REVIEW 3 major objections 4 minor 7 references
Determinants of Longevity amongst SSNIT Pensioners in Ghana
T0 review · 3 major / 4 minor · reviewed 2026-08-12 · deepseek-v4-flash
Pith's one-line read The paper claims that basic salary, years of service, age at death, and gender predict whether a SSNIT pensioner survived under eight years after retirement, with a fitted logistic model that is 83 percent accurate.
desk verdict A useful Ghanaian mortality descriptive, but the central predictive model is circular: age at death is a linear transform of the outcome in a fixed-retirement-age sample, so the reported 83% accuracy is mostly label leakage. read the letter →
The pith
A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.
The reading
What carries the argument
The central object is the binary logistic regression model, which transforms the probability of an event into a log-odds scale and expresses it as a linear combination of predictors. The paper sets the event as surviving less than eight years after retirement, uses four predictors (basic salary, service years, gender, age at death), and interprets each coefficient through its odds ratio, $\exp(\beta)$. A companion multiple linear regression predicts the continuous number of years survived, and the paper compares it against decision tree, random forest, and support vector regressions, finding the linear model has the lowest mean squared error.
What would settle it
Refit the logistic model on the same pension records with age at death removed, or replace it with age at retirement, and evaluate out-of-sample accuracy on a holdout set; if accuracy falls to near the base rate, the reported 83 percent classification depends on the definitional overlap rather than on salary, service years, or gender.
Extended reading notes
Core claim
On the paper's own terms, the central discovery is that a binary logistic regression with four administrative predictors can sort pensioners into short and long post-retirement survival groups with 83 percent accuracy. Each additional year of service raises the odds of dying within eight years of retirement by 22.36 percent; higher basic salary raises those odds by a small but statistically significant amount; male pensioners have 46.95 percent higher odds than female pensioners; and each additional year of age at death lowers the odds of short survival by about 42 percent. The same predictors account for roughly 55 percent of the variance in the continuous outcome, years survived after retirement.
Load-bearing premise
The analysis assumes age at death can serve as an ordinary predictor even though, with retirement fixed at 60, it is the same quantity that defines the outcome, years survived after retirement; this overlap, rather than any independent biological signal, may be what makes the model look accurate.
Editorial extensions
If this is right
- If the logistic model is correct, the pension provider can estimate an individual's probability of dying within eight years of retirement using four fields already in its records.
- The service-years effect implies that long-career contributors tend to draw pensions for fewer years, which would reduce the expected annuity burden from that group.
- The female-to-male gap in death rates supports using sex-specific mortality assumptions when pricing annuities or setting reserves.
- The eight-year threshold offers a practical cut-off for classifying pensioners as higher-risk versus lower-risk in future mortality studies.
Reading between the lines
- A direct test the paper does not run: remove age at death from the model, since with retirement fixed at 60, years survived after retirement and age at death are the same clock; this would reveal how much of the reported accuracy comes from the other three predictors.
- An implication the author leaves implicit is that higher salary and longer service may be proxies for occupation, education, or health-care access, so the associations should not be read as causal without a longitudinal design.
- A testable extension beyond the paper's design is to apply the same four-variable logistic model to pensioners who retired after 2020 and measure out-of-sample accuracy, giving a truer estimate of predictive value.
Editorial analysis
A structured set of objections, weighed in public.
Referee Report
Summary. The paper analyzes SSNIT pensioner data (2015–2020) to estimate mortality rates, identify determinants of longevity, and construct predictive models for post-retirement survival. It fits a multiple linear regression and a binary logistic regression with predictors basic salary, number of years of service, gender, and age at death; the outcome is either years survived after retirement or a binary indicator of surviving less than 8 years. The paper claims all four predictors are statistically significant and reports a logistic model accuracy of 83%.
Significance. If the analysis were valid, the paper would offer useful evidence on pensioner mortality determinants in Ghana, a context with limited empirical work. The paper also provides descriptive mortality-rate tables and compares several regression approaches. However, the central predictive claim is undermined by a fundamental label-leakage problem in the model specification, so the reported significance and accuracy do not support the stated conclusions.
major comments (3)
- [III.A and Eq. (8), Table 6] The model includes 'age of pensioner before death' (lambda_4) as a predictor of whether the pensioner survived less than 8 years after retirement. Section III.A states that all analysis was based on the mandatory pensionable age of 60 and that early retirement was excluded. For every decedent in the sample, years survived after retirement is therefore age at death minus 60. The binary outcome 'less than 8 years' is then equivalent to 'age at death < 68' (up to rounding). Including age at death as a covariate is direct label leakage: the model uses a deterministic transform of the outcome to predict the outcome. This mechanically produces the large age coefficient (logistic coefficient -0.5445, OR 0.5801) and inflates the reported 83% accuracy. The claim that basic salary, service years, gender, and age jointly predict longevity is not supported unless the model is re-estimated without age at death.
- [Section IV.A.2 and Table 3] The fitted linear regression equation in the text gives the basic salary coefficient as +0.0000682, but Table 3 reports the coefficient as -6.8217e-05. These are opposite signs for the same parameter. This inconsistency means the reader cannot determine the actual estimated effect of salary, and it calls into question the reliability of the reported table entries.
- [Table 6] For the basic salary predictor, the reported Wald statistic is 0.1451 while the reported p-value is 0.0000. A Wald statistic this small would correspond to a p-value very close to 1, not 0.000. The table therefore contains an internal statistical inconsistency that prevents verification of the claimed significance.
minor comments (4)
- [Throughout] There are frequent typographical and formatting errors, including duplicated table numbers (two Tables numbered 4), inconsistent notation (e.g., 'N0 of years' in Table 6), and uneven spacing in equations.
- [Section III.B.2, Eq. (6)] The logistic model is specified as g(x) = beta0 + beta1 + beta2 + beta3 + beta4, with no variables shown; this should be g(x) = beta0 + beta1*lambda1 + ... + beta4*lambda4 to be consistent with Eq. (8).
- [Section IV.A.2, Table 4] The mean squared error values in the text for the linear regression (12.17) and random forest (12.42) do not match the RMSE of 3.6 reported in Table 3; the relationship between MSE and RMSE should be clarified.
- [References] Several references have incomplete details (e.g., Antolin (2007) lacks a title), and at least one citation in the text ('Madrigal, Matthews, Patel, Gaches, & Baxter, 2011') is not matched to a fully formatted reference.
Circularity Check
Age-at-death is an affine transform of the outcome under the paper's fixed-retirement-age restriction, so the reported age coefficients and 83% accuracy are definitional artifacts.
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self definitional
[Section III.A; Section IV.A.2 (logistic model Eq. (1)/(8), Table 6, and fitted linear model)]
"Furthermore, less emphasis was placed on early retirement, as to that fact all analysis was based on the normal mandatory pensionable age of 60 in Ghana. ... where, λ1 = basic salary of pensioner, λ2 = the number of years of service in the workforce, λ3 = the gender of the pensioner, λ4 = age of pensioner before death. Again, longevity is categorized as yi = { 1 if the pensioner had survived less than 8 years after retirement, 0 if the pensioner had survived 8 or more years after retirement }."
The paper restricts the analysis to pensioners retiring at the mandatory age of 60. For every such pensioner, years survived after retirement is exactly age at death minus 60, and the binary outcome 'less than 8 years' is equivalent to 'age at death < 68'. The model then includes age at death (λ4) as a predictor of that same outcome. This makes age a deterministic affine transform of the response, so the large age coefficient (0.8115 in the linear model), the age odds ratio (0.5801), and much of the reported accuracy (0.83) are forced by construction rather than discovered. The apparent predictive contribution of age cannot be evidence for the paper's claim that the four listed predictors jointly determine post-retirement survival.
full rationale
The paper's central predictive claim rests on a logistic model that includes 'age of pensioner before death' as a predictor of whether a SSNIT pensioner survived less than 8 years after retirement. Section III.A explicitly states that all analysis was based on the normal mandatory pensionable age of 60 and that early retirement was not emphasized. Given that restriction, the response variable, years survived after retirement, is equal to age at death minus 60, and the binary outcome is equivalent to an age threshold of 68. Thus including age at death as a covariate is label leakage: the model uses a deterministic transformation of the outcome to predict the outcome. This explains the large age coefficient and the high reported accuracy and makes the statistical significance of age tautological in this sample. The other three predictors (salary, service years, gender) are not themselves circular, but their reported effects are estimated conditional on the age variable and the headline 83% accuracy cannot be separated from the definitional age effect. Because the paper presents age as one of the significant determinants and the accuracy as evidence for the joint model, the central claim is substantially circular by construction. No self-citation issues are present; the circularity is purely definitional.
Assumptions & free parameters
free parameters (3)
- Eight-year survival threshold =
8 years
- Linear regression intercept and coefficients =
intercept -29.53; salary 6.8217e-05 (text) or -6.8217e-05 (Table 3); service years -0.45973; gender -0.57593; age…
- Logistic regression intercept and coefficients =
intercept 28.65; salary 1.076e-06; service years 0.2019; gender 0.3849; age -0.5445
assumptions (4)
- domain assumption All analysed pensioners retired at the mandatory age of 60
- domain assumption SSNIT secondary data are complete and accurate for deaths and pensioner counts
- standard math Standard logistic regression assumptions hold (independence, linear logit, no severe multicollinearity)
- domain assumption Deceased pensioner records are an unbiased sample for longevity analysis
Cite this review
Pith. "Pith review of Determinants of Longevity amongst SSNIT Pensioners in Ghana." pith.science (2026). https://pith.science/paper/RDO3F454
@misc{pith2026241117750,
author = {Pith},
title = {Pith review of: Determinants of Longevity amongst SSNIT Pensioners in Ghana},
year = {2026},
howpublished = {\url{https://pith.science/paper/RDO3F454}},
note = {Machine review of arXiv:2411.17750}
}
read the original abstract
This paper statistically analysed pensioner longevity in Ghana. It fundamentally sought to ascertain the significant determinants of longevity amongst Ghanaian pensioners, specifically, SSNIT pensioners by estimating the mortality rate of SSNIT pensioners, determining the factors that significantly affect the longevity of the average SSNIT pensioner and constructing a predictive model for predicting the longevity of SSNIT pensioners in Ghana. Secondary data was obtained from the leading pension provider in Ghana, SSNIT. The results of the study revealed that the total number of male deaths was significantly greater, about four times more, than the total number of female deaths. There was sufficient evidence that there exists a lower rate of death among female pensioners as compared to male pensioners. Furthermore, a significant number of the SSNIT pensioners used in the analysis survived less than 8 years after retirement before their death and the average basic salary of the pensioners who lived less than 8 years after retirement was GH 7741.827 cedis and served for 35.65 years on average. On the contrary, it was observed that pensioners who lived more than 8 years after retirement had an average basic salary of GH 5544.20 cedis and served for 31.49 years on average. In conclusion, predictors such as basic salary, the number of years of service in the workforce, the age of the pensioner before death and the gender of the pensioner were statistically significant in predicting the number of years a SSNIT pensioner survived after retirement before death that is, whether a particular SSNIT pensioner survived less than 8 years or 8 years and above after retirement. The authors recommend to employees that, their health should be of great priority as every increase in the service year increases the likelihood of a SSNIT pensioner surviving less than 8 years after retirement by 22.36%.
Figures
Reference graph
Works this paper leans on
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[1]
Mortality Rates Age-Specific Death Rates The age-specific death rate is the total number of deaths of people of a specified age or age group in a specified geographical area divided by the population of the same age or age group in the same geographical area and multiplied by 1,000. 𝐴𝑆𝑆𝐷𝑅 = 𝑇𝑜𝑡𝑎𝑙 𝐷𝑒𝑎𝑡ℎ𝑠 𝑖𝑛 𝑠𝑝𝑒𝑐𝑖𝑓𝑖𝑒𝑑 𝑎𝑔𝑒 𝑔𝑟𝑜𝑢𝑝 𝑇𝑜𝑡𝑎𝑙 𝑛𝑢𝑚𝑏𝑒𝑟 𝑜𝑓 𝑝𝑒𝑟𝑠𝑜𝑛𝑠 𝑖𝑛 𝑡ℎ...
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[2]
Regression - Based Models Binary Logistic Regression The binary logistic regression model shows how the outcome variable which is a binary categorical variable depends on the sets of explanatory variables(predictors). It comprises of the distribution of Y is a Binomial, the link function (logit) and the systematic components 𝜂 = 𝑙𝑜𝑔𝑖𝑡(𝜋) = 𝐼𝑛 ( 𝜋 1−𝜋) = 𝛽...
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[3]
Assessing the logistic model Goodness-of-fit is mostly used in describing how effective our model is. It is assessed over the constellation-fitted values determined by the covariates in the model, not the total collection of covariates. In o rder to assess goodness-of- fit as explained above the idea of what it means to say that a model fits. Suppose we d...
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[4]
Model Evalution Metrics Mean Squared Error (MSE) The most common metric for regression is MSE. An estimator’s mean squared error (MSE) measures the average of the squares of the errors or the average squared difference between the estimated values and the actual values. The MSE is a measure of the quality of an estimator – it is always non-negative, and v...
work page 2022
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[6]
Mortality Rates The mortality rate as explained earlier in this section is the proportion of the number of people who died within a particular cohort by the total number of people within that cohort at a given time. It is observed in Table 2 that, over the five years, th e female pensioners' mortality rate is relatively lower than that of the male pension...
work page 2022
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[7]
Regression Analysis Linear Regression Some results from the regression analysis of the data collected is presented in this subsection of the paper. The significance of the variable of interest was assessed and the overall adequacy of the models was examined and presented. Furthermore, the findings of the model fitting, model selection and prediction accur...
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[2008]
suggested that certain characteristics should be present in a decent model in order to determine its suitability. Among the attributes are the following: Invariance with past data, Implementation simplicity, Parsimony, Transparency, Sample path and forecast intervals, and Uncertainty. Therefore, this paper explores the Regression-based models in determini...
work page 2018
Reviewed August 12, 2026 · model on record in the stance chip above.
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