There used to be a study that showed that women were at higher risk of getting divorced if they got a serious sickness, but I think that study had an error in its numbers. We got a new study on the topic, and it's not in favor of men either.
Method
We utilized data from the European Survey of Health, Ageing, and Retirement (SHARE), spanning Waves 1 (2004–2005) to 9 (2021–2022), and employed discrete-time event-history analysis to model the risk of silver splits, separately among couples aged 50–64 and 65+ (N = 31,915 and 48,361 couple-years, respectively). We inspected three health dimensions: self-rated health, Global Activity Limitations Index, depression.
Results
We found a non-negligible and gendered association between health and union dissolution among couples aged 50–64. Couples in which the woman reported poor self-rated health or faced severe activity limitations, whereas the man maintained good health, exhibited a higher risk of silver splits compared to couples in good health. Conversely, the risk of silver splits did not change significantly when the man experienced poor self-rated health or activity limitations compared to couples in good health. Results among older couples suggested that the health/silver split link weakens with age.
Conclusion
Gendered health-related selection effects appear among older European couples, as men struggle more than women with a partner's declining health, potentially jeopardizing the couple's stability.
https://onlinelibrary.wiley.com/doi/10.1111/jomf.13077?af=R
Here's an article discussing this study, and they've also linked another one.
Women composed 53% of the patient population. Divorce or separation occurred at a rate similar to that reported in the literature (11.6%). There was, however, a greater than 6-fold increase in risk after diagnosis when the affected spouse was the woman (20.8% vs 2.9%; P < .001). Female gender was found to be the strongest predictor of separation or divorce in each cohort. Marriage duration at the time of illness was also correlated with separation among brain tumor patients (P = .0001). Patients with brain tumors who were divorced or separated were more likely to be hospitalized, and less likely to participate in a clinical trial, receive multiple treatment regimens, complete cranial irradiation, or die at home (P < .0001).
https://pubmed.ncbi.nlm.nih.gov/19645027/
Thankfully, I don't know couples who got divorced over women's health issues, but I know several couples who went through husbands' serious health problems and they stuck together. These wives went through their partners' poor health and long-term unemployment. I know an older couple where the woman has to take care of her husband who got through several strokes and now can't eat himself. He has a bad temper, but she still takes care of him.
Do you have any personal experience on the topic?
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