderate to high $R^2$. However, under high correlation, small samples, and low $R^2$, their selected variables and estimates differed, though prediction accuracy remained comparable. When $\gamma \ne 1$, the differences between NNG and ALASSO became more pronounced, with ALASSO generally performing better. Assuming linear relationships between predictors and the outcome, the results suggest that NNG may offer no practical advantage over ALASSO. The $\gamma$ parameter in ALASSO allows for adaptability to model complexity, making ALASSO a more flexible and practical alternative to NNG.