Performance assessment of Bayesian meta-analytic predictive model on kdr mutation in insecticide-resistant malarial vectors in sub-Saharan Africa

Abstract

Mosquito populations’ selective pressure arising from the widespread and prolonged use of insecticides, especially pyrethroids, for both agricultural usages and public health outcomes, has immensely contributed to the emergence and heavily spread of insecticide resistance. In this study, a systematic review identified eight eligible case–control or cohort studies published between 2015 and 2025 across sub-Saharan Africa that reported both allele and/or genotype frequencies of L1014F and L1014S. The predictive performance and inferential robustness of a Bayesian meta-analytic model were applied and evaluated on two knockdown resistance (kdr) mutations, L1014F and L1014S, in the Anopheles mosquito populations. Using the Markov Chain Monte Carlo (MCMC) sampling to compute pooled concordance statistics, odds ratios, and perform funnel plot asymmetry tests (Egger, Macaskill, Debray). The results revealed that L1014F showed a stronger and more consistent association with phenotypic resistance compared to L1014S, with odds ratios (OR) as high as 4.44 (95% CI 3.40–5.80). However, concordance statistics for both mutations demonstrated wide confidence intervals (L1014F: 0.141; CI − 0.095 to 0.459; L1014S: 0.169; CI − 0.399 to 0.688), indicating moderate predictive reliability. The Bayesian framework effectively synthesized complex and heterogeneous resistance data, confirming the operational relevance of KDR mutations in resistance surveillance. The global significance of these results enhances the predictive analytics in resistance management, such that resistance evolution is temporally and spatially dynamic. The integration of Bayesian modelling into existing entomological surveillance systems shifts the paradigm towards more adaptive and anticipatory management. Although data sparsity and regional heterogeneity warrant cautious interpretation, integrating ecological and thermodynamic variables into predictive models is essential for enhancing future resistance forecasting.

Supplementary Information

The online version contains supplementary material available at 10.1186/s12936-025-05628-8.

Background

Malaria remains a significant public health concern worldwide, especially in tropical nations [1, 2]. The World Health Organization (WHO) estimates that in 2023, 29 of the 83 countries (including the territory of French Guiana) that were malaria endemic accounted for almost 95% of malaria cases and 96% of deaths globally. Five countries, which include Nigeria (25.9%), the Democratic Republic of the Congo (12.6%), Uganda (4.8%), Ethiopia (3.6%) and Mozambique (3.5%), accounted for just over half of 249 million cases. Four countries accounted for just over half of 597,000 malaria deaths globally: Nigeria (30.9%), the Democratic Republic of the Congo (11.3%), Niger (5.9%) and the United Republic of Tanzania (4.3%). Nigeria accounted for 39.3% of global malaria deaths in children aged under 5 years [3].

The influence of malaria goes beyond healthcare systems. In endemic places, it affects socioeconomic development, well-being, and health consequences. In Africa, the National Malaria Control Programmes (NMCPS) have developed strategic plans following WHO recommendations, which guide the control and prevention of malaria transmission. The strategic plans involve a combination of clinical treatment of the disease with vector surveillance and control, most often using insecticides [4, 5]. Insecticide-treated nets (ITNS), antimalarial drugs, larvicide (larval control), and indoor residual spraying (IRS) are some of the methods that have been identified as the historical art of vector control for malaria [6]. Nonetheless, resistance to these chemical interventions has become prevalent in vector populations, particularly among anopheline species that carry the malaria parasite [4]. This is partially because the development of insecticide resistance has reduced the effectiveness of IRS and ITNS in controlling malaria vectors [7, 8]. In addition, environmental factors such as climate change and deforestation contribute to the spread of malaria by altering mosquito breeding habitats and transmission patterns. These have heightened the limitations in coverage, accuracy, and real-time reporting [9, 10].

However, the widespread and prolonged use of insecticides, particularly pyrethroids, has caused a substantial selective pressure on mosquito populations, leading to the emergence and rapid spread of insecticide resistance [11, 12]. This resistance has shown a formidable obstacle to sustaining malaria control gains and achieving global eradication goals [13]. One major force driving the spread of insecticide resistance in mosquito populations is the extensive use of insecticides for both public health and agricultural purposes during the past decade [14, 15]. Pyrethroid resistance in malaria vectors is a significant risk because pyrethroids are among the insecticide classes recommended for ITNS and LLINS impregnation [15, 16]. One of the molecular mechanisms of pyrethroid resistance in Anopheles is target-site insensitivity of sodium channels [17–19]. Among the most studied mechanisms of insecticide resistance are target-site mutations, particularly knockdown resistance (KDR) mutations, which have been implicated in the reduced efficacy of pyrethroid-based interventions [20, 21]. Pyrethroids exert their toxic effect by hindering the voltage-gated sodium channels on the mosquito's neurons, which generally produces fast knockdown properties [22]. Mutations in the IIS6 transmembrane segment of the voltage-gated sodium channel (vgsc) gene result in target-site resistance known as knockdown resistance (kdr), which confers pyrethroid resistance to mosquitoes [23–25].

Target-site resistance is caused by mutations at the site of action of an insecticide, thereby reducing or preventing the insecticide's binding affinity [4, 26–28]. Conversely, metabolic resistance entails increased detoxification of insecticides by the vector through overexpression or conformational changes of the enzymes that can metabolize, sequester and excrete the insecticide [29, 30]. Behavioural resistance involves any modification in the insect’s behaviour that helps it to avoid exposure to insecticides. In malaria vectors, this is commonly observed as a change in biting patterns, for example, biting earlier and outdoors, thus avoiding any LLINS or IRS [30]. Cuticular resistance is seen when the insect’s cuticle thickens, reducing uptake of insecticide by limiting or preventing the absorption or penetration of insecticide [28, 30].

Two of the most prevalent kdr mutations in Anopheles involve nonsynonymous substitutions at amino acid position 1014 in the IIS6 transmembrane segment of the vgsc gene: a leucine-to-phenylalanine change (L1014F, also referred to as kdr-west) and a leucine-to-serine change (L1014S, also referred to as kdr-east) [23]. These mutations have been documented widely across Anopheles populations in Africa and are considered critical markers for tracking and modelling the dynamics of insecticide resistance [5]. Although molecular diagnostic tools have made it easier to detect the presence of kdr alleles, predicting their phenotypic resistance and spread within natural populations remains complex due to ecological, evolutionary, and epidemiological factors [31, 32]. However, there is an increasing need for a large-scale dataset for a statistical modelling approach which can support data-driven decision-making that accurately predicts resistance patterns that assist in vector control strategies [33, 34].

Bayesian modelling has emerged as a powerful statistical framework for understanding complex biological phenomena, especially when data are uncertain or incomplete. Bayesian approaches, unlike classical frequencies, incorporate prior knowledge to update the beliefs as new datasets become available, which properly allow more dynamic and flexible inferences [35, 36]. Traditional statistical approaches, such as Fisher’s exact test, are limited in their ability to handle sparse or heterogeneous data. Bayesian methods with respect to insecticide resistance can provide probabilistic predictions that can accommodate heterogeneous data sources, which quantify uncertainty regardless of the impact and spread of kdr mutations. This modelling paradigm is particularly well-suited for resistance surveillance in malaria vectors, where spatial and temporal variability, as well as gene-environment interactions, play significant roles in shaping resistance outcomes [37].

Furthermore, studies have shown that Bayesian methods incorporate ecological covariates, which involve land use, vector control, and climatic change into predictive frameworks, thereby enriching our understanding of the factors driving kdr mutation prevalence and distribution [38, 39]. These models also integrate information from bioassay results, molecular data, and entomological indices to provide comprehensive insights into resistance risk [5, 40]. This multidimensional approach enables policymakers and vector control managers to design tailored interventions that are responsive to local resistance profiles and capable of mitigating the operational impact of resistance on malaria transmission.

Despite the promise of Bayesian approaches, there is a limited number of studies that have systematically applied this framework to evaluate the predictive performance of kdr mutations. Most existing models either focus on descriptive statistics or use deterministic approaches that may not adequately account for the uncertainties and variabilities inherent in resistance data [43–45]. Moreover, there is often a disconnect between genotypic data on kdr frequencies and phenotypic outcomes observed in field bioassays. Bayesian modelling helps bridge this gap by explicitly linking genotype distributions with phenotypic resistance outcomes and estimating the probability of resistance under various environmental and operational scenarios [41, 42]. Such probabilistic assessments are essential for forecasting future trends and adapting vector control strategies accordingly. This study evaluated the predictive performance and inferential robustness of a Bayesian meta-analytic model applied to two kdr mutations, which involved L1014F and L1014S, in Anopheles mosquito populations. The analysis focused on estimating the concordance statistic (c-statistic) to measure the model’s discriminative power and examined convergence and potential publication bias through multiple statistical diagnostics.

Methods

Search strategy

A comprehensive search of the literature was conducted to locate relevant studies that examined the relationship between Anopheles mosquitoes and pyrethroid resistance and knockdown resistance (KDR mutations). A variety of databases, including PubMed, Web of Science, Google Scholar, and the Cochrane Library, were searched. The following keywords were used to search the databases: pyrethroid resistance, sub-Saharan Africa, Anopheles mosquitoes, L1014F, L1014S, and kdr mutation. The search was limited to studies published between January 2015 and January 2025. The literature search yielded 511 publications in all databases, including two from the Cochrane Library, eight from Web of Science, 33 from PubMed, and 468 from Google Scholar.

Eligibility criteria

This study was specifically confined to studies that addressed Anopheles mosquitoes, pyrethroid resistance, Kdr mutation, L1014F, L1014S, and sub-Saharan Africa. Therefore, the eligibility criteria involved the selection of articles that exclusively explored pyrethroid resistance in malaria vectors, with a specific focus on kdr mutation, which involved L1014F and L1014S; therefore, studies outside of sub-Saharan Africa and non-Anopheles mosquitoes were excluded, resulting in the retrieval of eight articles. Figure 1 illustrates the search results and the inclusion and exclusion criteria are presented in Tables 1 and 2.

Fig. 1.

Illustration of PRISMA flow for Bayesian Analysis

Table 1.

Inclusion criteria for selected studies

Eligibility criteria	Inclusion criteria
Study design	Cohort or case–control studies reporting both genotypic (L1014F and L1014S) and phenotypic (bioassay) data
Mutation resistance	Studies assessing the relationship between kdr mutations (L1014F, L1014S) and pyrethroid resistance
Insecticide resistance assessment	Pyrethroid resistance was evaluated using standard WHO or CDC bioassay protocols
Genotypic data	Reports allele and/or genotype frequencies of L1014F and L1014S
Mosquito species	Anopheles mosquitoes only

Table 2.

Exclusion criteria for selected studies

Eligibility criteria	Exclusion criteria
Study design	Editorials, review articles, case reports, and abstracts
Mutation resistance	Studies not assessing mutation-resistance relationships or focusing on unrelated resistance mechanisms
Insecticide resistance assessment	Studies lacking standardised bioassay protocols
Genotypic data	Does not report mutation frequency or genotypic data
Mosquito species	Other mosquito genera or non-vector species

Data extraction

Relevant summary-level data from previously published studies on L1014F and L1014S mutations were collected for inclusion in the meta-analysis. The extracted data included estimates of model performance such as concordance statistics, confidence intervals, odds ratios, and study-level characteristics [46]. All data were standardized for input into a Bayesian random-effects framework as illustrated in Tables 3 and 4.

Table 3.

Summary of Selected Studies on Sample Characteristics and Anopheles Mosquito Populations

Study (author & year)	Location & period	Mosquito species	Case sample size	Control sample size	Key notes/methodology
Opondo et al. [58]	Sierra Leone	Female An. spp.	200	75	Prior exposure to pyrethroids such as: deltamethrin, permethrin and alpha-cypermethrin
Diallo et al. [59]	Senegal	Female An. spp.	888	176	The resistance mutations at the Voltage-gated Sodium Channel 1014
Soumaila et al. [60]	Niger, West Africa	An. gambiae sensu lato (s.l.)	630	1017	Two- to five-day-old adult females; tested in parallel using Chlorfenapyr and pyrethroid
Perugini et al. [61]	Burkina Faso	Female An. gambiae spp.	115	78	Captured via pyrethrum spray, sticky boxes, and human landing catches indoors and outdoors
Hemming-Schroeder et al. [62]	Kenya (Port Victoria and Chulaimbo)	Female An. gambiae spp.	446	72	Included Kisumu strain susceptible controls; known kdr mutations in An. arabiensis
Somda et al. [63]	Burkina Faso	An. gambiae s. l	50	50	Mosquitoes had prior pyrethroid exposure; both case and control groups included
Korti et al. [64]	Sudan	Female An. spp.	149	110	WHO bioassay; insecticide-untreated control papers used for the control group; mosquitoes aged 24–48 h
Mawejje et al. [65]	Uganda	Female An. gambiae spp.	432	202	Parallel testing using permethrin and deltamethrin of case and control groups

Table 4.

Extracted Odds ratio and 95% Confidence interval for all allelic frequencies

Author, year	Allele contrasts	ORs (Cis)	Allele contrasts	ORs (Cis)
	L1014F		L1014S
Opondo, [58]	LL	1.83 (0.94–0.99)	SS	1.43 (0.01–0.04)
	LS	0.70 (0.57–0.98)	FS/FF	0.08 (0.00–0.05)
	LF	0.98 (0.95–1.00)
Diallo, [59]	LL	0.46 (0.17–0.66)	SS	0.19 (0.01–0.45)
	LS	0.17 (0.07–0.57)	FS	0.17 (0.06–0.51)
	LF	0.22 (0.02–0.89)	FF	0.14 (0.00–0.41)
Soumaila, [60]	LL	3.32 (0.61–0.64)	SS	1.42 (0.67–0.71)
	LS	1.67 (0.12–0.62)	FS	1.09 (0.025–0.69)
	LF	1.80 (0.21–0.62)	FF	1.81 (0.65–0.78)
Perugini, [61]	N/D	N/D	N/D	N/D
Hemming-Schroeder, [62]	LL	3.50 (1.80–7.10)	SS	1 (Ref.)
	LS/LF	3.90 (0.78–5.61)	FS/FF	0.53 (0.19–1.36)
Somda, [63]	LL	1 (ref.)	SS	1 (ref.)
	LS/LF	1.00 (0.50–0.84)	FS/FF	0.154 (0.153–0.156)
Korti, [64]	LL	4.44 (3.40–5.80)	SS	N/D
	LS	6.56 (5.01–8.96)	FS	N/D
	LF	4.22 (5.40–10.79)	FF	N/D
Mawejje, [65]	LL	1.40 (0.85–2.30)	SS	3.44 (1.02–6.11)
	LS	1.25 (0.77–2.03)	FS	1.17 (0.23–3.94)
	LF	1.64 (0.99–2.71)	FF	1.41 (0.40–2.97)

Bayesian meta-analysis framework

A Bayesian random-effects meta-analysis was conducted using Markov Chain Monte Carlo (MCMC) sampling to estimate the pooled concordance statistic for each mutation. This approach accounts for both within-study and between-study variability and yields posterior distributions for all parameters of interest [47, 48]. The model parameters for the framework include the outcome variable (c-statistics), non-informative priors specified for all parameters used, and a random-effects term that captures between-study heterogeneity. Posterior estimates were derived using multiple MCMC chains, and each run was for sufficient iterations to ensure convergence. Also, thinning procedures and burn-in were applied to reduce autocorrelation and ensure independence of samples [48]. For each included study i = 1…, k_i = 1, we extracted the genotype–phenotype association estimate (odds ratio, concordance statistic). The Bayesian random-effects model was formulated as:

$$\text{yi}\sim \text{N}(\theta \text{i},\sigma \text{i}2)$$

where; Y_i = observed log odds ratio (or concordance statistic) from study i, σ_i²​ = within-study sampling variance (from published CIs), θ_i​ = true effect size for study iii.

The true study-specific effects were modelled hierarchically:

$$\theta i\sim \text{N}\left(\mu ,{\tau }^2\right)$$

where; μ = pooled mean effect size across studies (overall association), τ² = between-study heterogeneity variance.

Priors;

$$\mathrm{\mu }\sim \text{N}(0,102),\mathrm{\tau }\sim \text{Half}-\text{Cauchy}(0,2.5)$$

Assessment of predictive performance and heterogeneity

The primary summary measure was the posterior mean of the concordance statistic with 95% credible intervals (CI) and 95% prediction intervals (PI). Concordance values close to 0.5 indicate poor discriminative performance, while higher values suggest improved predictive accuracy, as seen in Table [3]. Prediction intervals were used to reflect uncertainty in estimating effect sizes in new studies.

Assessment of small-study effects and publication bias

Four funnel plot asymmetry tests were used to assess potential publication bias or small-study effects for each mutation, each designed to detect different patterns of bias and heterogeneity, which include:

Egger’s regression test (unweighted)

This classical test evaluates funnel plot asymmetry by regressing the standard normal deviate (effect size divided by its standard error) on the inverse of the standard error [49, 50]. In the absence of small-study effects, the funnel plot is supposed to have a symmetric funnel shape; thus, the intercept from Egger’s regression is 0. On the other hand, small-study effects lead to missing studies in a certain direction and thus an asymmetric funnel plot [52]. Therefore, the intercept of Egger’s regression is away from 0; a larger intercept in absolute magnitude indicates more severe small-study effects [51].

The unweighted Egger’s regression test formula is expressed as:

$$\text{Ei}÷\text{SEi}=\beta 0+\beta 1·\text{Sei1 -}\epsilon \text{i}$$

where: E_i​ = Effect size estimate from study i (such as log odds ratio, risk ratio, standardized mean difference). SE_i = Standard error of the effect size estimate. E_i ÷ SE_i​ = Standard normal deviate (SND) or “precision-adjusted effect size.” 1 ÷ SEi = Precision of the study. β₀​ = Intercept, which reflects funnel plot asymmetry (if significantly different from zero, bias is indicated). β₁ = Slope, which reflects the underlying “true” effect. ϵi = Error term.

A statistically significant intercept indicates asymmetry consistent with small-study effects or publication bias, as Egger’s unweighted for L1014F was observed in Figures a and b, and L1014S was observed in Figs. 2c and d.

Fig. 2.

Forest plots of genotype–phenotype associations for kdr mutations: (a) L1014F and (b) L1014S. Each square represents the study-specific effect size (odds ratio on a log scale), with horizontal lines indicating 95% credible intervals. The diamond represents the pooled effect from the Bayesian random-effects model

Egger’s regression test with multiplicative overdispersion

This test modifies the original Egger regression to address inflated Type I errors under high heterogeneity by adjusting the standard errors using a multiplicative overdispersion factor [45, 53]. The adjusted model helps reduce spurious detection of bias caused by between-study variability.

The regression model is:

$$\text{Ei}÷\text{SEi}=\mathrm{\beta }0+\mathrm{\beta }1·\text{SEi}1+ϵ\text{i}$$

with an adjusted variance assumption:

$$\text{Var}\left(\text{Ei}\right)=\tau 2·\text{SEi}-2$$

where: E_i​ = Effect size estimate from study i (such as log odds ratio, risk ratio, standardized mean difference). SE_i = Standard error of the effect size estimate. E_i ÷ SE_i​ = Standard normal deviate (SND) or “precision-adjusted effect size.” 1 ÷ SEi = Precision of the study. β₀​ = Intercept, which reflects funnel plot asymmetry (if significantly different from zero, bias is indicated). β₁ = Slope, which reflects the underlying “true” effect. ϵi = Residual error term. τ2 = Multiplicative overdispersion parameter (accounts for between-study heterogeneity).

Macaskill’s regression test

Macaskill’s test regresses the log-transformed effect size on the inverse of the study sample size, offering an alternative approach to Egger's method [54]. A significant slope indicates that smaller studies report systematically larger effects, showing a small-study bias. This method is more robust when heterogeneity is present.

The Macaskill’s Regression Test Formula:

$$\text{Ei}=\mathrm{\beta }0+\mathrm{\beta }1·\text{ni}1+ϵ\text{i}$$

where: E_i = Effect size estimate of study i (e.g., log odds ratio, risk ratio, mean difference). N_i = Sample size of study i. 1n_i = Inverse of sample size (a measure of study precision). β_i = Intercept (represents the pooled effect size if no publication bias). β1​ = Slope (the test statistic for publication bias; a significant slope indicates bias). ϵi = Error term.

Debray’s asymmetry test

Designed explicitly for prediction model meta-analyses, Debray’s test incorporates standard errors and study-level covariates to assess structural sources of funnel plot asymmetry, and each test's significance was evaluated at 0.05 [55].

The test regresses the predictive performance measure (such as logit-transformed C-statistic or log-odds ratio of discrimination slope) against the precision of the study:

$$\text{Yi}=\mathrm{\beta }0+\mathrm{\beta }1·\text{SEi}1+ϵ\text{i}$$

where: Y_i​ = Effect size (such as logit of C-statistic, log DOR, or other prediction performance measure) in study i. SE_i = Standard error of the effect size in study i. β₀ = Intercept (average effect if no asymmetry). β1 = Slope capturing the association between study size/precision and predictive performance. ϵi = Random error term.

Model for concordance statistics

For the concordance statistic (c_i), bounded between 0 and 1, a logit transformation was used:

$$\text{logit}(\text{ci})=\text{ln}(ci÷1-\text{ci})$$

and modelled as: $\text{Logit}\left(\text{ci}\right)\sim \text{N}\left(\mu \text{c},\tau \text{c2}\right)$

with;

$$\mu \text{c}\sim \text{N}(0,102),\tau \text{c}\sim \text{Half}-\text{Cauchy}(0,2.5)$$

MCMC diagnostics and model convergence

MCMC diagnostics were conducted to ensure the reliability of the posterior estimates [51, 56]. Running means plots were carried out to assess the stabilization of the cumulative posterior mean over the iterations. Evaluation of the correlation between successive MCMC samples using autocorrelation plots, with low autocorrelation indicating efficient mixing. However, a Gelman-Rubin diagnostic plot was conducted to quantify the convergence across multiple chains using the potential scale reduction factor (PSRF), with values near 1.0 indicating convergence.

Posterior distributions were estimated using Markov Chain Monte Carlo (MCMC) sampling:

$$\text{p}\left(\mu ,\tau |y\right)\alpha \text{i}=1\prod \text{kN}\left(\text{yi|}\theta \text{i,}\sigma \text{i2}\right)·\text{N}\left(\theta \text{i}|\mu ,\tau 2\right)·\text{p}\left(\tau \right)$$

from the posterior, we obtained: Pooled effect size (μ) with 95% credible intervals, Prediction intervals reflecting heterogeneity, Concordance statistics summarizing predictive discrimination, Funnel plot asymmetry tests for bias (Egger, Macaskill, Debray).

Statistical validation and visualization

The statistical validation and visualization were conducted using JASP software (version 0.18.3.0) for Bayesian estimation and advanced bias diagnostics [57]. The Bayesian meta-analysis focused on comparing the frequency of resistant (kdr) versus susceptible alleles in both case (resistant) and control (susceptible) groups across multiple selected studies for the L1014F and L1014S mutations. A Bayesian random-effects model was implemented to estimate pooled concordance statistics, reflecting the discriminatory ability of prediction models for each mutation. This approach generated posterior distributions for pooled estimates, along with 95% credible intervals (CI) and prediction intervals (PI). Model convergence was assessed using Markov Chain Monte Carlo (MCMC) diagnostics, including running means plots, autocorrelation plots, and the Gelman-Rubin statistic. This was confirmed when the potential scale reduction factor (PSRF) approached 1.0. Four funnel plot asymmetry tests to assess possible publication bias or small-study effects for each mutation, which include Egger’s Regression Test (Unweighted), Macaskill’s Regression Test, Egger’s Regression Test with Multiplicative Overdispersion, and Debray’s Asymmetry Test. Sensitivity analysis was performed to evaluate the influence of individual studies on the pooled ORs to assess the robustness of the results and identify potential outliers or overly influential data points.

Results

Summary of the selected studies

Studies with relatively large sample sizes were selected for this analysis, and they were all conducted in sub-Saharan Africa with a specific interest in pyrethroid resistance and preference for kdr mutations from 2014 to 2025. The following describes the characteristics of the included studies from 2015 to 2025; studies with comparatively large sample sizes that focused on pyrethroid resistance and kdr mutation preference were chosen for this study. The features of the studies are described in Table 3.

Summary of the extracted odds ratio and 95% confidence interval

Table 4 presents the extracted odds ratios (ORs) and 95% confidence intervals (CIs) for allelic contrasts associated with two knockdown resistance (kdr) mutations, L1014F and L1014S, in Anopheles mosquito populations across multiple studies. Each row corresponds to a different study author, detailing the strength of association between specific allele combinations and phenotypic resistance outcomes.

Table 5 presents heterogeneity measures for the kdr mutations L1014F and L1014S. Statistics include Cochran’s Q, between-study variance (τ²), heterogeneity standard deviation (Τ), inconsistency index (I²), and the H² statistic. Very high I² values indicate substantial heterogeneity across selected studies. Figure 3 shows the funnel plot asymmetry tests using Egger’s regression method.

Table 5.

Heterogeneity test for KDR Mutations

	L1014F	L1014S
Q	80.950	20354.025
τ2	0.010	1.328
Τ	0.098	1.152
I2 (%)	92.309	99.954
H2	13.003	2192.346

Q: Cochrane's test; I² and H²: Haggins and Thompson statistics; T: Heterogeneity standard deviation; τ²: Heterogeneity variance

Fig. 3.

shows the funnel plot asymmetry tests using Egger’s regression method. Subplots (a) and (b) show Egger’s unweighted regression for L1014F and L1014S, respectively, while (c) and (d) show Egger’s regression with multiplicative overdispersion for L1014F and L1014S. Each plot displays study effect sizes against standard errors, with the regression line indicating the presence or absence of small-study effects

Discussion

This Bayesian perspective review reveals a broader range of field studies, which examine the distribution and prevalence of insecticide resistance in Anopheles mosquito populations across sub-Saharan Africa. Most of these studies primarily focus on confirming the occurrence of target-site resistance mechanisms, which particularly involve the knockdown resistance (kdr) mutations, most notably L1014S (often referred to as kdr-east), commonly seen in the East African countries such as Kenya, Tanzania, Uganda, and Sudan. The L1014F (kdr-west) has been commonly reported in the West African countries such as Benin, Burkina Faso, Côte d'Ivoire, Gambia, Ghana, Guinea, Liberia, Mali, Niger, Nigeria, Senegal, and Togo, which represent two of the most widely studied genetic alterations in Anopheles gambiae complex mosquitoes. These mutations occur within the voltage-gated sodium channel (VGSC) gene at codon 1014 in the IIS6 transmembrane segment, where leucine is substituted with serine (L1014S) or phenylalanine (L1014F) [5, 23]. This region is the molecular target site of pyrethroid insecticides and DDT, and the amino acid substitutions reduce the binding affinity of these insecticides, thereby diminishing their knockdown effect. Consequently, mosquitoes carrying either of these alleles display delayed or failed knockdown when exposed to pyrethroids, manifesting as phenotypic resistance under WHO susceptibility bioassays [31].

Meanwhile, several modelling frameworks have been employed in recent and advanced research, which include Bayesian spatial models, generalized linear models, and generalized additive models [13, 66, 67]. These models assist in investigating the geographical variation in insecticide resistance patterns, and this offers important insights into the various areas of elevated resistance risks. However, a recurring limitation observed is the static nature of these models. Once formulated, many are rarely updated with new data, reducing their capacity to reflect the evolving resistance dynamics. In this study, the concordance statistic (c-statistic) was selected as the primary summary measure of predictive discrimination because of its intuitive interpretation as the probability that a randomly selected resistant mosquito would have a higher predicted probability of resistance than a susceptible one. However, the study reported that the c-statistic has limitations, particularly in meta-analyses of heterogeneous datasets. Despite the well-documented role of kdr mutations in resistance, the Bayesian predictive model performance suggests that integrating these molecular markers into dynamic models remains insufficiently explored. Dynamic modelling, which accommodates temporal data updates and feedback mechanisms, yet its application remains sparse in studies on malaria vectors, provides a powerful tool to anticipate resistance evolution under varying selection pressures [13].

Across the studies included in this Bayesian predictive model performance, a high frequency of the L1014F mutation was observed in both case and control groups, with notable odds ratios (ORs) reported by Hemming-Schroeder et al. [62] [OR 3.50 (1.80–7.10)] and Korti et al. [64] [(OR 4.44 (3.40–5.80]. These values are indicative of a strong association between the homozygous L1014F genotype and phenotypic resistance. This trend is consistent with the study of Dabire et al. [68], which reported that L1014F may be a contributing mechanism underlying the permethrin resistance. Fadel et al. [69] reported that a study of high frequency of L1014F is the driving force of pyrethroid resistance in the Anopheles coluzzii population from the Guinea savanna of Cameroon and a review of the current situation and the perspectives for malaria control conducted by Zoure et al. [70] demonstrated that the L1014F mutation significantly contributes to pyrethroid resistance in An. gambiae sensu stricto populations in West Africa. Moreover, a systematic review by Hancock et al. [13] also found a high prevalence of L1014F in resistance hotspots, especially where LLINS and IRS have been intensively used. In contrast, the L1014S mutation presented less consistent associations. While Soumaila et al. [60] and Mawejje et al. [65] reported moderate-to-high ORs for L1014S 1.42 (0.67–0.71) and 3.44 (1.02–6.11), respectively, other studies, such as Diallo et al. [59] and Somda et al. [63], recorded notably lower associations or reference-level odds. The variation suggests possible regional differences in selection pressures or ecological conditions influencing the propagation of the L1014S allele. A recent study by Odero et al. [71] highlights the divergent distribution of L1014S compared to L1014F, with the former being more frequent in Anopheles arabiensis populations in East Africa and often showing weaker phenotypic associations. These findings from Odero’s study agree with the report made by Kabula et al. [73] and Perugini et al. [61] that L1014S is more associated with An. arabiensis due to geographical variation in various sub-Saharan Africa. The Bayesian random-effects model indicated very high between-study heterogeneity. For L1014F, the posterior variance component was τ² = 0.010, corresponding to an I² of 92.309%. For L1014S, heterogeneity was even greater with τ² = 1.328 and I² of 99.954%. The extremely high I² values (> 90%) for both mutations reflect substantial heterogeneity across studies, which may arise from ecological differences (species composition, transmission settings), methodological inconsistencies (bioassay protocols, genotyping methods), and regional variations in insecticide pressure. While Bayesian methods accommodate such heterogeneity, the very high values indicate that pooled estimates must be interpreted cautiously.

According to Hancock et al. [13], models can still be informative in data-poor settings by incorporating known ecological and entomological parameters, allowing for extrapolation and prediction in unsampled regions. In addition, the heterozygous genotypes (LS for L1014F and FS for L1014S) reveal a less consistent pattern and lower odds ratios across selected studies. The LS genotype in the study conducted by Diallo et al. [59] had [OR 0.17 (0.07–0.57)], which shows a less recessive mode of action for the resistant allele, thus, these findings align closely with the study investigated by Donnelly et al. [72] and Roca-Acevedo et al. [32], who recorded that homozygous kdr mutations are more predictive of phenotypic resistance than heterozygous states. Kdr mutations alone may not serve as sufficient predictors of phenotypic resistance because the expression of resistance in mosquito populations is shaped by a combination of genetic, ecological, and behavioural factors. While L1014F and L1014S mutations reduce the binding efficacy of pyrethroid insecticides at the sodium channel target site, their predictive power is often constrained by the concurrent presence of alternative resistance mechanisms such as metabolic detoxification, cuticular thickening, or altered insecticide penetration. Moreover, ecological drivers, including insecticide usage patterns in agriculture and public health, seasonal vector dynamics, and local species composition, can significantly influence the observed strength of association between kdr alleles and phenotypic outcomes. Behavioural traits such as changes in biting time, resting behaviour, or host preference also interact with genetic mechanisms to shape resistance profiles in the field.

The Concordance Statistic (supplementary Table 1) for L1014F showed a mean estimate of 0.141 (95% CI −0.095 to 0.459), while for L1014S the mean was 0.169 (CI −0.399 to 0.688). These wide confidence intervals encompassing zero indicate moderate to low predictive value of either marker in isolation, particularly when meta-analytical variability is taken into account. This is because of confounding variables such as gene-environment interactions, sampling differences, and inconsistent resistance bioassay methods. The high heterogeneity (observed in earlier analyses, not shown in the current summary but consistent with the literature) aligns with previous meta-analyses by Bkhache et al. [73] and Churcher et al. [74], who found significant between-study variation when comparing genotype and resistance phenotype across mosquito field populations. Mechanistic models in relation to the challenges reveal an important alternative. Unlike data-driven models that depend on large empirical datasets, mechanistic models simulate biological or ecological processes using theoretical formulations. These models are capable of simulating the spread of resistance based on genetic selection dynamics, behaviours of the mosquito population, and insecticide use patterns. Gene flow, genetic dominance, and fitness cost significantly enhance the predictive performance of resistance models, even in the absence of extensive surveillance data [75]. Nevertheless, the model requires proper and strong theoretical assumptions and expertise in resistance mechanisms, vector ecology, and insecticide mode of action.

Egger’s test, Debray’s test, and Macaskill’s test are methods performed in funnel asymmetry plots, as seen in supplementary Table 2, which are used in meta-analyses to visually assess the small-study effects or potential publication bias. Figure 3 illustrates the unweighted and multiplicative overdispersion (Egger) test. The Egger (unweighted) test for L1014F yielded a t-statistic of 2.117 (p = 0.102), which reveals that the test is not statistically significant at the threshold of 0.05, although it borders on the moderate concern for publication bias. This result corresponds with the report made by Wasserstein & Lazar [76] that warns against the misuse of statistical significance and p-value. In contrast, the multiplicative Egger overdispersion produced a non-significant t-statistic (0.220, p = 0.837); thus, this shows limited evidence for small-study publication bias. Fisher [77] reported that the significance of the evidence against the null hypothesis could only be approximated by the p-value. The implication of p < 0.05 was simply that the experiment should be repeated. The discovered effects were unlikely to be the result of pure chance if further research produced significant p-values as well [78]. However, neither Egger’s unweighted nor multiplicative overdispersion tests were statistically significant (t = – 0.743, p = 0.499 and t = – 1.340, p = 0.251, respectively). This finding shows that there is a relative symmetry and lower likelihood because of publication bias from small studies across selected studies in the case of the resistant alleles.

Furthermore, selecting drivers or predictor variables affects the model accuracy. Studies have shown that the predictors, such as demographic, environmental, ecological, and climatic factors, which include vector species composition, land use, human population density, temperature, and rainfall [79–81], are frequently used. Meanwhile, many models fail to incorporate other important factors, which involve resistance management history, vector migration, and larval habitat productivity in their studies. Thus, gene flow and migration have shown how resistance alleles disseminate across different regions, which often override local selection pressures [82, 83]. Temperature-dependent metabolism affects the detoxification ability of mosquitoes and the toxicity of insecticides, as reported by Hancock et al. [13]. Higher temperature reduces the effectiveness of insecticides and favours resistant phenotypes; it accelerates the enzymatic breakdown of insecticide compounds. No review study has integrated the principle to understand the biophysical processes which are thermodynamically driven into the resistance prediction models. Thermodynamic parameters can be incorporated into the predictive frameworks, which can add to the explanatory power and increase the recognition of temperature as the modulator of insecticide performance [5]. The model risk without the foundational values shows non-representative outcomes or produces a skewed result. Therefore, accurate insecticide resistance modelling demands systematic surveillance, longitudinal monitoring efforts, and a large-scale baseline dataset which captures the past, present, and future trends across various regions in sub-Saharan Africa.

Conclusion

This study has systematically applied a Bayesian modelling framework to assess the predictive power of two major KDR mutations involving L1014F and L1014S in Anopheles mosquito populations from sub-Saharan Africa. The analysis affirms that the L1014F mutation is a more reliable marker of phenotypic pyrethroid resistance than L1014S, with higher and more consistent odds ratios reported across several studies. Nevertheless, both mutations displayed considerable variability in their predictive accuracy, as evidenced by wide credible intervals and moderate concordance statistics. A key limitation of this Bayesian meta-analysis is the small number of eligible studies (n = 8). While Bayesian modelling provides a flexible framework for sparse data, the low number of studies weakens the foundation for robust inference and limits the interpretability of funnel plot asymmetry tests, which may be underpowered or unstable. However, this study demonstrates the application of a Bayesian random-effects model to synthesize genotype–phenotype associations in insecticide resistance surveillance. In addition, metabolic resistance mechanisms were not incorporated into the Bayesian model because resistance is often multifactorial, restricting the analysis to target-site mutations may overestimate or underestimate their predictive power. The low concordance statistics observed in our analysis may, in part, reflect the absence of metabolic markers, which account for substantial unexplained variability in phenotypic outcomes.

The application of advanced meta-analytical tools, including multiple funnel plot asymmetry tests and MCMC diagnostics, revealed essential issues in model convergence, publication bias (asymmetry in effect size estimates), and data quality (statistical robustness, methodological consistency, and data completeness). Specifically, the Macaskill and Debray tests flagged potential reporting biases in both datasets, revealing the need for more transparent and comprehensive resistance surveillance systems. The inclusion of temporal dynamics, environmental covariates, and migration patterns could substantially improve the realism and utility of future models. Moreover, mechanistic modelling, which simulates biological processes and vector behaviour, provides a valuable alternative in settings where empirical data are sparse or inconsistent.

Author contributions

Conceptualization; methodology and analysis; original draft preparation, review and editing: D.I.T. and E.F.A. Both authors have read and agreed to the published version of the manuscript.

Funding

This research did not receive any specific grant from funding agencies in the public, commercial, or not-for-profit sectors. No external funding was provided for the study design, data collection, analysis, and interpretation of this manuscript.

Data availability

All data used in this study are derived from publicly available peer-reviewed publications included in the meta-analysis. The compiled dataset and relevant analysis scripts used for the Bayesian meta-analytic predictive modelling are available from the corresponding author upon reasonable request.

Declarations

Consent to publish

Not applicable. This study does not involve any individual person’s data in any form (including individual details, images, or videos), and thus does not require consent to publish.

Competing interests

The authors declare no competing interests.